Proceedings of the International Academy of Ecology and Environmental Sciences, 2014, Vol. 4, Iss. 3

Proceedings of the International Academy of

Ecology and Environmental Sciences

Vol. 4, No. 3, 1 September 2014

International Academy of Ecology and Environmental Sciences

Proceedings of the International Academy of Ecology and Environmental Sciences ISSN 2220-8860 Volume 4, Number 3, 1 September2014

Editor-in-Chief WenJun Zhang Sun Yat-sen University, China International Academy of Ecology and Environmental Sciences, Hong Kong E-mail: [email protected], [email protected] Editorial Board Taicheng An (Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, China) Jayanath Ananda (La Trobe University, Australia) Ronaldo Angelini (The Federal University of Rio Grande do Norte, Brazil) Nabin Baral (Virginia Polytechnic Institute and State University, USA) Andre Bianconi (Sao Paulo State University (Unesp), Brazil) Iris Bohnet (CSIRO, James Cook University, Australia) Goutam Chandra (Burdwan University, India) Daniela Cianelli (University of Naples Parthenope, Italy) Alessandro Ferrarini (University of Parma, Italy) Marcello Iriti (Milan State University, Italy) Vladimir Krivtsov (Heriot-Watt University, UK) Suyash Kumar (Govt. PG Science College, India) Frank Lemckert (Industry and Investment NSW, Australia) Bryan F. J. Manly (Western EcoSystems Technology Inc. and University of Wyoming, USA) T.N. Manohara (Rain Forest Research Institute, India) Ioannis M. Meliadis (Forest Research Institute, Greece) Lev V. Nedorezov (University of Nova Gorica, Slovenia) George P. Petropoulos (Institute of Applied and Computational Mathematics, Greece) Edoardo Puglisi (Università Cattolica del Sacro Cuore, Italy) Zeyuan Qiu (New Jersey Institute of Technology, USA) Mohammad Hossein Sayadi Anari (University of Birjand, Iran) Mohammed Rafi G. Sayyed (Poona College, India) R.N. Tiwari (Govt. P.G.Science College, India) Editorial Office: [email protected] Publisher: International Academy of Ecology and Environmental Sciences Address: Flat C, 23/F, Lucky Plaza, 315-321 Lockhart Road, Wanchai, Hong Kong Tel: 00852-6555 7188; Fax: 00852-3177 9906 Website: http://www.iaees.org/ E-mail: [email protected]

Proceedings of the International Academy of Ecology and Environmental Sciences, 2014, 4(3): 95-105

IAEES www.iaees.org

Article

Morphometry and meristic counts of Bombay duck, Harpodon

nehereus (Hamilton, 1822) along Sunderban region of West Bengal,

India

V. Vinaya Kumar1,4, A. Devivaraprasad Reddy2, Sampurna Roy Choudhury1, C. H. Balakrishna3, Y. Satyanaryana3, T.S. Nagesh1, Sudhir Kumar Das1 1Department of Fishery Biology and Resources Management, Faculty of Fishery Sciences, WBUAFS, Kolkata – 94, West Bengal,

India 2Department of Fish Processing Technology, College of Fishery Science, SVVU, Muthukur-524 344, Andhra Pradesh, India 3Fisheries Development Officer, Joint Director Fisheries, Fishing Harbor, Vishakapatnam, Andhra Pradesh, India 4Fishery Resources Assessment Division, Central Marine Fisheries Research Institute, Cohin, Kerala, India

E-mail: [email protected]

Received 4 January 2014; Accepted 10 February 2014; Published online 1 September 2014

Abstract

Fisheries sector have been gaining importance globally due to their role in national economy, foreign exchange

earnings and employment generation besides providing nutritious food and cheap protein not only to the fisher

folk but also to the rapidly growing population. Bombay duck fishery supported by single species, Harpodon

nehereus, contributes about 4-5 % of the estimated average annual marine landings of India. With a peculiar

discontinuous distribution fishery is utmost importance in two maritime states of India i.e. Gujarat and

Maharashtra contributing 92% of the total landings and the remaining 8% landings were from West Bengal

and Orissa coasts. H. nehereus forms a commercial fishery along Hooghly estuarine systems. The present

study aims on the morphometric and meristic counts of H. nehereus. During the period of investigation, 373

fish samples with length range (145 to 302 mm) and weight range (28 to 212 gm) were examined. Highest

significant correlation (P<0.01) was observed between reference length and other morphometric parameters of

both sexes. Percentage range difference in male's morphometric characters like post orbital length (15.24) and

snout length (15.04) are environmentally controlled and others like standard length (11.09), pre-dorsal length

(12.18), height of pelvic fin (13.39) and height of pectoral fin (12.10) are intermediate controlled (genetic and

environmental factors). But in case of females, none of the characters are controlled by environmental factors

and parameters like pre-dorsal length (10.37) and post orbital length (12.37) are intermediate controlled,

remaining parameters in both sexes are genetically controlled (hereditary). Meristic counts includes dorsal fin

with 10-13 soft rays, pelvic fin with 9 soft rays, pectoral fin with 10-12 soft rays and anal fin with 13-15 soft

rays.

Keywords Bombay duck; Harpodon nehereus; morphometry; meristic counts; Sunderban region.

1 Introduction

Proceedings of the International Academy of Ecology and Environmental Sciences ISSN 22208860 URL: http://www.iaees.org/publications/journals/piaees/onlineversion.asp RSS: http://www.iaees.org/publications/journals/piaees/rss.xml Email: [email protected] EditorinChief: WenJun Zhang Publisher: International Academy of Ecology and Environmental Sciences


IAEES www.iaees.org

1 Introduction

As we are proceeding in this millennium, finfish and other aquatic products will be in acute short supply as

domestic and International demand for both high and low valued species increasing due to raising populations,

living standards and disposable incomes. Bombay duck, Harpodon nehereus is a key contributor in Indian

marine fish landings ranging from 4-5% commonly along North-West and North-East coast (Fig. 1). Bombay

duck production was 1, 15,296 tonnes in 2012, contributing nearly 3-4% of the total marine landings of India

(CMFRI Annual Report, 2013). Though well relished and considered a delicacy in Western India, its culinary

qualities have not been recognized in West Bengal. H. nehereus forms a lucrative fishery along Sunderban

region of North-East coast of India. Bombay duck is a very soft and highly perishable due to high moisture

content in its muscle. It is having good importance and relished by different sections of people as table fish and

also valuable as laminated or dried from (Kumar et al., 2012a).

Fig. 1 Sampling site i.e. Diamond harbor (22o 12’53.92’’ N & 88o 12’22.74’’ E)

Fig. 2 A view of Harpodon nehereus during measuring of morphometric & meristic parameters.

96


IAEES www.iaees.org

The fishery, biology and population characteristics of the H. nehereus from the Saurashtra coast were

extensively studies (Balli et al., 2011; Ghosh et al., 2009; Bapat, 1970; Khan, 1985, 1986a, 1986b, 1987 and

1989). Along Hooghly matlah estuarine region of North-East cast of India, food and feeding habits was studied

(Pillay, 1951, 1953; Kumar et al., 2012b)and population dynamics was also estimated (Krishnayya, 1968).

Studies on the morphometry and meristic counts are vital for the differentiation of taxonomic units. Studies on

variation in morphological characters are critical in order to elucidate patterns observed in phenotypic and

genotypic variations among coastal fish populations (Beheregaray and Levy, 2000). There were no studies

related with morphometry and meristic counts of Bombay duck, H. nehereus stocks along North-East coast of

India. The present work aims to full fill the research gap, upgrade the biological information of species and

also study the factors which influence the stock dynamics.

2 Materials and Methods

2.1 Sampling site and size

The present work aims on some aspects of morphometric and meristic characters of H. nehereus for the period

of one year (August, 2008 to July, 2009). The samples were collected from the Daimond harbour area (22o

12’53.92’’ N & 88o 12’22.74’’ E), Sagar Islands, Bokkhali, 8-Jetighat and local fish markets, which were

mainly procured from different areas of Sundarban region of South 24 – Paraganas district (Fig. 1). Samples

were captured mostly by stationary bag-net, locally called Beenjal, Behundijal which are non-selective

multispecies small meshed nets.

Current experiment, total of 373 specimens of H. nehereus was sampled for the 12 months period (August,

2008 to July, 2009). More than 30 specimens were examined in the laboratory during each month. Samples

were collected twice in a month and examined usually at fortnightly intervals. Total length and standard length

were measured in market itself by using the millimeter scale (Fig. 2). Total weight was measured with a

monopan balance for individual fish in grams.

2.2 Sampling method

For study of the morphometric and meristic characters the standard procedure (Lowe-McConnel, 1971) was

followed. All linear measurements were rounded to the nearest mm. Among different morphometric characters,

standard length, head length, pre-dorsal length, length base of dorsal fin, length base of anal fin, pectoral fin

length, dorsal height, pectoral fin height, least depth of caudal peduncle, post orbital length, snout length, eye

diameter were measured. Four meristic characters such as dorsal fin rays, pectoral fin rays, pelvic fin rays and

anal fin rays were estimated. Total length and head length were used as reference length. Total length was

measured from tip of the snout to the tip of the caudal fin. The diameter of the eye was measured in horizontal

axis. The regression of various morphometric characters on standard length was obtained by least square

method with the formula Y = a + bX, where, ‘Y’ is different morphometric measurements and ‘X’ is the

reference length; ‘a’ is the constant value; ‘b’ is the exponent.

2.3 Statistical analysis

Correlation co-efficient between variables were calculated and regression equations were found out following

standard methods. Isometric growth was tested by employing Fisher’s t test. Significant difference among

mean of different biological parameters were tested employing standard statistical tools like Student’s‘t’ test,

and ANOVA (Snedecor and Cochran, 1967), etc.

3 Results and Discussion

Studies on the morphometric and meristic characters of fishes provide substantial information with regard to

the exact nature of stocks and their geographical distributions. Morphometric differences are seen with in the

97


IAEES www.iaees.org

species and even within different sexes of species due to interactive genetic and environmental effects. The

knowledge of exact genetically and environmental controlling characters are essential for the identification of

species of a genus and the populations with in a species. Current study reveals that the biometry values H.

nehereus showed a proportional positive increase with total length of fish. The mean, percentage range,

percentage difference and standard error values of different morphological characters of H. nehereus are

presented in Fig. 3, 4 and Table 1, 2.

The regression coefficient ‘b’ of different variable characters (Yi) on the total length (X) was highest in

case of standard length. The ‘b’ values for standard length on total length are 0.5747 for male and 0.9067 for

females respectively. Least depth of caudal peduncle (Y) on total length (X), showing lowest ‘b’ value i.e.

0.0281 for males and 0.0389 for females. While considering the post orbital length, snout length and eye

diameter in terms of percentage of head length, post orbital length shows highest ‘b’ values, which were

0.7744 for males and 0.8015 for females.

The present study revealed the highest correlation of standard length on total length in case of both male

(r =0.965) and female (r =0.961) and also observed the highest correlation of post orbital length on head length

in case of both male (r =0.948) and female (r =0.957). The lowest value of the correlation for the male was

noticed in the case of height of pelvic fin (r =0.771) on total length and snout length (r =0.642) on percentage

of head length. In female lowest correlation value was observed in case of length base of anal fin (r =0.597) on

total length and snout length (r =0.572) on percentage of head length. Morphometric analysis of the present

study revealed that the correlation values were greater in male than female when calculating the percentage on

total length and head length. Only the post orbital length giving the more value in case of female (r =0.957)

when compare to male (r =0.948). All the regression coefficient ‘b’ values, correlation differentiation ‘R2’ and

coefficient of correlation ‘r’ values are represented in Table 3.

Nikolsky (1963) stated that the males and females often differ in the length and shapes of fins. Phenotypic

plasticity during present investigation occurred due to the environmental factors because fishes were procured

from different water bodies of Sunderban areas of Hooghly-Matlah estuarine system. Johal et al. (1994),

classified three categories of morphometric characters based on percentage range difference i.e. genetically

controlled characters (<10% range difference), intermediate (10.1% to 14-99% range difference) and

environmentally controlled characters (>15% percentage difference). In current study, in male parameters like

post orbital length (15.24%) and snout length (15.04%) are environmentally controlled and the other

parameters like standard length (10.09%), pre-dorsal length (12.18%), height of pelvic fin (13.39%) and height

of pectoral fin (12.10%) were controlled by intermediate factors, but in case of female pre-dorsal length

(10.37%) and post orbital length (12.37%)were controlled by intermediate factors. Other than these parameters,

all the remaining parameters in both male and female were controlled by genetic factors (hereditary).

Meristic characters of H. nehereus (Table 4) in the current study includes dorsal fin with 10-13 soft rays,

pelvic fin with 9 soft rays, pectoral fin with 10-12 soft rays and the anal fin with 13-15 soft rays. The

variations in the number of meristic characters have been documented by many workers (Abdurahiman et al.,

2004), who opined that the environmental factors particularly that the temperature influences meristic

characters in the process of their growth in fishes. The variations can also be exhibited by various stocks found

in different geographical areas (Sarker et al., 2004).The present study agreed with the previous work (Bapatet

al., 1970). The meristic counts in both of the sexes were found to be quite similar resembling the earlier work.

98


IAEES www.iaees.org

99


IAEES www.iaees.org

Fig. 3 Morphometric analysis of Bombayduck, Harpodon nehereus in Male.

100


IAEES www.iaees.org

Fig. 4 Morphometric analysis of Bombayduck, Harpodon nehereus in Female.

101


IAEES www.iaees.org

Table 1 Morphometric analysis of Harpodon nehereus (Male).

Table 2 Morphometric analysis of Harpodon nehereus (Female).

Parameters

Mean

SE

Percentage Range (min-max)

Percentage range difference

% on Total length

Standard length 83.685 0.146 78.07 - 89.16 11.09

Head length 17.390 0.083 20.94 - 13.6 7.34

Pre-dorsal length 37.796 0.128 30.26 - 42.44 12.18 Length base of Dorsal fin 12.766 0.057 10.96 - 16.06 5.13 Length base of Anal fin 14.250 0.065 11.83 - 17.25 5.42

Height of Dorsal fin 16.474 0.074 13.22 - 19.17 5.95 Height of Pelvic fin 25.510 0.125 18.61 – 32.00 13.39 Height of Pectoral fin 24.266 0.158 18.18 - 30.28 12.1

Least depth of Caudal fin 4.693 0.021 4.00 - 5.92 1.92

% on Head length

Post-orbital length 79.575 0.210 73.33 - 88.57 15.24 Snout length 20.693 0.163 13.08 - 28.12 15.04

Eye diameter 12.487 0.090 10.00 - 18.52 8.52

Parameters

Mean

SE

Percentage Range (min-max)

Percentage range difference

% on Total length

Standard length 84.304 0.191 80.00 - 89.41 9.41 Head length 17.751 0.129 14.28 - 20.82 6.54 Pre-dorsal length 37.986 0.176 31.09 - 41.46 10.37 Length base of Dorsal fin 12.436 0.079 10.60 - 14.53 3.93 Length base of Anal fin 13.634 0.105 11.06 - 17.09 6.03 Height of Dorsal fin 15.805 0.103 12.36 - 17.95 5.59 Height of Pelvic fin 24.447 0.153 20.00 - 28.51 8.51 Height of Pectoral fin 23.347 0.147 19.20 - 27.87 8.67 Least depth of Caudal fin 4.679 0.030 4.02 - 5.53 1.51 % on Head length

Post-orbital length 79.453 0.229 75.51 - 87.88 12.37 Snout length 19.273 0.197 14.63 - 24.24 9.61 Eye diameter 12.227 0.112 9.75 - 15.15 5.4

102


IAEES www.iaees.org

Table 3 Regression equation of morphometric parameters of Harpodon nehereus.

Table 4 Meristic characters of Harpodon nehereus.

Parameters

Male Female

Regression equation

R2 r Regression equation

R2 r

Standard length (Y) on Total length (X)

Y=5.6675+0.5747x

0.932

0.965

Y= -1.5976+0.9067x

0.922

0.961

Head length (Y) on Total length (X)

Y=0.7397+0.1406x

0.746

0.864

Y= -1.5685+0.2398x

0.657

0.811

Pre-dorsal length (Y) on Total length (X)

Y=2.2972+0.2728x

0.831

0.912

Y= -0.5698+0.4025x

0.711

0.844

Length base of Dorsal fin (Y) on Total length (X)

Y=1.0956+0.0765x

0.661

0.813

Y=0.3788+0.1093x

0.530

0.729

Length base of Anal fin (Y) on Total length (X)

Y=1.5891+0.068x

0.589

0.773

Y=0.7489+0.1066x

0.356

0.597

Height of Dorsal fin (Y) on Total length (X)

Y=1.5413+0.0927x

0.649

0.806

Y=1.2706+0.1079x

0.394

0.628

Height of Pelvic fin (Y) on Total length (X)

Y=2.4058+0.142x

0.594

0.771

Y=1.862+0.1714x

0.440

0.663

Height of Pectoral fin (Y) on Total length (X)

Y=1.9848+0.1501x

0.607

0.779

Y=1.8812+0.1611x

0.415

0.643

Least depth of Caudal fin (Y) on Total length (X)

Y=0.4004+0.0281x

0.628

0.793

Y=0.1777+0.0389x

0.334

0.578

Post-orbital length (Y) on Head length (X)

Y=0.0602+0.7744x

0.898

0.948

Y=0.064+0.8015x

0.916

0.957

Snout length (Y) on Head length (X)

Y=0.3194+0.1204x

0.412

0.642

Y= 0.4097+0.1028x

0.327

0.572

Eye diameter (Y) on Head length (X)

Y=0.149+0.0832x

0.436

0.661

Y=0.1258+0.0917x

0.394

0.628

Parameter Meristic counts

Number of Dorsal fin rays 11 – 13 soft rays

Number of Pectoral fin rays 10 – 12 soft rays

Number of Pelvic fin rays 9 soft rays

Number of Anal fin rays 13 – 15 soft rays

103


IAEES www.iaees.org

4 Conclusion

Current study, shows high significant correlation (P<0.01) between reference length and other morphometric

features of the both sexes. On the percentage of range difference in case of male the morphometric characters

like Post orbital length and Snout length are environmentally controlled and the other characters like standard

length, pre-dorsal length, height of pelvic fin and height of pectoral fin are intermediate controlled. But, in case

of female none of morphometric characters are controlled by environmental factors and the parameters like

pre-dorsal length and post orbital length are intermediate controlled. However, the results clearly reveal that

the biometry values of H. nehereus showed a proportional positive increase with total length of fish.

References

Abdurahiman KP, Harishnayak T, Zacharia PU, Mohamed KS. 2004. Length-weight relationship of

commercially important marine fishes and shell fishes of the southern cost of Karnataka, India. World Fish

Centre Quarterly, 27(1): 9-10

Balli JJ, Chakraborthy SK, Jaiswar AK. 2011. Population dynamics of bombay duck Harpadontidaeneherus

(Ham. 1822) (Teleostomi/Harpadontidae) from Mumbai water, India. Indian Journal of Geo-Marine

Science, 40(1): 67-70

Bapat SV. 1970. The Bombay duck, Harpodon nehereus (Ham). Bulletin CMFRI, 21: 1-66

Beheregaray LB, Levy JA. 2000. Population genetics of the silverside Odontesthesargentinensis (Teleostei,

Atherinopsidae): evidence for speciation in an estuary of southern Brazil. Capeio, 441-447

CMFRI Annual Report, 2013. Central Marine Fisheries Research Institute, Cochin, Kerala, India

Ghosh S, Pillai NGK, Dhokia HK. 2009. Fishery and population dynamics of Harpadonnehereus (Ham.) off

the Saurashtra coast. Indian Journal of Fisheries, 56(1): 13-19

Johal MS, Tandon KK, Sandhu GS. 1994. Mahseer in lacustrine water, Gobindsagar reservoir. In: Mahseer –

the Game Fish (garhwal) (Nautiyal P, ed). 65-85, JagdambePrakashan, Dehradun, India

Khan MZ. 1987. A note on the Dol net fishery off Jaffrabad (Gujarat) with special reference to Bombay duck,

from 1979-‘80 to 1981-’82. Indian Journal of Fisheries, 34(2): 188-192

Khan MZ. 1986a. Dol net fishery off Nawabunder (Gujarat). Fishery Technology, 23: 92-99

Khan MZ. 1986b. Mortality and stock size estimates of the Bombay duck, Harpodon nehereus (Ham.) off

Nawabunder (Gujarat). Indian Journal of Fisheries, 33(3): 354-358

Khan MZ. 1985. Observations on the fishery of Bombay duck,Harpodon nehereus (Ham.) along the

Saurashstra coast. Indian Journal of Fisheries, 32 (4): 431-438

Khan MZ. 1989. Population dynamics of the Bombay duck, Harpodon nehereus (Ham.) off Saurashstra coast.

Indian Journal of Fisheries, 36 (2): 93-101

Krishnayya CH. 1968. Age and growth of Harpodon nehereus (Ham) and its fishery in the Hooghly estuarine

system. Journal of Zoological Society of India, 20(1&2): 129-147

Kumar VV, Reddy AD, Balakrishna C, et al. 2012a. Ecological parameters suitable for Bombayduck fishery,

Harpodon nehereus along Sunderban area of West Bengal, India. Environment and Ecology, 30(3B): 860-

864

Kumar VV, Reddy AD, Balakrishna C, et al. 2012b. Analysis of Diet composition, feeding dynamics and

proximate composition of Bombayduck, Harpodon nehereus along Sunderban area of West Bengal, India.

Achieves in Applied Science Research, 4(2): 1175-1182

104


IAEES www.iaees.org

Lowe-McConnel RH. 1971. Identification of Freshwater fishes. In: Methods for Assessment of Fish

Production in Freshwater (Ricker WE, ed). 450-489, Black well Scientific Publication, Edinburg, Oxford,

UK

Nikolsky GV. 1963. The Ecology of Fishes. Academic Press, New York, USA

Pillay TVR. 1951. A preliminary note on the food and feeding habits of the Bombay duck, Harpodon nehereus

(Ham.) in the river Matlah. Science and Culture, 17: 261-262

Pillay TVR. 1953. The food and feeding habits of the Bombay duck, Harpodon nehereus (Ham.) in the river

Matlah (Bengal). Proceedings of National Institute of Science in India, 19: 427-435

Sarker Y, Jaiswar AK, Chakraborthy SK, et al. 2004. Morphometry and length weight relationship of

Megalaspiscordyla (Linnaeus, 1758) from Mumbai coast. Indian Journal of Fisheries, 51(4): 481-486

Snedecor GW, Cochran WG. 1967. Statistical Methods. Oxford and IBH Publishing Co., Calcutta, India

105


IAEES www.iaees.org

Article

Classic models of population dynamics: assumptions about self-

regulative mechanisms and numbers of interactions between

individuals

L.V. Nedorezov

University of Nova Gorica, Vipavska Cesta 13, Nova Gorica SI-5000, Slovenia


Received 13 May 2014; Accepted 15 June 2014; Published online 1 September 2014

Abstract

Stochastic model of migrations of individuals within the limits of finite domain on a plane is considered. It is

assumed that population size scale is homogeneous, and there doesn’t exist an interval of optimal values of

population size (Alley effect doesn’t realize for population). For every fixed value of population size number

of interactions between individuals is calculated (as average in space and time). Correspondence between

several classic models and numbers of interactions between individuals is analyzed.

Keywords stochastic models; migrations; mechanistic models; self-regulative mechanisms.

1 Introduction

1 Introduction

Verhulst model (Verhulst, 1838) is one of the basic models in ecological modeling:

2xxdt

dx . (1)

In (1) )(tx is population size (or population density) at time t ; parameter is equal to difference between

intensity of birth rate and intensity of death rate; parameter , 0 const , is coefficient of influence of

self-regulative mechanisms on population dynamics; parameter /K (when 0 , and population

doesn’t eliminate for all initial values of population size) is maximum of population size which can be

achieved asymptotically. This is standard explanation of biological sense of model (1) parameters.

In (1) it is assumed that increasing of influence of self-regulative mechanisms on population size

changing (and, respectively, increasing of death rate) is proportional to population size squared (or population

density squared). This assumption is based on physical idea about paired interactions between physical objects.

In other words, it is assumed that number of interactions between individuals during rather short time period



IAEES www.iaees.org

0t is equal to tx 2 . Increasing of number of interactions leads, for example, to increase of intra-

population competition for food and space, to increase of speed of a spread of diseases in population and so on.

Thus, it leads to increase of influence of self-regulative mechanisms on population dynamics. But we have

some differences between physical and biological objects… Moreover, it isn’t obvious how we have to

determine “number of interactions” for individuals even in most primitive cases (when space is homogenous,

Alley effect doesn’t realize for considering population etc.; Allee, 1931; Odum, 1983).

Comparison of theoretical results obtained with model (1) with empirical and experimental time series

showed that in various cases this model doesn’t allow obtaining good fitting for existing datasets (see, for

example, Gause, 1934; Maynard, 1968, 1974; Pielou, 1977; Isaev et al., 1984, 2001; Brauer and Castillo-

Chavez, 2001; Nedorezov and Utyupin, 2011 and many others). In situations when model (1) allows obtaining

good fitting it is possible to point out some other models which can give better results (Nedorezov, 2011,

2012). Attempts in modifying of Verhulst’ model (1) led to appearance of some other models. In particular,

within the framework of Gompertz’ model (Gompertz, 1825) it was assumed that influence of self-regulative

mechanisms is proportional to product )ln(xx :

x

Kx

dt

dxln . (2)

In model (2) both parameters are positive. If initial value Kx 00 then Ktx )( at t . If Kx 0

then Ktx )( . Note, expression )ln(xx describes influence of self-regulative mechanisms if and only if

1x (Nedorezov, 1997; Nedorezov and Utyupin, 2011). Model (2) can be modified with saving all basic

properties:

1

1ln

x

Kx

dt

dx. (3)

In model (2) all parameters are positive, 0,, constK . Below model (3) will be called as “theta-

Gompertz model”. Within the framework of model (3) influence of self-regulative mechanisms is described by

the expression )1(ln xx , and this expression was used for fitting of datasets.

In Svirezhev’ model (Svirezhev, 1987) negative influence of self-regulative mechanisms was described

with expression 3x , and increase of population size was proportional to 2x , 0, const :

32 xxdt

dx . (4)

Within the framework of theta-logistic model (Rosenzweig, 1969; Gilpin, Ayala, 1973) which is modification

of Verhulst’ model (1), respective expression has the form x , where is positive parameter,

1 const . In literature (see overview Nedorezov and Utyupin, 2011) it is possible to find a lot of various

modifications of pointed out models (1)-(4) but in most cases influence of self-regulative mechanisms is

described as monotonic increasing function with respect to population size in any power.

Use of physical ideas for modeling of ecological processes can be very useful. In various situations it

allows obtaining important results. On the other hand, as it was pointed out above, interaction between

biological individuals doesn’t look like colliding of absolutely elastic balls. There exists a lot of various types

of interaction between individuals: it can be a competition for food and space; it can be transmission of

diseases from one individual to another one etc. Moreover, scale of population size changing may be a non-

homogenous set: for biggest part of analyzed species Allee effect is observed (Allee, 1931; Odum, 1983).

107


IAEES www.iaees.org

Influence of this effect (existence of favorable levels of local population size) leads to changing of distribution

of individuals in habitat, and respectively to changing of a number of interactions (like average of interactions

in space) between individuals. Thus, these remarks allow concluding that question about types of functions

which can be applied for description of influence of self-regulative mechanisms on population dynamics is

open.

Problem pointed out above cannot be solved analyzing empirical or experimental datasets: self-regulation

contains a lot of various biological mechanisms, real population density is unknown amount and out of control

etc. Limits of favorable zone (Allee effect) are unknown too. Thus, this problem can be solved using

mathematical model of migrations only. In such a situation all basic population parameters are under the

control, and computer experiments can be provided with important artificial assumptions. One of such models

is described and analyzed below.

2 Model

2.1 Description

Let N be a total population size, and constN during the time of providing of computer experiments. Let 2nmZ be an integer rectangular lattice on the plane 2R :

}1,1:),{(2 mjnijiZ nm .

We’ll assume that local population size is determined in knots ),( ji of the lattice 2nmZ only. Denote it as

)(txij for 2),( nmZji at time moment t . Thus, for all time moments t , ...2,1,0t , the following relation

is truthful:

Ntxn

i

m

jij

1 1

)( .

It means that there are no migrations outside the domain 2nmZ ; birth and death processes are absent too. We’ll

say that two elements of the lattice ),( 11 ji , 222 ),( nmZji are neighboring knots if and only if the following

relation is truthful:

12121 jjii .

Within the framework of model it will be assumed that migration processes from the knot ),( ji can be

observed to neighboring knots only. Within the framework of considering model we’ll assume that every

individual with equal probabilities can migrate to nearest knots or stay in initial knot. Thus, 2.0p .

2.2 Initial conditions

As it was pointed out above, for modeling of migration processes it was assumed that total population size N

is constant; thus, theoretical population density was known and equal to nmN / . Initial population

state was modeled with discrete uniform distribution: every individual with equal probabilities could appear in

every knot of the lattice 2nmZ . After determination of initial positions the process of individual’s migrations

was started. During T time steps (for providing calculations it was assumed that 20000T ) model was run

free. It is important moment because we have to have on the lattice the situation which is determined by the

rules of population migration only, and doesn’t depend on the initial state of population.

2.3 Number of interactions between individuals

Let’s assume that at any fixed time moment t local population size ltxij )( . The basic question is: how can

we calculate number of interactions between individuals? First of all, it is naturally to assume that there are no

108


IAEES www.iaees.org

interactions between individuals from different knots. The second, if epizootics play most important role in

self-regulation, we have a good background for assumption that every individual contacts with all other

individuals in determined knot. Thus, in this case the number of paired interactions is equal to 2/)1( ll .

Below results of computer experiments for this assumption about number of interactions are called “first

dataset”. But it isn’t a unique type of grouping of individuals and their paired interactions (Odum, 1983;

Maynard, 1968, 1974).

Together with pointed out variant of local interactions of individuals we’ll consider the following

situation. It will be assumed that in every knot individuals can stay separately (i.e. without contacts with other

individuals in a knot), or can stay in pair, or form a group of three individuals. Let and be stochastic

variables with geometric distribution with parameter q . Number of pairs assumed to be equal to

}2/,min{* l . Number of groups with three individuals was equal to },3/)2{( ** l . Other

individuals ( ** 32 l ) were assumed to stayed separately. In this case the number of paired interactions

was determined as ** 3 . Below results of computer experiments for this assumption about number of

interactions are called “second dataset”.

3 Results of Calculations

After 20000 free steps of model during 20000 steps number of interactions between individuals was calculated

as average in space and time (for both variants). For every fixed time moment number of interactions was

calculated for every knot of lattice, and total sum of interactions was divided on product mn . All 20000

values of averages were summarized and divided on 20000 respectively. This procedure was repeated a certain

number of times for various values of population size.

Population size N was changed from zero up to 100000 with step 1000. Respectively, population

density ]10,0[ and was changed with step 0.1. Results of calculations of numbers of interactions between

individuals are presented on Fig. 1.

Fig. 1 Results of computer experiments: changing of numbers of interaction between individuals in two different cases with respect to changing of population density.

For fitting of obtained samples (Fig. 1) four different functions pointed out above were used. Deviations

between theoretical functions and obtained samples were tested on Normality and symmetry of distributions

(Kolmogorov – Smirnov test, Lilliefors test, Shapiro – Wilk test, Mann – Whitney test, and Wald – Wolfowitz

109


IAEES www.iaees.org

test), and on existence/absence of serial correlation (Draper and Smith, 1986, 1987; Lilliefors, 1967; Shapiro et

al., 1968; Bolshev and Smirnov, 1983; Hollander and Wolfe, 1973; Bard, 1974). Note, that all computer

experiments were provided independently; thus, if any curve gives good fitting of obtained datasets no serial

correlations must be observed.

Table 1 Results of testing on normality for deviations (first dataset).

Models: Parameters minQ * KS1 L2 SW3

Verhulst 4993.0 18.0 15.0p 01.0p 510p

Theta-Gompertz

636.0 34.2

7.06 2.0p 01.0p 00006.0p

Svirezhev 058.0 1420.4 05.0p 01.0p 510p

Theta-logistic 5.0 ,

0.2

0.18 15.0p 01.0p 510p

1KS – Kolmogorov – Smirnov test; 2L – Lilliefors test; 3SW – Shapiro – Wilk test; minQ * is minimal value of minimized functional form.

For the case when 100 nm , and parameter of geometric distribution q is equal to 2.0 , results of

testing on Normality of deviations for four classic models (more precisely, deviations between computer

results of calculation of number of interactions and functions in classic models which describe the influence of

self-regulative mechanisms) are presented in Tables 1 and 2. Parameters of functions were determined with

Least Square Method.

Results presented in table 1 show that best approximations were obtained with Verhulst and Theta-

logistic models. For both models 999992.02 R . For Svirezhev model 9379.02 R , and for Theta-

Gompertz model 9997.02 R . As we can see in all cases correlation coefficient 2R is very close to one,

and it means that we have rather good approximation for first dataset. On the other hand, Lilliefors test and

Shapiro – Wilk test showed that in all four considering cases with 1% significance level we have to reject

hypotheses about Normality of residuals. Thus, from the standpoint of traditional imagination about good

model (Bard, 1974) all functions are not suitable for fitting of first dataset.

Table 2 Results of testing on Normality for deviations (second dataset).

Models: Parameters minQ * KS1 L2 SW3

Verhulst 0642.0 268.38 05.0p 01.0p 510p

Theta-Gompertz

3947.0 , 3468.0

0.1957 15.0p 01.0p 510p

Svirezhev 0072.0 117.35 05.0p 01.0p 510p

Theta-logistic 3758.0 ,

1543.1

0.327 15.0p 01.0p 510p

1KS – Kolmogorov – Smirnov test; 2L – Lilliefors test; 3SW – Shapiro – Wilk test; minQ * is minimal value of minimized functional form.

110


IAEES www.iaees.org

The similar situation is observed for results presented in Table 2: Lilliefors test and Shapiro – Wilk test

showed that in all four considering cases with 1% significance level we have to reject hypotheses about

Normality of residuals. The best result was obtained for Theta-Gompertz model with 999258.02 R . For

Theta-logistic model 99876.02 R . For Svirezhev model this characteristics is rather small: 5548.02 R .

Like in previous case, from the standpoint of traditional imagination about good model (Bard, 1974) all

functions are not suitable for fitting of second dataset.

It is important to note that assumption about Normality of deviations between theoretical curves and

experimental datasets (in considering situation we have to talk about results of computer experiments) is rather

strong. Softer assumption is following: distribution density must be symmetric with respect to origin. Results

of checking of hypotheses about symmetry for both datasets are presented in Tables 3 and 4.

Table 3 Results of testing on symmetry for deviations (first dataset).

Models: KS1 WW2 MW3 Verhulst 1.0p 9968.0p 3573.0p

Theta-Gompertz 005.0p 3792.0p 016.0p

Svirezhev 1.0p 3196.0p 5335.0p

Theta-logistic 1.0p 5352.0p 5156.0p 1KS – Kolmogorov – Smirnov test; 2WW – Wald – Wolfowitz test; 3MW – Mann – Whitney test

In creation of conclusions about properties of datasets we’ll follow to the next basic principle: if one of

using tests gives a negative result we have to reject Null hypothesis, and it doesn’t depend on results obtained

with other tests. In particular, Kolmogorov – Smirnov test showed that we have to reject hypothesis about

symmetry of residuals obtained for Theta-Gompertz model with very small significance level (Table 3). In

other cases we cannot reject Null hypothesis about symmetry even with 10% significance level.

Table 4 Results of testing on symmetry for deviations (second dataset).

Models: KS1 WW2 MW3 Verhulst 1.0p 5586.0p 7887.0p

Theta-Gompertz 001.0p 009.0p 0009.0p

Svirezhev 1.0p 8422.0p 9423.0p

Theta-logistic 001.0p 0049.0p 0005.0p 1KS – Kolmogorov – Smirnov test; 2WW – Wald – Wolfowitz test; 3MW – Mann – Whitney test

Results presented in Table 4 allow concluding that deviations obtained for Theta-Gompertz model and

Theta-logistic model haven’t symmetric distributions: we have to reject hypotheses about symmetry even with

1% significance level. It is interesting to note that biggest values of probabilities were obtained for Svirezhev

model which has biggest value of minimizing functional form (Table 2).

As it was pointed out above for every value of population size (density ) computer experiments were

provided independently (Fig. 1). Additionally, we can consider population density as independent variable, as

111


IAEES www.iaees.org

a sequence of fixed time moments. Independence of computer experiments means that deviations between

theoretical and experimental results are independent stochastic variables. Thus, we cannot have correlation in

sequence of residuals if used model gives good fitting of dataset.

Critical values for Durbin – Watson test for 100 experimental points and one predictor variable are

following: 65.1Ld and 69.1Ud for 5% significance level and 52.1Ld and 56.1Ud for 1%

significance level (Draper and Smith, 1986, 1987). For first dataset we have the following results: for Verhulst

model 0268.0d ; for Svirezhev model 3901.0d ; for Theta-logistic model 0268.0d . Thus, in all

cases we have to reject hypothesis about absence of correlation with 1% significance level. For second dataset

we have the following results: for Verhulst model 0047.0d ; for Svirezhev model 0153.0d . For this

dataset we have also to reject hypothesis about absence of serial correlation.

For checking hypothesis about absence/existence of serial correlation we also used serial test (Draper and

Smith, 1986, 1987). For first dataset we have the following results: for Verhulst model number of positive

deviations is equal to 49, 491 n , number of negative deviation is equal to 51, 512 n , number of groups is

equal to 50, 50u , and 0965.0z (standard normal stochastic variable). Taking into account that

47.0}1.0{ zP we can conclude that observed combination of deviations with different signs and their

groups has very big probability. Thus, in this case we have no reasons for rejecting hypothesis about absence

of serial correlation. The same results we have for Theta-logistic model. For Svirezhev model 851 n ,

152 n , 2u , 554.9z ; thus, for this model combination of deviations with different signs and their

groups has very small probability, thus, we have to reject hypothesis about absence of serial correlation.

For second dataset we have the following results: for Verhulst model number of positive deviations is

equal to 81, 811 n , number of negative deviation is equal to 19, 192 n , number of groups is equal to 2,

2u , and 623.9z ; probability that z less or equal to -9.623 is very small, 002.0}3{ zP . For

Svirezhev model 851 n , 152 n , 2u , 554.9z . For both models we have to reject hypotheses

about absence of serial correlations in sequences of residuals.

4 Conclusion

Computer experiments with stochastic model of migrations of individuals on a plane under conditions that

population size is constant (no birth and death rates, no migrations out of and in to considering domain,

homogenous structure of locations) allowed obtain two various datasets of interactions between individuals.

First dataset was obtained for the case when in every location every individual connected with all other

individuals. Second dataset was obtained for the situation when in locations individuals could stay separately

or organize group in two or three individuals.

A lot of classic models of population dynamics were constructed under the assumption that influence of

self-regulative mechanisms is determined by numbers of interactions between individuals. Approximation of

obtained datasets by various functions describing influence of self-regulative mechanisms (in Verhulst, Theta-

Gompertz, Svirezhev, and Theta-logistic models) showed that all functions are not suitable for fitting of

second dataset. For the first dataset Verhulst model and Theta-logistic model can be used for fitting. More

precisely, last models have good backgrounds for it; but from the standpoint of traditional imagination about

good and bad models (Bard, 1974) Verhulst and Theta-logistic equations are not suitable for approximation.

When requirements for used model are not so strong (in particular, when distribution of residuals must be

symmetric only, and in sequence of residuals serial correlation cannot be observed) these model can be used

for fitting.

Obtained results don’t allow concluding that used models cannot be applied for modeling of population

dynamics. We obtained the background for conclusion that within the frameworks of considered models

112


IAEES www.iaees.org

influence of intra-population self-regulative mechanisms haven’t strong correlation with numbers of

interactions between individuals.

References

Allee WC. 1931. Animal Aggregations: A Study in General Sociology. Chicago University Press, Chicago,

USA

Bard Y. 1974. Nonlinear Parameter Estimation. Academic Press, San Francisco, London, USA

Bolshev LN, Smirnov NV. 1983. Tables of Mathematical Statistics. Nauka, Moscow, Russia

Brauer F, Castillo-Chavez C. 2001. Mathematical Models in Population Biology and Epidemiology. Springer-

Verlag, NY, USA

Draper NR, Smith H. 1986. Applied Regression Analysis. V.1. Finance and Statistics, Moscow, Russia.

Draper NR, Smith H. 1987. Applied Regression Analysis. V.2. Finance and Statistics, Moscow, Russia

Gause GF. 1934. The Struggle for Existence. Williams and Wilkins, Baltimore, USA

Gilpin ME, Ayala FJ. 1973. Global models of growth and competition. Proceedings of the National Academy

of Sciences USA, 70: 3590-3593

Gompertz B. 1825. On the nature of the function expressive of the law of human mortality and on a new model

of determining life contingencies. Philosophical Transactions of the Royal Society London, 115: 513-585

Hollander M, Wolfe DA. 1973. Nonparametric statistical methods. John Wiley & Sons, New York-Sydney-

Tokyo-Mexico City, USA

Isaev AS, Khlebopros RG, Nedorezov LV, et al. 1984. Forest Insect Population Dynamics. Nauka,

Novosibirsk, Russia

Isaev AS, Khlebopros RG, Nedorezov LV, et al. 2001. Population Dynamics of Forest Insects. Nauka,

Moscow, Russia

Lilliefors HW. 1967. On the Kolmogorov-Smirnov test for normality with mean and variance

unknown. Journal of the American Statistical Association 64: 399-402

Maynard SJ. 1968. Mathematical Ideas in Biology. Cambridge University Press, Cambridge, USA

Maynard SJ. 1974. Models in Ecology. Cambridge University Press, Cambridge, USA

Nedorezov LV. 1997. Course of Lectures on Ecological Modeling. Siberian Chronograph, Novosibirsk, Russia

Nedorezov LV. 2011. Analysis of some experimental time series by Gause: Application of simple

mathematical models. Computational Ecology and Software, 1(1): 25-36

Nedorezov LV. 2012. Gause’ Experiments vs. Mathematical Models. Population Dynamics: Analysis,

Modelling, Forecast, 1(1): 47-58

Nedorezov LV, Utyupin YuV. 2011. Continuous-Discrete Models of Population Dynamics: An Analytical

Overview. State Public Scientific-Technical Library of Russian Academy of Sciences, Novosibirsk, Russia

Odum EP. 1983. Basic Ecology. Saunders College Pub., Philadelphia, USA

Pielou EC. 1977. Mathematical Ecology. John Wiley and Sons, NY, USA

Rosenzweig ML. 1969. Why the prey curve has a hump. American Naturalist, 103: 81-87

Shapiro SS, Wilk MB, Chen HJ. 1968. A comparative study of various tests of normality. Journal of the

American Statistical Association 63: 1343-1372

Svirezhev YuM. 1987. Nonlinear Waves, Dissipative Structures and Catastrophes in Ecology. Nauka, Moscow,

Russia

Verhulst PF. 1838. Notice sur la loi que la population suit dans son accroissement. Corresp. Math. et Phys., 10:

113-121

113


IAEES www.iaees.org

Article

Multivariate statistical analysis of surface water chemistry: A case

study of Gharasoo River, Iran

MH Sayadi 1, A Rezaei1, MR Rezaei1, K Nourozi2 1Environmental Department, University of Birjand, Birjand, Iran 2Department of Environmental Protection Kermanshah, Iran


Received 8 May 2014; Accepted 15 June 2014; Published online 1 September 2014

Abstract

Regional water quality is a hot spot in the environmental sciences for inconsistency of pollutants. In this paper,

the surface water quality of the Gharasoo River in western Iran is assessed incorporating multivariate statistical

techniques. Parameters like EC, TDS, pH, HCO3-, Cl-, SO4

2-, Ca2+, Mg2+ and Na+ were analyzed. Principal

component and factor analysis is showed the parameters generated 3 significant factors, which explained

73.06℅ of the variance in data sets. Factor 1 may be derived from agricultural activities and subsequent release

of EC, TDS, SO42- and Na+ to the water. Factor 2 could be influenced by domestic pollution and explained the

deliverance of HCO3-, Cl- and Mg2+ into the water. Factor 3 contains hydro-geochemical variable Ca2+ and pH,

originating from mineralization of the geological components of bed sediments and soils of watershed area.

Likewise, the clustering analysis generated 3 groups of the stations as the groups had similar characteristic

features. Pearson correlation analysis showed significant correlations between HCO3- and Mg2+ (0.775), Ca2+

(0.552) as well as TDS and Na+ (0.726). With reference to multivariate statistical analyses it can be concluded

that the agricultural, domestic and hydro-geochemical sources are releasing the pollutants into the Gharasoo

River water.

Keywords anthropogenic activities; geological components; Gharasoo River; PCA; water quality.

1 Introduction

1 Introduction

The surface water quality is truly a sensitive issue today because of its effects on human health and aquatic

ecosystems. Rivers are highly vulnerable to pollution attributing to their role in carrying off the municipal and

industrial wastewater and runoff from agriculture in their vast drainage basins. Anthropogenic influences, as

well as natural processes, deteriorate surface water and impair their use for drinking, industrial, agricultural


IAEES

and recre

Rezaei, 2

The

on receiv

water is

weatherin

From

widely u

et al., 20

to invest

natural in

similariti

sources (

possible

2 Materi

2.1 Stud

The Gha

is approx

diplomat

collects w

lies betw

above se

Rainfall

Proceedings

eational purpo

2014).

e environmen

ving water ar

most vulne

ng of crystal

m many met

used, being ca

06; Wenning

tigate the Gh

nfluences on

ies or dissim

(natural and

sources deter

ial and Meth

y Area

rasoo River s

ximately 20.7

tic area in we

water from K

ween latitudes

ea level (Fig.

occurs during

of the Internati

oses (Sayadi

ntal impacts o

re numerous

erable to po

materials, an

thods availab

apable of dete

g and Erickso

harasoo river

the river wat

milarities betw

anthropogeni

rmining wate

hods

system forms

7 kilometers a

estern Iran. G

Kermanshah a

s 46° 36´ - 47

. 1). The me

g the autumn

Fig

ional Academy

et al., 2010;

of agricultural

and inputs o

llution due

nd anthropoge

ble, Cluster A

ecting similar

on, 1994). In t

r water quali

ter quality. Th

ween monitor

ic) on water

er quality para

with joining

and runs thro

Gharasoo Rive

and Kurdista

7° 37´ N and

ean annual te

and winter (D

g. 1 Location o

y of Ecology and

Sayadi and S

l runoff, mun

of contamina

to natural p

enic influence

Analysis (CA

rities among s

this work, PC

ity and discr

he objective

ring periods a

quality param

ameters of the

of two main

ough the city

er is one of th

an provinces

d longitudes 3

emperature an

December to

f sample sites o

d Environmenta

Sayyed, 2011;

nicipal wastew

ants can be h

processes, su

es (Sundaray

A) and Princ

samples and/o

CA and hierar

riminate relat

of the study

and monitori

meters, and (

e Gharasoo R

branches of M

of Kermansh

he most impo

and delivers

34° 00´- 34°

nd rainfall ar

March).

on the Gharasoo

al Sciences, 20

; Sayyed and

water and ind

hazardous to

uch as precip

et al., 2006).

cipal Compon

or variables (

rchical cluste

tive magnitu

is to extract i

ng sites, (2)

3) source ide

River.

Merek and R

hah. Kermans

ortant tributar

it to Saymar

91´ E with t

re 14°C and

o River.

14, 4(3): 114-12

w

Sayadi, 2011

dustrial efflue

the environm

pitation inpu

nent Analysi

(Acque et al.,

er analysis ha

ude of anthro

information a

the influence

entification fo

Raz Avar Rive

shah city is l

ries of Sayma

reh River. Th

the height of

456.8 mm,

22

www.iaees.org

1; Sayadi and

ent discharge

ment. Surface

uts, erosions,

is (PCA) are

1995; Wang

ave been used

opogenic and

about; (1) the

e of possible

or estimating

ers. Its length

ocated in the

areh River. It

he study area

f 1322 meters

respectively.

d

e

e

,

e

g

d

d

e

e

g

h

e

t

a

s

.

115


IAEES www.iaees.org

Data sets of 9 parameters of the water quality were monitored monthly over a period of 2009-2010.

Monitoring stations are shown in (Fig. 1). The selected parameter for the determination of water quality

characteristics were EC, PH, TDS, bicarbonate (HCO3-), chloride (Cl‾), sulfate (SO4

2-), calcium (Ca2+),

magnesium (Mg2+) and sodium (Na+). The parameters were analyzed according to standard methods (APHA-

AWWA-WPCF, 1985; APHA, 1999). The results were evaluated via multivariate statistical analysis

techniques. All statistical computations were made using SPSS statistical software.

2.2 Principal Component Analysis (PCA)

PCA is designed to transform the original variables into new and uncorrelated variables called the principal

components, which are linear combinations of the original variables (Zhang, 2011; Vieira, 2012). It provides

information on the most significant parameters due to spatial and temporal variations that describes the whole

data set by excluding the less significant parameters with minimum loss of the original information (Helena et

al., 2000; Kannel et al., 2007). The principal component can be expressed as

Zij=ai1 x1j + ai2 x2j + … + aim xmj (1)

where z is the component score, a is the component loading, x is the measured value of the variable, I is the

component number, j is the sample number, and m is the total number of variables.

Factor analysis follows principal component analysis. The main purpose of factor analysis is to reduce the

contribution of less significant variables and to simplify even more the data structure coming from the

principal component analysis. This purpose can be achieved by rotating the axis defined by principal

component analysis according to well established rules, and constructing new variables, also called vary

factors. A small number of factors will usually account for approximately the same amount of information as

does the much larger set of original observations (Shrestha and Kazama, 2007). The Factor analysis can be

expressed as:

Zji = af1 f1i + af2 f2i + af3 f3i + … + afmfmi + efi (2)

where z is the measured value of a variable, a is the factor loading, f is the factor score, e is the residual term

accounting for errors or other sources of variable number, and m is the total number of factors.

2.3 Cluster Analysis (CA)

CA is a multivariate technique, whose primary purpose is to classify the objects of the system into categories

or clusters based on their similarities (Zhang, 2012), and the objective is to find an optimal grouping for which

the observation or objects within each cluster are similar, but the cluster is dissimilar to each other.

Hierarchical clustering is the most common approach in which clusters are formed sequentially. The most

similar objects are first grouped, and these initial groups are merged according to their similarities. Eventually

as the similarity decreases all subgroups are merged into a single cluster. CA was applied to surface water

quality data using a single linkage method. In the single linkage method, the distances or similarities between

two clusters A and B are defined as the minimum distance between a point A and a point in B:

D (A, B) = min {d (xi+xj), for xi in A and xj in B} (3)

where d (xi +xj) is the Euclidean distance in (3). At each step the distance is found in every pair of clusters and

the two clusters with smallest distance are merged. When over two clusters are merged the procedure is

repeated for the next step: the distances between all pairs of clusters are calculated again, and the pair with the

minimum distance is merged into a single cluster. The result of a hierarchical clustering procedure can be

displayed graphically using a tree diagram, also known as a dendrogram, which shows all the steps in the

hierarchical procedure (Alkarkhi et al., 2008; Johnson and Wichern, 2002).

116


IAEES www.iaees.org

3 Results and Discussion

Table 1 summarizes briefly the mean, maximum and minimum values besides standard deviation and variance

of the 9 measured parameters in the river water samples from the five stations. It is interesting to note that the

high standard deviations of the parameters indicating changeability in chemical composition between the

samples, shows the temporal variations which appears by lithogenic and anthropogenic sources.

Table 1 Simple statistical analysis of water quality parameters at different locations on the Gharasoo River.

Station EC pH TDS HCO3- Cl SO4

2- Ca Mg Na Station1

Mean Std. Variance Minimum Maximum

372 53.8 290 172 437

7.8 0.46 0.21 6.53 8.57

2.4 35.2 1.24 108 280

3.3 0.55 0.31 2.31 5.06

0.520.220.050.161.10

0.49 0.27 0.07 0.1 1.29

2.7 0.42 0.18 1.91 3.41

1.3 0.38 0.15 0.56 2.24

0.36 0.17 0.03 0.09 0.91

Station2

Mean Std. Variance Minimum Maximum

437 96 91.70 329 661

7.7 0.46 0.22 6.70 8.52

280 61 37.45211 423

3.73 0.8 0.6 2.56 5.43

0.560.250.060.160.96

0.49 0.27 0.07 0.14 0.92

2.9 0.43 0.19 2.01 3.55

1.47 0.65 0.42 0.78 2.80

0.43 0.31 0.09 0.16 1.16

Station3 Mean Std. Variance Minimum Maximum

404 56.61 321 320 540

7.79 0.36 0.13 7.04 8.40

285 36.18130 205 346

3.43 0.68 0.46 2.30 5.11

0.660.140.020.380.91

0.59 0.28 0.0810.20 1.36

2.94 0.42 0.18 2.37 3.37

1.42 0.42 0.18 0.81 2.40

0.38 0.08 0.01 0.25 0.59


434 111 124 312 663

7.86 0.37 0.13 7.19 8.66

275 71.5151.14199 424

3.58 0.93 0.87 2.10 6.46

0.520.220.050.221.00

0.72 0.52 0.28 0.16 2.71

2.77 0.50 0.25 1.41 3.49

1.56 0.58 0.34 0.56 3.00

0.55 0.53 0.28 0.06 2.20


494 491 241 340 520

7.37 0.13 0.02 7.32 7.80

336 199 397 320 390

4.00 0.29 0.08 3.44 4.38

0.430.040.010.360.50

0.91 0.14 0.02 0.64 1.11

3.00 0.08 0.01 2.80 3.13

1.94 0.41 0.17 1.00 2.50

0.45 0.03 0.00 0.39 0.49

3.1 Application of PCA to Gharasoo River data set

A particular problem in the surface water quality monitoring is the complexity associated with analyzing a

large number of measured variables (Saffran et al., 2001). Therefore, in this study, surface water quality data

were grouped using FA. The correlation matrix of variables was generated and factors were extracted by the

centroid method, rotated by Varimax. From the results of the FA, the first three eigenvalues were found to be

bigger than 1 (Fig. 2). According to the Fig. 2 and a subsequent interpretation of the factor loadings, the first

three components were extracted and the other components have been eliminated.

117


IAEES www.iaees.org

Fig. 2 Screen plot of the eigenvalue and component number.

Table 2 presents the total variance explained by the first three factors for both related and unrelated factor

loadings. The parameter loading three factors in the two from FA associated with each factor stations are well

defined and contribute slightly to other factors, which help not only in the interpretation of the results but also

in the identification of anthropogenic sources of pollution from the surface water quality data. FA generated

three significant factors, which explained 73.06℅ of the variance in data sets, where a correlation greater than

0.75 is considered “strong”; 0.75-0.50, “moderate”; and 0.50-0.30, as “weak” significant factor loading (Liu et

al., 2003).

Table 2 Extracted values of various FA parameters.

Component Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings

Total % of Variance Cumulative % Total % of Variance Cumulative %

1 3.85 42.86 42.86 2.81 31.23 31.23

2 1.53 17.03 59.89 2.47 27.49 58.72

3 1.18 13.16 73.06 1.29 14.33 73.06

Table 3 Loadings of 9 experimental variables on 3 significant Principal components,

rotated factor loadings matrix

Variables Factor 1 Factor 2 Factor 3 EC 0.831 0.360 0.087 pH -0.180 0.180 -0.687 TDS 0.858 0.306 0.102 HCO3

- 0.102 0.844 0.422 Cl 0.220 0.720 -0.221 SO4

2- 0.740 -0.184 0.198 Ca -0.040 0.389 0.716 Mg 0.240 0.820 0.046 Na 0.829 0.361 -0.136

118


IAEES www.iaees.org

As shown in tables 2 and 3, the first factor (Factor 1), accounted for 31.23 of the total variance, was high

positive loading in EC, TDS, SO42-and Na+ which were 0.831, 0.858, 0.740 and 0.829 respectively. This factor

represents the contribution of nonpoint pollution from agricultural areas. In these areas, farmers use sulfate

fertilizers, and the stream receives sulphate via surface runoff and irrigation waters. As a result shown increase

in SO42- concentrations may be due to agricultural activities (Krouse, 1997). The contribution of Na+ to this

factor can be considered a result of action-exchange processes in soil–water interface (Guo and Wang, 2004).

Factor 2 explains 27.49% of the total variance and is the positively correlated with HCO-, Cl¯ and Mg2+. This

factor represents the contribution of point pollution and the physico-chemistry of the stream. While point

pollution is from domestic wastewater, nonpoint pollution is from agricultural and livestock farms. Mg2+ is a

basic metal which increases alkalinity of the environment (Razmkhah et al., 2010). This factor may also be due

to anthropogenic activities such as domestic waste water or influents. Nevertheless, the release of domestic

effluents into the river water caused the dramatic Cl- increase. The loading for factor 3 was 18.92% with Ca2+

and pH. Thus, this factor contains hydro-geochemical variable Ca2+, originating, at a first glance, from

mineralization of the geological components of soils as well as moderate decrease of pH concentration. The

contribution of Ca2+ to this factor can be considered a result of action-exchange processes in soil–water

interface (Guo and Wang, 2004) as the results demonstrated an increase in EC, TDS, SO42- and Cl¯

concentrations due to agricultural and domestic waste water activities. Sources of dissolved SO42- in natural

river waters may include dissolution of sedimentary sulfates, oxidation of both sulfide minerals and organic

materials, and anthropogenic inputs.

3.2 Pearson correlation

Statistical analysis using Pearson correlation showed that the parameters in the water samples collected from

Gharasoo river were weak and moderately correlated to each other at p <0.01 and p <0.05 levels. A significant

positive correlation was found to exist between EC and TDS (0.918), HCO3- (0.432), Cl¯ (0.381), SO4

-2 (0.411),

Mg2+ (0.421), and a positive correlation was found between EC and Na+ (0.721) at p <0.01 (Table 4).

Similarly, there were significant correlations between TDS and HCO3- (0.387), Cl¯ (0.369), SO4

2-(0.434),

Mg2+ (0.385) and a positive correlation between TDS and Na+ (0.726) at p <0.01 in the collected water

samples of the study region. The level of TDS reflects the pollutant burden of the water. High levels of

dissolved and suspended solids in water systems increase the biological and chemical oxygen demand

(Jonnalagadda and Mhere, 2001). Similarly, some correlations were also observed (Table 4) between HCO3-

and Cl- (0.373), Na+ (0.387) and a positive strong correlation was found between HCO3- and Mg2+ (0.775)

and Ca2+ (0.552) at p <0.01. Likewise, Li and Zhang (2009) indicated a strong positive correlation between

HCO3-, Ca2+ and Mg2+in Geochemistry of the upper Han River basin, China. There were as well significant

positive correlations between Cl¯- Mg2+ (0.506), Cl--Na+ (0.453), SO4-2 - Na+ (0.529), and Mg2+ - Na+ (0.459)

at p <0.01 level (Table 4). Chloride concentration is higher in wastewater than raw water because sodium

chloride, the commonest component of the human diet passes unchanged through the digestive system (WHO,

2008).

It is interesting to note that in this study there is no significant correlation between pH and other

parameters. Similarly, Chigor et al. (2012) exhibited nil correlation between pH and other contaminated

parameters in surface water sources used for drinking and irrigation in Zaria, Nigeria.

3.3 Hierarchical cluster analysis (HCA)

Spatial similarity and monitoring stations grouping is shown in Fig. 3. In this study, the classification of

monitoring stations was performed incorporating HCA, and a dendrogram was composed.

119


IAEES www.iaees.org

Table 4 Pearson correlation between different water quality parameters of the study site.

Discriminate variables

EC pH TDS HCO3- Cl SO4

-2 Ca Mg Na

EC 1.00

pH -0.126 1.00 TDS 0.918** -0.177 1.00 HCO3

- 0.432** -0.140 0.387** 1.00 Cl 0.381** 0.070 0.369** 0.373** 1.00 SO4

-2 0.411** -0.086 0.434** -0.039 0.014 1.00 Ca 0.169 -0.096 0.148 0.552** 0.175 0.204* 1.00 Mg 0.421** -0.017 0.385** 0.775** 0.506** 0.166 0.180* 1.00 Na 0.721** -0.017 0.726** 0.387** 0.453** 0.529** 0.000 0.459** 1.00

**. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed).

Fig. 3 Dendrogram of the CA according to single linkage method.

The clustering procedure generated 3 groups of stations in a very convincing way, as the sites in these

groups have similar characteristic features and natural background source types. Cluster 1 (Stations 2, 3 and 4),

Cluster 2 (Station 1) and Cluster 3 (Station 5) correspond to a relatively low to high polluted regions. Hence,

the temporal variation in the Gharasoo river water quality was greatly determined by agricultural and

municipal activities as well as lithogenic sources which confirm the result of the PCA. In fact, Fig. 3 shows

that the patterns of pollution sources of Gharasoo river water.

4 Conclusion

In this study, multivariate statistical methods including factor, principal component and cluster analysis were

applied to surface water quality data sets obtained from the Gharasoo River in Iran. The results suggest that

anthropogenic activities such as agricultural and domestic pollution sources and lithogenic activities had

significant effects on water quality. Three factors explaining the 73.06℅ of the total variance in the surface

water quality data set were determined. Based on the above results, Factor 1 may be derived from agricultural

120


IAEES www.iaees.org

activities and release the EC, TDS, SO42- and Na+ to the environment. Factor 2 could be influenced by

domestic pollution and explained the deliverance of HCO-3, Cl¯ and Mg2+ into the surface water of Gharasoo

River. Factor 3 contains hydro-geochemical variable Ca2+ and pH, originating from mineralization of the

geological components of bed sediments and soils of watershed area. Cluster analysis grouped the monitoring

stations into 3 clusters of similarity based upon water quality characteristics at different stations. These results

reveal that agricultural, domestic and hydro-geochemical sources are responsible for pollutions in terms of

water quality in Gharasoo River.

Acknowledgment

The authors would like to appreciate the Department of Environment, Head Office, Kermanshah city for their

cooperation and support. Authors are appreciated the authorities of Research Council and Faculty of Natural

Resources and Environment, University of Birjand, due to their sincere cooperation. We also like to thank Dr.

Mrs. Mahavash F. Kavian for editing the paper.

References

Acque RS, Battegazzore M, Renoldi M. 1995. Integrated chemical and biological evaluation of the quality of

the River Lambro (Italy). Water Air and Soil Pollution, 83(3-4): 375-390

Alkarkhi A FM, Ahmad A, Easa A M. 2008. Assessment of surface water quality of selected estuaries of

Malaysia: multivariate statistical techniques. The Environmentalist, 29(3): 255-262

APHA-AWWA-WPCF. 1985. Standard methods for the Examination of Water and Wastewater (16th ed),

American Public Health Association, American Water Works Association, Water Pollution Control

Federation, USA

American Public Health Association (APHA). 1999. Standard methods for the examination of water and

wastewater (20th ed.). Washington D.C.: APHA, AWWA, Washington DC, USA

Chigor VN, Umoh VJ, Okuofu CA, et al. 2012. Water quality assessment: surface water sources used for

drinking and irrigation in Zaria, Nigeria are a public health hazard. Environmental monitoring and

assessment, 1845: 3389-3400

Guo H, WangY. 2004. Hydrogeochemical processes in shallow quaternary aquifers from the northern part of

the Datong Basin, China. Applied Geochemistry, 19(1): 19-27

Helena B, Pardo R, Vega M, Barrado E. 2000. Temporal evolution of groundwater composition in an alluvial

aquifer (Pisuerga River, Spain) by principal component analysis. Water Research, 34(3): 807-816

Johnson RA, Wichern DW. 2002. Applied Multivariate Statistical Analysis (Vol. 5). 1-13, Prentice Hall

Upper Saddle River, NJ, USA

Jonnalagadda SB, Mhere G. 2001. Water quality of the odzi river in the Eastern Highlands of Zimbabwe.

Water Research, 35(10): 2371-2376

Kannel PR, Lee S, Kanel SR, Khan S P. 2007. Chemometric application in classification and assessment of

monitoring locations of an urban river system. Analytica Chimica Acta, 582(2): 390-399

Krouse HR. 1997. Application of the stable isotope composition of S O 4 to tracing anomalous TDS in Nose

Creek , southern Alberta , Canada IRegional Bow River. Applied Geochemistry, 12(97): 567-575

Li S, Zhang Q. 2009. Geochemistry of the upper Han River basin, China. 2: Seasonal variations in major ion

compositions and contribution of precipitation chemistry to the dissolved load. Journal of hazardous

materials, 170(2-3): 605-611

121


IAEES www.iaees.org

Liu CW, Lin KH, Kuo YM. 2003. Application of factor analysis in the assessment of groundwater quality in a

blackfoot disease area in Taiwan. The Science of the Total Environment, 313(1-3): 77-89

Razmkhah H, Abrishamchi A, Torkian A. 2010. Evaluation of spatial and temporal variation in water quality

by pattern recognition techniques: A case study on Jajrood River (Tehran, Iran). Journal of environmental

management, 91(4): 852-860

Saffran K, Environment A, Cash K, Canada E. 2001. Canadian water quality guidelines for the protection of

aquatic life, CCME water quality Index 1, 0. User‘s Manual. Excerpt from Publication No. 1299, Canada

Sayadi MH, Rezaei MR. 2014. Impact of land use on the distribution of toxic metals in surface soils in Birjand

city, Iran. Proceedings of the International Academy of Ecology and Environmental Sciences, 4(1): 18-29

Sayadi MH, Sayyed MRG, et al. 2010. Short-term accumulative signatures’ of heavy metal in river bed

sediments, Tehran Iran. Environmental Monitoring and Assessment, 162: 465-473

Sayadi MH, Sayyed MRG. 2011. Comparative assessment of baseline concentration of the heavy metals in the

soils of Chitgar Industrial Area Tehran (Iran) with the comprisable reference data. Environmental Earth

Sciences, 63(6): 1179-1188

Sayyed MRG, Sayadi MH. 2011. Variations in the heavy metal accumulations within the surface soils from the

Chitgar Industrial Area of Tehran (Iran). Proceedings of the International Academy of Ecology and

Environmental Sciences, 1(1): 27-37

Shrestha S, Kazama F. 2007. Assessment of surface water quality using multivariate statistical techniques: A

case study of the Fuji river basin, Japan. Environmental Modelling & Software, 22(4): 464-475

Sundaray SK, Panda UC, Nayak BB, Bhatta D. 2006. Multivariate statistical techniques for the evaluation of

spatial and temporal variations in water quality of the Mahanadi river-estuarine system (India)--a case

study. Environmental geochemistry and health, 28(4): 317-330

Vieira VMNCS. 2012. Permutation tests to estimate significances on Principal Components Analysis.

Computational Ecology and Software, 2(2): 103-123

Wang YYS, Lou ZZP, Sun CC C, Wu MML, Han SH. 2006. Multivariate statistical analysis of water quality

and phytoplankton characteristics in Daya Bay, China, from 1999 to 2002. Oceanologia, 48(2)

Wenning RJ, Erickson GA. 1994. Interpretation and analysis of complex environmental data using

chemometric methods. TrAC Trends in Analytical Chemistry, 13(10): 446-457

World Health Organization. 2008. Guideline to drinking water quality (3rd ed., Vol. 1). World Health

Organization, Geneva, Switherlands

Zhang WJ. 2011. Simulation of arthropod abundance from plant composition. Computational Ecology and

Software, 1(1): 37-48

Zhang WJ. 2012. Computational Ecology: Graphs, Networks and Agent-based Modeling. World Scientific,

Singapore

122


IAEES www.iaees.org

Article

Detecting barriers and facilities to species dispersal: Introducing

sloping flow connectivity

Alessandro Ferrarini

Department of Evolutionary and Functional Biology, University of Parma, Via G. Saragat 4, I-43100 Parma, Italy

E-mail: [email protected], [email protected]

Received 28 April 2014; Accepted 2 June 2014; Published online 1 September 2014

Abstract

Connectivity in ecology deals with the problem of how biotic dispersals can happen, given actual landscape

properties and species presence/absence over such landscape. Recently I have introduced a modelling approach

(flow connectivity) to ecological connectivity that is alternative to circuit theory, and is able to fix the weak

point of the “from-to” connectivity approach. In addition, I’ve introduced “reverse flow connectivity” that

couples evolutionary algorithms to partial differential equations in order to fix the problem of subjectivity in

the attribution of friction values to landscape categories. I’ve also showed that flow connectivity can be used to

predict biotic movements happened in the past (backward flow connectivity). To date, there has been little

effort by conservation scientists towards detecting restoration opportunities by mapping barriers that strongly

reduce movement potential. In this paper, I introduce a new kind of theoretical and modelling approach called

“sloping flow connectivity”. The goal of such proposal is to individuate and map barriers and facilities to

species dispersals over the landscape. I define here a barrier as a landscape feature that impedes biotic

movements, the removal of which would increase the potential for biotic shifts. Using sloping flow

connectivity, it’s possible to plan greenways and ecological networks in an effective manner, since it is able to

enhance the real potential of each landscape elements to facilitate or obstruct both directional and overall

species movements.

Keywords biotic flows; dispersal facilities; flow connectivity; gene flow; landscape barriers; landscape

connectivity; partial differential equations; species dispersal.

1 Introduction

1 Introduction

Predicting how animals disperse is a pivotal issue for the management and conservation of fragmented

populations. Landscape heterogeneity and fragmentation affect how organisms are distributed in the landscape

(Fahrig and Merriam, 1985; Kennedy and Gray, 1997), determine the chance of a patch being colonized

(Hanski and Ovaskainen, 2000), reduce inbreeding in small populations and maintains evolutionary potential



IAEES www.iaees.org

(Couvet, 2002). In order to predict dispersal, it is important to not only consider an organism’s dispersal

capabilities, but also the complex interactions between its behaviour and the landscape pattern and use.

The modelling of animal dispersal provides a useful tool for investigating these complex interactions, and

it is an essential goal for biotic conservation planning (Kareiva and Wennergren, 1995; King and With, 2002).

Due to the difficulty in gathering experimental results on species dispersal, simulation models have become a

cost-effective approach to predict dispersal dynamics (Tischendorf, 1997; Wiegand et al., 1999; Tischendorf

and Fahrig, 2000). Simulation models with spatially-explicit landscapes enable the integration of the

relationships between species and the landscape, and provide representation of the spatial elements that

promote or constrain dispersal. Several dispersal models with spatially explicit landscapes have been

developed. Some consider dispersal behaviour according to habitat affinity or physiological states in order to

predict animal movements and provide guidelines for landscape and wildlife management (Gustafson and

Gardner, 1996; With et al., 1997; Gardner and Gustafson, 2004).

Recently I have introduced a modelling approach (flow connectivity; Ferrarini, 2013a) to ecological

connectivity that is alternative to circuit theory (McRae, 2006; McRae and Beier, 2007; McRae et al., 2008),

and is able to fix the weak point of the “from-to” connectivity approach. Landscape connectivity as estimated

by circuit theory relies on a strong assumption that is possibly untrue, unproven or very challenging to be

demonstrated: species dispersals are “from-to” movements, i.e. from source points (patches) of the landscape

to sink ones. Source and sinks are suitable areas present within a matrix that is partially or completely hostile

to the species. There are two aspects of this approach that are questionable. First, a source-sink habitats model

can be suitable to describe lowland landscapes where few suitable patches (e.g. protected areas) are surrounded

by a dominant, hostile (or semi-hostile) anthropogenic landscape. By the way, can we think the same of

mountain and hilly landscapes? Such landscapes are not composed of source and sink habitats, instead they’re

a continuum with a natural matrix where the source-sink habitats model loses its rationale. Second, assuming

that a species aims to go from “patch A” to “patch B” means that such species is supposed to plan such

dispersal path (i.e. global optimization). This could be true for short-range dispersals where the final point is

visible from the starting one, but for wide-range movements, and for plant species in particular, the dispersal

model postulated by circuit theory is unsuitable.

In addition, I’ve introduced “reverse flow connectivity” (Ferrarini, 2014a) that couples evolutionary

algorithms to partial differential equations in order to fix the problem of subjectivity in the attribution of

friction values to landscape categories. I’ve also showed that flow connectivity can be used to predict biotic

movements happened in the past (backward flow connectivity; Ferrarini, 2014b).

In this paper, I introduce a new kind of theoretical and modelling approach called “sloping flow

connectivity”. The goal of such proposal is to individuate barriers (to be removed) and facilities (to be

conserved) to species dispersal over the landscape. The reason behind sloping flow connectivity is that it

makes possible to plan greenways and ecological networks in an effective manner, since it is able to enhance

the real potential of each landscape elements to facilitate or obstruct directional and overall species movements.

2 Sloping Flow Connectivity: Mathematical Formulation

Let ( , , , )L x y z t be a real 3D landscape at generic time t, where [1,..., ]L n . In other words, L is a generic

(categorical) landcover or land-use map with n classes. At time T0,

0 0( , , , )L L x y z t (1)

Let be the landscape friction (i.e. how much each land parcel is unfavourable) to the species under

study. In other words, ( )L is a function that associates a friction value to each pixel of L. At time T0,

( )L

124


IAEES www.iaees.org

0 0( )L (2)

Let ( , , ( ))sL x y L be a landscape where, for each pixel, the z-value is equal to the friction for the species

under study. In other words, Ls is a 3D fictional landscape with the same coordinates and geographic

projection as L, but with pixel-by-pixel friction values in place of real z-values. Higher elevations represents

areas with elevated friction to the species due to whatever reason (unsuitable landcover, human disturbance

etc), while lower altitudes represent the opposite.

True-to-life coefficients for landscape friction can be calculated as in Ferrarini (2014a), where I defined P

as the predicted path for the species over the fictional landscape Ls, and P* the real path followed by the

species as detected by GPS data-loggers or in situ observations. The bias B between P and P* is hence

calculated as

*mod( )B Pdx P dx (3)

where the function mod indicates the module of the difference.

Hence:

* *

* *

where >

where >

Pdx P dx P PB

P dx Pdx P P

(4)

Now, true-to-life coefficients for landscape friction can be calculated by optimizing B, as follows:

set B to 0 (5)

or, at least,

minimize B (6)

The optimization of ( )L can be properly achieved using genetic algorithms (GAs; Holland, 1975). GAs

are powerful evolutionary models with wide potential applications in ecology and biology, such as

optimization of protected areas (Ferrarini et al., 2008; Parolo et al., 2009), optimal sampling (Ferrarini, 2012a;

Ferrarini, 2012b), optimal detection of landscape units (Rossi et al., 2014) and networks control (Ferrarini,

2011a; Ferrarini, 2013b; Ferrarini, 2013c; Ferrarini, 2013d; Ferrarini, 2013e; Ferrarini, 2014c). At time T0,

(7)

Now, sloping flow connectivity acts upon the optimized frictional landscape of eq. (7) as follows:

0( , , ( ))

( , )sL x y L

v x y

(8)

In other words, sloping flow connectivity calculates (pixel-by-pixel) the slope of the optimized frictional

landscape along the (vectorial) direction v that is a function of x and y dimensions:

v ax by

(9)

For instance, with a= 0 and b= 1 eq (8) calculates the frictional slope toward the N direction; with a = 1 and b=

1, eq. (8) calculates the frictional slope toward the N-E direction. Since a and b are real numbers, sloping

connectivity is able to calculate slope not only along the 8 cardinal directions (N, E, S, O, N-E, S-E, N-O, S-O),

but along any compass bearing.

In order to estimate the slope of a landscape cell along a particular direction, sloping flow connectivity acts as

follows:

0 0( , , ( ))s sL L x y L

125


IAEES www.iaees.org

0( , , ( ))

( , )s v

h

L x y L D

Dv x y

(10)

where Dv and Dh are the vertical and horizontal distances between the center-point of the focal cell and the

center-point of the adjacent cell in the specified direction.

Sloping flow connectivity takes a reasonably simple approach to estimate the % slope of a cell in a particular

direction: it assumes that the elevation values for all cells are good estimates of the elevation at the center-

points of the cells. If the direction is not a cardinal direction, then the slope is calculate from the focal cell

center-point to an interpolated point between 2 adjacent cell center-points. It can also be calculated in degrees

using the following alternative equation:

0( , , ( )) 180arctan( )*

( , )s v

h

L x y L D

Dv x y

(11)

Which is the ecological meaning of the slope direction (also known as, slope aspect or slope orientation)

calculated over the frictional landscape Ls? Clearly, it represents the least friction direction (LFD) to species

dispersal. To calculate the aspect from the frictional landscape Ls, I have used the equation from Evans (1972):

0

0

( , , ( ))

arctan( , , ( ))

s

s

L x y L

yLFD

L x y L

x

(12)

which is the angle by the x and y derivative of Ls via arctan, measured clockwise in degrees from North. Once

LFD is calculated, it can be then grouped into 9 categories (flat; N: 337.58–22.58, NE: 22.58–67.58, E:

67.58–112.58, SE: 112.58–157.58, S: 157.58–202.58, SW: 202.58–247.58, W: 247.58–292.58, NW:

292.58–337.58).

In order to apply sloping flow connectivity modelling to real landscapes, I wrote the ad hoc software

Connectivity Lab (Ferrarini, 2013f).

3 An Applicative Example

The Ceno valley is a 35,038 ha wide valley situated in the Province of Parma, Northern Italy. It has been

mapped at 1:25,000 scale (Ferrarini, 2005; Ferrarini et al., 2010) using the CORINE Biotopes classification

system. The landscape structure of the Ceno Valley has been widely analysed (Ferrarini and Tomaselli, 2010;

Ferrarini, 2011b; Ferrarini, 2012c; Ferrarini, 2012d).

From an ecological viewpoint, the most interesting event registered in the last years is the shift of wolf

populations from the montane belt to the lowland. Several populations have been recently observed in situ by

life-watchers, environmental associations and local administrations.

As an example of sloping flow connectivity, I have applied my model to a portion of the Ceno valley (Fig.

1) above 1000 m a.s.l. close to the municipality of Bardi where several small populations of wolves have been

recently observed. The area is a square of about 20 km * 20 km. Optimized friction values to wolf

presence are borrowed from Ferrarini (2012e) in the form of friction coefficients assigned to every land cover

classes. A discussion of wolf’s frictional coefficients is outside the goals of this paper, so I avoid presenting

them.

( )L

126


IAEES www.iaees.org

Fig. 1 The frictional landscape Ls has been built for wolf upon a 20 km * 20 km portion of the Ceno Valley (province of Parma, Italy) that represents here the real landscape L(x,y,z,t). The higher frictional values are in red, the lower ones are in blue. The frictional landscape has been built using both structural and functional properties of the landscape (Ferrarini, 2012e).

In order to simulate (directional) species movements along such landscape, I calculated sloping flow

connectivity along the 4 cardinal directions (N, S, E, O) using equations from (8) to (12).

Simulated northward (i.e., a= 0 and b= 1) connectivity is depicted in Fig. 2. Darker areas depict the

individuated barriers, lighter ones are the detected facilities. Barriers to northward wolf’s movements are

present in particular in the Eastern and Western portions of the study area. Instead, the central part of the study

area present less problems to northward wolf’s movements.

Simulated eastward (i.e., a= 1 and b= 0) connectivity is depicted in Fig. 3. It is clear that the study area is

particularly knotty with regard to eastward movements. Only the central portion allows for facilitated eastward

shifts. Southward (a= 0, b= -1) and westward (a= -1, b= 0) movements are simulated in Fig. 4 and Fig. 5.

Barriers and facilities are clearly detected.

127


IAEES www.iaees.org

Fig. 2 Simulated wolf’s northward movements (as indicated by the arrow). Darker areas represent the individuated barriers, lighter ones are the detected facilities.

Fig. 3 Simulated wolf’s eastward movements (as indicated by the arrow). Darker areas represent the individuated barriers, lighter ones are the detected facilities.

128


IAEES www.iaees.org

Fig. 4 Simulated wolf’s southward movements (as indicated by the arrow). Darker areas represent the individuated barriers, lighter ones are the detected facilities.

Fig. 5 Simulated wolf’s westward movements (as indicated by the arrow). Darker areas represent the individuated barriers, lighter ones are the detected facilities.

129


IAEES www.iaees.org

The computation of the LFD for the frictional landscape Ls using eq. (12) depicts for each portion of the

study area the most facilitated direction for wolf (Fig. 6).

It results clear that wolf’s movements towards South, South-West and West are the most probable (i.e.

facilitated) events in the study area. Instead, wolf’s movements towards North, North-East and East are highly

improbable. It’s also clear that there’s a kind of spatial clustering of movements probabilities, with certain

directions prevalent in particular portions of the study area (Fig. 6).

Fig. 6 Map of the most facilitated wolf’s movements in the study area. It has been achieved via sloping flow connectivity applied to the frictional landscape Ls of Fig. 1. For each pixel, the direction with the lowest friction to species dispersal is given.

The overall assessment of the least friction directions to wolf’s dispersal in the study area is given in Fig.

7, which refers to Fig. 6.

130


IAEES www.iaees.org

Fig. 7 Histogram of the most facilitated directions to wolf’s dispersal in the study area. Columns count the number of pixels in the sloping landscape of Fig. 6 with a particular direction for the most facilitated wolf’s dispersal.

4 Conclusions

Planning greenways and ecological networks in an effective manner is not an easy task, since it requires to

detect the real potential of each landscape elements to facilitate or obstruct both directional and overall species

movements. Conservation practitioners use two main strategies to promote connectivity. The first focalizes on

conserving areas that facilitate movement, the second focuses on restoring connectivity across areas that

impede movement. Most connectivity works have focused on the former strategy.

In this paper, I have introduced sloping flow connectivity that is on top of this requirement, as it is able to

produce simple and effective maps of barriers and facilities to directional and overall species dispersal.

Sloping flow connectivity takes advantage of two previously-introduced theoretical and methodological

frameworks for the prediction of species dispersal: flow connectivity and reverse flow connectivity.

References

Couvet D. 2002. Deleterious effects of restricted gene flow in fragmented populations. Conservation Biology,

16: 369-376

Evans I.S. 1972. General geomorphometry, derivations of altitude and descriptive statistics. In: Chorley R.J.

(Editor). Spatial analysis in geomorphology. 17-90, Harper & Row Publishers, New York, USA

Fahrig L, Merriam G. 1985. Habitat patch connectivity and population survival. Ecology, 66: 1762-1768

Ferrarini A. 2005. Analisi e valutazioni spazio-temporale mediante GIS e Telerilevamento del grado di

Pressione Antropica attuale e potenziale gravante sul mosaico degli habitat di alcune aree italiane. Ipotesi

di pianificazione. Ph.D. Thesis, Università degli Studi di Parma, Parma, Italy

Ferrarini A, Rossi G, Parolo G, Ferloni M. 2008. Planning low-impact tourist paths within a Site of

Community Importance through the optimisation of biological and logistic criteria. Biological

Conservation, 141:1067-1077

Ferrarini A, Bollini A, Sammut E. 2010. Digital Strategies and Solutions for the Remote Rural Areas

Development. Acts of Annual MeCCSA Conference, London School of Economics, London, UK

131


IAEES www.iaees.org

Ferrarini A, Tomaselli M. 2010. A new approach to the analysis of adjacencies. Potentials for landscape

insights. Ecological Modelling, 221:1889-1896

Ferrarini A. 2011a. Some thoughts on the controllability of network systems. Network Biology, 1(3-4): 186-

188

Ferrarini A. 2011b. Network graphs unveil landscape structure and change. Network Biology, 1(2): 121-126

Ferrarini A. 2012a. Biodiversity optimal sampling: an algorithmic solution. Proceedings of the International

Academy of Ecology and Environmental Sciences, 2(1): 50-52

Ferrarini A. 2012b. Betterments to biodiversity optimal sampling. Proceedings of the International Academy

of Ecology and Environmental Sciences, 2(4): 246-250

Ferrarini A. 2012c. Founding RGB Ecology: the Ecology of Synthesis. Proceedings of the International

Academy of Ecology and Environmental Sciences, 2(2): 84-89

Ferrarini A. 2012d. Landscape structural modeling. A multivariate cartographic exegesis. In: Ecological

Modeling (Zhang WJ, ed). 325-334, Nova Science Publishers Inc., New York , USA

Ferrarini A. 2012e. The ecological network of the province of Parma. Province of Parma, Parma, Italy (in

Italian)

Ferrarini A. 2013a. A criticism of connectivity in ecology and an alternative modelling approach: Flow

connectivity. Environmental Skeptics and Critics, 2(4): 118-125

Ferrarini A. 2013b. Controlling ecological and biological networks via evolutionary modelling. Network

Biology, 3(3): 97-105

Ferrarini A. 2013c. Computing the uncertainty associated with the control of ecological and biological systems.

Computational Ecology and Software, 3(3): 74-80

Ferrarini A. 2013d. Exogenous control of biological and ecological systems through evolutionary modelling.

Proceedings of the International Academy of Ecology and Environmental Sciences, 3(3): 257-265

Ferrarini A. 2013e. Networks control: Introducing the degree of success and feasibility. Network Biology, 3(4):

127-132

Ferrarini A. 2013f. Connectivity-Lab 2.0: a software for applying connectivity-flow modelling. Manual, Italy

(in Italian)

Ferrarini A. 2014a. True-to-life friction values in connectivity ecology: Introducing reverse flow connectivity.

Environmental Skeptics and Critics, 3(1): 17-23

Ferrarini A. 2014b. Can we trace biotic dispersals back in time? Introducing backward flow connectivity.

Environmental Skeptics and Critics, 3(2): 39-46

Ferrarini A. 2014c. Local and global control of ecological and biological networks. Network Biology, 4(1): 21-

30

Gardner RH, Gustafson E.J. 2004. Simulating dispersal of reintroduced species within heterogeneous

landscapes. Ecological Modelling, 171: 339-358

Gustafson EJ, Gardner R.H. 1996. The effect of landscape heterogeneity on the probability of patch

colonization. Ecology 77, 94–107

Hanski I, Ovaskainen O. 2000. The metapopulation capacity of a fragmented landscape. Nature, 404: 755-758

Holland J.H. 1975. Adaptation in Natural And Artificial Systems: An Introductory Analysis with Applications

to Biology, Control and Artificial Intelligence. University of Michigan Press, Ann Arbor, USA

Kareiva P, Wennergren U. 1995. Connecting landscape patterns to ecosystem and population processes.

Nature, 373: 299-302

Kennedy M, Gray R.D. 1997. Habitat choice, habitat matching and the effect of travel distance. Behaviour,

134: 905-920

132


IAEES www.iaees.org

King AW, With KA. 2002. Dispersal success on spatially structured landscapes: when do dispersal pattern and

dispersal behaviour really matter? Ecological Modelling 147: 23-39

McRae BH. 2006. Isolation by resistance. Evolution, 60: 1551-1561

McRae BH, Beier P. 2007. Circuit theory predicts gene flow in plant and animal populations. Proceedings of

the National Academy of Sciences of the USA, 104: 19885-19890

McRae BH, Dickson BG, Keitt TH, Shah VB. 2008. Using circuit theory to model connectivity in ecology and

conservation. Ecology, 10: 2712-2724

Parolo G, Ferrarini A, Rossi G. 2009. Optimization of tourism impacts within protected areas by means of

genetic algorithms. Ecological Modelling, 220: 1138-1147

Rossi G, Ferrarini A, Dowgiallo G, Carton A. et al. 2014. Detecting complex relations among vegetation,

soil and geomorphology. An in-depth method applied to a case study in the Apennines (Italy).

Ecological Complexity, 17(1): 87-98

Tischendorf L. 1997. Modelling individual movements in heterogeneous landscapes: potentials of a new

approach. Ecological Modelling 103: 33-42

Tischendorf L, Fahrig L. 2000. How should we measure landscape connectivity? Landscape Ecology 15, 633–

641

Wiegand T, Moloney K, Naves J, Knauer F. 1999. Finding the missing link between landscape structure and

population dynamics: a spatially explicit perspective. American Naturalist, 154: 605-627

With KA, Gardner RH, Turner M.G. 1997. Landscape connectivity and population distributions in

heterogeneous environments. Oikos, 78: 151-169

133

Proceedings of the International Academy of Ecology and

Environmental Sciences

The Proceedings of the International Academy of Ecology and Environmental Sciences (ISSN 2220-8860) is an open access, peer-reviewed online journal that considers scientific articles in all different areas of ecology and environmental sciences. It is the flagship journal of the International Academy of Ecology and Environmental Sciences. It dedicates to the latest advances in ecology and environmental sciences. The goal of this journal is to keep a record of the state-of-the-art research and promote the research work in these fast moving areas. All manuscripts submitted to Proceedings of the International Academy of Ecology and Environmental Sciences must be previously unpublished and may not be considered for publication elsewhere at any time during review period of this journal. The topics to be covered by this journal include, but are not limited to theory, methodology, technology, innovation, activity, and project in the following areas:

Animal ecology, plant/microbe ecology, wetland ecology, farmland ecology, forest/grassland ecology, marine ecology, pollution ecology, etc.

Biological conservation & preservation, ecosystem restoration, environmental policy, environmental toxicology, environmental pollution and control, natural resource, bioenergy research, environmental technology, waste management, environmental economics, environmental management & planning, environmental education, environmental engineering, global climate change, oceanography, etc.

Authors can submit their works to the email box of this journal, [email protected].

In addition to free submissions from authors around the world, special issues are also accepted.

The organizer of a special issue can collect submissions (yielded from a research project, a

research group, etc.) on a specific topic, or submissions of a conference for publication of special

issue.

Editorial Office: [email protected]

Publisher: International Academy of Ecology and Environmental Sciences

Address: Flat C, 23/F, Lucky Plaza, 315-321 Lockhart Road, Wanchai, Hong Kong

Tel: 00852-6555 7188

Fax: 00852-3177 9906


Proceedings of the International Academy of Ecology and Environmental Sciences ISSN 2220-8860 Volume 4, Number 3, 1 September 2014 Articles

Morphometry and meristic counts of Bombay duck, Harpodon nehereus

(Hamilton, 1822) along Sunderban region of West Bengal, India

V. V. Kumar, A. D. Reddy, S. R. Choudhury, et al. 95-105

Classic models of population dynamics: assumptions about selfregulative

mechanisms and numbers of interactions between individuals

L.V. Nedorezov 106-113

Multivariate statistical analysis of surface water chemistry: A case study of

Gharasoo River, Iran

MH Sayadi , A Rezaei1, MR Rezaei, K Nourozi 114-122

Detecting barriers and facilities to species dispersal: Introducing sloping flow

connectivity

Alessandro Ferrarini 123-133

IAEES http://www.iaees.org/

Proceedings of the International Academy of Ecology and Environmental Sciences, 2014, Vol. 4, Iss. 3

Documents

Transcript of Proceedings of the International Academy of Ecology and Environmental Sciences, 2014, Vol. 4, Iss. 3