Genes Genet. Syst. (2000) 75, p. 281–292

Edited by Naoyuki Takahata* Corresponding author. E-mail: mruiz@javercol.javeriana.edu.co

Genetic microsturcture in two spanish catpopulations. II: gametic disequilibrium

and spatial autocorrelation.

Manuel Ruiz-GarciaUnidad De Genetica (Biologia Evolutiva). Departamento De Biologia. Facultad De Ciencias. Pontificia

Universidad Javeriana. Cra 7A No 43-83. Bogota D. C. Colombia.Cigeem, Carrer Guatemala No 13 B, C. P: 43882, Segur De Calafell (Tarragona),

Catalunya. Spain.

(Received 29 September 1999, accepted 31 August 2000)

In a previous publication, we described some aspects of the microgenetic struc-ture of two Spanish cat populations (in Barcelona and Alicante). In the presentstudy, the possible existence of gametic disequilibrium and spatial genetic structure

― ― ― ― ― ―for these populations, at the coat colour pattern and length genes O, A, T, D, L, S and

―W, was analyzed. There was little gametic disequilibrium between pairs of theseloci, despite certain pairs that showed significant systematic gametic disequilib-

― ― ― ―rium (a–d and O–S), which appears to show the action of natural selection ondomestic cat populations. Nevertheless, we believe that the major cause of thesmall amount of gametic disequilibrium found was probably a combination of genedrift and gene flow. The results obtained here were clearly in disagreement withthose of Hedrick (1985), who concluded that epistatic selection was the cause ofthe gametic disequilibrium that he found in cat populations. We also found thatalthough Hardy-Weinberg equilibrium could not be demonstrated, the gametic dis-equilibrium statistics were not affected by this fact, adding credence to the esti-mates obtained.

We found no genetic spatial structure inside the city of Barcelona, as shown byanalysis of the spatial autocorrelation of the individual loci, and analysis of thecoordinates of the two first axes of a multidimensional scale. However, somegametic disequilibrium statistics showed certain spatial patterns, which leads us toconsider the possibility of several evolutionary processes acting upon some ofBarcelona’s cat colonies.

INTRODUCTION

In a previous publication complementary to this one(Ruiz-Garcia & Alvarez, 1999), certain aspects of thegenetic structure of two populations of feral cats studiedat the micro-geographic level in the Spanish cities ofBarcelona and Alicante were examined. In that report,

―the existence of Hardy-Weinberg equilibrium at the Olocus, gene diversity, genetic heterogeneity, and gene flowbetween colonies and subpopulations in those cities, aswell as the presence of selection acting differentially onthe loci array studied, were analyzed. In the presentstudy, the main aspects studied were as follows:

1/ To analyze the possible existence of gametic disequi-librium for pairs of allelic combinations at the individualcolony level (Barcelona), at the individual subpopulation

level (Barcelona and Alicante), and at the global level inthe cat populations of both those Spanish cities. For sev-eral of these gametic disequilibrium statistical values, andassuming that genetic drift was the preponderant cause ofthe observed gametic disequilibrium, to estimate the pos-sible effective number sizes of the analyzed sample struc-tures. In addition, all of these analyses enabled us toexamine the possible correlations between gametic dis-equilibrium statistics and the sample sizes employed. Inprinciple, an inverse negative correlation between thesetwo variables should be expected (Hedrick, 1985).

2/ At the colony level in Barcelona, to analyze thepossible spatial structure, by means of spatial auto-correlation, of the seven allelic frequencies analyzed, of thecoordinates of the colonies at the first two axes (I and II)obtained from a multidimensional scale analysis, aswell as to analyze the possible spatial structure ofseveral average estimates for gametic disequilibrium.Furthermore, the possible similarity between the

282 M. R.-GARCIA

correlograms of the 7 alleles was analyzed in order to tryto clarify whether or not spatial evolutionary events existwhich affect, simultaneously or not, the aforementionedalleles (Sokal et al. 1986, 1987, 1989).

MATERIALS AND METHODS

The populations, areas sampled and the genetic charac-teristics studied were described in Ruiz-Garcia & Alvarez

― ― ― ― ― ―(2000). To summarize, these loci were O , A , T , D , L , S,

―and W and they control the color, length and pattern ofthe coat in the cats (Robinson, 1977; Wright and Walters,1982; Ruiz-Garcia, 1994a).

Gametic disequilibrium. The seven loci analyzed areunlinked because they are on different chromosomes, orfar apart on the same chromosome (Robinson, 1977).Nevertheless, we studied the possible existence of gameticdisequilibrium, that is to say, the statistically significantassociation of alleles from different loci, in order to inves-tigate the possibility that different evolutionary eventscould affect these diverse alleles simultaneously.Previously, only one study of this nature was carried outby Hedrick (1985) in four other cat populations. In thepresent study, we analyzed the possible existence of ga-metic disequilibrium at the microgeographical level in thecat populations of Barcelona and Alicante. Accordingly,the following statistics were calculated: D̂ , the extent ofgametic disequilibrium (Turner, 1968; Hedrick, 1985), Q̂,a statistical value that is associated with D and that isdistributed like a chi-square with 1 degree of freedom(Hill, 1974) and r̂ , the correlation coefficient for gameticdisequilibrium (Hill and Robertson, 1968). The corre-sponding statistical equations were used:

D̂ = x̂4 - p̂2 q̂2 ; Q̂ = 4n D̂2 / (p̂1 (2-p̂1) q̂1 (2-q̂1)) and r̂ = D̂/(p̂1

p̂2 q̂1 q̂2)1/2

where x̂4 is the maximum likelihood estimate of the fre-quency of the double recessive gamete, p̂2 and q̂2 are thefrequency estimates of the recessive alleles in the two locianalyzed, p̂1 and q̂1 , are the frequencies of the dominantalleles in the same loci and the complements of estimated

―recessive alleles, and n is the total sample size. With theseven diallelic loci analyzed, 21 different diallelic combi-nations could be obtained. However, it was only possibleto obtain 14 allelic combinations (O-tb , O-d, O-l, O-S, a-d,a-l, a-S, tb-d, tb-l, tb-S, d-l, d-S, l-S, l-W) due to the exist-ence of phenotypic epistasis phenomena between some ofthose genes.

The statistical significance of the gametic disequilib-rium was measured by the Q̂ statistic. A value of Q̂ >3.84 with 1 degree of freedom was considered significant(P<0.05) for each individual test carried out. Not-withstanding, these different tests might be considered asmultiple tests of the same hypothesis. For this, we also

used Bonferroni’s standard multiple method (Miller, 1980;Zar, 1984; Weir, 1990; Vrijenhoek and Graven, 1992).With these criteria of multiple tests, the chosen signifi-cance level was α ’=0.00357 (0.05/14) within each indi-vidual colony, individual subpopulation and in the total ofeach population, which corresponds to a Q̂ value of > 9.5with 1 degree of freedom. Using these different criteriafor significance, we calculated the percentage (%) of pairsof allelic combinations which showed statistically signifi-cant gametic disequilibrium at the individual colony level(Barcelona), at the individual subpopulation level(Barcelona and Alicante) and at the total population level(Barcelona and Alicante). Percentage values that did notexceede a type I error of 5% indicate that no significantamount of gametic disequilibrium existed within the com-bination tested. The mean values were calculated for allthe pairs of loci analyzed by the ̂D, ̂r statistics and Σ Q̂ with14 degrees of freedom. All these mean values were cal-culated in order to be able to analyze the evolutionarycauses for the values found for gametic disequilibrium(Hill and Robertson, 1968; Ohta and Kimura, 1969;Hedrick et al., 1978; Hedrick, 1985, 1987; Hastings, 1981,1986; Weir, 1990; Weir and Cockerham, 1989). Weexamined whether the gametic disequilibrium statisticsfound at the different population levels analyzed were cor-related in any way with the sample sizes used, such ashas been found by certain authors (Hedrick, 1985). All ofthe results pertaining to the gametic disequilibriaobtained in the present study were compared in terms oftheir magnitude and direction to those found by Hedrick(1985) for the cat populations of Amsterdam, Lahore,Montreal and Portsmouth in order to analyze the possiblenature of any gametic disequilibrium detected.

Spatial autocorrelation. Spatial autocorrelation of theallelic frequencies analyzed at the colony level inBarcelona.

Four analytical techniques were applied to perform aglobal spatial autocorrelation analysis (Sokal & Oden,1978ab; Sokal and Wartenberg, 1983; Sokal et al. 1986,1987, 1989, Sokal & Jacquez, 1991; Upton & Fingleton,1985, 1989; Epperson, 1990, 1993; Ruiz-Garcia & Klein,1997; Ruiz-Garcia and Jordana, 1997, 2000; Legendre &Legendre, 1984; Legendre & Fortin, 1989):

1/ Estimation of statistic heterogeneity in eachlocus. For this, we used the χ2 values obtained from a Fst

analysis.2/ Calculation of autocorrelation coefficients and

correlograms. The Moran’s I index (Sokal and Oden,1978ab) was employed in the current study. Four classesof distances (CDs) were defined as follows: 1 CD: 0-2014m; 2 CD: 2014–4408 m; 3 CD: 4408–5792 m; 4 CD: 5792–7306 m. Different networks for connecting colonies ineach CD were used. They were the Gabriel-Sokal net-work (Gabriel and Sokal, 1969; Matula & Sokal, 1980) and

283Gametic disequilibrium in cat populations.

Delaunay’s triangulation with elimination of the crossingedges (Miles, 1970; Ripley, 1981; Watson, 1981; Upton& Fingleton, 1985; Isaaks & Srivastava, 1989). Theresults were practically identical for both methods. Theconnection matrix was binary (Ruiz-Garcia, 1994b). Todetermine the statistical significance of autocorrelation,the Bonferroni procedure was used (Oden, 1984). Thepercentage of significant autocorrelation coefficients wasobtained to determine if it was superior to the 5% type Ierror.

3/ Similarity analysis between the variable surfaces.The similarity of the gene surfaces was studied by usingthe product-moment correlation coefficient of Pearson(r).

4/ Similarity analysis of correlograms. To determinethe similarity between the correlograms, we calculated the Manhattan distance matrices between correlogramvariable pairs generated with the Moran’s I index. Thisanalysis was useful to investigate if each one of thegenetic variables studied has been subjected to the samespatial evolutionary agents. Sokal and Wartenberg(1983) and Sokal et al. (1986, 1987, 1989) showed bymeans of simulation studies that correlogram pairs gener-ated by the same evolutionary spatial processes have Man-hattan distances lower than 0.1 in the case of Moran’s Iindex. For this reason, we considered the percentage (%)of Manhattan distance values lower than these amountsto be comparable to the 5% type I error.

Spatial autocorrelation of other genetic statistics.Different spatial autocorrelation analyses were applied todifferent genetic statistics at the colony level inBarcelona. In order to analyze a possible global spatialstructure for all of the seven loci analyzed, a spatialautocorrelation analysis was applied to the coordinatesobtained for the 11 cat colonies analyzed in Barcelona foraxes I and II, generated by a multidimensional scaleanalysis. Other spatial autocorrelation analyses wereapplied to the gametic disequilibrium statistics D̂, |D̂| , r̂ ,and |r̂|.

RESULTS

Gametic disequilibrium. The analysis of gameticdisequilibrium in the two cities studied was applied atdifferent sampling levels: total population, individualsubpopulation level and individual colony level.Furthermore, the mean values were obtained for the 14diallelic combinations analyzed in each one of the popula-tion structures (Table 1). The common denominator of allof these results was the existence of little, or very little,significant gametic disequilibrium.

――――――――――――――――――――――Total population level: In the case of Barcelona, usingthe criterion of significance of the individual tests (α =0.05) of the 14 allele combinations studied, only 3 were

― ― ― ―significant (o – tb : D̂ = 0.0268, P<0.05; O – S : D̂ = 0.0218,

― ―P<0.01; d – l : D̂ = –0.0388, P<0.05). Therefore, a signifi-

―cant disequilibrium unfavorable was detected between O

―(Orange allele) and tb (blotched tabby allele). Overall, asignificant structure of gametic disequilibrium did not ex-ist globally in the sample of cats which was analyzed inBarcelona (3/14 = 21.4%). This percentage is not signifi-cantly different from the type I error of 5% (χ2 = 1.65 , 1 dfNS). Therefore, the dynamics of most of these genes areindependent of those of the other genes analyzed. In fact,the three cases of gametic disequilibrium which werefound, although significant, showed relatively smallvalues. If the statistical significance was determined bymeans of Bonferroni’s multiple standard tests’ procedure,the percent of the allelic pairs which showed gametic dis-equilibrium decreased even more: it was only 7.15% (1/14). The only allele combination which demonstrated sig-nificant gametic disequilibrium was O–S (+).

In the case of Alicante, no significant gametic disequi-librium was detected among the pairs of alleles studiedeither with individual tests or by the procedure ofBonferroni’s multiple standard tests.

―――――――――――――――――――Subpopulation level: In the case of Barcelona at theindividual subpopulation level the general findings wereas follows. No subpopulation showed a percentage ofpairs of alleles with a gametic disequilibrium significantlysuperior to the 5% error level. That is to say that littlegametic disequilibrium exists. In the A subpopulation,with α =0.05, a percentage of 21.42% (3/14) was obtained(O–d [–]; d–S [–] and l–S [–]). This value did not differsignificantly from the error type of 5%. With Bonferroni’scriterion, a percentage of only 14.28% was obtained (2/14;O–d; d–S). In the B subpopulation, 21.42% of the allelepairs showed significant gametic disequilibrium (O–S [+];tb–S [–]; l–S [–]). With Bonferroni’s procedure, this per-centage value was only 7.14% (1/14; tb-S). SubpopulationC did not show any pair of alleles with significant gameticdisequilibrium. Subpopulation D yielded a value of14.28% (d–S [–]; l–S [–]) with α=0.05. With Bonferroni’sprocedure, neither value was significant. Finally, in theE subpopulation, a value of 14.28% was obtained (O–S [+];a–d [–]), both for individual significance as well as forBonferroni’s procedure.

In the case of Alicante, no subpopulation reached a per-centage value of allelic pairs with a significant gameticdisequilibrium superior to the 5% error level. Again, wefound very little gametic disequilibrium. SubpopulationA had only 7.14% (1/14; a-S (+)), for α =0.05. Subpopula-tion B yielded 21.43% (3/14; O-S [-], a–d [–] and d–S [–]),for α =0.05. Subpopulation C did not show any case ofsignificant gametic disequilibrium. Subpopulation Dshowed only one case of significant gametic disequilibrium(7.14%; O–S [+]), for α =0.05. No pair of alleles showed asignificant gametic disequilibrium for any subpopulationwith Bonferroni’s method. It is apparent that none of these

284 M. R.-GARCIA

Table 1. Gametic disequilibrium statistics (GDS) in Barcelona and Alicante cat populations. Mean values for 14 pair combinationsin each of the population sampling structures studied. D= mean value of the gametic disequilibrium; D= absolute value ofthe mean value of the gametic disequilibrium; r= mean correlation coefficient for gametic disequilibrium; r= absolutevalue of mean correlation coefficient for gametic disequilibrium; ΣQ= Total gametic disequilibrium with 14 degrees offreedom. (A) Total gametic disequilibrium statistics in both Spanish cat populations. (B) Total mean gametic disequilib-rium statistics in both Spanish cat populations. (C) Mean gametic disequilibrium statistics in individual cat subpopula-tions of Barcelona and Alicante. (D) Mean gametic disequilibrium statistics in individual cat colonies of Barcelona.A. Total gametic disequilibrium

BARCELONA ALICANTE

^D ^Q df ^r ^D ^Q df ^rO–tb 0.027 4.36* 1 0.168 O–tb 0.028 1.23 1 0.125O–d 0.003 0.10 1 0.019 O–d 0.001 0.01 1 0.009O–l 0.015 3.05 1 0.142 O–l 0 0 0 0O–S 0.022 12.67*+ 1 0.152 O–S –0.015 1.58 1 –0.087a–d –0.024 2.92 1 –0.116 a–d –0.006 0.13 1 –0.038a–l –0.003 0.04 1 –0.019 a–l 0 0 0 0a–S –0.001 0.01 1 –0.005 a–S 0.015 1.36 1 0.082tb–d –0.007 0.09 1 –0.036 tb–d 0.037 1.10 1 0.179tb–l 0.041 2.80 1 0.287 tb–l 0 0 0 0tb–S –0.014 0.71 1 –0.071 tb–S 0.037 1.86 1 0.156d–l –0.039 4.56* 1 –0.248 d–l 0 0 0 0d–S –0.009 0.64 1 –0.051 d–S 0.008 0.17 1 0.041l–S –0.012 0.81 1 –0.078 l–S 0 0 0 0l–W 0.000 0.08 1 0.023 l–W 0 0 0 0

B. GDS

D |D| r |r| ΣQ

Total mean for Barcelona –0.0000±0.0208 0.0155±0.0132 0.0120±0.1367 0.1010±0.0886 32.87 (14 df)Total mean for Alicante 0.0075±0.0158 0.0105±0.0138 0.0335±0.0756 0.0514±0.0638 7.44 (8 df)

C. Mean GDS subpopulationsD |D| r |r| ΣQ (14 df)

Subpopulation A BARCELONA –0.0239±0.0814 0.0591±0.0590 –0.1706±0.4933 0.3524±0.3754 64.01*+ALICANTE 0.0163±0.0366 0.0248±0.0310 0.0944±0.1990 0.1426±0.1652 12.43

Subpopulation B BARCELONA –0.0110±0.0486 0.0389±0.0293 –0.0615±0.3086 0.2776±0.1823 37.11*ALICANTE –0.0122±0.0364 0.0217±0.0314 –0.0935±0.2717 0.1556±0.2391 19.27

Subpopulation C BARCELONA –0.0119±0.0356 0.0198±0.0316 –0.0502±0.1714 0.0967±0.1484 4.48ALICANTE 0.0052±0.0460 0.0265±0.0373 0.0247±0.2226 0.1344±0.1753 6.53

Subpopulation D BARCELONA –0.0104±0.0411 0.0302±0.0287 –0.0564±0.2584 0.1946±0.1731 18.94*ALICANTE 0.0116±0.0270 0.0162±0.0244 0.0679±0.1223 0.0785±0.1153 10.16

Subpopulation E BARCELONA –0.0057±0.0388 0.0293±0.0247 –0.0255±0.2406 0.1814±0.1521 53.90*+

D. Mean GDS colony for BarcelonaD |D| r |r| ΣQ (14 df)

Colony B1 –0.0218±0.0788 0.0320±0.0750 –0.0909±0.3465 0.1459±0.3256 19.00Colony B2 –0.0124±0.0566 0.0383±0.0423 –0.0519±0.3189 0.2168±0.2324 27.44Colony B3 –0.0141±0.0805 0.0521±0.0614 –0.0742±0.4406 0.3047±0.3163 35.99*+Colony D1 0.0030±0.0370 0.0238±0.0277 0.0446±0.2495 0.1653±0.1870 11.15Colony D2 –0.0243±0.0743 0.0396±0.0669 –0.1398±0.3255 0.1908±0.2963 20.08Colony E1 0.0029±0.0293 0.0148±0.0250 0.0228±0.1383 0.0731±0.1181 3.54Colony E2 –0.0153±0.0758 0.0486±0.0588 – 0.0297±0.3555 0.2496±0.2454 15.01Colony E3 –0.0042±0.0389 0.0312±0.0219 –0.0266±0.2484 0.1981±0.1420 23.22Colony E4 –0.0093±0.0476 0.0290±0.0381 –0.0804±0.4016 0.2199±0.3408 62.69*+

*p<0.05; +p< 0.00357 (Bonferroni standard multiple method)

pairs of alleles showing significant gametic disequilibriumwere the same as for the cat subpopulations in Alicante,with the exception of O–S. Even, for this pair, in one case(subpopulation B), the value was negative and in the othercase it was positive. In the Barcelona subpopulations,although the gametic disequilibrium was relatively small,

some significant allele combinations were found which af-fected the same loci in the same way. This was the casewith l–S (–) in 3 of the 5 subpopulations, d–S (–) in 2 of the5 subpopulations and O–S in 2 of the 5 subpopulations.

――――――――――――Colony level: At this level no individual colony wasfound which showed a significant percentage of allele pairs

285Gametic disequilibrium in cat populations.

Table 2. Regression equations and correlation coefficients between gametic disequilibrium statistics defined in Table 1 and the samplesizes used. NS = not significant; s.s = sample size. (A) Total Barcelona and Alicante subpopulations. (B) Total Barcelonacolonies; (C) Small Barcelona colonies. (D) Large Barcelona colonies.

A. Subpopulations^D |^D| ^r |^r| ΣQ

BARCELONA SUBPOPULATIONS –0.0185048 0.038789 –0.112817 0.225275 22.12837+0.00004141 (s.s) –0.000023208 (s.s) +0.00028167 (s.s.) ±0.0007535 (s.s.) +0.095664 (s.s.)

r 0.6704 –0.1711 0.547 –0.087 0.4284r2 0.4495 0.0293 0.2993 0.0076 0.1835

significance NS NS NS NS NS

ALICANTE SUBPOPULATIONS ^D |^D| ^r |^r| ΣQ

–0.010334 0.034718 –0.0553769 0.1857019 7.177555–0.00006064 (s.s) –0.0001477 (s.s) –0.000381786 (s.s.) –0.00069109 (s.s.) +0.0095607 (s.s.)

r –0.1466 –0.9823 –0.1392 –0.616 0.0304r2 0.0214 0.965 0.0193 0.3794 0.0009

significance NS t=7.42; 2 df; p<0.05 NS NS NS

B. Total Barcelona Colonies ^D |^D| ^r |^r| ΣQ

–0.0168112 0.034748 –0.061479 0.1584884 8.6936+0.00007511 (s.s) +0.000009557 (s.s) +0.000041092 (s.s.) +0.00066375 (s.s.) +0.269424 (s.s.)

r 0.2764 0.0245 0.0229 0.2846 0.4609r2 0.0764 0.0006 0.0005 0.0810 0.2124

significance NS NS NS NS NS

C. Small Barcelona Colonies (n = 5 ; less than 50 individuals)^D |^D| ^r |^r| ΣQ

–0.015759 0.059976 –0.01552086 0.296539 28.82409+0.000044839 (s.s) +0.0007870 (s.s) –0.0011427 (s.s.) –0.0039469 (s.s.) –0.44557 (s.s.)

r 0.034 –0.4628 –0.1514 –0.4518 0.4597r2 0.0011 0.2142 0.0229 0.2041 0.2113

significance NS NS NS NS NS

Large Barcelona Colonies (n = 6 ; more than 50 individuals)^D |^D| ^r |^r| ΣQ

–0.016633 0.051785 –0.078735 0.297105 36.61116+0.00007366 (s.s) +0.00014621 (s.s) –0.0002155 (s.s.) –0.0006192 (s.s.) +0.009238 (s.s.)

r 0.2606 –0.3421 0.0991 –0.2845 0.0138r2 0.0679 0.1171 0.0098 0.0809 0.0002

significance NS NS NS NS NS

with gametic disequilibrium significantly different fromthe error level of 5%. For colonies A and C, since theycoincided with the subpopulation level, the results wereexactly the same. Colony B1 had a case of significantgametic disequilibrium (7.14%; a–d (–)) consideringα = 0.05 as well as α’ = 0.0036. Colony B2 showed a per-centage of 14.28% (2/14; O–S (+); a–d (–)). Colony B3 alsoshowed 14.28% of allelic combinations with significantgametic disequilibrium (2/14; tb–S (–); l–S (–)). Colony D1showed 7.14% pairs of significant allelic combinations (1/14; l–S (–)). For colony D2, a percentage of 7.14% wasobtained for α = 0.05. The only case of significant gameticdisequilibrium was a–d (–). Colony E1 did not have anycase of significant gametic disequilibrium. Colony E2had a value of 7.14% (1/14; a–d (–)) according to both meth-ods for calculating statistical significance. In colony E3there were 14.28% allelic pairs with significant gametic

disequilibrium with α=0.05 (2/14; O–S (+); tb–S (–)). Incolony E4 only one case of significant gametic disequilib-rium was found (7.14%; O–d (–)). Therefore, the smallamount of gametic disequilibrium present in the cat popu-lation of Barcelona was again demonstrated at anothersample level. Notwithstanding, certain gametic disequi-libria were repeated, and with the same sign, at the colonylevel. This was the case for a-d in 4 of the 11 coloniesstudied, and l–S in 3 of the 11 colonies studied. In con-trast, the pairs of the combinations which had moregametic disequilibrium were different in the case of theBarcelona population in their performance according tothe sample levels being dealt with. Only the l-S pairappeared with a certain frequency at both the colony andsubpopulation levels.

Also, the mean values of D̂, |D̂|, r̂, |r̂| and ΣQ̂ in all ofthe sample levels in the two cities studied (Table 1) showed

286 M. R.-GARCIA

Table 3. Spatial autocorrelation analysis with 4 distanceclasses (DC) for the seven alleles studied (O = orange;a = non-agouti; tb = blotched tabby; d = dilution; l =long hair; S = White spotting; W = dominant white)at the colony level in Barcelona with Moran´s I in-dex. Distance classes in meters. CgramProb = over-all correlogram

Moran’s IDistance 2014 4408 5792 7306 CgramProb

O 0.02 –0.18 –0.28 0.05 0.812a –0.38 0.02 –0.12 0.06 0.475tb –0.24 –0.11 –0.11 0.05 0.911d –0.41 0.10 0.02 –0.12 0.402l –0.21 –0.03 –0.34 0.17 0.298S 0.02 0.25* 0.03 –0.69** 0.004W –0.30 0.05 –0.10 –0.07 0.239

average –0.21 0.02 –0.13 –0.08

probability. * p<0.05; **p<0.01

a small gametic disequilibrium. If we analyze the statis-tical significance of Σ ̂Q with 14 df by means of Bonferroni’sprocedure, it was not detectable at the global level eitherin Barcelona or in Alicante. In Alicante, statistical sig-nificance was not detected in any of the subpopulationsanalyzed either. In Barcelona, significant gameticdisequilibrium was indeed found in the A, B and E sub-populations, although this was caused by high gametic dis-equilibrium, but the disequilibrium was found in very fewpairs of allelic combinations. At the colony level inBarcelona, only colonies A, B3 and E4 gave significantΣQ̂ values. Just as in the subpopulation case, only veryfew pairs of allelic combinations were the causes of thesesignificant values.

In Table 2, the regression equations and the correlationcoefficients between the mean statistical values of gameticdisequilibrium and the sample sizes used are given. Incontrast to the conclusion of Hedrick (1985), in Barcelona,no statistical association was found at the colony and sub-population levels between the values of the mean statis-tics of gametic disequilibrium and the sample sizes. Inthe case of the population of Alicante, at the subpopula-tion level, a significant correlation in the sense predictedby Hedrick was only observed for |D̂|. However, in that

―case, n (the number of pairs of comparisions) was only4. Therefore, that value might prove to be totally spuri-ous.

Spatial autocorrelation. The spatial autocorrelationanalysis of the seven alleles studied (Table 3) for 4 CD, byusing Moran’s I index, showed percentages of significantspatial autocorrelation coefficients that did not differ fromthe error I of 5%. Therefore, spatial structure was notseen among the cat colonies analyzed in Barcelona. Only

―the S locus showed a significant overall correlogram.Basically, statistical significance was established for the

high negative autocorrelation between 6000 and 7300m. That is to say, the S locus showed a significant case ofdifferentiation at long distance. It was a curious obser-vation that for many of those alleles, the most negativespatial autocorrelation values were those which belongedto the first 2400 m. Thus, the existence of the greatestgenetic diversity was found among the colonies which wereclosest to each other geographically.

The similarity analysis between the variable surfacesshowed a weak correlation between the frequenciessurfaces. The percentage of significant correlations (O vstb, r=–0.739; a vs S, r=–0.659; l vs W, r=0.813) was 14.29%(3/21). This value was not significantly higher than theerror type of 5%.

The percentage of correlogram pairs with Manhattandistances under 0.1 (Moran’s I index) was never superiorto the 5% error type. This percentage was 19% (4/21) (χ2

= 1.96 1 df, NS). The pairs of variables a–tb , a–W, tb–W,d–W gave Manhattan distances of less than 0.1. Thus,the spatial evolutionary dynamics among those seven vari-ables were highly independent.

As a method for determining the possible simultaneousspatial structure of those seven alleles, a spatialautocorrelation analysis was used with the coordinates ofthe axes I and II of the multidimensional scale analysis ofthe 11 cat colonies analyzed in Barcelona (Table 4). Itseems clear that no evidence was found which supportsthe existence of a significant spatial structure for thesecat colonies. One finding which strongly supported thisinference was that the more negative spatial auto-correlation values were found for the first distance classes(maximum genetic diversity between the nearest colonies).

One way of analyzing the causes which might have gen-erated the gametic disequilibrium found would be toexamine whether there is some type of spatial structurein the statistics used to mesure this disequilibrium,D, |D̂|, r̂, |r̂|, and ΣQ̂ in the individual colonies(Table 5). Only the r statistic gave a significant overallcorrelogram. The most outstanding was the significantlynegative spatial autocorrelation value of the last distanceclass (5792–7306 m). Also, D̂ showed a negative spatial

Table 4. Spatial autocorrelation analysis of the two first axesfrom a non-metric multidimensional scaling analysis(MSD) at the colony level in the Barcelona cat popula-tion with 4 distance classes, with Moran´s I index.Distance classes in meters. CgramProb = overallcorrelogram probability.

Moran’s I

Distances 2014 4408 5792 7306 CgramProbMSD AXE I –0.36 –0.02 –0.26 0.22* 0.171MSD AXE II –0.10 –0.15 –0.03 –0.11 1.000

average –0.23 –0.09 –0.15 0.06

* p<0.05; **p<0.01

287Gametic disequilibrium in cat populations.

Table 5. Spatial autocorrelation analysis of the percentage ofsignificant gametic disequilibrium statistic (PSGD)(A), and ^D, |^D|, ^r, |^r|, SQ statistics (B) with 4distance classes (DC) with Moran´s I index at thecolony level in Barcelona. DC in meters. CgramProb= Overall correlogram probability.

A.

Moran’s I

Distances 2014 4408 5792 7306 CgramProbPSGD 0.10 0.07 –0.28 –0.27 0.751

B.Moran’s I

Distances 2014 4408 5792 7306 CgramProbD 0.02 0.30* –0.26 –0.45* 0.077|D| –0.03 0.20 –0.29 –0.28 0.236r 0.02 0.20 –0.06 –0.55* 0.040|r| 0.01 –0.05 –0.19 –0.17 1.000ΣQ 0.08 –0.40 0.18 –0.24 0.221

average 0.02 0.05 –0.12 –0.34

* p < 0.05; p** < 0.01.

autocorrelation value in the last distance class and a posi-tive value for 2 DC (2014–4408 m). The statistics |D̂|,|r̂|, and ΣQ̂ did not give significant spatial structures.To differentiate it, therefore, from that shown accordingto the individual or joint allelic frequencies (MDS coordi-nates), the gametic disequilibrium that was found, eventhough relatively small or very small, did indeed show acertain spatial structure.

DISCUSSION

Gametic disequilibrium The clearest conclusion fromthis analysis of gametic disequilibrium is that this type ofevent does not affect in any appreciable manner the groupsof pairs of loci analyzed in either of the two citiesstudied. Nor does it affect groups of loci at the differenthierarchical levels that were established. These resultsclearly disagree with those of Hedrick (1985), who found arelatively high proportion of loci pairs presenting signifi-cant gametic disequilibrium (7/28 = 25%) for the cat popu-lations in Amsterdam (Holland), Lahore (Pakistan),Montreal (Canada), and Portsmouth (England). Innumerous cases, he observed strong negative associations

― ― ―between a–S and positive associations between l–

― ― ― ― ―S. Furthermore, in the case of a–d and a–l , Hedrick(1985) often did not observe significant differences, but didnote that these pairs consistently had the same sign(positive). This led him to suggest that epistatic selec-tion acting in the same direction in all populations couldbe the most important cause of the gametic disequilibriumencountered. Our results, however, do not appear to sup-port that hypothesis. The significant combinations at theglobal level in Barcelona did not coincide in any case with

those encountered in the populations analyzed by Hedrick(1985). At the global level in Alicante, no pair of allelesshowed significant levels of gametic disequilibrium. For

― ―example, the relation between a–S was not significant forthe combined data from Barcelona and Alicante. The

― ―highly significant and positive results for l–S in the popu-lations analyzed by Hedrick (1985) were negative, andmostly nonsignificant, for the populations studied

― ― ―here. Furthermore, whereas a–d and a–l showed consis-tently positive values in the study of Hedrick, in Barcelonaand Alicante those values were negative and

― ―nonsignificant. In the study of this author, the pair d–ldid not show a systematic direction of variation, whereasin Barcelona and in Alicante the systematic direction wassignificantly negative. Likewise, the pairs of combina-tions did not agree in sign between Barcelona and

― ―Alicante. For example, while O–S in Barcelona waspositive and significant, in Alicante it was negative and

― ―nonsignificant. Moreover, a–S was negative in Bar-celona, whereas in Alicante it was positive, but

― ―nonsignificant. The pair tb–d yielded a negative, andnonsignificant, value for Barcelona, but a positive andnonsignificant value for Alicante. The opposite was true

― ―for both cities with regard to the pair tb – S. In addition,at different levels of the sample populations in Barcelona,with respect to each other, the pairs of loci that exhibitedsignificant gametic disequilibrium were different.Individually, in the subpopulations as well as in the indi-vidual colonies in Barcelona, no consistent trends wereobserved in terms of the appearance in those loci pairswith significant gametic disequilibrium. In addition, theaverage gametic disequilibrium statistics determined forBarcelona and Alicante were less than those reported byHedrick (1985) for other populations of cats. This sug-gests to us that the action of epistatic selection as indi-cated by Hedrick was not the main determining elementfor the small proportion of gene pairs that exhibited sig-nificant gametic disequilibrium. Hedrick (1987) subse-quently also rejected epistatic selection as the main causalfactor for gametic disequilibrium encountered in the catpopulations that he analyzed. Hedrick (1985) rejectedmutations, hitch hiking, genetic drift, and gene flow as themain causes for the generation of gametic disequilibriumin the populations that he analyzed. We agree that mu-tations and hitch hiking probably are not the main causesof the small amount of gametic disequilibrium found inthe cat populations of Barcelona and Alicante. Firstly,disequilibrium was exhibited only in rare alleles (Hedrick,1983). Secondly, the disequilibrium was exhibited in locipairs tightly linked on the same chromosomes (Hedrick,1980; Thompson, 1977), which was not the case for the locianalyzed here.

However, it is possible that under certain circum-stamces not considered by Hedrick (1985), gene drift orgene flow could have been the main, but not the only cause

288 M. R.-GARCIA

Table 6. Estimates of population sizes (N) in colonies and subpopulations in Barcelona and in subpopulations in Alicanteand total in both populations assuming N = Ne/0.6 and Ne calculated from gametic disequilibrium correlationsr and |r|, and assuming as a unique cause of gametic disequilibrium, gene drift. These N estimates werecompared with those obtained from a census carried out by the author in the same colonies and subpopula-tions. No = There is not agreement between the census and the estimates of population size obtained from thegametic disequilibrium statistics; Yes = The population size estimate coming from a census agrees quite wellwith that obtained indirectly from the gametic disequilibrium statistics. ↑ = there was not agreement byexcess (the size of the N estimated from the gametic disequilibrium statistics was higher than that estimatedfrom the census); ↓ = there was not agreement by defect (the size of the N estimated from the gametic disequi-librium statistics was less than that estimated from the census) .

BARCELONAColonies Ne from N from agreement Ne from N from agreement

r Ne between Ns |r| Ne between Ns

A 17 28 No (↓) 4 6 No (↓)B1 60 100 Yes 23 31 No/Yes (↓)B2 185 309 Yes 11 17 No (↓)B3 91 151 Yes 5 9 No (↓)C 198 330 Yes 53 89 No/Yes (↓)

D1 250 415 Yes 18 30 No (↓)D2 26 42 No (↓) 14 23 No (↓)E1 954 1590 No (↑) 93 155 YesE2 565 942 No (↑) 8 13 No (↓)E3 702 1169 Yes 13 21 No (↓)E4 77 128 No (↓) 10 17 No (↓)

SubpopulationsB 132 219 Yes 8 13 No (↓)D 157 261 Yes 13 21 No (↓)E 766 1276 Yes 15 25 No (↓)

TOTAL 3444 5742 No 49 139 No (↓)

ALICANTESubpopulations

A 56 93 No (↓) 25 41 No (↓)B 57 95 No (↓) 21 34 No (↓)C 813 1356 No (↑) 28 46 No (↓)D 108 180 No (↓) 81 134 No (↓)

TOTAL 445 742 No 189 538 No (↓)

of the gametic disequilibrium observed in the presentstudy.

In populations at equilibrium, the expected value of thesquare of the correlation coefficient for gametic disequilib-rium is E(r2) = (1/[1 + 4 Ne c]) (Ohta and Kimura, 1969),

―― ―where Ne is the effective population size and c is the re-combination for the loci being considered. In the presentcase, we assume that c = 0.5 (genes not linked), so that the

―effective population size can be stated as a function of r,Ne = (1–r2)/(2 r2). Hedrick (1985) used the mean absolutevalue of r (0.018) and obtained a value for Ne of 27.3cats. This value was entirely too small for the cat popu-lations under consideration, and as a result he rejectedgenetic drift as a main factor causing the observed gameticdisequilibrium. What would happen if one applied theseequations to the different estimates of r encountered atthe different sample population levels analyzed inBarcelona and Alicante ?. The results are shown in Table6. The total population size, N, was calculated on thebasis of N = Ne/0.6. This is a ratio found for other

――――――――――mammals. Several examples are as follows: Mus muscu-

――― ―――――――――――――lus (N = Ne/0.65; Charlesworth, 1980), Sciurus caro-

―――――――― ―――――――――――linensis (N = Ne/0.59; Charlesworth, 1980), Alces alces

――――――――――――――――――――――(N= Ne/0.4; Ryman et al., 1981), Odocoileus virginianus(N = Ne/0.35; Ryman et al., 1981) and Homo sapiens (N =Ne/0.52, or N = Ne/0.60; Nei and Murata, 1966 andCharlesworth, 1980, respectively). In addition, we em-ployed the expression :

V(k) = (4N – 2Ne – 2)/(Ne), where V(k) is the variance ofthe progenies. This variance in cats is usually greaterthan two (V(k) > 2), and therefore Ne < N. If we considerthat the size of the population is constant, then the breed-ing progeny, when they reach sexual maturity, have a k =2 (k, mean number of individual progeny). If progeny arecounted at an earlier stage, k should be greater than 2and as V(k)/k is related to k, the obtained V(k)/k must beadjusted to a ratio of k = 2 (Crawford, 1984). Addition-ally, if we consider that the survival of each kitten israndom and independent of that of its siblings, then theexpression

V(k)/k = 1 + (k/k ’)[(V(k ’)/ k ’) – 1), where k ’ and V(k ’)are the mean and variance of the number of progeny enu-

289Gametic disequilibrium in cat populations.

merated at an early stage of the life-cycle, is useful to cal-culate the relation among Ne and N. On the other hand,if the progeny average is decreased from k ’ to k * by thedeath of entire families, and subsequently to k by indi-vidual death independently of the family survival, theexpression V(k)/k = 1 + (k/k *)[(V(k ’)/k ’) + (k ’ – k * – 1)] isalso useful for calculating the ratio between Ne andN. Both models are probable in cats. For instance, forthe first case, if k = 2, k ’ = 5 and V(k ’) = 3 , normal valuesfor cats, V(k)/k = 0.84 and Ne/N = 0.5952. For this rea-son, we used Ne/N = 0.60 for a first estimation of the sizeof each one of the populations analyzed at the global, sub-population and colonial levels. For obtaining a secondestimation, we used other parameter values. If weselect the values k =2 , k ’ = 2, k * = 4 and V(k ’) = 3, nor-mal values for cats, we have V(k)/k = 1.3 and Ne/N =0.3846. For this reason, we used Ne/N = 0.40 for a sec-ond estimate of the population sizes. Needless to say, wecompared these theoretical N estimates with the popula-tion estimates that were obtained during several censusesmade of the Barcelona and the Alicante cat populationswhile we were carrying out the genetic analysis shownhere . If we use the gametic disequilibrium r coefficient,and we compare the population sizes obtained by thismethod with those obtained from the censuses, 6 of the 11colonies analyzed in Barcelona exhibited a population sizewhich could have been caused by genetic drift. The re-maining five colonies had values of N that were either verysmall, or very large, in relation to the demographic analy-ses based on the censuses carried out in these cat colonies(Ruiz-Garcia, unpublished). At the subpopulation level,several estimates for N appeared to be more or less valid(B, C), but others (D, E) probably were less than those ob-tained from the censuses. The theoretical value for the Asubpopulation was extremely small.

The gametic disequilibrium estimate for the total popu-lation in the sampled area of Barcelona suggested an N ofapproximately 6000 cats. If, for example, we assume N =Ne/0.4, the value of N would instead be about 9000cats. This is a reasonable estimate, but one that prob-ably underestimates the actual number of cats in thesampled area of Barcelona. In the case of Alicante, all ofthe estimates at the subpopulation, as well as at the totalpopulation level were less than what one would expectbased on the results of the censuses that were carriedout. If we assume that N = Ne/0.4, the value for N wouldbe 1200 cats, which is much lower than that expected forthe sampled areas in Alicante. Therefore, in some casesthere was a correlation between the observed census val-ues and those obtained from the estimates made by usinggametic disequilibrium. In other cases, however, therewas no correlation between the two values, which weresometimes overestimates, but generally were not, as wasthe case in Hedrick’s work (Hedrick, 1985), where thesetheoretical estimates were extremely small.

In order to determine the possible importance of geneflow as a cause of the observed gametic disequilibrium,Hedrick (1985) developed the expression ∆ = 2 D̂1/2 , where∆ is the difference between the allele frequencies of thecompared loci assuming that this difference should occur(∆ = 0.326) between hypothetical populations of cats inorder to explain the observed substantial levels of gameticdisequilibrium solely as a result of gene flow. In the caseof Barcelona and Alicante with |D̂|, the values of ∆ were0.249 and 0.209, which are also very high values thatwould be directly contrary to the relatively strong homo-geneity and high gene flow that characterize the cat popu-lations studied here. However, the assumptions made byHedrick represent an extreme simplification of the actualsituation in which cat populations are found:

1/ Colonies and subpopulations of cats in a city probablydo not originate only as a mixture of two groups withdifferent origins. Rather, they come from an extensivemixture of individuals from different stocks and with dif-ferent proportions; thus, they are different from m = 0.5.

2/ The differences between pairs of different loci do notnecessarily have to be of the same magnitude.

3/ It is very probable that many stocks that can join inthe formation of a colony, or a subpopulation, originatewith a certain amount of gametic disequilibrium of a sto-chastic (genetic drift), or selective nature, prior to the ef-fective constitution of gene flow.

We believe that a part of the relatively small gameticdisequilibrium observed could originate from an intermix-ing due to the action of genetic drift (especially at the levelof the smallest colonies), as well as gene flow. It could beproposed, however, at least for Barcelona at the colonylevel, that four of the colonies showed a significantly nega-

― ―tive association for a–d and that, furthermore, for three

― ―of them significantly negative values for l–S wereobserved. At the subpopulation level, in three cases

― ―negative values for l–S were observed, and in two cases

― ―significantly negative values existed between d–S, whilein two cases significantly positive values were found for

― ―O–S. It is possible that for certain pairs of alleles sometype of epistatic selection could be acting. However, ifdifferent colonies, or subpopulations, had originated his-torically from the same source, or from very similarsources, and if these sources exhibited gametic disequilib-rium of the same nature, then different colonies and sub-populations of a given city could systematically presentgametic disequilibrium in the same direction. In orderto propose that the systematic appearance of gameticdisequlibrium in different allele combinations was aidedby epistatic selection, it would be expected that thisappearance would be repeated in colonies and subpopula-tions of different cities. It is difficult to understand howselection would promote different combinations in differ-ent parts of the same city and between differentpopulations. The comparisons between Barcelona and

290 M. R.-GARCIA

Alicante do not show repetition, or a systematic nature, inthe signs of the different pairs of allelic combinations.This could be taken to indicate that selection does not playan important role. However, the action of natural selec-tion can not be dismissed in those pairs of allele combina-tions where significant and same-sign results wereobserved.

Hedrick (1985) proposed that the possible epistaticselection that could be noted in the populations of cats thathe studied could be attributed to artificial selection viahuman preference more than to natural selection basedon different genotypical fitness. Several authors, how-ever, have asserted the possible action of some type ofnatural selection in favor of the dark phenotypes in urbanareas (Metcalfe and Turner, 1971; Clark, 1975, 1976;Blumenberg and Lloyd, 1980; Symmond and Lloyd,1987). This would mean that the combinations of thosepairs of alleles that confer greater darkness of fur wouldbe favored by natural selection. For example, this typeof selection could favor negative allele combinations, such

― ― ― ― ― ― ― ― ― ―as O–d , a–d , d–S , and d–tb, or positive ones, such as a–S,

― ― ― ― ― ―tb–S, O–tb, and O–S. In the study by Hedrick (1985,1987), none of these combinations were significant in themanner required for the urban natural selection of darkphenotypes. For this reason, Hedrick proposed that theselection must be due to human preferences. At thecolony level in Barcelona, as mentioned earlier, a certain

― ―level of significantly negative values was exhibited for a–dthat would be expected precisely under natural selectionthroughout the urban effect. Furthermore, two of the 11colonies analyzed exhibited significantly negative values

― ―for tb–S , which one would not expect based on naturalselection. At the subpopulation level in Barcelona, sev-

― ―eral of these groups exhibited significantly negative (d–S),

― ―or positive (O–S), gametic disequilibrium, which would bein accordance with that expected under naturalselection. At the total level in Barcelona, two of the threecombinations that exhibited significant gametic disequi-

― ― ― ―librium (O–S and o–tb) could respond to this single selec-tion criterion. At the subpopulation level in Alicante, insome cases a significant combination was noted that couldrespond in the manner expected for natural selection: for

― ― ― ― ― ―example, a–d and d–S in the B subpopulation and a–S inthe A subpopulation. However, other combinations wereobserved in the opposite direction from that expected

― ―under such selection: for example, O–S in the B sub-population. Despite all of this, no systematic pattern wasnoted in these pairs of expected combinations due to theurban effect, nor between different colonies and subpopu-lations in the same city, nor between different cities. Allof this leads us to conclude that the low level of gameticdisequilibrium observed could respond mainly to differen-tial gene flow, to genetic drift in the smallest populationgroups, and perhaps to certain specific allele combina-tions, which are strongly determined by natural selection

based on the urban effect. The role of epistatic selectionbased on human preferences as indicated by Hedrick(1985), however, can be dismissed, at least for the two Ibe-rian cat populations. Only through detailed study inother cities and the analysis of successive generations of agiven population could one determine the precise role ofselection, and the type of selection present, in the occur-rence of gametic disequilibrium for certain pairs of allelecombinations. It is important to emphasize that at eachpopulation level the pairs of allele combinations that weresignificant were different. This could mean that at eachpopulation level, the causes of the gametic disequilibriumcould also be different. This probably supports more theprocesses of gametic disequilibrium via gene flow and dif-ferential stochastic processes at each population level thanthe role of selection as a cause of this disequilibrium.These results could only be explained through differentialselection at each population level. It is hard to imagine,however, a type of selection of this nature in the context ofthe present study.

Spatial autocorrelation The spatial autocorrelationanalysis with different classes of distances applied to theallele frequencies and to the coordinates of axis I and II ofa multidimensional scale analysis clearly demonstratedthat no significant spatial structure existed at the colonylevel in Barcelona. This is what would be expected in amodel where gene flow is high and random. The low per-centage of significant correlograms and the nonsignificantpercentage of Manhattan distances less than 0.1 (Moran)clearly demonstrated that each of these variables has beenaffected differentially in terms of the spatial history of thepopulation. It is important to emphasize, however, thatsome gametic disequilibrium statistics did exhibit a spa-tial structure, which shows that for several of them therewas a pattern of long distance differentiation. This is duemainly to the fact that one of the colonies in an extremegeographic position (A colony; Barcelona harbor) exhibitedmean values for the gametic disequilibrium statisticswhich were higher than those for the remainingcolonies. This is a colony relatively isolated from theothers and it is apparently subjected to much moredemanding and adverse environmental conditions thanthe other colonies analyzed. The slight increase in ga-metic disequilibrium for this colony could be due to thefollowing:

1/ Genetic drift greater than in the other colonies. Theextreme environental conditions under which these catslive could result in greater levels of extinction processes,in which case stochastic processes would increase.

2/ Due to these extreme conditions, there could be agreater role for selection.

3/ There could be greater gametic disequilibriumthrough gene flow due to the arrival of cats of differentgeographic origins through the numerous ships of differ-

291Gametic disequilibrium in cat populations.

ent nationalities that arrive at the Port of Barcelona (oneof the busiest on the Mediterranean).

It would be desirable to study other cat populations todetermine if the results obtained for Iberian cats are spe-cific to that population, or if, on the other hand, they canbe generalized to other populations of urban cats. Itwould also be desirable to undertake long-term studies ofthe population analyzed here to determine whether thecharacteristics observed remain constant through time, orvary according to the generation.

I want to express my thanks to Dr. K. Klein (Mankato, USA),Dr. A. Sanjuan (Vigo, Spain), Dr. R. Robinson (London, England)for opinions and discussion of this manuscript. Special thanksgo to Prof. Diana Alvarez (Bogotá DC., Colombia) for help withtables and Dr. Jeff Jorgenson (Bogotá DC., Colombia) for helpwith English syntax. This work was partially financed by grantsfrom COLCIENCIAS to the author (Convenios No 139–94 and140–96). This work is dedicated to the memory of the late Dr.Roy Robinson.

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