The two-edged effect of tourism

for national park management: the case of the rock partridge in the Austrian Alps

Doris A. Behrens Birgit Friedl Michael Getzner

Discussion Paper No. 2008.01 February 2008

DEPARTMENT OF ECONOMICS KLAGENFURT UNIVERSITY

The two-edged effect of tourism

for national park management: the case of the rock partridge in the Austrian Alps

Doris A. Behrens Birgit Friedl Michael Getzner

Discussion Paper No. 2008.01 February 2008

Corresponding Author:

Doris Behrens, Department of Economics, Klagenfurt University, Universitaetsstr. 65–67, A-9020 Klagenfurt, Tel. +43 463 2700 4123, Fax +43 463 2700 4148, doris.behrens@uni-klu.ac.at

Abstract:

Attracting visitors to a national park can open up additional sources of funding for species conservation. However, tourism may also bring ecologically negative impacts to the park. In this paper, we discuss this two-edged effect of nature-based tourism by means of a stylized model which frames the interaction of a representative species, its habitat, and park visitors in an alpine ecosystem. In an application to the protection of the rock partridge population in the Mallnitz Tauern Valley (National Park Hohe Tauern, Austria), we investigate the scope for static policies that combine both higher visitor numbers and species protection. A policy-mix of visitor infrastructure improvements and habitat creation performs best in terms of combined effects regarding recreation, conservation and funding.

Keywords: bioeconomic model, species conservation, nature-based tourism, optimal policy mix, protected area management, case study, Mallnitz Tauern valley, Hohe Tauern national park, rock partridge

JEL Codes: C61; Q26; Q28

Acknowledgements: We would like to thank Brigitte Gebetsroither and Stefan Lieb for their help, suggestions and inputs to the current paper, and the Jubiläumsfonds der Österreichischen Nationalbank (project No. 11216) for financial support. The views expressed in the paper do not imply an endorsement by the funding agency. Moreover, we are indebted to participants of the OR 2005 at Bremen (Germany), the DIVERSITAS First Open Science Conference at Oaxaca (Mexico), the OeGOR-Workshop on ‘Challenges in the Optimization of Health and Bio-Systems’ in Graz (Austria), and the World Conference of Environmental and Resource Economists at Kyoto (Japan).

1. Introduction

In Alpine regions the protection of charismatic species such as the golden eagle or the bearded vulture is a challenging but well-funded task (Pachlatko, 1991; Robin et al., 2004; Frey, 1999). As compared to these charismatic and fund-attracting birds, less popular species derive less attention and usually attract smaller conservation budgets (e.g., Metrick and Weitzman, 1998; Dawson and Shogren, 2001; Ando and Getzner, 2005). The rock partridge (Alectoris graeca saxatilis, listed in the EU Flora Fauna Habitat directive)1 is a prime example for such a ‘non-charismatic species,’ and thus throughout the paper the terms ‘partridges’ and ‘non-charismatic species’ are used synonymously. But why does the rock partridge so balefully lack of charisma?

The rock partridge is a shy game bird (small in physical as well as in population size) living in a habitat consisting of sub-alpine and mountain pasture ranges in hilly areas (Hafner, 1994). During breeding season (when hikers disturb nesting and feeding) and during winter rest (when partridges are disturbed by skiers) these birds are vulnerable to visitors. This threat by visitors contradicts the requirement in the EU Birds’ directive which requires non-declining population numbers of the rock partridge. While, from a scientific point of view, the partridges are regarded as an important indicator species for natural alpine habitats largely untouched by human use, the species is not known by the general public. Thus, visitors to a national park area might not approve visitor restrictions necessary for the partridge’s survival.2

On the other hand, at least indirectly, visitors are important for the protection of the rock partridge: Considering that national parks are highly dependent on federal subsidies,3 public expenditures have to be justified as important for the general public. Thus, the more visitors ‘vote by their feet’ for protected areas, the more are federal authorities willing to supply funding, also for unknown species like the rock partridge.

In the context of protected area management, ecosystem damage caused by visitors is an unintended side-effect rather than an explicit economic activity such as hunting. In the literature, most of the multi-species models address this second case of harvesting (e.g., Brock and Xepapadeas, 2004, Hoekstra and van den Bergh, 2005); the first case of unintended damage is only covered by some authors who address wildlife conservation and its (negative) economic consequences (see, e.g., Conrad and Salas, 1993; Rondeau, 2001; Bulte and van Kooten, 2002; Shogren et al., 2003; Skonhoft, 2005; Friedl and Behrens, 2007). The present paper contributes to this field by developing a descriptive food-chain model of a non-charismatic species, its habitat, and the interaction with park visitors in order to investigate consequences of different conservation and visitor policy measures. We start with the description of the ecological model augmented by the impacts of visitors and by conservation and tourism policies. In section 3, we investigate the equilibrium of the resulting bioeconomic model for the case without any policies (as a reference point for the rest of the analysis). Section 4 aims at identifying an ‘ecologically

1 Rock partridges only occur in the Alps and mountains of Italy and the Balkan. According to BirdLife International (2004, 2005) the Austrian breeding population size is estimated to 900-1,200 pairs. 2 This, of course, depends on the perception of visitors regarding the aims of a national park. If strict conservation is perceived positively by visitors, restricting access to certain areas might increase the credibility of park policies and therefore also lead to stronger preferences for the park. 3 For all Austrian national parks annual federal contributions are about € 10.11million, with € 2.6million going to the Hohe Tauern national park; total annual public expenditure amount to about € 26million (ITR, 2001).

neutral’ (and easy to implement) mix of visitor and conservation policies4 that maximizes the net benefits for the park administration. This optimal policy mix is designed as a static one since the national park management claims that permanent adjustment of the control measures is impossible. This impossibility rests on the fact that typical conservation measures such as habitat creation take time to evolve their effectiveness and cannot be implemented instantaneously. Suggestions for further research and the derivation of policy recommendations for practical decision making in conservation conclude the paper.

2. The bioeconomic model

2.1 A food-chain model augmented by the negative impact of tourism

In this section, we develop a dynamic bioeconomic model that captures the interaction of a non-charismatic species and visitors in a national park, where visitors come for hiking and other types of non-consumptive wildlife recreation.5 Without intention, park visitors have a detrimental impact on the ecosystem, either by e.g. disturbing species (during sensitive phases of the life-cycle) and destroying its habitat, or through the demand for visitor infrastructure such as hiking trails, picnic sites, parking areas and shelters. Moreover (and in case of a ‘non-charismatic species’ often primarily), visitors are attracted by landscape (which is suitable as habitat of the species under consideration) and by wildlife found therein (where the partridges are assumed to be a proxy for), but also by the attractiveness of visitor infrastructure. Each component of the bioeconomic model will be described in turn, starting with the ecological system impaired by visitors.

Let the modeled species, denoted by S(t), depend on the park area which is suitable as habitat, denoted by H(t). From the viewpoint of visitors, the habitat forms the appealing landscape. In contrast to large predators, non-charismatic species such as the rock partridge do not impair their habitat and thus, species numbers do not negatively feedback on the habitat. While the maximum extent of the suitable habitat area is fixed at some upper level, denoted by ω, the actual size of this area H(t) is generally considerably smaller than ω and can change over time, e.g. due to changes in vegetation and climate, and restoration measures. This motivates the modeling of the ‘habitat dynamics’ by means of a logistic function. Thus, in absence of visitors, the area suitable as habitat for the species grows towards its carrying capacity, ω. Unfortunately, for ecological reasons the rock partridge breeding areas are often located in direct vicinity to the existing hiking trail network. Therefore, the bird population has to ‘compete’ with visitors for the landscape serving as its breeding grounds and retreat area. Thus, the ‘pristine’ carrying capacity is reduced by visitor influences, and we describe this damage by a function a(U(t)), with 0 ≤ a(U(t)) < 1, where U(t) denotes the number of visitors in percent of a baseline level U0 = 1 =

100%. Then, (1) can be used to describe H(t)’s growth rate, represented by

g(t), embodying the inverse relationship between habitat growth and the number of visitors, U(t):

4 The term ‘ecologically neutral’ refers to preserving the current population size of the non-charismatic species. 5 According to Duffus and Dearden (1990), non-consumptive wildlife recreation refers to recreational activities that do not harm wildlife on purpose, such as bird-watching, nature walks, photography or viewing in parks.

( ) ( )( ) ( )( )( )( )

−

−==tUa

tHtUtHgtg

11,)(

ωα , (1)

where 0>α is the natural growth rate of the habitat. Note that the term a(U(t)), capturing the negative impact of visitors, is zero only in absence of tourism and positive otherwise. Assuming that the marginal damaging effect (∂a/∂U) is increasing with the number of visitors, we implement a quadratic function to represent the percentage reduction of the habitat’s carrying capacity, ω :

( )( ) ( ) ]1 ,0[ 2 ∈= tUtUa ρ ,6 (2)

with 0>ρ denoting the marginal percentage reduction of carrying capacity

ω (per additional visitor). A standard feature of food-chain-type models is that the species

depending on the habitat grows logistically, too. Its carrying capacity is restricted endogenously by the supply of suitable breeding area (βH(t)) which is usually smaller than the current habitat H(t). This yields the following growth rate for the partridge population:

( ) ( )( ) ( )( )

−==

tH

tStStHftf

βγ 1,)( , (3)

where β∈ (0,1] denotes the conversion rate of habitat into carrying capacity of non-charismatic species, and 0>γ the natural growth rate of the non-charismatic species population.

Visitors are attracted by the existing diversity of ‘untouched’ landscapes, ecosystems, animal and plant species, including rare/threatened animals living therein, and by the quality of visitor infrastructure (hiking trails, picnic areas, nature trails, lodges, availability of information, vista points etc.). Thus, the number of visitors U(t) at time t is determined by a Cobb-Douglas-type7 ‘visitor demand function’ depending on the ecosystem conditions (H(t),

S(t)) and the availability of visitor infrastructure 0>ν (e.g. hiking trails):

( ) ( ) ( )( ) ( ) ( ) µµν

−== 1, tStHtStHUtU , (4)

with 0 <<µ ≤ 1 denoting the elasticity of H(t) with respect to the attraction of visitors by the habitat.

2.2 The bioeconomic model with conservation and visitor policies

Assume that the park management seeks to increase (or at least maintain) the number of visitors without damaging the bioeconomic system. This can be accomplished by combining measures for the protection of the ecosystem with measures for attracting additional visitors. The ecosystem can, for instance, be protected by habitat creation, which comprises all measures that increase the quality of the habitat (e.g. by means of changing vegetation) and the size of the area by designating larger areas as

6 Since (2) is usually not limited to values in the unit interval, we parameterize and truncate the function accordingly. 7 Note that the choice of the functional form is merely driven by empirics. A demand function linear in both arguments (H and S ) yielded counter-intuitive results, such that visitors were deterred by partridges (this would be suitable if we described visitors’ reaction to the existence of bears or other dangerous species but not for the inconspicuous partridge).

the core zones of a national park. The latter improves the conversion rate from habitat into species, β, i.e. the endogenous carrying capacity for S, in (3) by a certain percentage (1+λ ), as introduced in (5b).

On the other hand, visitor infrastructure improvement helps to attract additional visitors; thus increasing the visitor infrastructure parameter in the visitor demand function (4) by a certain factor, (1+ψ ), as given by (5c). Positive values of ψ correspond to visitor infrastructure improvements and negative ones to visitor access restrictions, e.g. during sensitive periods. Describing the effects of increasing visitor infrastructure ψ and habitat creation λ on the ecosystem in such a way yields the following two-stage continuous-time bioeconomic model.

( ) ( )( )( ) ( ) ( ) 00,

11

2>

−−= HtH

tU

tHtH

ρωα& (5a)

( ) ( )( ) ( )

( ) ( ) 00,1

1 >

+

−= StStH

tStS

λβγ& (5b)

( ) ( ) ( ) ( ) ( ) 00,11 >+= −

UtStHtUµµ

ψν . (5c)

System (5a)-(5c) has been fully parameterized for the case study of the rock partridge population situated in the Mallnitz Tauern valley (Hohe Tauern national park, Austria) and the hiking visitors found there. A detailed description of data sources and calibration procedure can be found in Appendix A.2, the respective values are captured in Table 1.

Table 1: Parameter values for the rock partridge in the Mallnitz Tauern valley

Parameter Value Description

α 0.4621 Growth rate of the size of the landscape (= habitat), with the limits of growth given by pristine landscape

β 0.3843 Conversion rate of habitat into carrying capacity of rock partridge

γ 0.6200 Annual net growth rate of the rock partridge

ω 41.630 Pristine carrying capacity of the habitat (= total area of Mallnitz Tauern valley)

ν 0.0368 Scaling parameter in visitor demand function

µ 0.9500 Elasticity of (landscape (=habitat) in visitor demand function (= significance of the habitat for attracting visitors, compared to the species)

ρ 0.1303 Marginal reduction of carrying capacity of habitat due to visitors

H(0 ) 28.37 Size of rock partridge habitat in square kilometers at time t = 0

S(0 ) 12 Number of breeding pairs at time t = 0

2.3 Benefits and costs of conservation and visitor policies

In order to evaluate the different policy options from the point of view of the park management, we consider benefits in terms of additional revenues generated by additional visitors (relative to the initial state as indicated by the initial conditions for visitors and the non-charismatic species, U0 and S0, respectively), by either out-of-pocket expenses on visitor facilities or by donations of visitors to species protection measures. Accordingly, the net benefit (NB) for the planning horizon T is calculated as the difference

between the discounted stream of gross benefits and the discounted stream of costs of additional visitor infrastructure and of habitat creation:

( ) ( )( ) ( )( ) ( )2 2

0 0

0

T

r t

t

NB e U t S t S U t U dtκ ε θψ φ λ−

=

= − + − − + ∫ , (6)

where ε are average visitor expenditures (in park facilities), κ stands for the average willingness to pay (=donations) per additional breeding pair of the partridge, and θ and φ are the costs of providing additional visitor infrastructure (associated with an increase in visitor numbers by 1%) and of increasing the habitat by 1%, respectively. The first term in (6) refers to the aggregate donations by all visitors generated by an increase in the population size of the non-charismatic species relative to S0 (non-use values), while the second term refers to visitor spending related to visitor infrastructure due to an increase in the number of visitors relative to U0 (use values) yielding additional park revenues. Assuming that improvement of visitor infrastructure is subject to decreasing returns to scale, we associate quadratic cost with the provision of additional visitor infrastructure (ψ ).8 The cost of habitat creation is also modeled to develop in a quadratic manner, where λ = 0 is associated with the initial state.

Table 2: The policy parameters values for the rock partridge in the Mallnitz Tauern valley

Parameter Value Description

T 10 Length of planning horizon

r 0.04 Discount rate

κ 0.0017 Average willingness to pay for an additional rock partridge breeding pair

ε 0.0018 Average visitor infrastructure expenditures

θ 11.6474 Cost parameter of increasing visitor infrastructure

φ 633.890 Cost parameter of habitat creation

Table 2 shows the parameter values assigned to the net benefit function

(6) for the case study of the rock partridge in the Mallnitz Tauern valley (see Appendix A.2 for the calibration). To put these numbers into perspective, in the initial state the aggregated WTP is € 39,447 per additional breeding pair (for a total of 22,910 visitors), while the creation of suitable habitat for serving an additional breeding pair induces a cost to the park management of approximately € 44,545. Thus, income generated by additional visitors through new visitor infrastructure is essential to cover these costs.

3. The long run equilibrium behavior

3.1 The bioeconomic equilibrium: the reference case

By using (5c) in (5a) and setting the time derivatives of (5a) and (5b) equal to zero, we gain two isoclines in (H, S )-space, see Appendix A.1. In the

8 Note that this does not (only) come from the fact that setting up new trails becomes more and more inefficient, but from a crowding effect of visitors (i.e., additional trails and additional visitors do no behave proportionally). If the level of maintenance work falls below its baseline level, less hiking trails are available. This reduces maintenance cost for ψ < 0 (since the sgn function is responsible for the

negative sign, sgn[ψ ] = –1), and the additional costs are thus costs reductions.

relevant subsection of the phase space, {(H, S ) | 0 < H ≤ ω, 0 < S}, the model exhibits a unique bioeconomic equilibrium:

( )( )

( )( ) ( )( ) ( )( ) ( ) ( ) ( ).

1

1

11411

12

ˆ

ˆ

2221242

2

+++++++

+=

+ λβωψρνλβλβλβ

ωλβ

µµµ

µ

S

H(7)

Equilibrium (7) always exists as 0β ≠ and does not depend on the growth rates α and γ (as a consequence of using a food-chain model, not a predator-prey model). As can be seen from (7), additional visitor infrastructure (ν and ψ ) as well as an increase in the marginal damage caused by visitors (ρ ) affect the bioeconomic equilibrium (both H and S ) in a negative way, while both an increase in the habitat’s carrying capacity (ω) and an increase in the elasticity of the number of visitors with respect to the habitat (µ ) have a positive impact on the long-run size of the species population and its habitat. An improvement of habitat quality (λ ) as well as a more efficient conversion from habitat into species (β ) have the expected positive effect on the long-run size of the ‘non-charismatic’ species population, S . Interestingly, 0/ˆ <∂∂ λH and 0/ˆ <∂∂ βH . This is because the increase in efficiency of transforming area into partridges allows for adapting more of the area suitable as habitat with additional visitor infrastructure (eventually increasing the number of tourists).

Investigating the responsiveness of the bioeconomic equilibrium (7) determined for the Mallnitz Tauern ecosystem (parameter values listed in Table 1; ψ = λ = 0), we find that 1%-changes in the size of the respective parameter values have an under-proportional effect on the equilibrium (which is given by 33.94ˆ =H km², 31ˆ =S breeding pairs, and visitors

191.ˆ =U ). Thus all results derived here about the long-run behavior of the ecosystem under investigation are fairly robust with respect to parameter changes. Moreover, we find that the initial state of the Mallnitz Tauern ecosystem (H(0) = 28.37km², S(0) = 12, U(0) = 1=100%) is already ‘quite close’ to its bioeconomic equilibrium state. The size of habitat has the potential to increase by approximately 20% yielding a comparable increase in visitor demand by 19% and an additional breeding pair. Note that even in absence of visitors the Mallnitz Tauern valley is not capable of hosting more than

61ˆ =S breeding pairs, because ‘excess breeding pairs’ will migrate to neighboring valleys.

3.2 The bioeconomic system away from the (reference) equilibrium

For the Mallnitz Tauern ecosystem parameter values (see Table 1) and setting ψ = λ = 0, depicts the isoclines for H and S (determined in Appendix 1), as well as the trajectories approaching the bioeconomic equilibrium (identified by the white circle located at the intersection of the isoclines in the interior of the ecologically relevant region of our model). The shape of the trajectories (together with standard local stability analysis) indicates that for the Mallnitz Tauern ecosystem parameter values the equilibrium is a stable node (see Figure 1 and Appendix A.1).

Let us investigate the (H, S )-phase plane in more detail. For any point above the 0=S& isocline (the grey line with positive slope), the rock partridge population is declining, while below it is increasing (grey shaded area). Accordingly, points to the left of the 0=H& isocline (the steep grey

line) lead to an increase in the size of the habitat while points to the right of it lead to a decrease. Thus, for any point above of the 0=S& isocline and to the left of the 0=H& isocline (e.g. data estimated for the Mallnitz Tauern ecosystem in the initial state as indicated by the grey circle) the transition towards the bioeconomic equilibrium is described by a trajectory that initially implies a decline in the number of species until the trajectory surpasses the S& -isocline, i.e. until the habitat’s size and quality is sufficient to support the growth of the partridge population. After that point of return ( 0=S& ), the habitat as well as the species increases towards the bioeconomic equilibrium. This is the mathematical equivalent of a population’s ‘healthy shrinkage’ if habitat is not available in sufficient quality and/or quantity.

10 20 30 40H

2

4

6

8

10

12

14

16

S

Habitat large enough to support sustainable growth of

bird population

Bird population too large for current size of habitat

t = 0

0S =& 0H =&

Figure 1: Phase diagram for base case parameter values plus initial value (t=0)

Due to the good shape of the initial state of the Mallnitz Tauern

ecosystem (recall that the current population size is just one breeding pair away from its bioeconomic equilibrium level, 31ˆ =S ) it seems plausible that attracting additional visitors generating additional regional income might be beneficial for the national park managementespecially because the existence and maintenance of a protected area is fundamentally based on the acceptance and the support of the local population.9 Since non-declining population numbers are grounded on the Bird’s Directive, any management strategy attracting more visitors has to be accompanied by a practicable intervention guaranteeing that increasing the number of visitors does not cause damage to the ecosystem.

9 Quoting Klaus Eisank, manager in the Hohe Tauern national park: “Nicht von den Steinhühnern leben wir, sondern von den Touristen” (“We do not make our living from rock partridges but from tourists.”)

4. Results of the policy scenarios for the Mallnitz Tauern valley

The main interest for the park management is thus to develop practicable strategies guaranteeing that even though additional visitors might be attracted to the park area, the species population comes sufficiently close to a particular level after a certain number of years.10 We define that seeking such an easy-to-implement policy corresponds to finding fixed combinations of increasing visitor infrastructure and habitat creation capable of reaching its ‘bioeconomic reference equilibrium level’, in which the negative impact of visitor infrastructure improvement on the equilibrium population size is just compensated for by habitat creation. We call this case a ‘species neutral’ visitor policy. Note that this ‘neutrality’ or ‘equivalence’ of management policies is guaranteed only in the equilibrium state and not along the transients (because both policies are assumed to be constant over time due to the significant cost that can be associated with a permanent adjustment of interventions). Moreover, we do not formulate an explicit condition for the habitat as this is indirectly implied via the requirements on S.

4.1 A ‘species neutral’ policy mix

Recall that all regulations necessary to increase visitor infrastructure are embodied in the parameter ψ, while habitat creation is represented by positive values of the parameter λ. To find constant species neutral

management policies (SN-POL) we determine all combinations of ψ and λ that yield the same equilibrium level for S as the ‘reference’ equilibrium

(which is determined by (7) for ψ = λ = 0). The condition 0

ˆˆ==− =

λψSS

POLSN is

satisfied, if the function

( )

( )( )

( )( ) ( )( ) ( )( ) ( ) ( )221242

21

2

22222

11411

12

2

4,

ψρνλβλβλβ

ωλβ

ρωβν

ρωνββββψλ

µµµ

µ

µµµ

++++++

+−

+−−=

+

+

F

(8)

is equal to zero. Thus, all combinations ( λψ

~,~ ), for which F(ψ, λ ) = 0,

constitute SN-POLs. Figure 2 depicts these combinations by the (slightly convex) dark line for the Mallnitz Tauern ecosystem and policy parameters given in Table 1 and 2, respectively. We observe that the percentage increase in partridge habitat necessary to compensate for an additional percent of infrastructure in terms of the equilibrium rock partridge population is not constant, but has to marginally grow in ψ~ .

Having found all combinations of SN-POLs given by {( λψ~

,~ )| F(λ,ψ) = 0,

λ ≥ 0, ψ ≥ 0, 0)(,0)( == tt ψλ && }, we seek to find the combination that additionally maximizes the park management’s additional net-benefit (defined by the finite integral (6)):

10 As the permanent adjustment of conservation measures such as habitat creation is hardly possible, we assume that the strategies we are looking for are constant over time. Furthermore, the permanent monitoring of the state of an endangered species, which is a prerequisite for a dynamic policy, is difficult and costly.

( ) ( ){ }( ) ( )( ) ( )( ) ( )[ ]∫

=

−

=+−−+−

T

t

tr

FdtUtUStStUe

0

2200

0,|~,~ max λφψθεκ

ψλψλ (9a)

subject to

( ) ( )

( ) ( ) ( )( )( ) ( ) 00,

~11

121

>

+−

−=−

HtH

tStH

tHtH

µµψνρω

α& (9b)

( ) ( )( ) ( )

( ) ( ) 00,~1

1 >

+

−= StStH

tStS

λβγ&

. (9c)

Figure 2: Combination of ecologically neutral policy mixes (black line) and the associated welfare gained (grey line) for the Mallnitz Tauern valley parameter set Table 1)

Since (9a-c) cannot be solved analytically due to the complexity of the functional forms involved, we aim at illustrating the results of solving (9a-c) numerically for the parameterization for the Mallnitz Tauern ecosystem (Figure 2). The optimal static management policy mix allows for an increase of visitor infrastructure by ≈*~ψ 25%. Only combined with a habitat creation policy of increasing the habitat conversion rate β by ≈*~

λ 8.2% this measure accomplishes the bioeconomic (reference) equilibrium size of the rock partridge population of 13 breeding pairs. The maximum net benefit gained (above the level of € 227,139 which comes from maintaining current policy for the next ten years), however, amounts to € 53,056. This corresponds to an improvement of the park management’s net benefits by roughly one quarter over the next ten years. Furthermore, Figure 2 illustrates that the net benefit gained (grey line) is only positive if the visitor infrastructure does not increase by more than ≈ψ~ 48% (or, equivalently, with ≈λ

~16.3%).

Any desired increase in visitor infrastructure going beyond this threshold level reduces net-benefits (in terms of the net benefit function (6)).

10% 20% 30% 40%

2.5

5.0

7.5

10.0

12.5

15.0

Largest combination of ψ~

and λ~

that yields a net-benefit gain compared to the status quo

status

quo

ψ~

λ~

)~

,~( ** λψ

Net-benefit gained in € 10,000 (compared to the status quo) as

function of ψ~

(and the associated λ~

)

4.2 The trade-offs involved: steady state effects

To illustrate the antagonistic forces of additional visitor infrastructure and habitat creation during the transient phase of control, we split the optimal static policy mix, associated with a 25.0~ * ≈ψ increase in visitor infrastructure and an extension of the habitat by 082.0

~* ≈λ , into its components. In particular, the ‘pure’ habitat creation policy (denoted by HAB) takes *~

λ , but sets *~ψ equal to zero while the ‘pure’ visitor attracting policy (VIS) is given by 0

~* =λ and *~ψ at its optimal level. The case of the species neutral policy mix (POL) refers to VIS’s and HAB’s joint application yielding the optimal SN-POL. As a reference case, we also report on the case without policy 0

~~ ** == λψ (NoP). The results on the equilibrium levels of H, S, and U are summarized in Table 3.

Table 3: Effects on bioeconomic equilibrium values, benefits and costs

Policy Scenario Parameter

Values H S U BCR ∆NB

No policy (NoP) *~ψ = 0

*~λ = 0

33.9 13 1.2 – 1

Additional visitor infrastructure (VIS)

*~ψ = 0.25 *~

λ = 0 – 7.6% – 7.6% + 15.5% – 4.1 – 0.14

Habitat creation (HAB)

*~ψ = 0 *~

λ = 0.082 ± 0% + 8.2% + 0.4% 15.3 2.23

Policy Mix (POL) *~ψ = 0.25

*~λ = 0.082

– 7.6% ± 0% + 16.0% 7.77 1.24

According to Table 3, the equilibrium number of visitors (U ) is increasing in the (optimal) species neutral policy mix (POL) case and the ‘pure policies’ (relative to the no policy case), but increasing strongest in applying jointly VIS and HAB. The equilibrium size of the species is larger in HAB than in NoP due to an increase in the size of the habitat. VIS leads to smaller habitat and significantly smaller species number than NoP. The policy mix of both instruments leads to an equal number of species as in NoP, while the habitat is smaller due to additional visitor infrastructure (but has improved in quality due to HAB). The number of visitors is highest for the policy mix (since visitors are also attracted by the species), and lowest for HABitat creation as a single instrument.

Considering benefits and costs of the different policies, it is remarkable that only the species-conserving policies are cost-effective (the benefit cost ratios BCR are considerably larger than one). This result depends, however, on parameter values. Moving on the (slightly convex) dark line in Figure 2 left of )

~,~( ** λψ , also for VIS the BCR becomes positive. Moreover, while for

POL the change in net benefits compared to NoP is positive ( NB∆ = 1.24), this policy mix is outperformed by HABitat creation ( NB∆ = 2.23). If, however, the park administration cannot collect donations for species protection and thus only considers expenditures by visitors (i.e., we set κ = 0), the costs of the measures lead to an outranking of all policy options by the no policy case.

4.3 The trade-offs involved: transition phase

Let us now investigate the transition towards the new bioeconomic equilibrium for the different policies. While the time paths for the habitat (and visitors) coincide for NoP and HAB (and VIS and POL, respectively), the adjustment of the species population is particularly interesting (as the rock partridge is a core issue of our analysis). VIS gives the same equilibrium species population size as the no-policy case, but during transition POL outperforms the no-policy case (see Figure 3). Most interestingly, Figure 3 shows that HAB is capable of making the conversion from habitat into species more efficient, which allows the species to monotonously grow towards S .

Figure 3: Time path for species for no policy case (NoP), increase in visitor

infrastructure (VIS), habitat creation (HAB) and policy mix (POL)

Figure 4: Time path for net benefit for no policy case (NoP), increase in visitor

infrastructure (VIS), habitat creation (HAB) and policy mix (POL)

2 4 6 8 10

20

40

60

€ (in thousand)

HAB

POL

NoP

VIS

t

t

VIS

S

12.5

13.0

13.5

14.0 HAB

POL

NoP

2 4 6 8 10

Comparing the net benefits across policies (Figure 4), the slight increase in benefits in NoP is driven by the increases in S, H and U over time, without causing any costs. For HAB, the benefit increase is mainly driven by the relative increase in S, leading to a strong increase in the aggregate willingness to pay for species conservation by the visitors. The policy mix (POL), despite leading to an increase in U, while S is kept constant, only ranks second, due to the compound costs of the measures. Note, however, that this result hinges on the relative strength of the benefit and cost parameters. If, for instance, the costs of the visitor measure were small compared the costs of conservation the policies with a primary focus on visitors would outperform the conservation oriented policies.

In a nutshell: The well-balanced combination of visitor attraction and habitat creation (at their optimal levels *ψ% and *λ% ) serves the decision-maker not just as a compromise solution between nature-based tourism and conservation requirements (by avoiding a deterioration of the living conditions for the non-charismatic rock partridge, stabilizing its population size at the reference equilibrium level) but can create benefits at least as high as in the no-policy case. This is an important result, since (as we already mentioned) the existence and maintenance of a park area is fundamentally based on the acceptance of the local population. It also serves as an important policy advice since it shows that managing a park can not only increase the number of visitors but also lead to ecological gains. Moreover, this strategy can be regarded not only as ecologically

neutral but also as superior in the transition towards the equilibrium, since the level of breeding pairs and of total benefits are higher for POL than NoP.

5. Summary and conclusions

The literature regarding land-use, development and conservation often sketches a picture of a trade-off between conservation on the one hand, and development and land-use on the other (opportunity cost of conservation). However, conservation and tourism are not necessarily contradictory: Sometimes, they are complements (or at least they can be). Improving visitor infrastructure can attract more visitors who are willing to pay for their recreation benefits, and for provision of information and education. Directly, visitors spend money on parking and entry fees, tolls, guided tours and information materials. Indirectly, increased awareness and education leads to higher WTP for species on the basis of non-use values. Such expenditure can be used (and is actually used) for funding of nature conservation measures. The negative impacts of tourism in ecologically sensitive areas are, however, as important. While budget-generating, tourism also brings ecologically negative impacts to a protected area.

In this paper, we discussed this two-edged effect of tourism in national parks, and tried to evaluate different policy options in a concrete environment, the Mallnitz Tauern valley in the Hohe Tauern national park, and regarding a concrete species, the rock partridge. It turns out, on the basis of our numerical example, realistic empirical parameters and a GIS model of the region, that there are policies that combine both higher visitor numbers and larger numbers of species.

Interestingly, a ‘pure’ conservation policy, as well as the combined ‘balanced’ approach, are cost-effective. The discounted stream of benefits of these policies are each larger than their costs (over a planning period of ten years), but this result does not hold for the ‘pure’ visitor attraction policy. This means that concentrating only on tourism leads to inferior results not only in ecological, but also economic terms. Furthermore, mixed policies of

increasing conservation efforts and attracting new visitors to the area can not only increase net benefits of the park management, but can also increase habitat quality and the number of species living in a certain area. However, the scope for increasing habitat on behalf of new visitor infrastructure is limited––eventually net benefits become negative and visitors’ donations can no longer compensate for the damages caused to the ecosystem.

The definition of benefits of recreation and conservation also determines the ranking of the policy options. If visitors acknowledge non-charismatic species, and the park administration can collect visitors’ willingness to pay for the conservation of this species, policies that include conservation measures are better than visitor measures alone. If the revenues are restricted to entrance fees and other direct expenditures (corresponding to a case in which κ = 0), conservation policies become less favorable, and tourism projects such as extending visitor infrastructure are better in terms of net benefits. Ultimately, the park managers should use visitor information programs as a means to widen the potential for turning non-use benefits into actual donations. An important implication of these results is that the park management is not only advised to fulfill ecological goals based on international agreements or to obey legal regulations, but that the credibility of park policies as well as the attractiveness of the park for visitors depend directly on the ecological measures such as species conservation programs. Policies that only concentrate on attracting visitors without ecological constraints will not be perceived as serious park policies, therefore diminishing visitors’ WTP for conservation programs.

Finally, several directions for further research can be identified. First, other species might require different protection measures, like species re-stocking or reintroduction which alter not only the modeling but also the magnitude of costs. Secondly, while the species under considerations is unknown to the general public (and thus the stated WTP is considerably lower than for charismatic species), it is not unpopular either. The scope for financing species conservation by attracting visitors can be expected fundamentally smaller for large predators like lynxes, wolfs, or bears. Thirdly, the objective we used is suitable for the management of an existing national park, but might require considerable modifications for other types of protected land, be it private land or protected areas of larger scale and more restrictive protection status, or protected areas that are not well-known to the general public.

Appendix A.1: Local Stability Analysis of the bioeconomic model

Since the initial conditions are always positive ( 0, 00 >SH ) and the first quadrant is an invariant set we restrict our analysis to {(H, S) | 0 < H ≤ ω, S >

0}. First we derive the equations for the isoclines:

( ) ( )( )( ) ( )

{0

110

0

2=

−−⇔=

>

tHtU

tHtH

ρωα&

(A1)

( ) ( )( ) ( )

( ){

( ) ( ) ( )tHtStStH

tStS λβ

λβγ +=⇔=

+

−⇔=>

101

10

0

& (A2)

where ( ) ( ) ( ) ( ) µµψν

−+= 11 tStHtU . (A3)

Thus, the number of visitors for which the size of the bird population remains constant corresponds to the case ψ = 0 and can be computed as ( ) ( )tHtU µβν −= 1 according to (A2). Moreover, the intersection of the

isoclines uniquely defines the equilibrium state ( )SH ˆ,ˆ as given in (7) in the main text. The Jacobian matrix evaluated at the stationary point is given by

( )( )( )

( )( ) ( )( )

( )

+

Θ−−

−+Θ

Θ−−

+−Θ−−

ℑ

−

λβ

γγ

ω

µλβα

ω

µα

1ˆˆ

1

221

1

211

=ˆ2

1

2

HH

, (A4)

where ( )( ) ( )22222 11ˆ ψρνλβµ ++≡Θ −

H .

The local stability behavior of the bioeconomic model can be determined in the usual manner by linearization of the system around the equilibrium state (7). The corresponding characteristic polynomial, ( ) 0ˆdetˆtr2 =ℑ+ℑ−= λλλP , may be solved analytically yielding the spectrum

of eigenvalues,

ℑ−ℑ±= ℑ ˆdet4ˆtr 2

21

2

ˆtr2,1λ .

The determinant and trace of the Jacobian matrix at the equilibrium state for the bioeconomic model are given by

( )( ) ( )( ) ( )( ) ( )( ) ( ) ( )(( ) ( ) ( )( ) ( )( ) ( )( ) ( ) ( )( ))222124222222

222124241

2

114112112

1141112

1ˆdet

ωψρνλβλβλβωψρνλβ

ωψρνλβλβλβλβαγω

µµµ

µµµµ

+++++++++

++++++++=ℑ

+

+−−

(A5)

( )( ) ( )( ) ( )( ) ( )( ) ( ) ( )( )

( )( ) ( ) ( )(( )( ) ( )( ) ( ) ( ) )))222124

222222

22212422

2

1141

1141

1

114111

2

1ˆtr

ωψρνλβλβ

ωψρνµλβλβα

λβ

ωψρνλβλβλβγλβ

ω

µµ

µ

µµµµ

+++++

+++++−

−

+++++++

−+=ℑ

+

+−

(A6)

For the chosen parameter values and λ ∈ {0,0.25} and ψ ∈ {0,1}, we get according to (A5)-(A6), 1ˆdet0 <ℑ< and 0ˆtr <ℑ . Moreover, 0ˆdet4ˆtr 2 >ℑ−ℑ and thus both eigenvalues are real and negative. Accordingly, we have an improper node which is asymptotically stable.

Appendix A.2: Parameterization for the rock partridge in the Mallnitz Tauern Valley (Austria)

For the rock partridge population in the Mallnitz Tauern valley, the initial state of the ecological system can be parameterized as follows: H(0) = 28.37, S(0) = 12. According to a GIS model (Behrens et al., 2006), approximately three quarters of the Tauern valley can currently be identified as potential habitat suitable for the rock partridge population (ω = 41.63 km²) leading to a carrying capacity of the rock partridge of 16 breeding pairs.11

The current state of the Mallnitz Tauern valley implies a breeding area that is 13% smaller than the pristine carrying capacity, thus ρ = 0.1303 (Behrens et al., 2006). Moreover, in the initial state, the habitat (i.e., its biomass per km²) is growing slowly, assumingly at a rate that is a reasonably low number for high altitude forest and brush ecosystems of 0.1 (10%), see, e.g., Umweltkontrollbericht (2004). Accordingly, the intrinsic growth rate for t= 0 can be estimated as 4621.0=α . The annual survival rate of the rock partridge population is, on average for male and female, γ= 62% (Hafner, 1994). Since the partridge’s carrying capacity is 16 breeding pairs (Behrens et al., 2006), we can set 16=Hβ . Thus, for H = 41.63 km², the natural growth rate of the rock partridge is equal to

3843.0→β . According to a visitor count in 2003 (Lehar et al., 2004), the annual

number of visitors to the Mallnitz Tauern valley is 22,910, which we define as 100% for analytical convenience, U(0) = 1=100%. Visitor demand is then calibrated as follows. As visitors are highly in favor of the nice landscape (i.e. the habitat) but are quite neutral with respect to the partridge we set µ= 0.95 and we get ν=0.0368 for the initial state (H(0) = 28.37, S(0) = 12, U(0) = 1).

The average (hiking) visitor to the Hohe Tauern spends € 22.87 per day (Lehar et al. 2004). Most of the costs are private costs which cannot be devoted to financing visitor infrastructure, such as meals and beverages, fuel, and cable car tickets. However, some spending categories can be related to visitor infrastructure maintained by the park management: parking fees, guides and hiking tours, and entrance fees, leaflets, souvenirs issued by the park management, yielding infrastructure expenditures per visitor of ε = 0.00180 (in 1,000 Euros).

From a contingent valuation survey (n = 211) among the visitors to the Hohe Tauern national park the mean willingness to pay for an increase in the rock partridge population from 12 to 16 breeding pairs in the Mallnitz

Tauern valley was investigated (for details, see Behrens et al., 2006). The mean WTP per breeding pair can be estimated to be € 1.72 (lump sum, not annual payment), or κ = 0.00172.

11 For a habitat suitability analysis by means of a GIS model (see Behrens et al., 2006). According to slope steepness, vegetation (brushwood and small bushes are the suitable retreat area for the partridge), and human influences from existing trekking trails and skiing tour routes, the suitable habitat and maximum population size were estimated. The same model was applied to different protection measures (e.g. seasonal closings) and visitor infrastructure (new trails and outdoor activities) to estimate the impact on breeding area, overall habitat and species numbers.

According to Getzner et al. (2002) the cost of setting up an additional hiking trail is of the order of € 1,000-2,000 per kilometer. Since this is a very conservative estimation, we take the larger value and for the annual fixed cost per km. Annual maintenance cost (variable cost) amounts to approximately 5% of investment cost, i.e., € 75-100 per km (Getzner et al., 2002). Then, the annual cost of increasing the trail network to 41.896 km (associated with U = 1.5) can be calculated as

( ) ( )1 41.896 2,000 / 100 12,568.80C Tψ = + = yielding 1.0388ψ = € (for T=10) and thus 11.64743θ ≅ .

The cost of habitat creation can be estimated in a straight forward way. An increase in the breeding area by 1 km² increases the rock partridge population by 1.1 breeding pairs (Behrens et al., 2006). In particular, we calculate the size of the parameter λ for our initial conditions (t = 0, H(0) = 28.37 and S(0) = 12) and for β = 0.3843 and γ = 0.62, as 0.29162λ = . According to Getzner et al. (2002) habitat maintenance cost is € 40,000-70,000 per km² and per year, and as a first approximation we take the lower value for the variable costs. Moreover, per additional km² of habitat start-up and one-time measures of € 90,000 p.a. are necessary. Proceeding analogously as for the estimation of the cost parameters for new visitor infrastructure, the cost parameter can thus be calibrated as 633.89φ ≅ .

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