1. Introduction
From an economic perspective, biodiversity conservation can be considered a public good since its consumption does not entail rivalry or exclusion (Dasgupta, Reference Dasgupta2021; Strange et al., Reference Strange, Ermgassen, Marshall, Bull and Jacobsen2024). Public goods lack markets that could provide information regarding their relative scarcity (Arrow et al., Reference Arrow, Cropper, Eads, Hahn, Lave, Noll, Portney, Russell, Schmalensee, Smith and Stavins1996; Hanley and Perrings, Reference Hanley and Perrings2019; Dasgupta, Reference Dasgupta2021), making it difficult to estimate their economic value and evaluate policies aimed at their conservation (Fraser et al., Reference Fraser, Roberts and Brock2023).
Since biodiversity is an essential input for many ecosystem services, its economic value can be estimated based on the value of such ecosystem services (Bateman and Mace, Reference Bateman and Mace2020). Nevertheless, several attempts have been made to value biodiversity directly (Jacobsen et al., Reference Jacobsen, Boiesen, Thorsen and Strange2008; Jacobsen et al., Reference Jacobsen, Lundhede, Martinsen, Hasler and Thorsen2011; Bakhtiari et al., Reference Bakhtiari, Jacobsen, Strange and Helles2014; Strange et al., Reference Strange, Ermgassen, Marshall, Bull and Jacobsen2024). In many of these studies, biodiversity conservation serves as a source of non-use value (existence and bequest); therefore, economic value estimation has relied on stated preference (SP) techniques, such as contingent valuation (CV) or choice experiments (CEs).
SP techniques require the implementation of surveys that present hypothetical markets in which respondents declare preferences for changes in the quantity or quality of biodiversity proxies (Kahneman and Knetsch, Reference Kahneman and Knetsch1992; Hanemann, Reference Hanemann1994; Rolfe and Windle, Reference Rolfe and Windle2012; Martin-Ortega et al., Reference Martin-Ortega, Mesa-Jurado and Berbel2015). Furthermore, CE, a more recent technique compared to CV, can identify trade-offs between the attributes of alternatives (Jin et al., Reference Jin, He, Wang and Gong2018) and has been used more frequently in recent investigations (Emang et al., Reference Emang, Lundhede and Thorsen2020; Dechasa et al., Reference Dechasa, Senbeta and Guta2021). Discrete CEs allow for the structured evaluation of complex, non-market environmental attributes, making them particularly suitable for testing ecological constructs such as species interaction networks.
Previous research using SP to value biodiversity conservation is extensive and diverse (e.g., Olar et al., Reference Olar, Adamowicz, Boxall, West, Lessard and Cantin2007; Bakhtiari et al., Reference Bakhtiari, Jacobsen, Strange and Helles2014; Borzykowski et al., Reference Borzykowski, Baranzini and Maradan2018). Rather than attempting an exhaustive review, this study concentrates on two critical themes within this literature: (1) how biodiversity is represented in SP studies, and (2) how different proxies affect the capacity of SP designs to meet validity criteria such as sensitivity to scope and plausibility.
A growing consensus in the literature stresses that how biodiversity is represented in valuation studies affects the estimated economic value (Strange et al., Reference Strange, Ermgassen, Marshall, Bull and Jacobsen2024). Frameworks such as the Essential Biodiversity Variables (Turak et al., Reference Turak, Harrison, Dudgeon, Abell, Bush, Darwall, Finlayson, Ferrier, Freyhof, Hermoso, Juffe-Bignoli, Linke, Nel, Patricio, Pittock, Raghavan, Revenga, Simaika and De Wever2017) promote the inclusion of functional and holistic indicators of biodiversity change. Among these, the network of species interactions – a proxy capturing ecosystem functionality and resilience – remains underexplored in SP studies, despite its theoretical relevance.
However, different representations of biodiversity in SP will present some challenges. SPs are based on the random utility model (RUM) proposed by McFadden (Reference McFadden1974), which allows respondents to express their preferences in monetary terms (i.e., willingness to pay (WTP) and willingness to accept (WTA)). These values have been used to evaluate public policies for biodiversity conservation (Lew et al., Reference Lew, Layton and Rowe2010; Spencer-Cotton et al., Reference Spencer-Cotton, Kragt and Burton2018). Nevertheless, SP applications have been criticised for generating results inconsistent with the economic theory (Diamond et al., Reference Diamond, Hausman, Gregory, Denning and Hausman1993; Szabó, Reference Szabó2011; Ferrini and Turner, Reference Ferrini and Turner2018).
Arrow et al. (Reference Arrow, Solow, Portney, Leamer, Radner and Schuman1993), in a report for the National Oceanic and Atmospheric Administration (NOAA), and Johnston et al. (Reference Johnston, Boyle, Adamowicz, Bennett, Brouwer, Cameron, Hanemann, Hanley, Ryan, Scarpa, Tourangeau and Vossler2017) proposed a series of recommendations to ensure that the results of an SP study can inform public policy. This study focuses on two of these issues: rationality and plausibility.
Rationality refers to the results consistent with the assumption that an individual should pay more for more units or higher quality of goods. This is also called sensitivity to scope (Lew and Wallmo, Reference Lew and Wallmo2011; Ojea and Loureiro, Reference Ojea and Loureiro2011; Hjerpe et al., Reference Hjerpe, Hussain and Phillips2015). Some researchers have claimed that when interviewees do not perceive changes in a good, it is a symptom of conflict with behavioural economic theory, which weakens the results of SP studies (Loomis et al., Reference Loomis, Lockwood and DeLacy1993; Ojea and Loureiro, Reference Ojea and Loureiro2009). Others have argued that a reduction in marginal utility (a sign of satiety) can explain insensitivity to scope (Rollins and Lyke, Reference Rollins and Lyke1998; Olar et al., Reference Olar, Adamowicz, Boxall, West, Lessard and Cantin2007; Jacobsen et al., Reference Jacobsen, Lundhede, Martinsen, Hasler and Thorsen2011). This satiety could occur after passing a certain threshold; for instance, a minimum viable number of individuals in a species’ population (Ojea and Loureiro, Reference Ojea and Loureiro2009).
Insensitivity to scope has been observed in many SP studies across various contexts and is particularly prevalent in biodiversity conservation valuation (Kahneman and Knetsch, Reference Kahneman and Knetsch1992; Martin-Ortega et al., Reference Martin-Ortega, Mesa-Jurado and Berbel2015; Borzykowski et al., Reference Borzykowski, Baranzini and Maradan2018). The problem appears to have been exacerbated by the complexity of representing biodiversity in SP studies (Jacobsen et al., Reference Jacobsen, Boiesen, Thorsen and Strange2008; Bartkowski et al., Reference Bartkowski, Lienhoop and Hansjürgens2015).
For instance, species and habitat are two common representations of biodiversity. Economic valuation studies referencing biodiversity with species have used different subcategories, including the number of flora or fauna species affected by an intervention (Christie et al., Reference Christie, Hanley, Warren, Murphy, Wright and Hyde2006; Hausmann et al., Reference Hausmann, Slotow, Fraser and Di Minin2017), iconic or emblematic species and broad categories of fish (McDaniels et al., Reference McDaniels, Gregory, Arvai and Chuenpagdee2003) and mammals (Giraud and Valcic, Reference Giraud and Valcic2004; Frontuto et al., Reference Frontuto, Dalmazzone, Vallino and Giaccaria2017). Other studies have utilised a small number of species in a specific location or even an entire country (Olar et al., Reference Olar, Adamowicz, Boxall, West, Lessard and Cantin2007; Hoyos et al., Reference Hoyos, Mariel, Pascual and Etxano2012). Regarding habitat, studies have characterised biodiversity by the size of an ecosystem (length or surface) (Rolfe et al., Reference Rolfe, Bennett and Louviere2000; Rolfe and Windle, Reference Rolfe and Windle2012; Shoyama et al., Reference Shoyama, Managi and Yamagata2013); iconic regions such as wilderness areas (Diamond et al., Reference Diamond, Hausman, Gregory, Denning and Hausman1993; McFadden, Reference McFadden1994), rivers (Brown and Duffield, Reference Brown and Duffield1995), wetlands (Powe and Bateman, Reference Powe and Bateman2004; Whitehead et al., Reference Whitehead, Groothuis, Southwick and Foster-Turley2009) and forests (Borzykowski et al., Reference Borzykowski, Baranzini and Maradan2018); and places that species traditionally inhabit (Thiene et al., Reference Thiene, Meyerhoff and De Salvo2012; Hausmann et al., Reference Hausmann, Slotow, Fraser and Di Minin2017).
Notably, these common proxies seem to be insufficient for representing biodiversity. A common concern about these definitions is that they are not well linked to a more ecological definition of biodiversity.Footnote 1 Species representations have often been equivalent to a single and plain component of biodiversity or the number of individuals of one or more species. Habitat has usually referenced a broad area with a non-specific definition of biodiversity (Ring et al., Reference Ring, Hansjürgens, Elmqvist, Wittmer and Sukhdev2010; Bartkowski et al., Reference Bartkowski, Lienhoop and Hansjürgens2015). Both approaches can generate representations of levels of biodiversity that could be indistinguishable from interviewees’ perspectives and become a source of insensitivity to the scope. For example, biodiversity representations from uncharismatic and unrecognised species or places (habitats) could include variations that are perceived to be equal by interviewees (Boyle et al., Reference Boyle, Bishop, Hellerstein, Welsh, Ahearn, Laughland, Charbonneau and O’Conner1998; Jacobsen et al., Reference Jacobsen, Boiesen, Thorsen and Strange2008; Ojea and Loureiro, Reference Ojea and Loureiro2009). In this sense, limitations in interviewees’ adequate appreciation of biodiversity and hypothetical markets could translate into null or even negative marginal utility, obtaining responses that contradict a well-being perspective (Carson and Mitchell, Reference Carson and Mitchell1995).
In this paper, in addition to two common proxies – the number of threatened flora and fauna species – we include the network of species interactions, measured as the percentage of persistent species encounters in the community network. Although several authors have suggested using functionality to measure biodiversity (Czajkowski and Hanley, Reference Czajkowski and Hanley2009; Rambonilaza and Brahic, Reference Rambonilaza and Brahic2016; Bakhtiari et al., Reference Bakhtiari, Jacobsen, Thorsen, Lundhede, Strange and Boman2018), no consensus has emerged regarding its definition in the valuation literature. To the best of our knowledge, this is the first study to utilise this proxy of biodiversity, based on the foundations of ecology and ecosystem architecture as outlined by Jordano (Reference Jordano2016). The loss of key ecological interactions may precede the local extinction of species that depend on the key ecological services provided, signalling the loss of ecological functions (Jordano, Reference Jordano2016). We argue that the network of species interactions represents ecological community structure and biodiversity functionality, as described by Bakhtiari et al. (Reference Bakhtiari, Jacobsen, Strange and Helles2014). The concept of functionality reaches beyond isolated groups of species or areas, aiming to capture agents’ interrelationships that generate stability and resilience in ecosystems to represent changes and impact on human well-being more adequately (Bartkowski et al., Reference Bartkowski, Lienhoop and Hansjürgens2015). Whether described qualitatively or quantitatively, functionality can be a more effective option for representing biodiversity, although interviewees may not be familiar with the concept (Ring et al., Reference Ring, Hansjürgens, Elmqvist, Wittmer and Sukhdev2010; Jordano, Reference Jordano2016). Some previous evidence has suggested otherwise (Bakhtiari et al., Reference Bakhtiari, Jacobsen, Strange and Helles2014; Bartkowski et al., Reference Bartkowski, Lienhoop and Hansjürgens2015; Lavado-Solis et al., Reference Lavado-Solis, Orihuela, Vásquez-Lavín and Dávila2021). More importantly, representing a network of species interactions could be particularly useful, especially in valuation applications concerning megadiverse environments.Footnote 2 In these contexts, biodiversity loss may be perceived differently by respondents due to the overwhelming number of species involved, which can challenge their cognitive ability to process changes based on species counts alone. We hypothesised that this definition of functionality would respond better to scope and plausibility tests.
Arrow et al. (Reference Arrow, Solow, Portney, Leamer, Radner and Schuman1993) proposed that reliable SP estimates must exhibit sensitivity to scope and an adequate degree of responsiveness to the magnitude of change being valued. In a later clarification, Arrow et al. (Reference Arrow, Leamer, Schuman and Solow1994) acknowledged that the term plausible responsiveness would have better conveyed the behavioural credibility expected of WTP estimates. However, the NOAA panel did not offer formal criteria for evaluating plausibility. Whitehead (Reference Whitehead2016) and Burrows et al. (Reference Burrows, Newman, Genser, Plewes, McFadden and Train2017) suggested using the scope elasticity of WTP (
${E_{WTP}}$) as an empirical measure of plausibility. In the presence of diminishing marginal utility, most environmental goods are expected to yield 
${E_{WTP}}$ values below one. Whitehead (Reference Whitehead2016) conducted simulations under linear and quadratic utility forms, suggesting plausible 
${E_{WTP}}$ typically ranges between 0.2 and 1.0. Although Burrows et al. (Reference Burrows, Newman, Genser, Plewes, McFadden and Train2017) proposed a lower plausibility bound of 0.2, they noted that this threshold is somewhat arbitrary and lacks strong theoretical justification. Overall, the literature underscores the importance of context-specific judgment when evaluating the plausibility of scope effects.
Dugstad et al. (Reference Dugstad, Grimsrud, Kipperberg, Lindhjem and Navrud2021) further formalised 
${E_{WTP}}$ within the CE framework, emphasising that assuming constant (unitary) elasticity – common in linear models – can obscure insufficient scope sensitivity. Estimating arc-elasticities across discrete attribute levels allows researchers to evaluate whether WTP responds in a behaviourally consistent way, particularly when marginal utility may decline. This approach complements conventional model fit statistics and provides a more nuanced validity test.
In conclusion, this study evaluates whether the network of species interactions passes scope sensitivity and plausibility tests using a CE approach. We compare respondents’ WTP for three proxies of biodiversity conservation, including species richness (i.e., number of flora and fauna species), habitat and network of species interactions. This study makes four novel contributions. First, we value biodiversity conservation in a megadiverse environment. Second, we link our concept of functionality to recent definitions of a network of species interactions that is derived from ecological literature (Bakhtiari et al., Reference Bakhtiari, Jacobsen, Strange and Helles2014; Jordano, Reference Jordano2016). Third, we estimate a latent class (LC) model to determine interviewees’ heterogeneity based on socioeconomic characteristics. Finally, we evaluate scope sensitivity and plausibility using different econometric models, with particular emphasis on the LC model – both in its standard and attribute non-attendance (ANA) specifications – due to their ability to uncover preference heterogeneity and cognitive processing relevant for biodiversity policy.
Our case study concerns Manu National Park (hereafter Manu), which was established as a UNESCO Natural Heritage Site in 1987 and is the Protected Natural Area with the greatest biodiversity in Peru (SERNANP, 2014).
The remainder of this paper is organised as follows. Section 2 presents the materials and methods and the study’s design. We present our results in Section 3. Section 4 of the discussion compares our benchmark results with those of previous literature. Section 5 presents the conclusions.
2. Materials and methods
2.1. Study area
Manu has an area of 1.8 million hectares (ha) and is located in southeastern Peru, encompassing part of two regions, Cusco and Madre de Dios (Figure 1). This Protected Natural Area has the greatest biodiversity in Peru, containing a large proportion of the Peruvian Amazon’s flora and fauna. A diverse number of wildlife species inhabit Manu, with nearly 160 species of mammals, more than 1,000 species of birds (mostly residents), about 140 species of amphibians, 50 species of snakes, 40 species of lizards, 6 species of turtles, 3 species of alligators and 210 species of fish. Furthermore, the number of insects in the Manu is very high; estimated at about 30 million species, including more than 1,300 species of butterflies, 136 species of dragonflies, at least 300 species of ants (more than 40 species were found in a single tree) and more than 650 species of beetles. As for flora, the records indicate at least 162 families, 1,191 genera and 4,385 identified species (SERNANP, 2014). Up to 250 varieties of trees have been identified in a single ha.Footnote 3 Likewise, the Manu hosts 10 per cent of the world’s bird species and is the third largest Protected Natural Area in Peru, after Alto Purús National Park and Pacaya Samiria National Reserve, and its tropical forests are among the most undisturbed, only inhabited by indigenous populations in isolation, with a notable diversity of Amazonian ethnic groups (SERNANP, 2014).
Manu location.
2.2. Modelling approach
The CE is a model based on attributes of alternatives, and it has been frequently used in non-market valuation since the 1990s (Boxall et al., Reference Boxall, Adamowicz, Swait, Williams and Louviere1996; Hanley et al., Reference Hanley, Wright and Adamowicz1998). The random utility function is described as follows:
\begin{equation}{U_{ijt}}\, = \,{V_{ijt}}\, + \,{\varepsilon _{ijt}},\end{equation}where Uijt is the utility of individual i when choosing alternative j in the choice occasion t; Vijt is the deterministic component; and εijt is the stochastic term. The respondent selects the alternative that they perceive as providing the maximum benefit.
Different probabilistic models can be used depending on the assumptions concerning the distribution of the error terms. A widely used technique has been the conditional logit (CL) model, which assumes an extreme Value Type I distribution for error terms (McFadden, Reference McFadden1974). In this model, the estimation of the coefficients (β) is conducted using the maximum likelihood method, with the following likelihood function:
\begin{equation}L\left( \beta \right) = \mathop \prod \nolimits_{i = 1}^N \mathop \prod \nolimits_{t = 1}^T \frac{{{e^{\beta^{\prime}{x_{ijt}}}}}}{{\mathop{\sum}\nolimits_{l}{e^{\beta^{\prime}{x_{ilt}}}}}},\end{equation}where β is a vector of coefficients associated with individuals’ attribute levels and characteristics; xijt represents the explanatory variables; i denotes individuals; j and l denote choice sets; and t denotes decision occasions. The term inside the product is the probability of individual i choosing alternative j in decision occasion t.
This study uses CL, mix logit (MXL) and LC models (McFadden and Train, Reference McFadden and Train2000; Crespo-Cebada et al., Reference Crespo-Cebada, Díaz-Caro, Robina-Ramírez and Sánchez-Hernández2020) to calculate the mean WTP for biodiversity conservation. In the CL model, the preference structure is the same for all respondents, which may suffer from the independence of irrelevant alternatives problem. The MXL model corrects this limitation by estimating a distribution for the coefficients (random parameters) that captures respondents’ heterogeneity (Train, Reference Train2009).
Following standard practice in SP valuation, we specified all non-monetary attribute coefficients as normally distributed. This distribution accommodates both positive and negative preferences and captures attitudinal heterogeneity in biodiversity valuation. In contrast, the price coefficient was held fixed to preserve utility monotonicity and avoid convergence issues or implausibly large WTP estimates – problems commonly observed when using random price terms (Scarpa and Thiene, Reference Scarpa and Thiene2005; Train and Weeks, Reference Train, Weeks, Scarpa and Alberini2005; Daly et al., Reference Daly, Hess and Train2012). This specification enhances both interpretability and theoretical coherence (Hess et al., Reference Hess, Train and Polak2006; Hole, Reference Hole2007).
Assume this normal distribution, represented as f(β|b, W), where β is a vector containing the random coefficients (including those of alternative intercepts), b corresponds to the vector of the means, and W indicates the covariance matrix. Because it is not possible to obtain an analytical expression for the unconditional choice probability, the estimation process uses simulation methods to assess the integral of the probability for given values of b and W. In this case, 
${P_{ijt}}$ is the probability of individual i choosing alternative j, which is defined as follows:
\begin{equation}{P_{ijt}} = \int \frac{{{e^{\beta^{\prime}{_i}{x_{ijt}}}}}}{{\mathop{\sum}\nolimits_{j = l}^{J}{e^{\beta^{\prime}{_i}{x_{ilt}}}}}}f(\beta |b,W)d\beta .\end{equation}In contrast, the LC model captures heterogeneity using a discrete distribution over unobservable endogenous (latent) classes of respondents (Ben-Akiva et al., Reference Ben-Akiva, McFadden, Abe, Böckenholt, Bolduc, Gopinath and Steinberg1997; Ryan and Amaya‐Amaya, Reference Ryan and Amaya‐Amaya2005). Respondents’ preferences are assumed to be homogeneous within each class but can differ across a finite number of classes, which are determined by the data, while membership in a segment depends probabilistically on respondents’ observable socioeconomic or attitudinal and behavioural characteristics (Barreiro-Hurlé and Gómez-Limón, Reference Barreiro-Hurlé and Gómez-Limón2008; Lundberg et al., Reference Lundberg, Veríssimo, Vainio and Arponen2020).
The probability of choice varies among classes in this case; that is, the probability of individual i in class q choosing alternative j is given by 
$(P_{ijt}^q$), which is determined as follows:
\begin{equation}P_{ijt}^q = \frac{{{e^{\beta^{\prime}{_q}{x_{ijt}}}}}}{{\mathop{\sum}\nolimits_{l = 1}^J{e^{\beta^{\prime}{_q}{x_{ilt}}}}}}.\end{equation} q classes exist, in which the probability of choosing each alternative differs from other classes since the coefficients differ (
${\beta _q})$. We also estimate the probability of belonging to each class using a logit model that uses socioeconomic variables as explanatory variables.
We estimate the CL, MXL and LC models, and end up focusing on the LC specification due to its flexibility in capturing unobserved preference heterogeneity. Unlike MXL, which assumes a continuous distribution of tastes across individuals, the LC model partitions the population into a finite number of classes with distinct, internally homogeneous preference structures. This discrete segmentation is particularly useful in environmental valuation, where respondents may interpret biodiversity attributes differently depending on their ecological awareness, personal values, or familiarity with conservation issues (Boxall and Adamowicz, Reference Boxall and Adamowicz2002; Scarpa and Thiene, Reference Scarpa and Thiene2005).
To determine the appropriate number of classes, we estimated LC models with two to five segments and compared them using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). To further validate the robustness of preference estimates, we estimated an additional LC model incorporating ANA, following Scarpa et al. (Reference Scarpa, Gilbride, Campbell and Hensher2009) and Lew and Whitehead (Reference Lew and Whitehead2020). This specification allows for the possibility that respondents may have systematically ignored one or more attributes when making their choices. Accounting for ANA helps distinguish between genuine preference stability and lack of attribute salience, thus improving the behavioural credibility and interpretability of class-specific estimates.
Each model also enables the estimation of the average marginal WTP for a change in the attribute 
${x_{ijt}}$. Under the random utility framework, WTP is calculated as the negative ratio between the attribute coefficient and the marginal utility of income (Louviere et al., Reference Louviere, Hensher and Swait2000):
\begin{equation}WTP\, = \, - {\beta _x}/{\beta _{price}}\end{equation} where 
${\beta _x}$ is the estimated coefficient for the attribute and 
${\beta _{price}}$ is the coefficient for the cost attribute.
By comparing respondents’ WTP for different levels of biodiversity attributes, we can test whether they are statistically different and determine scope sensitivity (rationality). Economic theory indicates that if an individual is willing to pay something to obtain a certain environmental good (i.e., biodiversity conservation), then the individual should be willing to pay more to obtain a higher quantity and/or quality of that good (Lew and Wallmo, Reference Lew and Wallmo2011; Ojea and Loureiro, Reference Ojea and Loureiro2011; Hjerpe et al., Reference Hjerpe, Hussain and Phillips2015); otherwise, scope insensitivity prevails, which is a type of embedding effect (Kahneman and Knetsch, Reference Kahneman and Knetsch1992; Hanemann, Reference Hanemann1994).
Our null hypothesis is that insensitivity to scope exists for each chosen attribute, which can be expressed as 
${H_0}:\,WT{P_{level1}}\, = \,WT{P_{level2}}\, = WT{P_{level3}}$. The levels refer to the different attribute amounts included in the survey. For instance, level 1 may represent the lowest level of the attribute, while levels 2 and 3 represent the medium and highest levels. If this hypothesis is rejected and 
$WT{P_{level1}}\, \lt \,WT{P_{level2}}\, \lt \,WT{P_{level3}}$, we can conclude that respondents’ preferences demonstrate scope sensitivity. However, statistical significance alone may not be sufficient.
Whitehead (Reference Whitehead2016) and Burrows et al. (Reference Burrows, Newman, Genser, Plewes, McFadden and Train2017) suggested using the scope elasticity of WTP (
${E_{WTP}}$) as an empirical measure of plausibility. This elasticity is defined as:
\begin{equation}{E_{WTP}} \equiv \,\frac{{\% {{\Delta }}WTP\left( {q,z} \right)}}{{\% {{\Delta }}q}} = \left( {\frac{{\partial WTP\left( {q,z} \right)}}{{\partial q}}} \right) \cdot \,\left( {\frac{q}{{WTP\left( {q,z} \right)}}} \right).\end{equation} For a non-marginal improvement in environmental quality and/or quantity, say from 
${q^0}$ to 
${q^1}$, where 
${q^1}$ > 
${q^0}$, with an associated change in WTP from 
$WT{P^0}$ to 
$WT{P^1}$ (
$WT{P^1}$ ≥ 
$WT{P^0}$), the midpoint formula can be utilised to define a scope arc-elasticity (
${\bar E_{WTP}}$) as follows:
\begin{equation}{\bar E_{WTP}} \equiv \,\frac{{\% {{\Delta }}WTP\left( {q,z} \right)}}{{\% {{\Delta }}q}} = \left( {\frac{{\partial WTP\left( {q,z} \right)}}{{\partial q}}} \right) \cdot \,\left( {\frac{{\bar q}}{{\overline {WTP} }}} \right),\end{equation} where 
${{\Delta }}q = {q^1} - {q^0} \gt 0$, 
${{\Delta }}WTP = WT{P^1} - WT{P^0} \gt 0$ and 
$\bar q$ and 
$\overline {WTP} $ are, respectively, average environmental quality and/or quantity 
$\left( {\frac{{{q^0} + {q^1}}}{2}} \right)$ and average 
$\left( {\frac{{WT{P^0} + WT{P^1}}}{2}} \right)$.
Although 
${E_{WTP}}$ can also be estimated using log-log utility specifications – where the elasticity corresponds to the ratio of coefficients on logged attributes and prices – this approach requires continuous, strictly positive variables. In this study, we rely on dummy-coded categorical levels and therefore, adopt Dugstad et al.’s (Reference Dugstad, Grimsrud, Kipperberg, Lindhjem and Navrud2021) arc-elasticity method. This allows for flexible modelling of non-linear preferences and clearer interpretation of behavioural responses. Nevertheless, log-log formulations remain a promising avenue for future robustness checks.
This provides a unit-free metric to evaluate whether the WTP changes are economically meaningful and consistent with diminishing marginal utility. Elasticities within the range 0.2 to 1.0 are typically interpreted as plausible under standard microeconomic assumptions. To assess whether elasticity estimates exceeding unity reflect statistically significant deviations from theoretical expectations, we calculated standard errors and 95 per cent confidence intervals for all 
${E_{WTP}}$ values using the delta method. This approach enables a formal evaluation of whether scope elasticities are statistically distinguishable from one, or whether they fall within plausible ranges due to estimation uncertainty, as suggested in the literature (Whitehead, Reference Whitehead2016; Dugstad et al., Reference Dugstad, Grimsrud, Kipperberg, Lindhjem and Navrud2021).
2.3. Choice experiment design
To describe the likely changes in biodiversity in the Manu, we identified the most important elements of biodiversity in collaboration with ecologists who have studied the biodiversity and environmental conditions of the Manu.Footnote 4 As this study focuses on biodiversity conservation, we present diversity indicators that capture conservation-sensitive factors, including specified values for the number of threatened species or the percentage of the network of species interactions maintained as a proxy of the network of species interactions (i.e., thresholds for the loss of species interactions in the network of species interactions). We pretested the list of potential attributes using two focus groups, one comprising the general public and the other a multidisciplinary team, resulting in a list of five attributes with three or six levels each. The selected attributes in Table 1 represent potential changes in different biodiversity proxies that our focus group respondents identified as meaningful.
Attributes and levels of biodiversity of the Manu for the optimal CE design
The first and second attributes are the number of threatened flora and fauna species. For example, cedar and mahogany are two threatened flora species, and spectacled bears and jaguars are two species of threatened fauna. Each of these two attributes has three levels: 8, 16 and 24 threatened species. The level with 24 threatened species represents the status quo (SQ), indicating a worse biodiversity condition than the other two levels.
The third attribute is the novel biodiversity proxy: the network of species interactions. This construct captures key ecological dynamics such as keystone species loss, interaction richness and network connectivity – critical for stabilising food webs and preventing secondary extinctions (Tylianakis et al., Reference Tylianakis, Laliberté, Nielsen and Bascompte2010; Jordano, Reference Jordano2016). Although empirical thresholds for network stability are difficult to define (Allesina and Tang, Reference Allesina and Tang2012), expert input and literature suggest that losing 30–40 per cent of species interactions may trigger systemic ecological disruptions. Based on this, we defined three levels of interaction retention: 60, 80 and 100 per cent, representing degraded, intermediate and intact network conditions, respectively. These levels were refined through expert consultation and cognitive pretesting during the survey piloting phase. Importantly, these percentages reflect aggregate interaction retention at the landscape scale of Manu, rather than spatially homogeneous values. While local areas with lower species richness may still exhibit high functionality due to keystone species or interaction hubs, the modelling approach aimed to convey overall network resilience and systemic degradation.
The fourth attribute represents habitat loss from deforestation, referring to the number of ha deforested annually. Increased deforestation implies more habitat loss and biodiversity. We presented three possible levels, including annual losses of 286 ha, 700 ha and 1400 ha (SQ), to represent the amount of felled trees. The SQ for deforestation was based on historical averages observed in buffer zones of the park.
The final attribute is the contribution, determining respondents’ WTP for the four combined biodiversity attributes. Logically, if individuals want to reduce the negative impact of biodiversity loss to zero, they should be willing to contribute more money. The alternative payments ranged from 0 (SQ) to 32 Peruvian Soles (PEN) (1 USD = 4.10 PEN, on average, between July and August 2021) per month. Contributions were framed as an additional charge on the household electricity bill, collected monthly over a 12-month period, to fund a real biodiversity conservation initiative in Manu. Six possible levels were presented (PEN 0, 8, 12, 16, 24, 32).
Attributes were explained to respondents using audiovisual material, pointing out that the Universidad Nacional Agraria La Molina from Peru (UNALM) and Servicio Nacional de Áreas Naturales Protegidas por el Estado (SERNANP) are evaluating project implementation to reduce negative impacts on Peruvian biodiversity that includes a real-time surveillance system using drones and increased security personnel and park rangers. Our video included a narrative cheap-talk script that noted, ‘It is VERY IMPORTANT that you take into account your home budget and contributions you would make’.
Although the survey was framed as hypothetical and did not include an explicit consequentiality script or follow-up questions regarding perceived policy relevance, several features were incorporated to enhance perceived consequentiality. First, the initiative was framed as a real and plausible government-supported program. Second, its institutional affiliation with UNALM and SERNANP – two nationally recognised public agencies in biodiversity and conservation – provided credible implementation support. Third, consistent with the recommendations of Carson and Groves (Reference Carson and Groves2007), consequentiality was reinforced through institutional framing, realistic policy mechanisms and contextually grounded scenarios. These design elements aimed to reduce hypothetical bias and increase respondent engagement with the biodiversity conservation choices.
The survey design included 16 choice sets blocked into four questionnaires. An example choice card is presented in Figure 2. We applied a D-optimal design using Ngene software (Puckett and Rose, Reference Puckett, Rose, Hess and Daly2010). The third alternative is a constant SQ, which was added to every choice set, with no variation in the attribute levels for this alternative. Each respondent was presented with four choice sets, each of which included three alternatives.
Choice card example.
2.4. Survey implementation
The survey was conducted online in July and August 2021, in response to restrictions imposed by the COVID-19 pandemic. Participants were recruited through an opt-in online panel, which does not constitute a probability-based sample. We acknowledge this as a methodological limitation and interpret our findings accordingly. Despite this constraint, the survey achieved a relatively high response rate of 65 per cent, and we collected detailed sociodemographic information to characterise respondents and assess their comparability with the broader urban population of Lima.
The target population comprised residents of Metropolitan Lima, which includes both Lima, the capital of Peru, and the neighbouring constitutional province of Callao – together accounting for more than one-third of the national population. Of the 1,501 individuals who initiated the survey, 1,005 completed all sections, yielding 4,020 usable choice observations, as each respondent answered four discrete choice sets. This completion rate (65 per cent) exceeds that reported in comparable SP studies (e.g., Jacobsen et al., Reference Jacobsen, Lundhede, Martinsen, Hasler and Thorsen2011, Reference Jacobsen, Lundhede and Thorsen2013; Weller and Elsasser, Reference Weller and Elsasser2018).
Among respondents, 60 per cent were male, with an average age of 32 years. Approximately 69 per cent were single, and 83 per cent reported having completed higher education, with women showing higher levels of education than men. Only 18 per cent reported monthly incomes exceeding PEN 6,000. A large majority (86 per cent) indicated they were born in coastal regions. Regarding environmental attitudes and behaviours, 98 per cent of respondents agreed that biodiversity conservation is important, 36 per cent had visited a protected natural area within the past 5 years, and 2 per cent reported membership in an environmental organisation.
Compared to official statistics, our sample overrepresents individuals with higher educational attainment and income levels. In Metropolitan Lima, 42 per cent of the labour force has completed higher education, and most earn less than PEN 3,000 per month (LimaCómoVamos, 2022). Internet access – required to participate in the online survey – is available in only 72 per cent of households in the region (INEI, 2021a). Thus, our sample is not representative of the full urban population but rather reflects the preferences of a more affluent and environmentally engaged segment. Table 2 provides a comparative summary of sample characteristics and population benchmarks.
Comparison between the sample and the Metropolitan Lima population
a Estimate based on the urban young-adult population structure in Metropolitan Lima (INEI, 2021b).
b No official statistics available for visits to protected areas or environmental group membership for Metropolitan Lima.
Although 27 respondents expressed protest responses – stating that biodiversity conservation is a responsibility of the government and should not be financed by citizens – they were retained in the final sample, as their inclusion did not materially alter the results.
3. Results
3.1. Model results
Table 3 summarises the key results using the MLX and the LC. Full CL model results are reported in appendix table A3 for reference. MXL serves as a benchmark for preference heterogeneity prior to introducing the LC specification. In the MXL model, all biodiversity-related coefficients are statistically significant except for flora_16. Regarding standard deviations (SDs) of the random parameters, most are statistically significant (indicating heterogeneity), except for habitat_286. Importantly, none of the SDs for the network of species interaction levels are significant, suggesting greater agreement among respondents on the importance of this attribute. The cost coefficient remains negative and statistically significant, as expected.
Econometric results for mixed logit, and latent class models
Regarding the sociodemographic interactions, higher income is associated with a lower probability of choosing the SQ. Similarly, older respondents are less likely to choose the SQ, while higher educational attainment also decreases the likelihood of opting for the SQ alternative.
The LC model outperforms both the CL and MXL models in terms of AIC and BIC. We estimated a two-class solution. Although the four-class model yielded the lowest AIC and BIC values (AIC = 10336.96, BIC = 10695.71) (see appendix table A1), we selected the two-class model because it offered superior interpretability, particularly because some price coefficients in the three-class and four-class models displayed unexpected positive signs (see appendix table A2). The two-class model also produced well-proportioned segments (74.4 per cent and 25.6 per cent). Therefore, the two-class specification was considered the most robust, interpretable and policy-relevant.
Class 1 (LC1), representing the majority of the sample (74.4 per cent), is characterised by relatively low sensitivity to price and consistently strong preferences for biodiversity conservation attributes. Salary is the only statistically significant sociodemographic predictor of class membership, with higher-income respondents more likely to belong to LC1. In contrast, in class 2 (LC2), the coefficients for flora and fauna attributes are not statistically significant. However, the network of species interactions remains significant across both classes – with a stronger effect in LC1 – confirming its salience and robustness across specifications.
We further explored heterogeneity by estimating a LC model with ANA. Compared to the standard LC model, this specification slightly reduced the proportion of respondents assigned to LC2 – from 25.6 per cent to 25.1 per cent – and marginally improved model fit, as reflected in lower AIC and BIC values. The ANA LC model confirms that respondents in LC2 tend to disregard standard proxies such as flora and fauna richness – reflected in zero or non-significant coefficients – while still assigning significant positive value to the network of species interactions and habitat conservation. This finding underscores that interaction networks are perceived as more salient or understandable even by respondents with lower engagement or cognitive attention to biodiversity detail.
3.1.1. Scope sensitivity
Based on the benchmark econometric results, we estimate the marginal WTP for each attribute (Table 4) to examine sensitivity to scope. A statistically significant result in the first row of each model indicates the scope sensitivity between the lowest and medium or highest levels of each category. A statistically significant coefficient in the second row of each category shows the scope sensitivity between the medium and highest levels. The findings reveal sensitivity to scope for all attributes (P < 0.10) in the MXL model in the first row, with the exception of flora_16. Evaluating the scope sensitivity moving from the medium to the highest level (second row) of each attribute, the sensitivity to scope persists for fauna and for the network of species interactions (P < 0.01).
Scope sensitivity tests
The LC model reveals additional insights. Scope sensitivity is evident for the LC1 in almost all cases, while LC2 shows it only for the network of species interactions and habitat (P < 0.01). This heterogeneity highlights that scope sensitivity is not uniform across respondents, but class-dependent – an important insight for refining policy targeting and testing the behavioural validity of SP designs in biodiversity valuation.
3.1.2. Plausibility
Table 5 illustrates the attributes and levels presenting statistically significant and economically plausible scope elasticity of WTP (
${E_{WTP}}$), defined as values between 0.2 and 1.0 (Whitehead, Reference Whitehead2016; Dugstad et al., Reference Dugstad, Grimsrud, Kipperberg, Lindhjem and Navrud2021). This criterion is best fulfilled by the network of species interactions and, to a lesser extent, by fauna attributes. Although the MXL model indicates scope sensitivity for some attributes, WTP does not consistently increase for the highest quality levels – particularly for flora – suggesting limited behavioural plausibility under standard assumptions of diminishing marginal utility.
Plausibility test
In contrast, the LC model reveals substantial heterogeneity. LC1, comprising 74.4 per cent of the sample, demonstrates strong behavioural coherence: respondents are willing to pay significantly more for higher levels of three out of four biodiversity measures (flora, fauna and species interactions). This suggests a more than proportional response to improvements and underscores the presence of a conservation-minded segment. Notably, the network of species interactions consistently satisfies both scope sensitivity and plausibility across all levels in LC1. Meanwhile, LC2 shows limited engagement: only the medium level of species interactions meets the plausibility threshold, while upper levels yield implausibly low or even negative elasticities.
4. Discussion
Our findings inform the ongoing debate on the validity of SP methods for valuing biodiversity conservation in ecologically complex settings. Building on Arrow et al. (Reference Arrow, Solow, Portney, Leamer, Radner and Schuman1993), we assess whether respondents’ choices satisfy scope sensitivity and plausibility criteria (Whitehead, Reference Whitehead2016; Dugstad et al., Reference Dugstad, Grimsrud, Kipperberg, Lindhjem and Navrud2021). Although SP techniques like CV and CE are widely used to estimate non-use values (Boyle et al., Reference Boyle, Bishop, Hellerstein, Welsh, Ahearn, Laughland, Charbonneau and O’Conner1998; Borzykowski et al., Reference Borzykowski, Baranzini and Maradan2018; Weller and Elsasser, Reference Weller and Elsasser2018), meaningful biodiversity representation remains a challenge in megadiverse contexts (Bartkowski et al., Reference Bartkowski, Lienhoop and Hansjürgens2015; Lavado-Solis et al., Reference Lavado-Solis, Orihuela, Vásquez-Lavín and Dávila2021).
In our CE, the network of species interactions was the only biodiversity proxy consistently aligned with rational and plausible behaviour. It generated the highest WTP values and showed strong scope sensitivity, especially in LC1, aligning with prior work on functionality-based indicators (Bakhtiari et al., Reference Bakhtiari, Jacobsen, Strange and Helles2014; Bakhtiari et al., Reference Bakhtiari, Jacobsen, Thorsen, Lundhede, Strange and Boman2018). In megadiverse contexts, species or habitat counts may lack behavioural salience, while functionality-based proxies are more cognitively accessible (Ojea and Loureiro, Reference Ojea and Loureiro2009).
The LC model outperformed traditional specifications and revealed marked heterogeneity. Roughly 75 per cent of respondents (LC1) exhibited scope-consistent and plausible WTP for most biodiversity conservation attributes, while a second group (LC2) displayed weaker or implausible responses. To test robustness, we estimated an LC model with ANA, which slightly reduced LC2’s share (to 25.1 per cent) and improved model fit. Results confirmed that LC2 respondents systematically disregarded standard proxies like flora and fauna richness but still assigned significant value to the network of species interactions. This consistency across classes – even under ANA constraints – suggests that functionality-based proxies hold greater cognitive salience and perceived legitimacy, even among less engaged respondents, echoing concerns in the literature about the limited recognisability of species counts (Boyle et al., Reference Boyle, Bishop, Hellerstein, Welsh, Ahearn, Laughland, Charbonneau and O’Conner1998; Jacobsen et al., Reference Jacobsen, Boiesen, Thorsen and Strange2008).
Socioeconomic patterns were consistent with previous studies (Barreiro-Hurlé and Gómez-Limón, Reference Barreiro-Hurlé and Gómez-Limón2008): LC1 had higher income, education and concern for biodiversity; LC2 showed lower engagement and scope insensitivity. This segmentation has policy implications in megadiverse countries, where a portion of the population may not perceive additional conservation benefits beyond a threshold.
Despite its strong performance, the network of species interactions may remain abstract for ecologically less literate respondents. While it elicited internally consistent WTP, this does not preclude hypothetical bias.
We note several modelling limitations. Random parameter independence may overlook interdependencies among ecological proxies (Jordano, Reference Jordano2016; Turak et al., Reference Turak, Harrison, Dudgeon, Abell, Bush, Darwall, Finlayson, Ferrier, Freyhof, Hermoso, Juffe-Bignoli, Linke, Nel, Patricio, Pittock, Raghavan, Revenga, Simaika and De Wever2017). Although we included an ANA specification, more flexible models (Hole, Reference Hole2011; Lew and Whitehead, Reference Lew and Whitehead2020) could better distinguish genuine indifference from heuristic-driven simplification.
Lastly, we did not apply formal nested model comparisons (Johnston et al., Reference Johnston, Börger, Hanley, Meginnis, Ndebele, Siyal and de Vries2024) to test whether functionality-based proxies improve explanatory power. Future work should examine whether such proxies enhance both model fit and internal validity relative to conventional biodiversity measures.
5. Conclusion
This study tested whether different biodiversity proxies satisfy scope sensitivity and plausibility criteria in an ecologically complex setting. Using a CE in Manu National Park, Peru, we compared four proxies: threatened flora, threatened fauna, habitat and the network of species interactions.
Among these, the network of species interactions – grounded in ecological theory and indicative of ecosystem functionality – elicited the most consistent and plausible responses. It passed internal scope tests and produced elasticity estimates within expected theoretical ranges, even under an LC specification with ANA. This suggests that functional ecological relationships may enhance SP validity, particularly in megadiverse contexts where conventional proxies can overwhelm or disengage respondents.
Our results reveal substantial preference heterogeneity: a majority exhibited coherent WTP patterns, while others showed price sensitivity or inattentiveness to biodiversity attributes. The ANA model confirmed that functionality-based proxies remained salient even for less engaged respondents.
Overall, the study advances methodological and applied knowledge in biodiversity valuation. It demonstrates that novel ecological constructs – such as network of species interactions – can be effectively integrated into SP frameworks, guiding future valuation efforts in biodiversity and cognitively demanding settings. Nonetheless, several limitations remain, including discrete attribute levels, limited public familiarity with ecological functionality and the non-probabilistic urban sample. Future studies should broaden their geographic and cultural scope to include rural and Indigenous communities, whose ecological relationships and knowledge systems are essential to understanding biodiversity values more comprehensively. Addressing these challenges will be key to improving the validity, inclusivity, and policy relevance of SP methods.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/S1355770X25100296.
Acknowledgements
The authors express their gratitude to Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica (CONCYTEC) and Fondo Nacional de Desarrollo Científico, Tecnológico y de Innovación Tecnológica (FONDECYT) from Peru, for the funding provided under Grant Agreement No. 200-2015-FONDECYT. Additionally, they acknowledge the support from the Doctoral Program in Economics of Natural Resources and Sustainable Development at the Universidad Nacional Agraria La Molina (UNALM). Felipe Vásquez-Lavín is also grateful for support from the projects ANID PIA/BASAL AFB240003 and ICN2019_015 ICM_ANID.
