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Volume 28, Issue 8 p. 1940-1947
Communication
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Should I shoot or should I go? Simple rules for prey selection in multi-species hunting systems

Charlotte H. Chang

Corresponding Author

Charlotte H. Chang

Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, 08544-2016 USA

National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, Tennessee, 37996-3410 USA

E-mail: [email protected]Search for more papers by this author
Sarah E. Drohan

Sarah E. Drohan

Program in Applied and Computational Mathematics and Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, 08544-1000 USA

Search for more papers by this author
First published: 04 October 2018
Citations: 4
Corresponding Author: Charlotte H. Chang.

Abstract

Across the tropics, unregulated hunting targeting many different species presents a major conservation challenge. Prioritizing resources for monitoring and enforcement is difficult when multiple prey species are exploited. However, identifying which prey species are subject to hunting pressure can be achieved with diet choice models. We evaluate hunter diet sets using data from Southwest China and compare two diet choice models: optimal foraging theory and a relatively new diet model originating from economic optimal stopping problems. The optimal stopping diet choice model required fewer field parameters than optimal foraging models and more accurately reflected hunter catch in Southwest China. The optimal stopping model also indicated that hunters should be less selective when they experience a larger opportunity cost for their time. Finally, we illustrate a new method to evaluate harvest impact from single sites with limited data using dietary thresholds. This technique could be used to evaluate whether or not the community of exploited wildlife has shifted in its trait distribution, providing a means to anticipate trait-biased defaunation from minimal data.

Introduction

The unsustainable harvest of wildlife threatens global biodiversity, particularly in the tropics (Maxwell et al. 2016, Ripple et al. 2016). One challenge is that tropical hunting systems tend to harvest a wide range of species; researchers have found hunters exploiting as many as 65 targeted taxa across mammals, birds, and reptiles at individual sites (Bennett and Robinson 2000, Fa et al. 2002). As such, evaluating hunter prey selection is critical to prioritize limited resources for management. One tactic to simplify this problem is to focus on a single trait of interest, such as body mass, ornamentation, or antler size (Alvard 1995, Koster et al. 2010, Levi et al. 2011). Globally, body size is both an important determinant of prey value and a significant predictor of which species are threatened by overexploitation (Cardillo et al. 2005, Ripple et al. 2015).

By collapsing species into a single trait, diet choice models provide a way to rank species or taxa, so that researchers can determine which species (or individuals in an intraspecific context) are subject to hunting pressure and which are not. To date, characterizing hunter prey selection has primarily been performed using optimal foraging theory to determine which prey items should be included in a profit- or calorie-maximizing hunter's diet set (Stephens and Krebs 1986, Alvard 1995, Levi et al. 2011). However, this approach is relatively data demanding, requiring estimates of profitability, handling time, and encounter rate for each species.

A new and alternative diet choice model originates from optimal stopping time problems. Hunting can be viewed as a sequence of decisions; each time a potential prey is seen, does the hunter (1) shoot and gain a reward or (2) not shoot and wait for another prey? Pursuit hunting can thus be represented by an optimal stopping time problem wherein a rule for decision making (when to stop observing and take a shot) leads to an optimal expected reward. There is a rich literature in mathematics and economics considering sequential decision making. A prominent example particularly suited for pursuit hunting is the job search dilemma (Lippman and McCall 1976): how many jobs should a searcher consider before taking the next acceptable offer? More broadly, many have applied this framework to questions about search and foraging in ecology, such as mate or food selection (Pyke et al. 1977, Green 1984, Dombrovsky and Perrin 1994), as well as resource economics (Clarke and Reed 1990).

Applying the optimal stopping time problem to hunter diet choice yields a minimum trait threshold (denoted by economists as a “reservation value,” ε, Lippman and McCall 1976). Hunters should only target organisms above the minimum trait threshold. For instance, if hunters value body mass, and an individual hunter's ε was 10 kg, then they should only shoot when they observe any animal larger than 10 kg. In contrast with optimal foraging theory, stopping time problems only require (1) the wildlife trait distribution, (2) the opportunity cost for time spent hunting, and (3) a means to ensure that hunter opportunity costs and trait values have the same units. Although optimal stopping models are well suited for integration with data due to limited parameter requirements (Diekert et al. 2016), this exploration has not yet been performed.

Both of the hunter diet choice models, optimal foraging theory and optimal stopping problems, produce a minimum threshold for wildlife traits. Above this threshold, prey should be subject to hunting pressure. Using these thresholds for hunter prey selection provides a means to examine hunting sustainability from limited snapshot data. In the optimal stopping model, the threshold for harvesting prey is given by a “reservation value.” In optimal foraging theory, the lowest-ranked prey included in the diet set (which we denote last-place prey) gives this lower bound. A statistical bootstrapping approach can leverage dietary thresholds and historical or comparison wildlife distribution data to assess hunting impacts.

Monitoring communities of harvested wildlife poses intense personnel and cost demands. Catch data are some of the cheapest and easiest data for conservation practitioners to collect in highly threatened ecosystems (Fa et al. 2002, Cowlishaw et al. 2005, Kümpel et al. 2009, Harris et al. 2015). To date, the main tool for structured inference on the state of populations from catch data require time series. Catch data time series can construct catch-per-unit-effort (CPUE) indices, or be evaluated with rapid assessment techniques (Jones et al. 2008). One pitfall of CPUE is that this technique requires extensive temporal samples with known relationships with catchability and stock-abundance (Weinbaum et al. 2013).

In many instances, using CPUE to evaluate hunting sustainability is infeasible because of data limitations, namely too few observations without consistent temporal monitoring. This is a prominent issue facing hunting managers, who often have one-off observations from sites, paired with information on a reference state of wildlife communities from past data, a focal protected area, or a comparative site. Ingram et al. (2015) provide a method to pool across multiple sites to evaluate trends in body mass and harvest pressure for multi-species assemblages, but these approaches cannot be used to inform management at a single site with snapshot data.

When decisions are sought for a specific site with limited data, dietary thresholds provide a way to evaluate changes in prey composition relative to a reference point. We present a novel method that uses hunter diet thresholds to enhance the monitoring value of catch data, which we term “bag back-casting.” In this method, diet thresholds are combined with a baseline for the wildlife community to generate an expected catch distribution. This expected distribution is then compared against observed bag data. Practitioners could use the bag back-casting method to determine whether or not substantial changes had occurred in the community trait spectrum.

Xishuangbanna Dai Autonomous Prefecture in Southwest China typifies many problems facing tropical managers. Xishuangbanna is a biodiversity hotspot where hunters target 50 or more taxa, including several charismatic species of conservation concern (e.g., gaur Bos frontalis and Green Peafowl Pavo muticus, Kai et al. 2014). Although there is limited insight on hunter prey selection, it is known that hunters value larger prey body mass (Chang et al. 2017). Yet there are major knowledge gaps impeding management in this region, including limited or no information on offtake trends over time and the status of exploited wildlife populations.

We address three research questions using data from Xishuangbanna: (1) What do the two models (optimal foraging vs. optimal stopping) predict for hunter diets? (2) Which of two models more accurately characterizes hunter catch profiles? (3) How and when can bag back-casting be used to infer overexploitation of highly valued taxa? We summarize the mathematical motivation for both models below.

Optimal stopping time model

Using optimal stopping problems to represent hunter prey selection is particularly suited for situations when hunting is one of several activities vying for an individual's time. Let the random variable X denote a trait of interest to hunters (e.g., monetary or caloric rewards for body mass, trophy value for antler size), and ε the trait threshold that must be met or exceeded before a hunter will shoot (e.g., a stag must exceed the ɛ antler size to be shot). If S represents the decision to shoot and ¬S abstaining from shooting, then the utility (U) of shooting at this threshold must equal the utility of abstaining; U ( S | ε ) = U ( ¬ S | ε ) . Hunters pay a constant cost per day, c. Note that a hunter only goes into the field if E[X] > c, where E[X] denotes the expected value of X (Lippman and McCall 1976).

The original problem is set up as a one-off decision in an infinite time horizon. As such, shooting ends the problem and whichever animal is selected is gained as a benefit. For a given animal (x) whose trait value is a (example units: grams of protein, dollars, plumage coloration, antler size), the decision to harvest this animal yields U(S | x = a) = a, as the hunter's reward is defined by the animal's trait value. For all observations of individual animals, denoted by x = a
U ( ¬ S | a ) = 0 U ( x ) d F ( x ) c
where dF(x) is the probability density function at trait level x. When trait values are finite, then it is not optimal to stay in the field forever; instead, it is optimal to shoot when x ε .
The reservation value is explicitly related to the hunter's per-period cost as
c = ε ( x ε ) d F ( x ) (1)
(Appendix S1). Using Eq. 1, we can find ε, which is the reservation value or the trait value that minimizes this function (Replication code in Data S1; Section 2).

Optimal foraging theory

Let preyn denote an individual of speciesn (multi-species harvesting) or an individual with trait valuen (intraspecific selection). Prey are ranked in descending order based on the ratio of the reward for preyn vs. its handling time (hn), given by Rn/hn (Charnov 1976, Stephens and Krebs 1986, Levi et al. 2011). Handling times are the sum of all the time it takes to successfully process a prey item, from search to preparing the carcass. λn denotes the encounter rate for preyn. Similar to the stopping time framework, an optimal forager behaves myopically: their problem is whether or not to include preyn given that prey1…n-1 are already in their diet. Upon encountering preyn, the hunter should shoot if the benefits of taking preyn exceed the expected benefit of waiting for a more preferred prey species
R n h n i = 1 n 1 R i λ i 1 + i = 1 n 1 T i (2)
T i = λ i h i .

Methods

Case study data: Hunting in Xishuangbanna, China

To parameterize and compare the two diet choice models as well as the bag back-casting method, we used data on hunting from Southwest China (Appendix S2: Table S1). Historically, hunting in Xishuangbanna was primarily for subsistence, but in the past 30 yr, the local economy has transitioned to profitable smallholder rubber (Hevea brasiliensis) farming, which has released the local population from poverty (Xu et al. 2014). Every hunter is first and foremost a smallholder farmer (Chang et al. 2018), and has affordable and reliable access to animal protein from domestic livestock and poultry; there is no protein insufficiency in the region (Hammond et al. 2015). One distinguishing feature of hunting in Xishuangbanna is that hunters appear to be motivated by extra-economic factors such as the leisure value of pursuit hunting, and do not sell their products to a market (Kai et al. 2014). There is a strong preference for wild meat to domestic alternatives among hunters and the local population, yet the local hunters do not appear to purchase wild meat, and instead consume what they harvest (Zhang et al. 2008, Chang et al. 2017).

For the case study, ethical approval was obtained for the human subjects research and observational avian and mammalian transects (Princeton University Institutional Review Board #6682 and #7274, Xishuangbanna Tropical Botanical Garden #2015.2 and #2015.52, Princeton University Institutional Animal Care and Use Committee #1925-13).

Optimal stopping time parameter estimation

The optimal stopping diet choice model requires (1) an estimate of the hunter's opportunity cost for going hunting (c) and (2) the value of wildlife based on their traits (in this case, body mass in kg, represented by the random variable X). The units of c should match the units of X. In our case, we used monetary units as the foregone wages from agriculture were well characterized while the value of hunting prey was more difficult to describe but was positively correlated with body mass. We found a range of opportunity costs, c, ∈ [2, 68] US$ from interview data (Appendix S2).

Wildlife values (U(x)) were estimated from black market data in Xishuangbanna. However, this market sources wildlife products from poorer regions in Laos and Myanmar; its prices would tend to be less than local hunters’ value for wild meat. We thus used a scalar multiplier, γ, that related the value of bushmeat to a comparable domestic alternative; we sought to capture how much more hunters in China value wild meat over the black market estimates (Appendix S2).

With these parameters (c, opportunity cost, U(x), wildlife value, dF(x), probability density of traits), we determined dietary thresholds ( ε) for hunters by minimizing Eq. 1. More details on the parameters used in the optimal stopping model are provided in Appendix S2.

Optimal foraging theory diet choice model parameter estimation

For optimal foraging theory, the necessary parameters are the value of prey, the handling times required for processing prey, and encounter rates for each category of prey. Handling times are generally estimated from hunter follows. Due to the sensitivity of illegal hunting in Southwest China, hunter follows were infeasible. Thus, we used surrogate parameter values from shotgun hunters at other tropical sites (Koster et al. 2010, Levi et al. 2011). We identified the optimal foraging diet set for hunters by using these parameters in Eq. 2. Appendix S2 contains information on how these parameters were calculated.

Results

Hunter diet choice in Southwest China

Optimal stopping model

The optimal stopping model predicts different diet thresholds based on the opportunity cost of hunting for each individual hunter. Hunters with lower opportunity costs can afford to wait and should target high-value, large-bodied prey (Fig. 1A). Conversely, high opportunity costs should reduce selectivity, producing a smaller body size threshold for shooting (as small as 12 g).

Details are in the caption following the image
Dietary thresholds from optimal stopping and a comparison against bag data. (A) Reservation body masses and the opportunity cost of each hunting trip. The color of each cell depicts the diet threshold under different scaling factors (γ) and per-period costs. γ represents how much more valuable wildlife is per kilogram compared to domestic alternatives. Areas colored dark gray represent parameter space where hunting is not predicted. (B) The complementary cumulative density (P(X > x)) of different levels of per-trip catch biomass (kg) across 57 hunting trips in Xishuangbanna, China. The colored dots represent diet thresholds identified for optimal foraging theory or optimal stopping theory (OST). For OST, the thresholds were (1) the lowest value found when γ = 1, or (2) the lowest value found at the median opportunity cost (US$ 16.32 per trip, γ = 2.5).

The optimal stopping model also predicts when hunting should not be pursued because a hunter's time is more valuable than the prey. The gray zones denote regions where hunting is not economically justified (Fig. 1A). This situation arises when the mean of the trait value distribution is less than the individual hunter's per-period cost. The model predicted that hunting should not be pursued for individuals whose per-period costs were greater than US$ 7 per trip at γ = 1, corresponding to the unadjusted value distribution of wildlife based on black market sale data.

However, we had uncertainty in our estimation of wildlife value due to (1) limitations of the black market sale data, and (2) intangible benefits attached to the act of hunting and consuming bushmeat. When we used a scalar adjustment term (represented by γ → 10), the model predicted hunting activity across the full range of opportunity costs. Greater values of γ increased the reservation value, as an inflated valuation of prey means that it is worth a hunter's time to be more selective in targeting prey. Note that the opportunity cost of each trip was held within the range of US$ 2–68; only the trait value distribution was multiplied by γ.

Optimal foraging theory

The optimal foraging model indicated that only boar and muntjac should be included in the optimal diet, equivalent to a reservation value of 17.6 kg.

Comparison of both diet models against hunter bag data

In our bag data, hunters captured both birds (ranging in size from 25 g to 1.25 kg) and mammals (boar and muntjac). Hunters caught 0–3 prey items per trip, and in 60% of the trips, only one animal was harvested; on 23% of the trips, the hunters returned empty-handed. Because the hunting bag data were collected anonymously to protect respondents, we could not identify the opportunity cost associated with each recorded trip. Bags from successful hunts had a median catch of 561 g (mean: 30 kg, range: [0.28, 136.5] kg).

The optimal foraging theory predictions did not align with the bag data; the diet choice threshold, 17.6 kg, was larger than 75% of the catch records (Fig. 1B). On the other hand, the optimal stopping diet thresholds captured much more of the catch distribution (Fig. 1B; minimum optimal stopping threshold captures ~90% of the catch biomass).

Bag Back-Casting: Enhancing the Utility of Hunter Bag Data

Bag data can be a cost-effective method for monitoring changes in harvested wildlife communities (Jenkins et al. 2011). We present a method that leverages bag data and dietary thresholds to infer the state of harvested wildlife communities at individual sites. This method can address situations where researchers have (1) historical or comparative (e.g., space-for-time approach using a high quality and/or undisturbed site) data on wildlife communities, (2) limited, or even snapshot, bag data (which precludes CPUE analyses), and (3) information to estimate dietary thresholds for hunters. Researchers can use this method to evaluate whether a site is overexploited in the absence of transect data for the site of interest.

Bag back-casting proceeds by generating a dietary threshold for hunters from the “null” (baseline) wildlife transect data. Using dietary thresholds and the baseline community data, a null bag is simulated and compared against the observed bag. We use our bag data from Xishuangbanna as an example. Appendix S2 describes how the baseline wildlife data was obtained.

Using the baseline wildlife data (Fig. 2A), we estimated dietary thresholds for hunters using Eq. 1 across the opportunity cost range (specifically the minimum, US$2, median US$16.32, mean US$24.19, and maximum US$68). The dietary thresholds were 132.5 kg (minimum opportunity cost), 112.3 kg (median), 101.3 kg (mean), and 39.7 kg (maximum). Subsequently, we bootstrap sampled values in the baseline wildlife body mass distribution that exceeded each dietary threshold to construct “null” bags. Finally, we evaluated whether or not the catch data indicated that there was a change in the community of exploited wildlife by comparing the observed catch against these simulated catch data (Fig. 2B).

Details are in the caption following the image
Bag back-casting uses dietary thresholds to enhance inference from limited bag data. (A) As body mass is a salient trait to hunters in Southwest China and strongly predicts prey value, we show the distribution of body masses (measured in kg) in the baseline core zone (Null; Zhang et al. 2014) against our contemporary transect data (Observed) to illustrate the difference in the large-bodied tail of the distribution. Note that to use bag back-casting, one would only need the null data, and we assume that observed wildlife data are unavailable. (B) The distribution of body masses in the simulated null hunting bags (baseline core zone wildlife data evaluated at the dietary thresholds corresponding to the minimum, median, mean, and maximum opportunity costs for hunting) as well as our observed bag data.

A Kruskal–Wallis test indicated that the observed catch data were not consistent with the null bags ( χ 4 2  = 1,729.2, P < 10−16) and post hoc Nemenyi tests showed that the mean biomass of the observed bag was much smaller than each of the null distributions (each P < 10−14, Pohlert 2014). As such, the Xishuangbanna bag data indicate that the community of exploited wildlife are not consistent with the baseline community in the well-protected core zone.

Discussion

Hunter behavior in Southwest China: dietary thresholds and catch

The range of reservation values produced by the optimal stopping time model corresponded to catch data. In contrast, the diet threshold yielded by optimal foraging theory was larger than the majority of catches made by Chinese hunters; however, this could be due to a mismatch between the surrogate and real handling times. The optimal stopping model provides a fruitful method to evaluate hunter decision making processes. It requires minimal data on hunter costs and wildlife communities, all of which correspond to the scale of typical data-gathering efforts in the tropics (Fa et al. 2002, Damania et al. 2003, Cowlishaw et al. 2005, Levi et al. 2011, Harris et al. 2015). On the other hand, recording search and handling times for a wide variety of species, necessary for optimal foraging, would pose onerous data collection demands, particularly when hunting is criminalized (Nuno and St John 2015). In addition, opportunity costs cannot be integrated into optimal foraging models. Moreover, the optimal stopping problem is suitable for considering both intra- and interspecific hunter selectivity as it can take in granular data such as measurements on individual animal body size while the optimal foraging model typically requires species-level averages. Intraspecific sex- and size-biases in harvest can affect sustainability just as much as interspecific preferences (Diekert et al. 2016).

In regions where hunting is primarily for subsistence or profit, greater opportunity costs tend to depress the time allocated to hunting (Damania et al. 2003). As the stopping time framework includes opportunity costs, researchers could evaluate how changes to alternative livelihood wage rates or penalties associated with illegal hunting would affect prey diet choice. A counterintuitive result is that elevated opportunity costs would likely be associated with less selective harvesting, so long as the expected value of hunting exceeds the per-period costs.

We highlight several major limitations of the Xishuangbanna dataset that constrain interpretation. The first is that mammal signs are less robust than structured distance sampling methods. Nonetheless, signs are the primary way that Xishuangbanna hunters perceive mammal abundance. Similarly, our estimates for hunter opportunity costs and wildlife value may be inaccurate. Individuals likely value their time differently and we did not directly measure their opportunity costs for hunting, which could be approached with willingness-to-accept questionnaires in future work (Sirén et al. 2004). We recommend that researchers evaluate the optimal stopping model in subsistence hunting locales that retain a diverse range of body masses with well-characterized costs for hunting. Both dietary models are specific to the systems within which they are parameterized and do not necessarily generalize across sites.

Given the data constraints, the stopping time model indicates that hunting in Southwest China is not economically rational due to a defaunated prey base. The reservation value, ε, existed for all per-period costs (up to US$68 per trip) only when wildlife values were multiplied by a scalar (γ ≥ 9.5). The scalar multipliers were intended to correct inaccurate wildlife value estimates which may be driven in part by non-monetary rewards for hunting such as cultural preferences for wild meat or the leisure value of hunting time (Koster et al. 2010, El Bizri et al. 2015, Duffy et al. 2016). Chang et al. (2018) found that the majority of the male population in Xishuangbanna no longer hunted; the benefits of hunting did not outweigh the costs of foregone income and penalties for illegal hunting and gun ownership. On the other hand, the stopping time results suggest that individuals who have continued hunting likely value aspects of hunting that are not solely material. These extra-economic values may help explain why hunting in Southwest China has continued despite intense defaunation and extremely low catch (Kai et al. 2014, Chang et al. 2017).

Bag back-casting as a tool for conservation

To date, it has been challenging to monitor highly speciose harvesting systems. Dietary thresholds, whether predicted by optimal foraging, stopping, or other models, can be leveraged to produce insight for individual sites with limited data. We demonstrated how the combination of a dietary threshold (estimated from the optimal stopping model in our example), an expected trait distribution, and observed bag data could be used to infer whether or not there had been changes to the community of harvested prey. Evidence of a shift in the trait distribution could then be used to evaluate the success of regulations seeking to sustainably manage hunting pressure. Comparisons in bag back-casting findings across multiple sites could be used to triage scarce resources for monitoring and enforcement. Agile and adaptive management is critically needed in the tropics, where limited financial resources and person-hours constrain the scope of field data collection (Rowcliffe et al. 2004, Kümpel et al. 2009, Harris et al. 2015).

Conclusion

Both optimal stopping and foraging theory can produce dietary thresholds for hunters that exploit a wide range of species. This threshold, also denoted by the term reservation value, can simplify the scope of monitoring and management. We found that the optimal stopping dietary model was particularly informative and required fewer field parameters than optimal foraging theory. Active hunters in Southwest China seemingly violate the key tenet that hunting is only justified when the mean value of the trait distribution exceeds the individual's opportunity cost. This finding reinforces previous research demonstrating that cultural and social intangibles were highly important to hunters in this region, although our mammalian and hunter cost data present significant limitations. Finally, we described a “bag back-casting” method wherein researchers could perform structured inference on the state of harvested communities relative to a baseline, even in data-poor settings. This enhances the monitoring value of catch data, and permit researchers to evaluate the efficacy of hunting management policies with minimal time and personnel investment.

Acknowledgments

The authors thank M. Burgess for suggesting the optimal stopping approach and D. Morris for his assistance with the derivations presented in Appendix S1. N. R. Deshmukh, U. Srinivasan, C. Brook, L. McManus, A. Tilman, T. Treuer, S. Levin, D. Wilcove, R.-C. Quan, and M. Zhang provided helpful feedback. T. O'Brien and two anonymous reviewers greatly improved the quality of the manuscript. Our funding sources were the US National Science Foundation (Graduate Research Fellowship Program, Doctoral Dissertation Improvement Grant DEB-1501552, and NSF Award #1211972 CNH: Social-Ecological Complexity and Adaptation in Marine Systems), National Fish and Wildlife Foundation, Burnand-Partridge Foundation, The Explorers Club, the Princeton University Center for Health and Wellbeing, and postdoctoral as well as short-term visitor support from the National Institute for Mathematical and Biological Synthesis (NSF Award #DBI-1300426), with additional support from The University of Tennessee, Knoxville.

    Data Availability

    Data are available in the online supporting information as Data S1 and both the replication code and data sets are mirrored at https://zenodo.org/record/1404451.