Abstract
Empirical studies of tropical forest hunting have shown the existence of marked spatial gradients of hunting effort, game harvest, and animal abundance, as hunters mostly hunt near villages, roads, and rivers. The mechanisms underlying these patterns have, however, hitherto been poorly known. This article presents a spatial bioeconomic model based on the concept of distance friction, that is, an increasing marginal cost of distance. The model is validated by comparison with an economic field experiment with Amazonian hunters and with previous empirical data on hunting. (JEL Q57)
I. Introduction
Hunting is an importance source of food or cash income for many poor people in remote tropical forest regions, where few alternatives are available (Bowen-Jones, Brown, and Robinson 2003; Fa, Currie, and Meeuwig 2003; Siren and Machoa 2008). Game animals are often an open access resource, as rules restricting harvest are either absent, ineffective, or not enforced (e.g., Noss 1997; Siren 2006), and wildlife is often harvested at unsustainable rates, leading to depletion of the resource base and a myriad of secondary effects on the ecosystems (Milner-Gulland et al. 2003; Wright 2003). Where strong populations of large animals still exist, this is more often due to sheer remoteness than because of any rules restricting hunting (cf. Peres and Lake 2003).
Assessments of the sustainability of hunting in tropical forests typically are based on comparison of total offtake of each species with its estimated current yield or maximum sustained yield (Robinson and Redford 1991; Bodmer 2003). Such purely biological models, however, have severe flaws and may in some cases fail to detect overharvest, whereas in other cases they may erroneously label offtake levels as unsustainable although they in fact are not (Milner-Gulland and Akcakaya 2001; Ling and Milner-Gulland 2006). In fact, it is necessary to also take into account the economic components of the system in order to understand the interactions between hunters and prey, and assess sustainability (Milner- Gulland et al. 2003; Ling and Milner-Gulland 2006). Bioeconomic harvest models integrate population biology with microeconomics in order to assess sustainability or to analyze how different resource management measures or changes in the economic incentives facing harvesters affect harvest behavior, the resource base, and the economic outcome for harvesters (e.g., Albers 2010; Ling and Mil- ner-Gulland 2006; Pezzey, Roberts, and Urdal 2000; Robinson, Albers, and Williams 2008; Robinson, Williams, and Albers 2002; Skon- hoft and Solstad 1996). One important variable in bioeconomic models of hunting is the so-called effort. Effort is thought of as a quantitative measure of human harvesting activities that is directly proportional to the mortality thus imposed on prey populations (The term “effort” is somewhat misleading, as it has little to do with actual physical effort made by hunters, but it is well established among scientists in the field). There is no consensus on how to measure hunting effort in real life, and there have been a myriad of ways to define and measure effort, based on either time or distance (Rist et al. 2008). Regardless of how hunting effort is measured, however, it is typically very heterogeneously distributed in space. This spatial variability in hunting effort has profound socioeconomic and ecological implications, but the underlying mechanisms that create this variability remain poorly understood.
Hunting tends to be most intense near human settlements and transport routes, then to rapidly decrease and approach zero beyond some 9km to 15 km from roads, rivers, or human settlements (Peres and Lake 2003; Siren, Hamback, and Machoa 2004). This hunting gradient leads to marked gradients of prey animal abundance, often with a quite narrow transition zone from areas almost void of a particular species to areas where the same species is very common (Siren, Hamback, and Machoa 2004; Levi et al. 2009). On the other hand, animal dispersal smooths out abundance gradients caused by hunting, such that the abundance at any particular site is not only affected by the local hunting intensity but also by the hunting intensity in surrounding areas (Novaro, Redford, and Bodmer 2000; Siren, Hamback, and Machoa 2004). Therefore, as Levi et al. (2011) pointed out, sustainability must be redefined as a “spatial and temporal concept rather than as a ’Yes or No’ question.” In order to properly assess the impacts and sustainability of hunting, it is therefore necessary to take into account the spatial distributions of hunters and prey, and their interactions (Ling and Milner-Gulland 2008). Little attention has been paid, however, to the mechanisms underlying the spatial distribution of hunting effort.
Models are instead based either on empirically observed distributions of hunting effort, without any theoretical explanation of why these patterns appear (Siren, Hamback, and Machoa 2004; Levi et al. 2009), or on nonvalidated assumptions regarding the factors limiting how far hunters walk before returning home. For example, Clayton, Keeling, and Milner-Gulland (1997), modeling commercial hunting of wild pigs in Indonesia, introduced a limit on the duration of a hunting trip, because meat cannot be preserved in eternity in the forest. Similarly, Ling (2004) used a bag size limit, where hunters return home once they have hunted the maximum amount of meat they are able to carry, to model ibex hunting in central Asia. Both assumptions are, however, contradicted by the not so uncommon observation that tropical forest hunters return home empty-handed. Meat perishability is seldom a problem, as meat can be preserved during long periods by drying it over open fire, though at the time cost for drying. The assumption on bag size limit seems more successful and explained fairly well the observed spatial distributions of both hunters and prey (Ling 2004). Indeed, for a large prey species such as the ibex, weighing up to 100 kg, it may be realistic to assume that hunters are quite satisfied once they have killed one individual. It is more problematic when a model based on a bag size limit is used for more general issues about hunting (Ling and Milner-Gulland 2008) as there is great variation in the weight of meat that hunters carry back from their hunting trips. Sometimes tropical hunters may carry entire white-lipped peccaries (Tayassu pecari) weighing over 30 kg, sometimes just one or a few small birds of a few hundred grams each, and sometimes, again, they may return home empty-handed. Tapirs (Tapirus terrestris) commonly weigh above 200 kg, which definitively is more than a single hunter can carry, but this does not prevent tapirs from being hunted. A hunter killing a tapir dries the meat over a fire to reduce its weight and increase its durability, or may return home to ask for help with carrying the meat (A. Siren, personal observations and unpublished data). Thus, available empirical experience suggests that bag size limits are seldom a major limiting factor on how far tropical forest hunters walk before returning home.
Instead of a binding constraint such as maximum durability of the catch, or a bag size limit, other models assume that the harvesters stop and turn back home at the point where costs outweigh benefits. The spatial variability in such models is created by some function that directly or indirectly either increases the marginal cost, or decreases the marginal benefit, of distance walked. Directly or indirectly, looking at distance walked or the time devoted to walk that distance refers, at least to some extent, to the opportunity cost of time for the hunter. In general, distance and time are correlated in a monotonic manner in these models—longer distances imply greater time devoted to hunting—although little is known about the shape of such relationships, as other factors may also affect the cost per unit of distance walked. Physical exhaustion, more equipment required for longer journeys, and greater danger are examples of additional factors affecting how, at the margin, distance may affect the cost for the hunter walking longer distances. In the model of Robinson, Albers, and Williams (2008) the time it takes to walk a certain distance (and thus also the cost of doing so) increases with the weight of the load carried, according to a power function, and this implies that harvesting beyond a certain distance becomes unprofitable. In another paper, Robinson, Williams, and Albers (2002) instead assume an increasing opportunity cost of time over time. Albers (2010), on the other hand, assumes a decreasing marginal benefit of distance. Common to all these models is that there is little empirical evidence to support the assumptions made regarding the factors limiting the distance walked by hunters or collectors of other forest products. A similar approach has been used in bioecon- omic fisheries models, which incorporate the concept of distance friction. Such models use a power function representing an increase with distance of nonmonetary costs per unit effort, for example, the costs of insecurity, loneliness, and lack of comfort (e.g., Seijo, Defeo, and Salas 1998; Cabrera and Defeo 2001). Our study will contribute to this literature by tackling the problem through the measurement of the relationship, at the margin, between distance and the cost for the hunter. By using a revealed preferences approach (see Varian 2006 for a review) and using an incentivized experiment, we will be able to establish if the per unit cost of the effort hunting is constant or if it changes with distance.
Much hunting in tropical forest is carried out for subsistence purposes, without any monetary transactions involved. In the case of commercial hunting, payments are typically made for the meat, not for the labor of actually hunting. Therefore, it is rather difficult to estimate the cost of hunting effort in monetary terms. One approach is to ask hunters about their subjective valuation of the gains and losses from hunting, and in particular the disutility from traveling by foot a certain distance, as while hunting, and back. Further, one can ask hunters about whether they would accept a certain monetary compensation for incurring in the cost of such effort. Such effort represents an opportunity cost that the hunter accepts in order to obtain a benefit. The minimal amount a person is willing to accept in order to put up with something negative is called this person’s willingness to accept (WTA). Although it is part of the standard terminology of economics (e.g., Randall and Stoll 1980), it should be noted that the term is semantically somewhat misleading. A higher WTA does not mean that somebody is more willing to accept something, but, on the contrary, that he demands a larger compensation in order to do so.
The use of hypothetical questions in order to elicit people’s WTA might suffer from biases well documented in the environmental economics literature (cf. Carson et al. 1996; Bishop and Heberlein 1979). Hanemann (1991) and Hanley, Shogren, and White (1997) provide the theoretical responses to why the measurements of WTA may differ from the other valuation option, namely, the willingness-to-pay elicitation method. In our case, such bias should not apply because the cost of hunting and the benefit of hunting are both essentially private, and therefore the substitution and income effects present in public goods and nonprivate goods situations do not apply here.
The empirical question of estimating distance friction could instead be tackled by designing and testing an economic experiment in which real incentives are introduced in a controlled laboratory setting but brought to the field. Such an experiment would explore the behavioral response to treatment conditions, while controlling for other relevant variables. The use of experiments has a long tradition in social and behavioral sciences, mostly in the laboratory using college students (Kagel and Roth 1995), but also has a growing use in the field and in the context of developing countries (Cardenas and Carpenter 2008). Although some economic field experiments have been conducted previously with tropical forest hunters using real incentives (e.g., Henrich et al. 2006, 2010; Siren, Cardenas, and Machoa 2006), none of these addressed the cost of hunting.
The purposes of this paper are, first, to present a simple spatial bioeconomic model of tropical forest hunting, based on the concept of distance friction, and compare this model with previous empirical findings. Second, we use a field experimental approach to estimate the cost of hunting in terms of the revealed preferences for the distance friction factor. For this purpose, we used the distance and the weight of the hunted prey as treatment variables and observed the actual willingness to accept a monetary compensation for walking a certain distance and carrying a certain weight in exchange.
II. A Bioeconomic Model
Our model is based on a standard textbook nonspatial and nonstochastic bioeconomic equilibrium model (Milner-Gulland and Mace 1998, ch. 1) to which we introduce a spatial dimension and distance friction. According to the standard model (see Appendix A), the population size, effort, and harvest, at bioe- conomic equilibrium, are expressed as
[1]
[2]
[3]where N is population size, r is the intrinsic rate of population growth, K is the carrying capacity, and q is the catchability coefficient. Furthermore, c is the cost per unit of effort and p is the price per unit of harvest. The cost and price need not represent actual cash transactions, but could also be shadow values.
Our spatial model is one-dimensional, consisting of an infinite number of equidistant and equally sized patches. This resembles the case where villages are located along some linear feature such as a river or a road, surrounded by large expanses of homogeneous wildlife habitat, and where villagers go out to hunt in a perpendicular direction from the river or road and return the same way without any detours. Following Seijo, Defeo, and Salas (1998), we use the following formula for how the total cost of transport from the origin of hunters to any particular site i (Ci) depends on the total distance traveled (Di):
[4]where φ is distance friction and a is a constant. We can then represent the (marginal) cost of hunting in any particular place i along the trail as the first derivative of equation [4]:
[5]where σ = φ - 1 and b = φa.
Fishery models, typically based on the notion of fishing grounds of limited spatial extent, distinguish between time spent on getting from port to fishing grounds and time effectively spent on fishing at the fishing grounds. In tropical forest hunting, habitat tends to be more homogeneous. Although environmental variation due to edaphic factors (Salovaara 2005) or anthropogenic modification of the vegetation cover (Rist et al. 2009) affect prey abundance, all habitats are potential hunting grounds, and human hunting affects game abundance more than does environmental variation. Therefore, it make much less sense to make a distinction between transport and active search for prey in tropical forest hunting models than in fishery models. We therefore assume that all movements by hunters have the dual purpose of searching for prey and of moving in a desired direction, that is, either in the direction of increasing prey abundance or back home. Finally, for any site i we define local hunting effort, Ei, as the number of times a hunter has passed the place in question. Then, by combining equation [5] with equations [1], [2], and [3], respectively, we get the following equations for local population, effort, and harvest, at bioeconomic equilibrium:
Here, σ = 0 corresponds to the nonspatial case where all equations are independent of Di. When σ Φ 0, Ni, Ei , and Hi respectively, change with Di as the first derivative:
The hypothetical case that σ < 0 is unrealistic, as this implies that hunting far away has a lower cost than hunting nearby. We will not further discuss this case. When σ > 0, the following inequalities are globally true:
,
Thus, population size will increase with distance, whereas hunting effort will decrease with distance. Harvest, on the other hand, is a concave function of distance, with a maximum when the derivative equals zero. The distances at which this occurs are
.arvest is zero at D1 = 0, because of depletion of the game population, and at where the game population is not hunted because the costs involved are higher than the potential benefits. The shape of the harvest curve can be represented by the ratio m = Dmaxharvest/Dunharvested:
When m ≈ 0, then the harvest peak occurs at a distance close to zero distance, that is, left skewed, whereas the harvest peak is right skewed when m ≈ 1. The value of m is determined by σ, such that
The shape of the harvest curve as a function of distance thus depends on the distance friction φ = a + 1 (Figure 1).
Model Results
It may be noted that this model does not take into account stochasticity, as it is made by introducing a spatial dimension into the not only nonspatial but also nonstochastic standard model of Milner-Gulland and Mace (1998). Conceptually, this can be interpreted as if each hunter decides a priori how far away to walk, that is, already before actually going out to hunt. An alternative assumption could have been that the hunter, after each hunting kill, makes a new decision about how far to continue before turning back home again. Reality, according to our observations in the area where we carried out the experimental study (see below), lies somewhere in between these two extremes. A hunter leaving on a hunting trip already has an idea about how far to go and, based on this, carries the necessary supplies. For a short hunting trip hunters may carry nothing else than a few shotgun shells and a small knife, whereas a longer trip may necessitate several shotgun shells, considerable food provisions, matches, a torchlight, a blanket and a spare set of dry clothes, a big machete for making firewood, and salt for preserving the hunted meat. Plans may change, however, and a hunter that happens to kill a large animal already in the beginning of what was going to be a long hunting trip may very well decide to turn around home again. Thus, assuming that hunters decide beforehand how far away they will go on each hunting trip does not perfectly resemble reality, but it is a simplification as good as any other alternative assumption.
III. Experimental Study
We carried out the experiment in Sarayaku (1°44’ S, 77°29’ W), a Kichwa community with about 1,000 inhabitants in five hamlets along the Bobonaza River, in roadless land in eastern Ecuador, 65 km southeast of the town of Puyo. The local economy and natural resource use practices in this community were thoroughly studied during the years 19982001 (Siren 2004, 2006, 2007; Siren, Hamback, and Machoa 2004; Siren and Machoa 2008). Shifting cultivation, hunting, and fishing formed the basis for what is largely a subsistence economy. Governmental salaries, cattle, fibers of the Aphandria natalia palm, handicrafts, tourism, and migratory work provided some cash income, much of which was used to buy hunting and fishing equipment, agricultural tools, clothes, boots, and the like. Almost all able-bodied men hunted, and thus there was at least one active hunter in as much as 89% of the households. Hunting provided about a third of the food of animal origin consumed in the community, and most of the rest came from fishing. Poultry was a minor complementary food source. Primary school children received one meal a day from international food aid during part of the year. Other than that, store-bought food constituted just a minuscule proportion of the food consumed in the community.
Since that study was conducted, the availability of wage work in the community has increased, fish culture has become a significant complement to wild fish and game meat, and the amount of store-bought food brought to the community from town has markedly increased. Nevertheless, most households still acquire most of their food by subsistence agriculture, fishing, and hunting. Very active hunters may at times go hunting several times a week, whereas others, at other times, may spend months without going hunting, all depending on what other sources of food are available and to what extent they at the time are involved in other work, such as, in particular, agriculture, or, for example, house construction, canoe-making, or wage work. The level of payment for unskilled labor in the community was in 2009 and 2010, when this experiment was conducted, normally $10/ day,1 although occasionally there were opportunities for considerably higher payments (up to $80/day) in, for example, externally funded construction work.
A limited survey in 2001 (Siren and Ma- choa 2008) indicated that hunted meat was more commonly exchanged between households than were other types of food. Also, hunted meat was sold less often than other food products and, instead, typically given away as gifts. In any case, the great majority of the hunted meat (83%) was consumed within the hunter’s own household, implying that most of the benefits from hunting remain within the household bearing the costs. More widespread meat sharing occurs during the four-day community festival, preceded by a 10-day hunting journey (Siren, in press). This traditional festival was by then celebrated in February every year, but nowadays it is held only every two years.
Until recently, hunting was basically unregulated, except that hunters were supposed to hunt primarily within their own areas of inherited use rights. Such areas typically extend from each home out to the forest in such a way that they get wider, and their limits more fuzzy, as the distance from settlements increases. Since 2003, however, there have been some local conservation initiatives, including the setting aside of two small wildlife reserves where all hunting is prohibited, a partial ban on hunting tapirs, and a ban on selling hunted meat outside the community itself. These restrictions are, however, quite limited in their scope, and their enforcement has been only partially successful. For most game species in most of the community’s hunting grounds, it is therefore still a fairly good approximation to consider wild game as an open access resource and hunters as self-interested optimal foragers or “economic men.”
The basic idea of the experiment was to elicit from hunters how they value, using the currency of cash money, the cost of walking different distances through the forest, that is, their WTA. The relevance of this experiment rests on the assumption that walking constitutes the main cost of hunting, as is also assumed in the model described in the previous section. Thus, in accordance with equation [8], if WTA, in terms of dollars/kilometer, is constant dCi/dDi, this means that the marginal cost of walking, ci, is independent of the distance D„ and that thus σ = 0, that is, there is no distance friction. On the other hand, if the WTA in terms of dollar/kilometer changes with distance, this implies that σΦ 0. If σ > 0, this is evidence of the existence of distance friction.
Based on previous experience in the community, we deemed that asking hypothetical questions very likely would lead to answers heavily biased by intentions to express political standpoints (in the style of, e.g., “I would go and carry it back without payment, because in our community we should collaborate with each other without demanding money,” or “I would charge hundreds of dollars, because we also deserve to earn money just as you gringos do”). Such hypothetical and strategic biases from using survey questionnaires have been documented in the early environmental valuation literature (Carson et al. 1996; and Bishop and Heberlein 1979). Instead, we designed the experiment in such a way that the questions about the WTA were not hypothetical, but rather dealt with using a real possibility of, on the day after the experiment session, walking a certain distance x along a forest trail and carrying back a load of a certain weight y, and for all this getting paid a certain amount of money z. The experiment was designed in such a way that the chances of making a profit were highest if one revealed one’s real WTA, as is further described below.
A prerequisite for getting meaningful answers to the questions about the participants’ WTA was that they knew the places in question, such that they could make informed judgments about the time and effort required in order to walk there and back. Therefore we are able to compare the change in economic well-being due to the physical effort against the economic gain from a monetary compensation with rather complete information about the private costs and gains of the transaction. Different families tend to use different hunting trails, but in order to carry out the experiment we needed a trail that was familiar to many different people. Therefore, as a reference for the WTA questions, we chose a particular trail that is not just a hunting trail, but that leads from Sarayaku to a neighboring community, and therefore is used by the public at large, rather than just a few families. By conducting the experiment along only one trail we reduce the bias in the statistical estimation due to variation in trail conditions.
Along the trail, which we mapped using a GPS receiver, we defined six sites to represent different distances used in the experiment. Five sites were in places where the trail crossed creeks with well-known names. The first site along the trail, however, was defined by the base of a steep upslope. This place was chosen to use as the origin in the data analysis, because the village itself was potentially unfeasible to use for this purpose. First, the village lies in a quite deep river valley, such that the topography at the beginning of the trail is quite different from the rest, which may affect expressed WTA levels. Second, people live quite dispersed, so the distances from their respective homes to sites along the trail actually differ by a few hundred meters, which may affect their respective WTA for the first section of the trail. Considering the possibility that the shape of the relationship between WTA and distance may vary with load weight, we defined three loads with different weights: a small piece of plastic (0 kg), and two tanks of different sizes filled with water (5 kg and 24 kg, respectively). The model described in this article does not take into account the effects of load weight. We defined 33 levels of cash payment. These varied slightly from one session to another, but levels were always calculated in a similar manner. First, we defined a minimum and a maximum level, and the rest of the values were set such that they increased in an exponential manner, specifically, the increase from one level to the next was defined by a fixed multiplying factor (≈ 0.17 ±0.1 in different sessions) and rounded off. The range of values was first defined based on preliminary trial games, and later adjusted. Maximum values ranged between $100 and $110, whereas minimum values were first set to $1.00, then lowered to $0.80, then $0.50, and finally the exponential function was combined with a linear function below values of $1.00, such that the list of values reached all the way down to $0.01.
In the afternoon before the first day of the experiment, local native field assistants walked from house to house to invite people to participate in a game at a local school house in the afternoon of the next day. The field assistants briefly explained the purpose of the game, and that the prerequisites for participating were that the person (1) was an active hunter, (2) had previously walked the trail in question, and (3) was not occupied with other activities the day after the experiment session in the school.
At the experiment sessions, we first presented the objectives of the “game” and explained the rules in Kichwa, the local language. We also gave a few trial questions, or, in most cases, ran an entire trial game, in order to make sure that the participants had understood the incentives they faced before playing the game for real. Each participant was randomly assigned one weight. Then participants one by one, alone with just the experiment leader and one assistant, were asked to answer yes or no to a number (usually around 30) of questions as to whether they would accept a certain payment for walking to a certain place and carrying back the assigned load. The different loads were also present, such that the participants could lift them and feel their weight in order to make informed judgments.
We wanted each answer to the WtA questions to be as independent as possible from the answers to previous questions by the same person, but we also wanted to minimize the number of questions in order not to exhaust or cause boredom to the participants. Therefore, we assumed that if a participant accepted a combination of a payment z1, distance x1, and weight y1, then he would also accept a larger payment z2 > z1 for the same distance x1 and weight y1. And, similarly, that if a participant rejected a combination of a payment zi, distance x1 and weight y1, then he would reject also a smaller payment z2 < z1 for the same distance x1 and weight y1. We did not assume, however, that if a participant accepted a combination of a payment z1, distance x1, and weight y1, he would necessarily accept the same payment z1 also for a shorter distance x2 < x1 and the same weight y1. The order of the questions was such that they shifted from one distance to another according to a predefined random series of numbers, whereas for each distance the order of question followed a scheme designed in order to, with as few questions as possible, gradually reduce the possible range and finally identify the minimum accepted payment level, and the maximum rejected payment level, z for every distance x.
After finalizing the questions, we proceeded to select which participants would the next day have the chance to actually walk the trail, carry back loads, and get payment for that. To keep costs down, and depending on the number of participants who had shown up, we sometimes first did a lottery, using pieces of paper with the text “yes” or “no” to randomly exclude half of the participants. Then, we did another lottery, this time for payment levels. This time, there was one lottery ticket for each predefined level of payment, ranging from 0.0i, 0.50, 0.80, or i.00 dollars up to i00 or ii0 dollars, and each participant drew one ticket for himself. Finally, we did a lottery regarding the length of the walk, using pieces of paper with the name of the six sites along the trail. For practical reasons, we selected only one site at each session, the same for all participants.
For each participant there was now defined a distance x (common for all participants), a load of the weight y (different for different participants), and a payment of z dollars (unique for each participant). Participants whose expressed minimum WTA for the combination of distance and weight in question was lower than the offered payment (WTAxy < zxy) was given the opportunity to, the next day, actually walk the distance x and carry back the weight y, for a payment of z dollars. However, participants whose expressed minimum WTA for the combination of distance and weight in question was higher than the payment now offered (WTAxy > zxy) were not given this opportunity, and in this consisted the incentive not to exaggerate one’s WTA. On the other hand, all participants were to be paid $i, just for having participated in the experiment without cheating. Thus, participants whose expressed WTA for the combination of distance and weight in question was lower than the payment now offered (WTAxy < zxy) but nevertheless refused to perform the walk, did not receive this $ payment, as a punishment for having cheated, and as an incentive not to underestimate one’s WTA.
Carrying out the walks involved agreeing with the participants on an approximate time they would start their walk, usually early, before dawn. Then the researcher and one assistant walked in advance, carrying empty water tanks, out to the site where the loads were to be picked up. There the tanks were filled with water and the caps were sealed with epoxy glue. Another assistant waited at some point along the trail in order to check that the participants did not break any of the rules that had been clearly explained the day before: not letting anybody else help with carrying the tank and not carrying anything else back from the forest except the water tank. This latter was important, because if people would have had the opportunity to also hunt, fish, or gather other forest products once in the forest, the incentive situation would have been totally different.
We carried out the same experiment one time in one hamlet, called Shiwakucha, and four times in another hamlet, called Centro Sarayaku. The same trail was used for all experiments, except that the first couple of kilometers followed a different route depending on which hamlet one departed from. In total, 34 persons participated in the experiments, out of which 7 participated more than once, although with loads of different weights each time, such that there was data for a total of 43 combinations of persons and weights, out of which 3i were from the Centro Sarayaku hamlet, and i2 from Shiwakucha. Four experimental subjects (all from the same experimental session in Shiwakucha) were, however, excluded from the analysis because after participating in the game they spontaneously admitted that they had not been able to make informed judgments because they had never walked the trail in question. Another subject from Shiwakucha was excluded because he provided extremely weird replies, accepting payments of $0.50 for the four longest distances, whereas he for one of the shorter distances rejected even a payment of $100, and he later explained that he had done so because he liked to walk in the forest but thought it would be meaningless to walk just a very short distance. Three subjects were excluded because they (all on the same day in Centro Sarayaku) consequently answered yes to any level of payment offered, and afterward explained that they had done so because they had not understood the rules of the game. This left for the analyses a total of 25 persons out of which 5 participated in two sessions, and two participated in three sessions, such that there were a total of 34 replications for the analysis.
For data analysis we calculated the minimum WTA of each subject as the arithmetic mean of the lowest accepted, and the highest rejected, sum of money and divided this with the length of the trajectory walked, in order to get a value of WTA per unit of distance (dollars/kilometer). The experimental data was modeled statistically in a linear mixed effects model, using the mean monetary sum per unit distance as response variable. The WTA per unit distance was modeled with distance and load as fixed effects and person as a random effect. Prior to analyses, distance and WTA per unit distance were loge-transformed. The results we present here are based on an analysis where the first section of the trail is excluded, because of the reasons explained above. In one case, this led to some negative values, as one subject had indicated a higher WTA for walking to the first point along the trail than for walking to some of the points further away. To analyze this, a positive number was added to all values for this subject, such that the lowest WTA became zero. To double-check, the same analysis was also run including the entire length of the trail in the analysis, which had the advantage that there were then no negative numbers to deal with. This analysis showed almost identical results, with only slightly lower statistical significance. At some sessions, our list of predefined money values proved to start at a too high value, as some subjects, for short distances, accepted even the lowest available values. Thus it was not possible to calculate their WTA as the average between the lowest accepted and the highest rejected value. To deal with this, we ran the same analysis three times, each time calculating the WTA for these cases in different ways: (1) equal to zero, (2) equal to the lowest accepted value, and (3) equal to half of the lowest accepted value. The results presented below are based on the latter of these three treatments, but the other treatments yielded almost identical results.
To test if WTA per unit distance varied with distance and load we used a linear mixed effects model (lme) with individuals as random effect. This analysis accounts for the fact that the same individual is involved in multiple measurements and an lme adjusts degrees of freedom and significances accordingly. In the analysis, we evaluated the significance of main factors by comparing the full model with a simplified model, excluding the tested factor, with an F-test. In some cases, the same person was involved in tests with different loads, and this aspect added strength to the analysis as the test then includes effects both within and between groups (persons). The analysis was performed in R, version 2.11.1, and the package lme (Pinheiro et al. 2009). The initial test indicated that the variances were unequal between subjects, and we therefore used the varIdent-function.
IV. Results
Previous empirical data (Figure 2) showed that total hunting effort decreases with distance, whereas catch per unit of effort, which can be used as a proxy for population size (e.g., Rist et al. 2010), increases with distance, at least up to a certain point where it seems to level out. Harvest decreases with distance, although it shows a plateau at intermediate distances. These patterns are similar to those resulting from our model when including distance friction (Figure 1 b-d), except that harvest in the model shows a unimodal distribution whereas the empirical data show that harvest uniformly decreases with distance.
Empirical Results
Regarding the results of the experimental study, the WTA per unit distance varied considerably across individual experimental subjects, and the observed relations with distance were both positive and negative (Figure 3). The linear mixed model, however, suggested that WTA per unit distance increased significantly with both distance and load, confirming the economic valuation theory of a monetary compensation for incurring the cost of hunting. When doubling the distance, the WTA increased by a factor of 2.7. That is, with a doubling of the distance, the WTA per unit distance increased by about 35% (σ =0.44 ± 0.04 [mean ± SE]), comparing the model with and without distance: Δdf = 1, log-likelihood ratio = 11.1, ΔAIC = 9.0, p < 0.001). This provides empirical evidence for the existence of distance friction where σ > 0, according to the model presented above.
Experimental Results
The WTA per unit distance similarly increased with about 12% from a zero load to the 5 kg load and by about 55% from a 5 to a 25 kg load (comparing the model with and without load: Δdf =1, log-likelihood ratio = 7.7, ΔAIC = 5.7, p < 0.01 (see Appendix B).
Through the lotteries, a total of 16 subjects were offered the opportunity to perform a walk along the trail and carry back a certain load, for a payment that was equal or above their expressed minimum WTA. Out of these, 14 subjects actually fulfilled and got their respective payments. One subject told us that he would not be able to go on the walk because of an important meeting, and another subject stayed home because of heavy rain on the day he was to make the walk. These two persons were therefore not paid the $1 for participating in the experiment.
V. Discussion
We have here provided a theoretical model of hunting that is tested against evidence from a field experiment where we ask participants, who all are real tropical forest hunters, to express and honor their willingness to accept an economic offer to exert a real effort to walk and carry a heavy weight through the forest where they usually hunt.
The results of the theoretical model, when including distance friction (Figure 1 b-d), seem to largely coincide with previous empirical findings (Figure 2). The empirically found harvest levels, however, seem to uniformly decrease with distance. This is not in full accordance with the model, which predicts that harvest first would increase at short distances and then decrease at longer distances. One possible explanation could be that the harvest peak is very close to the origin of the hunters, as would be the case if the distance friction σ is low (cf. Figure 1b), and that the spatial resolution of data collection and analysis of the empirical study is too low to detect this peak. Alternatively, the multispecies character of hunting in real life may cause empirical results to deviate from the model (cf. Rowcliffe, Cowlishaw, and Long 2003), as may also the effects of animal dispersal, in other words, there are source-sink dynamics (cf. Novaro, Redford, and Bodmer 2000; Siren, Hamback, and Machoa 2004). Finally, habitat heterogeneity due to human activities may play a role. A remote sensing study revealed that only 0.2% of the study area as a whole consists of agricultural fields, and 2.2% of anthropogenic secondary forest (fallows) of age < 20 years. However, the human impact on forest cover near the village is much greater. In the area represented by the leftmost data point in Figure 2, agricultural fields constitute 1.9% of the land area, and no less than 23.5% are fallows of age < 20 years (Siren, Hamback, and Machoa 2004; Siren and Bron- dizio 2009). Here, the species composition of hunts, as well as the hunting methods used, differs quite significantly from the rest of the study area, and this may be due to the differences in habitat quality as well as to the high hunting pressure that has lead to the extirpation of several game species (Siren, Hamback, and Machoa 2004).
The experimental study, on the other hand, further confirmed the validity of the model by providing empirical evidence for the existence of distance friction in the context of Amazonian hunters. This provides an explanation of the variability of hunting effort in space that has been observed in empirical field studies (Peres and Lake 2003; Siren, Hamback, and Machoa 2004). So, what is then the advantage of this explanation in comparison with other explanations provided regarding the cause of the commonly observed spatial gradients in hunting effort, such as meat perishability (cf. Clayton, Keeling, and Milner-Gulland 1997), bag-size limits (cf. Ling and Milner-Gulland 2008), increasing opportunity cost of time (cf. Robinson, Williams, and Albers 2002), decreasing marginal benefit of distance (Albers 2010), or decreasing walking speed with weight of load (cf. Robinson, Albers, and Williams 2008)ΠThe main advantage is that whereas all these previous explanations are assumptions unfounded in empirical evidence, we have in this article presented experimental evidence for the existence of distance friction, that is, an increasing marginal cost with distance. This does not mean that the other explanations are wrong. On the contrary, we believe that meat perishability does, in some contexts, affect hunting patterns. And our own experimental results also suggest that there is an increasing marginal cost to the weight of the load carried, which is in full accordance with the assumption made by Robinson, Albers, and Williams (2008) of decreasing walking speed, and thus increasing cost, with load weight, due to shorter distances walked per unit of time, and also somewhat similar to the assumption of a bag-size limit (cf. Ling and Milner-Gulland 2008). In addition to the opportunity cost of time, also the increasing physical exhaustion and dangers associated with hunting at longer distances, or the larger amount of equipment required for longer hunting journeys may also affect the marginal cost of distance. The concept of decreasing marginal benefit of distance (cf. Albers 2010) is actually mathematically similar to the distance friction included in our model, but the validity of the concept itself is questionable. In fact, if resource density increases with distance from settlements, as is typically the case for wild game, the marginal benefit of distance on the contrary increases (cf. Siren, Hamback, and Machoa 2004). Also the increasing marginal opportunity cost of time used in the model of Robinson, Williams, and Albers (2002) is mathematically somewhat similar to the distance friction of our model. Conceptually, the difference is that our model is more general, as it permits that an increasing marginal opportunity cost of time may be one factor contributing to an increasing marginal cost of distance, or distance friction, but it implicitly includes also any other possible contributing factors, such as those mentioned above.
From now on, that kind of model no longer needs to be based on unfounded assumptions, but can be based on the empirical relation between distance and marginal cost, namely, distance friction, which we have shown in this paper, thanks to our experiment in the field. In addition, once we know that such distance friction exists, we can use that as a source of further research for improving our understanding of the costs involved in tropical forest hunting. For example, it would be worthwhile to explore how much of the distance friction observed in our experiment did depend on increasing opportunity cost of time (cf. Robinson, Williams, and Albers 2002), and how much depended on something else, such as, for example, people’s valuation of the physical exhaustion that walking long distances involves. Also, another next step could be to do modeling, using experimental and empirical studies that involve the increasing marginal cost with distance (distance friction) as well as the increasing marginal cost of load weight, in order to better understand how these two factors combined put limits on how far into the forest hunters walk before turning back.
By implementing a field experiment with actual incentives and actions, we have taken a step further in the response to criticisms about the hypothetical nature of questions that elicit values through surveys or the abstractions made in laboratory experiments. But the external validity problem remains as a challenge. There are, of course, differences between this experiment and hunting in real life. The trail used for our experiment had been cleared by machete about one year prior to the first experimental sessions, and about two years before the last ones. It was therefore relatively easy to walk all along its length, whereas other hunting trails typically become smaller and smaller as one gets further away from the village, becoming sometimes almost indistinguishable even for experienced hunters. Real-life hunting also differs from the experiment in that as hunters reach deeper into the forest, they tend to gradually slow down walking speed in order to sharpen their attention and not make noise that may scare animals away. And, of course, stochasticity greatly influences hunting luck on individual hunting trips, and thus the hunters’ decisions on how far to walk. Taking such variations into account constitutes further challenges for future experimental and modeling studies. However, our experience with this experimental design suggests that the same protocol with these variations might be applied again in these and other communities, given the interest it raised among young as well as more experienced hunters, and the real incentives used in the exercise.
It has been shown that the best protection from hunting is offered by sheer remoteness from human settlements (Peres and Lake 2003; Siren, Hamback, and Machoa 2004). Many indigenous peoples in the Amazon are currently experiencing rapid population growth, leading to resource scarcity around settlements. A common way to cope with this is that some people leave large communities and establish new settlements in the interstitial areas between existing villages. (In the surroundings of the Sarayaku community, such formation of new villages has also had to do with newcomer religious mission organizations willing to create communities made up exclusively of their own adepts, or with oil companies paying compensation money to the leaders of each community, thus providing an economic incentive for forming new communities.) As the interstitial areas between villages get filled up with new settlements, the truly remote forest areas are becoming ever fewer and smaller. As location of settlements is easier to monitor than hunting effort or hunting technology, it has been suggested that putting restrictions on the establishment of new settlement could be an important component of conservation policy in tropical forest regions (Levi et al. 2009). In fact, the Sar- ayaku community itself has adopted the policy of not allowing the establishment of any new permanent settlements within its community lands, largely because of concerns about the consequences this could have on wildlife populations. So what is needed may not always be externally imposed prohibitions, but rather support for local conservation initiatives and adequate location of, for example, schools and health services in order to provide incentives for living in a few large settlements rather than in many small ones.
Managing wildlife by means of influencing the spatial distribution of human settlements would benefit from an improved understanding of how such different spatial distributions of settlements would affect wildlife populations. Empirical study of hunting effort and wildlife harvest (cf. Siren, Hamback, and Ma- choa 2004; Parry, Barlow, and Peres 2009) around settlements of different sizes would therefore be important. The weakness of such an empirical approach is, however, first, that it is expensive, as it requires the presence of highly skilled professionals in the field during prolonged periods of time. And, second, that it may be problematic to extrapolate the findings from such empirical studies into other areas, or into the future, when settlements may have grown even larger, and when economic conditions may have changed. In order to predict how human population growth and settlement spread may affect wildlife populations, Levi et al. (2009,2011) used spatial modeling. However, their models were based on the rather simplistic assumption that human population growth would lead to a doubling of the hunting effort, but no change in its spatial pattern. An alternative approach to predicting the spatial distribution of local hunting may be to use spatial bioeconomic modeling in order to identify the equilibrium distribution of hunting effort where the benefits of hunting everywhere are equal to its costs. In this paper we have made a first step toward this by showing empirically how the transport costs perceived by hunters are related to distance in a nonlinear manner, with direct implications to how an increase in population or the establishment of new settlements may impact spatially the effort in hunting.
The findings of our experiments could be used to provide better estimates than before about the spatial extent of hunting around settlements, and, consequently, the expected impacts on wildlife species. Also, understanding not only the economic benefits of hunting, but also its costs could be helpful when implementing conservation and sustainable use management programs for tropical forest wildlife, in order to maximize benefits and minimize the costs borne by the local people, and, if pertinent, adequately calculate corresponding levels of compensation.
Whether hunting effort becomes negligible at either, for example, 9 or 15 km distance from settlements and transport routes (cf. Peres and Lake 2003; Siren, Hamback, and Machoa 2004) makes a huge difference where villages, as in much of the Amazon, often lie at a distance of some 10-30 km from each other. The question of when, where, and why, hunters turn around and go home, therefore deserves a great deal of attention.
Acknowledgements
Anders Sireén’s field work was funded by a postdoctoral grant from the Swedish International Developmentopment Authority (SIDA), another postdoctoral grant from the Swedish Research Council for Environment, Anders Siren’s field work was funded by a post- Agricultural Sciences and Spatial Planning (FOR- doctoral grant from the Swedish International Devel- MAS), and by the Kone Foundation through a grant, within its program for research on the significance of biodiversity, to Professor Risto Kalliola at the department of geography at the University of Turku, Finland. The Kone Foundation this way also funded Siren while he analyzed data and worked with the manuscript. Lenin Gualinga, Milton Gualinga, and Reinaldo Guerra assisted with field work. We are also grateful for the support provided by the Government Council of the Sarayaku community and for the interest shown by the hunters who accepted participation in the experiment.
Appendix A
The standard model (Milner-Gulland and Mace 1998, ch. 1) assumes that a game population, in the absence of harvest, grows according to the logistic equation
where N is the game population size (density), r is the intrinsic growth rate, t is time, and K is carrying capacity. Hunting effort, E, is, by definition, a quantitative measure of human harvesting activities that is directly proportional to the mortality2 imposed on prey populations, according to the following expression:
The model also assumes open access conditions, meaning that there are no effectively enforced restrictions on harvest.3 The catchability coefficient, q, is defined as the proportion of the game population that is harvested per unit of effort, such that
At a population-dynamical equilibrium, harvest equals population growth, such that
This equation has (at most) two equilibria, N* = 0 and
[A1]which is positive when r − qE > 0. The profit of harvesting (Πh) when the game population is at biological equilibrium is equal to
where p is the price per unit harvest and c is the cost per unit effort. It should be noted that this price and cost need not represent actual cash transactions but could also be shadow values. When open access conditions prevail, each individual hunter acts self-interestedly, leading to a suboptimal bioeconomic equilibrium where profit equals zero, such that
and thus population size at the bioeconomic equilibrium is
[A2]By combining equations [A1] and [A2], one then gets the following equations representing effort and harvest, respectively, at bioeconomic equilibrium:
Appendix B
Statistical Model Describing Willingness to Accept: The Statistics When Comparing the Full Model with a Model Where One Factor Was Removed (upperpanel); The Coefficients in the Final Model (lower panel)
Footnotes
The authors are, respectively, researcher, School of Biological Sciences, Pontificia Catholic University of Ecuador, Quito, and Department of Geography, University of Turku, Turku, Finland; professor, Faculty of Economics, University of the Andes, Bogota, Columbia; professor, Department of Botany, Stockholm University, Stockholm, Sweden; and researcher, Department of Mathematics and Statistics, University of Turku, Turku, Finland.
↵1. All monetary amounts are in U.S. dollars.
↵2. The term “imposed mortality” refers to the ratio of the number of harvested prey during a certain time period divided by the total prey population. It should not be confused with the absolute number of harvested prey.
↵3. Noneconomists sometimes misunderstand the concept of open access, believing that it is equivalent to uncoordinated and intense harvest by many different individuals. But the term in fact refers just to the absence of enforced restrictions on harvest, regardless of the actual harvest intensity. Open-access conditions in areas near human settlements or transportation routes commonly lead to intense harvest and resource depletion, but open-access conditions as such are actually most common in sparsely populated and remote areas. Even areas that are so remote that there are no humans present, either to harvest or to enforce any restrictions on harvest, are, technically, subject to open-access conditions.
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