Ungulate population dynamics and optimization models

Optimal harvesting strategies for an ungulate population are estimated using stochastic dynamic programming. Data on the Llano Basin white-tailed deer (Odocoileus virginianus) population were used to construct a 2-variable population dynamics model. The model provided the basis for estimating optimal harvesting strategies as a feedback function of the current values of the state variables (prefawning older deer and juveniles). Optimal harvest strategies were insensitive to assumptions about the probability distributions of the stochastic variable (rainfall). The response of the population components to harvesting and the returns obtained from applying optimal strategies were explored through simulation. Mean annual harvest is about 15% of the population. Simplified harvesting strategies based on age-ratios as well as a simplified version based on optimal strategies—but assuming persisting equilibrium juvenile deer density—were compared to optimal strategies through examining values of information. Simplified harvesting strategies lead to a lower harvest over a 50-year simulation period.     

Optimal harvesting of ecologically interdependent fish species

The optimal exploitation of a two-species predator-prey system is considered, using Lotka-Volterra-type equations. Due to the density-dependence of ecological efficiency, both species should be harvested simultaneously over a range of relative prices. Beyond the limits of this price range, either the prey species should be utilized indirectly by harvesting the predator, or the predator should be eliminated to maximize the prey yield. Neglecting harvesting costs, the simultaneous harvest of prey and predators requires that a unit of prey biomass increase in value by being “processed” by predators. Certain results from single-species fishery models are shown not to apply to multispecies models. These are as follows: (i) Optimal regulation of a free access fishery may call for subsidizing instead of taxing the harvest of predator species. (ii) Increasing the discount rate may, at “moderate” levels, imply that the optimal standing stock of biomass increases instead of decreasing. (iii) A rising price or a falling cost per unit fishing effort of a species may raise and not lower the optimal standing stock of that species.     

Effects of climate change on moose populations: Exploring the response horizon through biometric and systems models

Interest in the response of moose to climate change has increased because of the potential role they play in the conservation of woodland caribou, and threatened loss to recreational and economic opportunities. The objective of this study is to develop a plausible, parsimonious, systems-level model of moose population dynamics that will be useful in exploring the response of moose populations to climate projections. The study begins with a statistical model of moose carrying capacity, which is then integrated into a systems-level model that predicts moose density based on explicit causal factors. Scenario analysis was conducted using a variety of assumptions concerning biotic and abiotic interactions, and under the A2 climate scenario all model scenarios predict a decline of moose density at the southern limits of the Ontario distribution and an increase at the northern extents. Predicted declines are a result of lower carrying capacity and higher heat stress, parasite loads and wolf predation. Given the sensitivity of the model to density-dependent factors, the indirect effect of parasites on decreased recruitment may have greater impact on moose than the direct effect of increased death rate. Results indicate that conservation planning for woodland caribou populations should account for possible increases in moose and wolf populations.     

Ecological and economic considerations on fishing and rearing of Tapes phillipinarum in the lagoon of Venice

A population dynamic model for Tapes philippinarum has been developed, using experimental data for the estimation of mortality, and literature information for recruitment. The population dynamic model has been coupled to a eco-physiological model of T. philippinarum previously developed, in order to simulate the evolution of individual size and number of individuals in each age class.The resulting age-size class model has been used to analyse the implication of different scenarios of fishing/harvesting of the bivalve in the lagoons of the Northern Adriatic Sea, where fishery and aquaculture represent important economic activities.Ten years long simulations have been performed, in which initial density, harvesting efficiency, minimum harvested size, were varied. Comparisons between the different strategies are made in term of total yields and bio-economic income. The model gives suggestions on the optimal fishing effort, in case of fishery, and on optimal seeding size and seeding moment, in case of aquaculture.A discussion of model results provides indications on harvesting policies which are appropriate from ecological-economical point of view. The final result is that economically more profitable strategies coincide with ecologically more conservative policies.     

Incorporating natural enemies in an economic threshold for dynamically optimal pest management

The control of pests by their natural enemies represents an important regulating ecosystem service that helps maintain the stability of crop ecosystems. These services, however, are often ignored in pest management decision making. In addition, the use of broad-spectrum insecticides can damage the populations of natural enemies, reducing the cost-effectiveness of insecticide investment if unaccounted for in treatment decisions.The existing literature on modeling of biological control of insect pests has generally focused on simulations of the population dynamics of pest and natural enemy species and the processes underlying pest control. But agriculture is a managed ecosystem where predator–prey relationships are heavily influenced by human managers. In modeling managerial choices, this study develops an intra-seasonal dynamic bioeconomic optimization model for insecticide-based pest management that explicitly takes into account both the biological control effect of natural enemies on pest density and the nontarget mortality effect of insecticides on the level of natural pest control supplied. The model captures predator–prey interactions, linking them to crop growth and yield damage functions, which in turn are evaluated in a dynamic optimization framework. We introduce a new decision rule for judicious insecticide decisions using a natural enemy-adjusted economic threshold. This threshold represents the pest population density at which insecticide control becomes optimal in spite of the opportunity cost of injury to natural enemies of the target pest. Using field data from Michigan, the model is applied to the case of soybean aphid (Aphis glycines, Matsumura), a recent invasive pest of soybean (Glycine max), whose management is of both economic and environmental importance to the North Central region of the United States. As illustrated by the numerical examples, such natural enemy-adjusted threshold is likely to lead to fewer recommendations for insecticide use than naïve models that ignore natural enemies, resulting in less insecticide use, while maintaining profitability for farmers that rely on chemical pest control methods.The bioeconomic model developed in this study can be used to conduct a wide variety of analyses such as identifying dynamically optimal spray strategies and estimating the implied economic value of natural control services. Furthermore, with the incorporation of inter-year carry-over factors, such as overwintering of pests and natural enemies, the current model can contribute to building multi-year models for studying long-term pest management.     

Economics of harvesting age-structured fish populations

A generic age-structured model is developed to derive analytical results on optimal harvesting. Given two age classes, knife-edge selectivity, and no stock-dependent harvesting cost, the steady state is a unique saddle point. Adding harvesting cost does not alter the uniqueness, given that the utility is linear. Under specific conditions such as nonselective gear, optimal harvesting is proved to be a stationary cycle that represents pulse fishing. Optimal steady states are different if age-structured information is ignored and optimization is based on traditional biomass variables. This implies that the existence of optimal sustainable harvesting depends on age-structured information. Given a specific set of conditions such as low interest rate and knife-edge selectivity, optimal harvesting converges toward a unique saddle point independently of the number of age classes.     

Economics of harvesting age-structured fish populations

A generic age-structured model is developed to derive analytical results on optimal harvesting. Given two age classes, knife-edge selectivity, and no stock-dependent harvesting cost, the steady state is a unique saddle point. Adding harvesting cost does not alter the uniqueness, given that the utility is linear. Under specific conditions such as nonselective gear, optimal harvesting is proved to be a stationary cycle that represents pulse fishing. Optimal steady states are different if age-structured information is ignored and optimization is based on traditional biomass variables. This implies that the existence of optimal sustainable harvesting depends on age-structured information. Given a specific set of conditions such as low interest rate and knife-edge selectivity, optimal harvesting converges toward a unique saddle point independently of the number of age classes.     

Optimal management of non-Markovian biological populations

Wildlife populations typically are described by Markovian models, with population dynamics influenced at each point in time by current but not previous population levels. Considerable work has been done on identifying optimal management strategies under the Markovian assumption. In this paper we generalize this work to non-Markovian systems, for which population responses to management are influenced by lagged as well as current status and/or controls. We use the maximum principle of optimal control theory to derive conditions for the optimal management such a system, and illustrate the effects of lags on the structure of optimal habitat strategies for a predator–prey system.     

The importance of considering multiple interacting species for conservation of species at risk

Conservation of species at risk of extinction is complex and multifaceted. However, mitigation strategies are typically narrow in scope, an artifact of conservation research that is often limited to a single species or stressor. Knowledge of an entire community of strongly interacting species would greatly enhance the comprehensiveness and effectiveness of conservation decisions. We investigated how camera trapping and spatial count models, an extension of spatial-recapture models for unmarked populations, can accomplish this through a case study of threatened boreal woodland caribou (Rangifer tarandus caribou). Population declines in caribou are precipitous and well documented, but recovery strategies focus heavily on control of wolves (Canis lupus) and pay less attention to other known predators and apparent competitors. Obtaining necessary data on multispecies densities has been difficult. We used spatial count models to concurrently estimate densities of caribou, their predators (wolf, black bear [Ursus americanus], and coyote [Canis latrans]), and alternative prey (moose [Alces alces] and white-tailed deer [Odocoileus virginianus]) from a camera-trap array in a highly disturbed landscape within northern Alberta's Oil Sands Region. Median densities were 0.22 caribous (95% Bayesian credible interval [BCI] = 0.08–0.65), 0.77 wolves (95% BCI = 0.26–2.67), 2.39 moose (95% BCI = 0.56–7.00), 2.64 coyotes (95% BCI = 0.45–6.68), and 3.63 black bears (95% BCI = 1.25–8.52) per 100 km². (The white-tailed deer model did not converge.) Although wolf densities were higher than densities recommended for caribou conservation, we suggest the markedly higher black bear and coyote densities may be of greater concern, especially if government wolf control further releases these species. Caribou conservation with a singular focus on wolf control may leave caribou vulnerable to other predators. We recommend a broader focus on the interacting species within a community when conserving species.     

The causes and consequences of partial prey consumption by wolves preying on moose

For a wide range of taxa, partial prey consumption (PPC) is a frequent occurrence. PPC may arise from physiological constraints to gut capacity or digestive rate. Alternatively, PPC may represent an optimal foraging strategy. Assessments that clearly distinguish between these causes are rare and have been conducted only for invertebrate species that are ambush predators with extra-intestinal digestion (e.g., wolf spiders). We present the first strong test for the cause of PPC in a cursorial vertebrate predator with intestinal digestion: wolves (Canis lupus) feeding on moose (Alces alces). Previous theoretical assessments indicate that if PPC represents an optimal foraging strategy and is not caused by physiological limitations, then mean carcass utilization is negatively correlated with mean kill rate and the utilization of individual carcasses is uncorrelated with time between kills. Wolves exhibit exactly this pattern. We explore how the typical portrayal of PPC by wolves has been not only misleading but also detrimental to conservation by promoting negative attitudes toward wolves.     

Cost-Effective Suppression and Eradication of Invasive Predators

Abstract: Introduced predators can have pronounced effects on naïve prey species; thus, predator control is often essential for conservation of threatened native species. Complete eradication of the predator, although desirable, may be elusive in budget‐limited situations, whereas predator suppression is more feasible and may still achieve conservation goals. We used a stochastic predator–prey model based on a Lotka‐Volterra system to investigate the cost‐effectiveness of predator control to achieve prey conservation. We compared five control strategies: immediate eradication, removal of a constant number of predators (fixed‐number control), removal of a constant proportion of predators (fixed‐rate control), removal of predators that exceed a predetermined threshold (upper‐trigger harvest), and removal of predators whenever their population falls below a lower predetermined threshold (lower‐trigger harvest). We looked at the performance of these strategies when managers could always remove the full number of predators targeted by each strategy, subject to budget availability. Under this assumption immediate eradication reduced the threat to the prey population the most. We then examined the effect of reduced management success in meeting removal targets, assuming removal is more difficult at low predator densities. In this case there was a pronounced reduction in performance of the immediate eradication, fixed‐number, and lower‐trigger strategies. Although immediate eradication still yielded the highest expected minimum prey population size, upper‐trigger harvest yielded the lowest probability of prey extinction and the greatest return on investment (as measured by improvement in expected minimum population size per amount spent). Upper‐trigger harvest was relatively successful because it operated when predator density was highest, which is when predator removal targets can be more easily met and the effect of predators on the prey is most damaging. This suggests that controlling predators only when they are most abundant is the “best” strategy when financial resources are limited and eradication is unlikely.     

On multiple objective optimization in aquatic ecosystems

Optimal control criteria and hierarchical dynamic control have been designed for a class of structural nonlinear predator-prey models (nutrient-herbivore-predator). The optimal open-loop control of the class of models considered is described. The optimal control design is realized using the hierarchical coordination strategies which are mathematically based on the gradient approach for the interaction prediction principle.     

Maximal yields from multispecies fisheries systems: rules for systems with multiple trophic levels.

Increasing centralization of the control of fisheries combined with increased knowledge of food-web relationships is likely to lead to attempts to maximize economic yield from entire food webs. With the exception of predator-prey systems, we lack any analysis of the nature of such yield-maximizing strategies. We use simple food-web models to investigate the nature of yield- or profit-maximizing exploitation of communities including two types of three-species food webs and a variety of six-species systems with as many as five trophic levels. These models show that, for most webs, relatively few species are harvested at equilibrium and that a significant fraction of the species is lost from the web. These extinctions occur for two reasons: (1) indirect effects due to harvesting of species that had positive effects on the extinct species, and (2) intentional eradication of species that are not themselves valuable, but have negative effects on more valuable species. In most cases, the yield-maximizing harvest involves taking only species from one trophic level. In no case was an unharvested top predator part of the yield-maximizing strategy. Analyses reveal that the existence of direct density dependence in consumers has a large effect on the nature of the optimal harvest policy, typically resulting in harvest of a larger number of species. A constraint that all species must be retained in the system (a "constraint of biodiversity conservation") usually increases the number of species and trophic levels harvested at the yield-maximizing policy. The reduction in total yield caused by such a constraint is modest for most food webs but can be over 90% in some cases. Independent harvesting of species within the web can also cause extinctions but is less likely to do so.     

Simulating conditions for the regulation of a moose population by Wolves

Computer simulations were used to explore how wolves could regulate moose populations in the presence or absence of hunting. In the model, vulnerability to predation varied with the age of the moose, and the numbers of animals killed per age-class were computed using the Nicholson-Bailey model. Vulnerability to hunting varied with sex and age of moose. Three possibilities were investigated: (a) when reproduction of both predator and prey were held constant; (b) when reproduction of wolves was directly related to winter survival; and (c) as for b, with the addition that wolves have access to garbage dumps in winter. The last set of hypotheses proved to be sufficient for the predator to regulate its prey.     

On Valuing Information in Adaptive‐Management Models

Abstract: Active adaptive management looks at the benefit of using strategies that may be suboptimal in the near term but may provide additional information that will facilitate better management in the future. In many adaptive‐management problems that have been studied, the optimal active and passive policies (accounting for learning when designing policies and designing policy on the basis of current best information, respectively) are very similar. This seems paradoxical; when faced with uncertainty about the best course of action, managers should spend very little effort on actively designing programs to learn about the system they are managing. We considered two possible reasons why active and passive adaptive solutions are often similar. First, the benefits of learning are often confined to the particular case study in the modeled scenario, whereas in reality information gained from local studies is often applied more broadly. Second, management objectives that incorporate the variance of an estimate may place greater emphasis on learning than more commonly used objectives that aim to maximize an expected value. We explored these issues in a case study of Merri Creek, Melbourne, Australia, in which the aim was to choose between two options for revegetation. We explicitly incorporated monitoring costs in the model. The value of the terminal rewards and the choice of objective both influenced the difference between active and passive adaptive solutions. Explicitly considering the cost of monitoring provided a different perspective on how the terminal reward and management objective affected learning. The states for which it was optimal to monitor did not always coincide with the states in which active and passive adaptive management differed. Our results emphasize that spending resources on monitoring is only optimal when the expected benefits of the options being considered are similar and when the pay‐off for learning about their benefits is large.     

Do yellow-bellied marmots respond to predator vocalizations?

We conducted four experiments to determine whether yellow-bellied marmots, Marmota flaviventris, discriminate among predator vocalizations, and if so, whether the recognition mechanism is learned or experience-independent. First, we broadcast to marmots the social sounds of coyotes, Canis latrans, wolves, Canis lupus, and golden eagles, Aquila chrysaetos, as well as conspecific alarm calls. Coyotes and eagles are extant predators at our study site, while wolves have been absent since the mid-1930s. In three follow-up experiments, we reversed the eagle call and presented marmots with forward and reverse calls to control for response to general properties of call structure rather than those specifically associated with eagles, we tested for novelty by comparing responses to familiar and unfamiliar birds, and we tested for the duration of predator sounds by comparing a wolf howl (that was much longer than the coyote in the first experiment) with a long coyote howl of equal duration to the original wolf. Marmots suppressed foraging and increased looking most after presentation of the conspecific alarm call and least after that of the coyote in the first experiment, with moderate responses to wolf and eagle calls. Marmots responded more to the forward eagle call than the reverse call, a finding consistent with a recognition template. Marmots did not differentiate vocalizations from the novel and familiar birds, suggesting that novelty itself did not explain our results. Furthermore, marmots did not differentiate between a wolf howl and a coyote howl of equal duration, suggesting that the duration of the vocalizations played a role in the marmots’ response. Our results show that marmots may respond to predators based solely on acoustic stimuli. The response to currently novel wolf calls suggests that they have an experience-independent ability to identify certain predators acoustically. Marmots’ response to predator vocalizations is not unexpected because 25 of 30 species in which acoustic predator discrimination has been studied have a demonstrated ability to respond selectively to cues from their predators.     

Evaluating the impact of caribou habitat restoration on predator and prey movement

Fragmentation of the boreal forest by linear features, including seismic lines, has destabilized predator–prey dynamics, resulting in the decline of woodland caribou (Rangifer tarandus caribou) populations. Restoration of human-altered habitat has therefore been identified as a critical management tool for achieving self-sustaining woodland caribou populations. However, only recently has testing of the response of caribou and other wildlife to restoration activities been conducted. Early work has centered around assessing changes in wildlife use of restored seismic lines. We evaluated whether restoration reduces the movement rates of predators and their associated prey, which is expected to decrease predator hunting efficiency and ultimately reduce caribou mortality. We developed a new method for using cameras to measure fine-scale movement by measuring speed as animals traveled between cameras in an array. We used our method to quantify speed of caribou, moose (Alces alces), bears (Ursus americanus), and wolves (Canis lupus) on treated (restored) and untreated seismic lines. Restoration treatments reduced travel speeds along seismic lines of wolves by 1.38 km/h, bears by 0.55 km/h, and caribou by 1.57 km/h, but did not reduce moose travel speeds. Reduced predator and caribou speeds on treated seismic lines are predicted to decrease encounter rates between predators and caribou and thus lower caribou kill rates. However, further work is needed to determine whether reduced movement rates result in reduced encounter rates with prey, and ultimately reduced caribou mortality.     

Biological interactions and environmental effects in the economics of pest control

The problem of pest control is tackled in a context of an ecosystem that consists of prey-predator populations with human interaction through pesticide application. The control, aimed at reducing pest damage, results in two undesirable external effects: reduction of beneficial predator population and environmental contamination. The untapped natural equilibrium is compared with equilibrium resulting from decentralized and centralized economic decision making. It is shown that, under certain conditions, myopic decision rules increase rather than decrease the pest damage. The “user cost” (or benefit) is shown to be crucial in determining the optimal centralized policy, and its relations to the various components of the system are analyzed. The components of the user cost are analyzed to determine the level of taxes or subsidies that will yield the optimal policy.     

Bioeconomic models of marine recreational fishing

The theory of recreational fishing is developed and conditions are derived for optimal management policy, with special attention given to functional relationships that must be empirically verified. Determinants of the optimal allocation between commercial and recreational fishing effort are derived. The theory is extended to include selected peculiar features of recreational fishing: Some anglers sell their catch; a small proportion of the fishing population accounts for a large proportion of the catch; and anglers throw back a fraction of what they catch. Optimal policies are derived under these more realistic conditions.     

Spatial and temporal changes in group dynamics and range use enable anti-predator responses in African buffalo

The reintroduction of large predators provides a framework to investigate responses by prey species to predators. Considerable research has been directed at the impact that reintroduced wolves (Canis lupus) have on cervids, and to a lesser degree, bovids, in northern temperate regions. Generally, these impacts alter feeding, activity, and ranging behavior, or combinations of these. However, there are few studies on the response of African bovids to reintroduced predators, and thus, there is limited data to compare responses by tropical and temperate ungulates to predator reintroductions. Using the reintroduction of lion (Panthera leo) into the Addo Elephant National Park (AENP) Main Camp Section, South Africa, we show that Cape buffalo (Syncerus caffer) responses differ from northern temperate ungulates. Following lion reintroduction, buffalo herds amalgamated into larger, more defendable units; this corresponded with an increase in the survival of juvenile buffalo. Current habitat preference of buffalo breeding herds is for open habitats, especially during the night and morning, when lion are active. The increase in group size and habitat preference countered initial high levels of predation on juvenile buffalo, resulting in a return in the proportion of juveniles in breeding herds to pre-lion levels. Our results show that buffalo responses to reintroduced large predators in southern Africa differ to those of northern temperate bovids or cervids in the face of wolf predation. We predict that the nature of the prey response to predator reintroduction is likely to reflect the trade-off between the predator selection and hunting strategy of predators against the life history and foraging strategies of each prey species.