Optimization model for a wolf-ungulate system

Public outcries against predator control create a need to devise management policies that optimally balance the cost (managerial and environmental) of predator control against the benefit of ungulate harvesting. To address this problem, an optimization procedure utilizing stochastic dynamic programming is described. Through this approach, optimal feedback strategies for a wolf-ungulate system in Alaska are estimated. The dynamic predator-prey model used in the analysis is based on parameter estimates from data collected over an eight-year period in Denali (Mt. McKinley) National Park. Stability analysis of the system revealed that stability properties depend on predator search efficiency. The effects of random fluctuations in winter severity and alternative objective functions are considered in the estimation of optimal feedback strategies. Optimal moose harvesting strategies appear to be dependent on wolf control costs. If no wolf control cost is assessed, optimal moose harvest is independent of wolf density. Optimal wolf control strategies are completely insensitive to moose density. The strategies are compared to current and simplified management policies.     

Uncertainty in age-specific harvest estimates and consequences for white-tailed deer management

Age structure proportions (proportion of harvested individuals within each age class) are commonly used as support for regulatory restrictions and input for deer population models. Such use requires critical evaluation when harvest regulations force hunters to selectively harvest specific age classes, due to impact on the underlying population age structure. We used a stochastic population simulation model to evaluate the impact of using harvest proportions to evaluate changes in population age structure under a selective harvest management program at two scales. Using harvest proportions to parameterize the age-specific harvest segment of the model for the local scale showed that predictions of post-harvest age structure did not vary dependent upon whether selective harvest criteria were in use or not. At the county scale, yearling frequency in the post-harvest population increased, but model predictions indicated that post-harvest population size of 2.5 years old males would decline below levels found before implementation of the antler restriction, reducing the number of individuals recruited into older age classes. Across the range of age-specific harvest rates modeled, our simulation predicted that underestimation of age-specific harvest rates has considerable influence on predictions of post-harvest population age structure. We found that the consequence of uncertainty in harvest rates corresponds to uncertainty in predictions of residual population structure, and this correspondence is proportional to scale. Our simulations also indicate that regardless of use of harvest proportions or harvest rates, at either the local or county scale the modeled SHC had a high probability (>0.60 and >0.75, respectively) of eliminating recruitment into >2.5 years old age classes. Although frequently used to increase population age structure, our modeling indicated that selective harvest criteria can decrease or eliminate the number of white-tailed deer recruited into older age classes. Thus, we suggest that using harvest proportions for management planning and evaluation should be viewed with caution. In addition, we recommend that managers focus more attention on estimation of age-specific harvest rates, and modeling approaches which combine harvest rates with information from harvested individuals to further increase their ability to effectively manage deer populations under selective harvest programs.     

Optimal control of Atlantic population Canada geese

Management of Canada geese (Branta canadensis) can be a balance between providing sustained harvest opportunity while not allowing populations to become overabundant and cause damage. In this paper, we focus on the Atlantic population of Canada geese and use stochastic dynamic programming to determine the optimal harvest strategy over a range of plausible models for population dynamics. There is evidence to suggest that the population exhibits significant age structure, and it is possible to reconstruct age structure from surveys. Consequently the harvest strategy is a function of the age composition, as well as the abundance, of the population. The objective is to maximize harvest while maintaining the number of breeding adults in the population between specified upper and lower limits. In addition, the total harvest capacity is limited and there is uncertainty about the strength of density-dependence. We find that under a density-independent model, harvest is maximized by maintaining the breeding population at the highest acceptable abundance. However if harvest capacity is limited, then the optimal long-term breeding population size is lower than the highest acceptable level, to reduce the risk of the population growing to an unacceptably large size. Under the proposed density-dependent model, harvest is maximized by maintaining the breeding population at an intermediate level between the bounds on acceptable population size; limits to harvest capacity have little effect on the optimal long-term population size. It is clear that the strength of density-dependence and constraints on harvest significantly affect the optimal harvest strategy for this population. Model discrimination might be achieved in the long term, while continuing to meet management goals, by adopting an adaptive management strategy.     

Demographic Effects of Harvesting Epiphytic Bromeliads and an Alternative Approach to Collection

Abstract: Hundreds of epiphytic bromeliads species are harvested from the wild for trade and for cultural uses, but little is known about the effects of this harvest. We assessed the potential demographic effects of harvesting from the wild on 2 epiphytic bromeliads: Tillandsia macdougallii, an atmospheric bromeliad (adsorbs water and nutrients directly from the atmosphere), and T. violaceae, a tank bromeliad (accumulates water and organic material between its leaves). We also examined an alternative to harvesting bromeliads from trees—the collection of fallen bromeliads from the forest floor. We censused populations of T. macdougallii each year from 2005 to 2010 and of T. violaceae from 2005 to 2008, in Oaxaca, Mexico. We also measured monthly fall rates of bromeliads over 1 year and monitored the survival of fallen bromeliads on the forest floor. The tank bromeliad had significantly higher rates of survival, reproduction, and stochastic population growth rates (λ_s) than the atmospheric bromeliad, but λ_s for both species were <1, which suggests that the populations will decline even without harvest. Elasticity patterns differed between species, but in both, survival of large individuals had high elasticity values. No fallen bromeliads survived more than 1.5 years on the forest floor and the rate of bromeliad fall was comparable to current harvest rates. Low rates of population growth recorded for the species we studied and other epiphytic bromeliads and high elasticity values for the vital rates that were most affected by harvest suggest that commercial harvesting in the wild of these species is not sustainable. We propose the collection of fallen bromeliads as an ecologically and, potentially, economically viable alternative.     

Interactive Effects of Harvest and Deer Herbivory on the Population Dynamics of American Ginseng

Abstract:  Few demographic models for any species consider the role of multiple, interacting ecological threats. Many forest herbs are heavily browsed by white-tailed deer ( Odocoileus virginianus ) and a number of these are also harvested for the medicinal, floral, or horticultural trades. Previous studies of the viability of American ginseng ( Panax quinquefolius ) have separately examined the effects of harvesting and deer herbivory. We followed individually marked ginseng plants in 6 populations for 8 years and documented deer browse levels, conducted helicopter surveys to estimate the deer herd size, and documented 2 ginseng harvests. We used this long-term data set to develop a stochastic demographic model that quantified the separate and interactive role of these threats to ginseng viability. Although harvesting and deer herbivory negatively affected ginseng population growth, their effects were not additive. Deer herbivory negatively affected population growth in the absence but not in the presence of harvesting. Life table response experiments revealed that in the presence of harvesting, deer herbivory had some positive effects on vital rates because browsed plants were less apparent to harvesters. Ginseng populations that were harvested responsibly (i.e., planting seeds from harvested individuals) had higher growth rates than those that were harvested irresponsibly. We concluded that both deer populations and harvesting must be managed to ensure sustainable populations of American ginseng. Our findings underscore the importance of long-term monitoring to assess threats to viability and the need for a broad ecological understanding of the complexity of ecosystem management.     

Habitat and population modelling of roe deer using an interactive geographic information system

Management of German roe deer (Capreolus capreolus) populations is a challenge for wildlife managers and foresters because population densities are difficult to estimate in forests and forest regeneration can be negatively affected when roe deer density is high. We describe a model to determine deer population densities compatible with forest management goals, and to assess harvest rates necessary to maintain desired deer densities. A geographic information system (GIS) was used to model wildlife habitat and population dynamics over time. Our model interactively incorporates knowledge of field biologists and foresters via a graphical user interface (GUI). Calibration of the model with deer damage maps allowed us to evaluate density dependence of a roe deer population. Incorporation of local knowledge into temporally dynamic and spatial models increases understanding of population dynamics and improves wildlife management.     

Mathematical modelling of the Ibera Caiman yacaré

A non-linear age structured model is presented for the Ibera Caiman yacaré population. We consider the placement of the nests (related to the temperature in the nest) as the determining factor for the sex of the hatchlings. The dynamical behavior and the effects of management strategies as harvest and eggs collection are studied through numerical simulation.     

Seasonal density dependence, timing of mortality, and sustainable harvesting

Birth-pulse populations are often characterized with discrete-time models, that use a single function to relate the post-breeding population size to the post-breeding size of the previous year. Recently, models of seasonal density dependence have been constructed that emphasize interactions during shorter time periods also. Here, we study two very simple forms of density-dependent mortality, that lead to Ricker and Beverton-Holt type population dynamics when viewed over the whole year. We explore the consequences of harvest timing to equilibrium population sizes under such density dependence. Whether or not individual mortality compensates for the harvested quota, the timing of harvesting has a strong impact on the sustainability of a harvesting quota. Further, we show that careless discretization of a continuous mortality scheme may seriously underestimate the reduction in population size caused by hunting and overestimate the sustainable yield. We also introduce the concept of the demographic value of an individual, which reflects the expected contribution to population size over time in the presence of density dependence. Finally, we discuss the possibility of calculating demographic values as means of optimizing harvest strategies. Here, a Pareto optimal harvest strategy will minimize the loss of demographic value from the population for a given yield.     

Exploiting sea otter populations: A simulation analysis

We used a Leslie matrix population model to investigate the impact of a range of harvest rates proposed for Alaskan sea otters (Enhydra lutris). The simulation included an analysis of several population mechanisms that might be important in the natural regulation of sea otter populations or in their reactions to harvesting. Significant differences in equilibrium population levels were found between compensatory mechanisms when fixed harvest rates were applied for 25-year periods. Adult harvests set at 2 and 4% of the total population showed that new stable population levels were rapidly attained. Harvest rates of 8 and 10%, however, resulted in marked population declines in simulated harvests. This analysis demonstrates that limited harvesting can be sustained by the population and that otter population compensation responses will be a critical determinant of sustainable harvest rates of sea otter populations.     

A Real Options Approach to the Valuation of a Forestry Investment

The theory of real options is used to model the optimal tree harvesting decision. The value of the option to harvest is estimated using a dynamic programming approach and a general numerical solution technique suitable for any type of stochastic process for prices. The conditions under which the optimal harvest time is independent of price are examined. In addition, the impact of assuming future lumber prices are mean reverting is considered. It is found that option value and optimal cutting time are significantly different under the mean reversion assumption compared to geometric Brownian motion.     

Optimal monitoring and control under state uncertainty: Application to lionfish management

State variables in many renewable resource management problems, such as the abundance of a fish stock, are imperfectly observed over time. In systems characterized by state uncertainty, decision makers often invest in monitoring to learn about the level of a stock. We develop a stochastic bioeconomic model of marine invasive species management under state uncertainty. The decision maker in our model simultaneously evaluates optimal investment in monitoring and population control. Using a recently-devised method for solving continuous-state Partially Observable Markov Decision Processes (POMDPs), we find that the ability to learn through monitoring can alter the role of population control in the optimal policy function, for example by reducing control intensity in favor of monitoring. Optimal monitoring depends on the management context, including in our application lionfish population structure. The rich transient dynamics of our model depend critically on the relationship between the initial conditions for information and invader abundance.     

A simulation model for the management of vicuña populations

The population dynamics of the vicuña was modelled based on field data from the Central Galeras Sector, Perú. Rains were simulated in order to obtain net primary productivity and grass availability which act upon density-dependent fecundity and mortality. The model produces a population growth curve that tends to stabilize at densities around 100 vicuñas per km². Harvest and shearing processes were simulated as part of the vicuña population management model. Harvest was based upon a fixed threshold density D_e below which no harvest occurs; for densities above D_e harvesting is applied at a rate proportional to the difference between D_e and the current population density (fixed escapement or ‘bang-bang’ harvest rule). Management optimization was analyzed by determining the optimal escapement density D_e, which maximized either net profits or the number of animals harvested. Analyzing the results as cumulative totals over 20 years of simulation, an optimum harvest production was obtained for a D_e of about 40 vicuñas per km², and maximum profit was obtained for a D_e around 70 vicuñas per km². Analyzing the results of 20 years of simulation as annual averages with an original population density of 40 vicuñas per km², the harvest production and profits were maximized for a D_e of 40 and 60 vicuñas per km², respectively.The model was validated using data from the Reserva Nacional San Guillermo, Argentina, where vicuña and guanaco populations coexist (although their interaction was not modelled). The sensitivity analysis was performed with three different techniques: (a) stepwise multiple linear regression, (b) visual graphic analysis based on a polar coordinates system, and (c) direct evaluation of the effect on management decisions. The curve shape parameters of the fecundity and mortality functions proved to be the most important ones in determining the outcome of the model.     

Optimal escapement levels in stochastic and deterministic harvesting models

A constant-escapement feedback policy is shown to be optimal in maximizing expected discounted net revenue from an animal resource whose dynamics are described by a stochastic stock-recruitment model, provided that unit harvesting costs satisfy certain conditions. The optimal escapement in this model is compared with that in the corresponding deterministic model and it is shown how the way in which unit harvesting costs vary with population abundance can be important in determining the relative sizes of the optimal escapements. In most cases, the optimal stochastic escapement is no less than the optimal deterministic escapement.     

Effects of Harvest of Nontimber Forest Products and Ecological Differences between Sites on the Demography of African Mahogany

Abstract: The demographic impacts of harvesting nontimber forest products (NTFP) have been increasingly studied because of reports of potentially unsustainable harvest. Nevertheless, our understanding of how plant demographic response to harvest is altered by variation in ecological conditions, which is critical for developing realistic sustainable‐use plans, is limited. We built matrix population models to test whether and how variation in ecological conditions affects population responses to harvest. In particular, we examined the effect of bark and foliage harvest on the demography of populations of African mahogany (Khaya senegalensis) in two contrasting ecological regions of Benin, West Africa. K. senegalensis bark and foliage harvest significantly reduced its stochastic population growth rates, but ecological differences between regions had a greater effect on population growth rates than did harvest. The effect of harvest on population growth rates (Δλ) was slightly stronger in the moist than in the drier region. Life‐table response experiments revealed that the mechanism by which harvesting reduced λ differed between ecological regions. Lowered stasis (persistence) of larger life stages lead to a reduction in λ in the drier region, whereas lowered growth of all life stages lowered λ in moist region. Potential strategies to increase population growth rates should include decreasing the proportion of individuals harvested, promoting harvester‐owned plantations of African mahogany, and increasing survival and growth by promoting no‐fire zones in gallery forests. Our results show how population responses to harvest of NTFP may be altered by ecological differences across sites and emphasize the importance of monitoring populations over the climatic range in which they occur to develop more realistic recommendations for conservation.     

Modeling the Effects of Trophy Selection and Environmental Disturbance on a Simulated Population of African Lions

Abstract:  Tanzania is a premier destination for trophy hunting of African lions (Panthera leo) and is home to the most extensive long-term study of unhunted lions. Thus, it provides a unique opportunity to apply data from a long-term field study to a conservation dilemma: How can a trophy-hunted species whose reproductive success is closely tied to social stability be harvested sustainably? We used an individually based, spatially explicit, stochastic model, parameterized with nearly 40 years of behavioral and demographic data on lions in the Serengeti, to examine the separate effects of trophy selection and environmental disturbance on the viability of a simulated lion population in response to annual harvesting. Female population size was sensitive to the harvesting of young males (≥3 years), whereas hunting represented a relatively trivial threat to population viability when the harvest was restricted to mature males (≥6 years). Overall model performance was robust to environmental disturbance and to errors in age assessment based on nose coloration as an index used to age potential trophies. Introducing an environmental disturbance did not eliminate the capacity to maintain a viable breeding population when harvesting only older males, and initially depleted populations recovered within 15–25 years after the disturbance to levels comparable to hunted populations that did not experience a catastrophic event. These results are consistent with empirical observations of lion resilience to environmental stochasticity .     

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.     

Examining the effects of alternative management strategies on landscape-scale forest patterns in northeastern Minnesota using LANDIS

Spatial modeling of forest patterns can provide information on the potential impact of various management strategies on large landscapes over long time frames. We used LANDIS, a stochastic, spatially-explicit, ecological landscape model to simulate 120 years of forest change on the Nashwauk Uplands, a 328,000 ha landscape in northeastern Minnesota that lies in the transition between boreal and temperate forests. We ran several forest management scenarios including current harvesting practices, no harvests, varied rotation ages, varied clearcut sizes, clustered clearcuts, and landowner coordination. We examined the effects of each scenario on spatial patterns of forests by covertype, age class, and mean and distribution of patch sizes. All scenarios reveal an increase in the spruce-fir (Picea-Abies) covertype relative to the economically paramount aspen-birch (Populus-Betula) covertype. Our results also show that most covertypes occur in mostly small patches <5 ha in size and the ability of management to affect patch size is limited by the highly varied physiography and landuse patterns on the landscape. However, coordination among landowners, larger clearcuts, and clustered clearcuts were all predicted to increase habitat diversity by creating some larger patches and older forest patches. These three scenarios along with the no harvest scenario also create more old forest than current harvesting practices, by concentrating harvesting on some portion of the landscape. The no harvest scenario retained large, fire-regenerated aspen-birch patches. Harvests fragment large aspen-birch patches by changing the age structure and releasing the shade-tolerant understory species. More sapling forest, and larger sapling patches resulted from the shortened rotation scenario.     

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.     

A method to estimate pre-exploitation population size

Antarctic fur seals (Arctocephalus gazella) were commercially exploited on the subantarctic island of South Georgia for over 100 years and nearly driven to extinction. Since the cessation of harvesting, however, their populations have rebounded, and they are now often considered a nuisance species whose impact on the terrestrial landscape should be mitigated. Any evaluation of their current population requires the context provided by their historic, pre-exploitation abundance, lest ecologists fall prey to shifting baseline syndrome in which their perspective on current abundance is compared only with an altered state resulting from past anthropogenic disturbance. Estimating pre-exploitation abundance is critical to defining species recovery and setting recovery targets, both of which are needed for the International Union for the Conservation of Nature's recent efforts to develop a green list of recovering species. To address this issue, we reconstructed the South Georgia fur seal harvest from 1786 to 1908 from ship logbooks and other historical records and interpolated missing harvest data as necessary with a generalized linear model fit to the historical record. Using an approximate Bayesian computation framework, harvest data, and a stochastic age-structured population model, we estimated the pre-exploitation abundance of Antarctic fur seals on South Georgia was 2.5 million females (95% CI 1.5–3.5 million). This estimate is similar to recent abundance estimates, and suggests current populations, and the ecological consequences of so many fur seals on the island, may be similar to conditions prior to human harvest. Although the historic archive on the fur sealing era is unavoidably patchy, the use of archival records is essential for reconstructing the past and, correspondingly, to understanding the present. Article impact statement: Defining species recovery requires an understanding of baseline population state, which can be estimated through statistical methods.