Assessing the effects of pseudo-absences on predictive distribution model performance

Modelling species distributions with presence data from atlases, museum collections and databases is challenging. In this paper, we compare seven procedures to generate pseudo-absence data, which in turn are used to generate GLM-logistic regressed models when reliable absence data are not available. We use pseudo-absences selected randomly or by means of presence-only methods (ENFA and MDE) to model the distribution of a threatened endemic Iberian moth species (Graellsia isabelae). The results show that the pseudo-absence selection method greatly influences the percentage of explained variability, the scores of the accuracy measures and, most importantly, the degree of constraint in the distribution estimated. As we extract pseudo-absences from environmental regions further from the optimum established by presence data, the models generated obtain better accuracy scores, and over-prediction increases. When variables other than environmental ones influence the distribution of the species (i.e., non-equilibrium state) and precise information on absences is non-existent, the random selection of pseudo-absences or their selection from environmental localities similar to those of species presence data generates the most constrained predictive distribution maps, because pseudo-absences can be located within environmentally suitable areas. This study shows that if we do not have reliable absence data, the method of pseudo-absence selection strongly conditions the obtained model, generating different model predictions in the gradient between potential and realized distributions.     

Species distribution modelling—Effect of design and sample size of pseudo-absence observations

We explored the effect of varying pseudo-absence data in species distribution modelling using empirical data for four real species and simulated data for two imaginary species. In all analyses we used a fixed study area, a fixed set of environmental predictors and a fixed set of presence observations. Next, we added pseudo-absence data generated by different sampling designs and in different numbers to assess their relative importance for the output from the species distribution model. The sampling design strongly influenced the predictive performance of the models while the number of pseudo-absences had minimal effect on the predictive performance. We attribute much of these results to the relationship between the environmental range of the pseudo-absences (i.e. the extent of the environmental space being considered) and the environmental range of the presence observations (i.e. under which environmental conditions the species occurs). The number of generated pseudo-absences had a direct effect on the predicted probability, which translated to different distribution areas. Pseudo-absence observations that fell within grid cells with presence observations were purposely included in our analyses. We discourage the practice of excluding certain pseudo-absence data because it involves arbitrary assumptions about what are (un)suitable environments for the species being modelled.     

Habitat classification modeling with incomplete data: pushing the habitat envelope.

Habitat classification models (HCMs) are invaluable tools for species conservation, land-use planning, reserve design, and metapopulation assessments, particularly at broad spatial scales. However, species occurrence data are often lacking and typically limited to presence points at broad scales. This lack of absence data precludes the use of many statistical techniques for HCMs. One option is to generate pseudo-absence points so that the many available statistical modeling tools can bb used. Traditional techniques generate pseudo-absence points at random across broadly defined species ranges, often failing to include biological knowledge concerning the species-habitat relationship. We incorporated biological knowledge of the species-habitat relationship into pseudo-absence points by creating habitat envelopes that constrain the region from which points were randomly selected. We define a habitat envelope as an ecological representation of a species, or species feature's (e.g., nest) observed distribution (i.e., realized niche) based on a single attribute, or the spatial intersection of multiple attributes. We created HCMs for Northern Goshawk (Accipiter gentilis atricapillus) nest habitat during the breeding season across Utah forests with extant nest presence points and ecologically based pseudo-absence points using logistic regression. Predictor variables were derived from 30-m USDA Landfire and 250-m Forest Inventory and Analysis (FIA) map products. These habitat-envelope-based models were then compared to null envelope models which use traditional practices for generating pseudo-absences. Models were assessed for fit and predictive capability using metrics such as kappa, threshold-independent receiver operating characteristic (ROC) plots, adjusted deviance (D(adj)2), and cross-validation, and were also assessed for ecological relevance. For all cases, habitat envelope-based models outperformed null envelope models and were more ecologically relevant, suggesting that incorporating biological knowledge into pseudo-absence point generation is a powerful tool for species habitat assessments. Furthermore, given some a priori knowledge of the species-habitat relationship, ecologically based pseudo-absence points can be applied to any species, ecosystem, data resolution, and spatial extent.     

Invasive species distribution modeling (iSDM): Are absence data and dispersal constraints needed to predict actual distributions?

Species distribution models (SDMs) based on statistical relationships between occurrence data and underlying environmental conditions are increasingly used to predict spatial patterns of biological invasions and prioritize locations for early detection and control of invasion outbreaks. However, invasive species distribution models (iSDMs) face special challenges because (i) they typically violate SDM's assumption that the organism is in equilibrium with its environment, and (ii) species absence data are often unavailable or believed to be too difficult to interpret. This often leads researchers to generate pseudo-absences for model training or utilize presence-only methods, and to confuse the distinction between predictions of potential vs. actual distribution. We examined the hypothesis that true-absence data, when accompanied by dispersal constraints, improve prediction accuracy and ecological understanding of iSDMs that aim to predict the actual distribution of biological invasions. We evaluated the impact of presence-only, true-absence and pseudo-absence data on model accuracy using an extensive dataset on the distribution of the invasive forest pathogen Phytophthora ramorum in California. Two traditional presence/absence models (generalized linear model and classification trees) and two alternative presence-only models (ecological niche factor analysis and maximum entropy) were developed based on 890 field plots of pathogen occurrence and several climatic, topographic, host vegetation and dispersal variables. The effects of all three possible types of occurrence data on model performance were evaluated with receiver operating characteristic (ROC) and omission/commission error rates. Results show that prediction of actual distribution was less accurate when we ignored true-absences and dispersal constraints. Presence-only models and models without dispersal information tended to over-predict the actual range of invasions. Models based on pseudo-absence data exhibited similar accuracies as presence-only models but produced spatially less feasible predictions. We suggest that true-absence data are a critical ingredient not only for accurate calibration but also for ecologically meaningful assessment of iSDMs that focus on predictions of actual distributions.     

Selecting pseudo-absence data for presence-only distribution modeling: How far should you stray from what you know?

An important decision in presence-only species distribution modeling is how to select background (or pseudo-absence) localities for model parameterization. The selection of such localities may influence model parameterization and thus, can influence the appropriateness and accuracy of the model prediction when extrapolating the species distribution across time and space. We used 12 species from the Australian Wet Tropics (AWT) to evaluate the relationship between the geographic extent from which pseudo-absences are taken and model performance, and shape and importance of predictor variables using the MAXENT modeling method. Model performance is lower when pseudo-absence points are taken from either a restricted or broad region with respect to species occurrence data than from an intermediate region. Furthermore, variable importance (i.e., contribution to the model) changed such that, models became increasingly simplified, dominated by just two variables, as the area from which pseudo-absence points were drawn increased. Our results suggest that it is important to consider the spatial extent from which pseudo-absence data are taken. We suggest species distribution modeling exercises should begin with exploratory analyses evaluating what extent might provide both the most accurate results and biologically meaningful fit between species occurrence and predictor variables. This is especially important when modeling across space or time—a growing application for species distributional modeling.     

Landscape-level impact of tropical forest loss and fragmentation on bird occurrence in eastern Guatemala

Tropical forest destruction and fragmentation of habitat patches may reduce population persistence at the landscape level. Given the complex nature of simultaneously evaluating the effects of these factors on biotic populations, statistical presence/absence modelling has become an important tool in conservation biology. This study uses logistic regression to evaluate the independent effects of tropical forest cover and fragmentation on bird occurrence in eastern Guatemala. Logistic regression models were constructed for 10 species with varying response to habitat alteration. Predictive variables quantified forest cover, fragmentation and their interaction at three different radii (200, 500 and 1000 m scales) of 112 points where presence of target species was determined. Most species elicited a response to the 1000 m scale, which was greater than most species’ reported territory size. Thus, their presence at the landscape scale is probably regulated by extra-territorial phenomena, such as dispersal. Although proportion of forest cover was the most important predictor of species’ presence, there was strong evidence of area-independent and -dependent fragmentation effects on species presence, results that contrast with other studies from northernmost latitudes. Species’ habitat breadth was positively correlated with AIC model values, indicating a better fit for species more restricted to tropical forest. Species with a narrower habitat breadth also elicited stronger negative responses to forest loss. Habitat breadth is thus a simple measure that can be directly related to species’ vulnerability to landscape modification. Model predictive accuracy was acceptable for 4 of 10 species, which were in turn those with narrower habitat breadths.     

Species-specific tuning increases robustness to sampling bias in models of species distributions: An implementation with Maxent

Various methods exist to model a species’ niche and geographic distribution using environmental data for the study region and occurrence localities documenting the species’ presence (typically from museums and herbaria). In presence-only modelling, geographic sampling bias and small sample sizes represent challenges for many species. Overfitting to the bias and/or noise characteristic of such datasets can seriously compromise model generality and transferability, which are critical to many current applications - including studies of invasive species, the effects of climatic change, and niche evolution. Even when transferability is not necessary, applications to many areas, including conservation biology, macroecology, and zoonotic diseases, require models that are not overfit. We evaluated these issues using a maximum entropy approach (Maxent) for the shrew Cryptotis meridensis, which is endemic to the Cordillera de Mérida in Venezuela. To simulate strong sampling bias, we divided localities into two datasets: those from a portion of the species’ range that has seen high sampling effort (for model calibration) and those from other areas of the species’ range, where less sampling has occurred (for model evaluation). Before modelling, we assessed the climatic values of localities in the two datasets to determine whether any environmental bias accompanies the geographic bias. Then, to identify optimal levels of model complexity (and minimize overfitting), we made models and tuned model settings, comparing performance with that achieved using default settings. We randomly selected localities for model calibration (sets of 5, 10, 15, and 20 localities) and varied the level of model complexity considered (linear versus both linear and quadratic features) and two aspects of the strength of protection against overfitting (regularization). Environmental bias indeed corresponded to the geographic bias between datasets, with differences in median and observed range (minima and/or maxima) for some variables. Model performance varied greatly according to the level of regularization. Intermediate regularization consistently led to the best models, with decreased performance at low and generally at high regularization. Optimal levels of regularization differed between sample-size-dependent and sample-size-independent approaches, but both reached similar levels of maximal performance. In several cases, the optimal regularization value was different from (usually higher than) the default one. Models calibrated with both linear and quadratic features outperformed those made with just linear features. Results were remarkably consistent across the examined sample sizes. Models made with few and biased localities achieved high predictive ability when appropriate regularization was employed and optimal model complexity was identified. Species-specific tuning of model settings can have great benefits over the use of default settings.     

Combining a generic process-based productivity model and a statistical classification method to predict the presence and absence of tree species in the Pacific Northwest,U.S.A.

Although long-lived tree species experience considerable environmental variation over their life spans, their geographical distributions reflect sensitivity mainly to mean monthly climatic conditions. We introduce an approach that incorporates a physiologically based growth model to illustrate how a half-dozen tree species differ in their responses to monthly variation in four climatic-related variables: water availability, deviations from an optimum temperature, atmospheric humidity deficits, and the frequency of frost. Rather than use climatic data directly to correlate with a species’ distribution, we assess the relative constraints of each of the four variables as they affect predicted monthly photosynthesis for Douglas-fir, the most widely distributed species in the region. We apply an automated regression-tree analysis to create a suite of rules, which differentially rank the relative importance of the four climatic modifiers for each species, and provide a basis for predicting a species’ presence or absence on 3737 uniformly distributed U.S. Forest Services’ Forest Inventory and Analysis (FIA) field survey plots. Results of this generalized rule-based approach were encouraging, with weighted accuracy, which combines the correct prediction of both presence and absence on FIA survey plots, averaging 87%. A wider sampling of climatic conditions throughout the full range of a species’ distribution should improve the basis for creating rules and the possibility of predicting future shifts in the geographic distribution of species.     

Model based grouping of species across environmental gradients

We present a novel approach to the statistical analysis and prediction of multispecies data. The approach allows the simultaneous grouping and quantification of multiple species’ responses to environmental gradients. The underlying statistical model is a finite mixture model, where mixing is performed over the individual species’ responses to environmental gradients. Species with similar responses are grouped with minimal information loss. We term these groups species archetypes. Each species archetype has an associated GLM that can be used to predict distributions with appropriate measures of uncertainty. Initially, we illustrate the concept and method using artificial data and then with application to real data comprising 200 species from the Great Barrier Reef (GBR) lagoon on 13 oceanographic and geological gradients from 12°S to 24°S. The 200 species from the GBR are well represented by 15 species archetypes. The model is interpreted through maps of the probability of presence for a fine scale set of locations throughout the study area. Maps of uncertainty are also produced to provide statistical context. The presence of each species archetype was strongly influenced by oceanographic gradients, principally temperature, oxygen and salinity. The number of species in each group ranged from 4 to 34. The method has potential application to the analysis of multispecies distribution patterns and for multispecies management.     

An improved approach for identifying suitable habitat of Sambar Deer (Cervus unicolor Kerr) using ecological niche analysis and environmental categorization: Case study at Phu-Khieo Wildlife Sanctuary,Thailand

To assess habitat suitability (HS) has become an increasingly important component of species/ecosystem management. HS assessment is usually based on presence/absence data related to environmental variables. An exception is Ecological Niche Factor Analysis (ENFA), which uses only presence data and which does not require absence data. Most HS modelling is based on input of all environmental parameters (EnvPs) without environmental categorization, and does not take into account species interaction and human intervention for an assessment of HS. In this study, the EnvPs are arranged into four features: geographical features, consumable features, human-factor features, and species–human interaction features. These features affect species with respect to movement, behavior and activity. The research presented here has used an already existing dataset of wildlife species and human activities/visitations, which was compiled during 2004–2006 in Phu-Khieo Wildlife Sanctuary (PKWS). Data from 2004 to 2005 were used to produce HS maps, while the data of 2006 were used for evaluating these maps. Sambar Deer (SD) was chosen to predict its own HS. Six HS maps of SD were analyzed using ENFA in the following manner: (1) inputting all EnvPs together, (2) inputting each feature, separately and (3) integrating the four resulting HS maps by model averaging. It was found that model averaging was capable of predicting the HS of SD more reliably than the model with all EnvPs put in together. Multiple linear regressions were computed between the HS map with all EnvPs and the HS maps with each feature. The results show that the HS map with only geographical features has the highest coefficient value (0.516) while the coefficient values of other HS maps with the above features are 0.296, 0.53 and −0.006, respectively. This indicates that the geographical features have an influence on the other features and that the predicting power is lower when all EnvPs are computed in the ENFA model. Therefore, in order to generate HS, each feature should at first be put into the model separately. Following that, the average of all features will be combined.     

Pesticide prediction in ground water in North Carolina domestic wells using artificial neural networks

This paper illustrates the application of artificial neural networks (ANN) for prediction of pesticide occurrence in rural domestic wells from the available limited information. Among the three ANN models (a feed-forward back propagation [BP], a radial basis function [RBF] and an adaptive neural network-based fuzzy inference system [ANFIS]) employed for this investigation, the BP neural network was found to be superior to RBF and ANFIS type networks for the detection of pesticide occurrences in wells. For improved model prediction efficiency, optimization of network structure (e.g., number of hidden layers and number of nodes in each hidden layer) and spread (the width of the radial basis function) are important for BP and RBF type of network, respectively. A four layer BP network with a 3:2 neurons ratio of the first hidden layer to the second hidden layer produced better prediction performance efficiencies in terms of the pesticide detection efficiency (E_f), the root mean square error (RMSE), and the correlation coefficient (R) and the overall E_f of the BP neural network was found greater than 85%. Sensitivity analysis was performed to measure the relative importance of one input parameter over the other in pesticide occurrence in wells. It was shown in terms of the prediction efficiencies (E_f, RMSE, and R) of a four-layer BP neural network that the time of sample collection (TSC; month of the year), the depths of wells, and pesticide travel times (PTT) were more important parameters in the prediction of the pesticide occurrences in rural domestic wells. This means that the wells having shallow ground water table are more vulnerable to pesticide occurrence.     

An Adaptive‐Management Framework for Optimal Control of Hiking Near Golden Eagle Nests in Denali National Park

Abstract: Unintended effects of recreational activities in protected areas are of growing concern. We used an adaptive‐management framework to develop guidelines for optimally managing hiking activities to maintain desired levels of territory occupancy and reproductive success of Golden Eagles (Aquila chrysaetos) in Denali National Park (Alaska, U.S.A.). The management decision was to restrict human access (hikers) to particular nesting territories to reduce disturbance. The management objective was to minimize restrictions on hikers while maintaining reproductive performance of eagles above some specified level. We based our decision analysis on predictive models of site occupancy of eagles developed using a combination of expert opinion and data collected from 93 eagle territories over 20 years. The best predictive model showed that restricting human access to eagle territories had little effect on occupancy dynamics. However, when considering important sources of uncertainty in the models, including environmental stochasticity, imperfect detection of hares on which eagles prey, and model uncertainty, restricting access of territories to hikers improved eagle reproduction substantially. An adaptive management framework such as ours may help reduce uncertainty of the effects of hiking activities on Golden Eagles.     

GIS-based modeling of the geographic distribution of Quercus emoryi Torr. (Fagaceae) in México and identification of significant environmental factors influencing the species’ distribution

The greatest concentration of oak species in the world is believed to be found in Mexico. These species are potentially useful for reforestation because of their capacity to adapt to diverse environments. Knowledge of their geographic distribution and of species–environment relations is essential for decision-making in the management and conservation of natural resources. The objectives of this study were to develop a model of the distribution of Quercus emoryi Torr. in Mexico, using geographic information systems and data layers of climatic and other variables, and to determine the variables that significantly influence the distribution of the species. The study consisted of the following steps: (A) selection of the target species from a botanical scientific collection, (B) characterization of the collecting sites using images with values or categories of the variables, (C) model building with the overlay of images that meet the habitat conditions determined from the characterization of sites, (D) model validation with independent data in order to determine the precision of the model, (E) model calibration through adjustment of the intervals of some variables, and (F) sensitivity analysis using precision and concordance non-parametric statistics applied to pairs of images. Results show that the intervals of the variables that best describe the species’ habitat are the following: altitude from 1650 to 2750 amsl, slope from 0 to 66°; average minimum temperature of January from −12 to −3 °C; mean temperature of June from 11 to 25 °C; mean annual precipitation from 218 to 1225 mm; soil units: lithosol, eutric cambisol, haplic phaeozem, chromic luvisol, rendzina, luvic xerosol, mollic planosol, pellic vertisol, eutric regosol; type of vegetation: oak forest, oak–pine forest, pine forest, pine–oak forest, juniperus forest, low open forest, natural grassland and chaparral. The resulting model of the geographic distribution of Quercus emoryi in Mexico had the following values for non-parametric statistics of precision and agreement: Kappa index of 0.613 and 0.788, overall accuracy of 0.806 and 0.894, sensitivity of 0.650 and 0.825, specificity of 0.963, positive predictive value of 0.945 and 0.957 and negative predictive value of 0.733 and 0.846. Results indicate that the variable average minimum temperature of January, with a maximum value of −3 °C, is an important factor in limiting the species’ distribution.     

Comparing discriminant analysis, neural networks and logistic regression for predicting species distributions: a case study with a Himalayan river bird

We assessed the occurrence of a common river bird, the Plumbeous Redstart Rhyacornis fuliginosus, along 180 independent streams in the Indian and Nepali Himalaya. We then compared the performance of multiple discrimant analysis (MDA), logistic regression (LR) and artificial neural networks (ANN) in predicting this species’ presence or absence from 32 variables describing stream altitude, slope, habitat structure, chemistry and invertebrate abundance. Using the entire data (=training set) and a threshold for accepting presence in ANN and LR set to P≥0.5, ANN correctly classified marginally more cases (88%) than either LR (83%) or MDA (84%). Model performance was assessed from two methods of data partitioning. In a ‘leave-one-out’ approach, LR correctly predicted more cases (82%) than MDA (73%) or ANN (69%). However, in a holdout procedure, all the methods performed similarly (73–75%). All methods predicted true absence (i.e. specificity in holdout: 81–85%) better than true presence (i.e. sensitivity: 57–60%). These effects reflect species’ prevalence (=frequency of occurrence), but are seldom considered in distribution modelling. Despite occurring at only 36% of the sites, Plumbeous Redstarts are one of the most common Himalayan river birds, and problems will be greater with less common species. Both LR and ANN require an arbitrary threshold probability (often P=0.5) at which to accept species presence from model prediction. Simulations involving varied prevalence revealed that LR was particularly sensitive to threshold effects. ROC plots (received operating characteristic) were therefore used to compare model performance on test data at a range of thresholds; LR always outperformed ANN. This case study supports the need to test species’ distribution models with independent data, and to use a range of criteria in assessing model performance. ANN do not yet have major advantages over conventional multivariate methods for assessing bird distributions. LR and MDA were both more efficient in the use of computer time than ANN, and also more straightforward in providing testable hypotheses about environmental effects on occurrence. However, LR was apparently subject to chance significant effects from explanatory variables, emphasising the well-known risks of models based purely on correlative data.     

Different escape tactics of two vole species affect the success of the hunting predator, the least weasel

In the ongoing evolutionary arms race between predators and their prey, successful escape from the predator leads to the evolution of improved escape tactics in prey, but also predators become more effective in following and attacking the prey. Antipredatory behavior of prey is considered to be the strongest towards their most dangerous predators. However, prey species can differ both in vulnerability and efficiency of escape to a shared predator. We studied escape reactions of two vole species, the bank vole (Myodes glareolus) and the field vole (Microtus agrestis), under a simulated predation risk of the least weasel (Mustela nivalis nivalis). We conducted a laboratory experiment where a vole was given a possibility to escape from a weasel by fleeing to a horizontal tunnel or climbing the tree. Subsequently to the vole escape decision, we released a weasel to the same tunnel system to test how the weasel succeeded in following the vole. Weasel presence changed the behavior of voles as especially bank voles escaped by climbing. Instead, the majority of field voles fled into the ground-layer tunnel. The different escape tactics of the voles affected the success of the weasel, because climbing voles were less often successfully followed. We suggest that the difference in escape tactics has evolved as an adaptation to different habitats; meadow-exploiting field voles using ground-level escape while bank voles living in three-dimensional forest habitat frequently use arboreal escape tactics. This is likely to lead to different habitat-dependent vulnerabilities to predation in Microtus and Myodes vole species.     

Population dynamics of splitnose rockfish (Sebastes diploproa) in the Northeast Pacific Ocean

We developed an age-structured population model of splitnose rockfish, Sebastes diploproa, in the Northeast Pacific Ocean. Splitnose rockfish is a bycatch species that co-occurs with several commercially important species that are currently declared overfished. Bycatch species are typically not the focus of stock assessment efforts because of their limited economic importance, but they may suffer the same population declines as species with which they co-occur. To examine the dynamics of splitnose rockfish for the first time, we analyzed data from three groundfish fisheries and four research surveys conducted in the Northeast Pacific Ocean. To develop a model, we used Stock Synthesis, a statistical framework for the construction of a population dynamics models utilizing both fishery-dependent and fishery-independent data. In the model, we reconstructed the total catch of the species back to 1900, estimated the dynamics of the stock spawning output and recruitment and evaluated biomass depletion relative to the stock's unfished state, as well as sources of uncertainty in model outputs. The results indicate that the splitnose rockfish is currently not overfished even though it has experienced several periods of abrupt decline in its biomass. Revisiting age data from earlier years, monitoring fishery discard, and investigating the spatial dynamics of splitnose rockfish is important to further improve the understanding of this species’ population dynamics, and decrease uncertainty in model results.     

Deer herbivory alters forest response to canopy decline caused by an exotic insect pest.

Hemlock woolly adelgid (HWA; Adelges tsugae) infestations have resulted in the continuing decline of eastern hemlock (Tsuga canadensis) throughout much of the eastern United States. While the initial impacts of HWA infestations have been documented, our understanding of forest response to this disturbance remains incomplete. HWA infestation is not occurring in isolation but within a complex ecological context. The role of potentially important interacting factors, such as elevated levels of white-tailed deer herbivory, is poorly understood. Despite the potential for herbivory to alter forest successional trajectories following a canopy disturbance, little is known about herbivory-disturbance interactions, and herbivory is rarely considered in assessing forest response to a co-occurring disturbance. We used repeated censuses of deer exclosures and paired controls (400 paired plots) to quantify the impact of deer herbivory on tree seedling species abundance in 10 eastern hemlock ravines that span a gradient in HWA-induced canopy decline severity. Use of a maximum likelihood estimation framework and information theoretics allowed us to quantify the strength of evidence for alternative models developed to estimate the impacts of herbivory on tree seedling abundance as a function of varying herbivore density and canopy decline severity. The exclusion of deer herbivory had marked impacts on the abundance of the studied seedling species: Acer rubrum, Acer saccharum, Betula lenta, Nyssa sylvatica, Quercus montana, and Tsuga canadensis. For all six species, the relationship between seedling abundance and deer density was either exponential or saturating. Although the functional form of the response varied among seedling species, the inclusion of both deer density and canopy decline severity measures consistently resulted in models with substantially greater support. Canopy decline resulted in higher proportional herbivory impacts and altered the ranking of herbivory impacts by seedling species. Our results suggest that, by changing species' competitive abilities, white-tailed deer herbivory alters the trajectory of forest response to this exotic insect pest and has the potential to shift future overstory composition.     

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.