Considering ecological dynamics in resource selection functions

1.  Describing distribution and abundance is requisite to exploring interactions between organisms and their environment. Recently, the resource selection function (RSF) has emerged to replace many of the statistical procedures used to quantify resource selection by animals.
2.  A RSF is defined by characteristics measured on resource units such that its value for a unit is proportional to the probability of that unit being used by an organism. It is solved using a variety of techniques, particularly the binomial generalized linear model.
3.  Observing dynamics in a RSF – obtaining substantially different functions at different times or places for the same species – alerts us to the varying ecological processes that underlie resource selection.
4.  We believe that there is a need for us to reacquaint ourselves with ecological theory when interpreting RSF models. We outline a suite of factors likely to govern ecologically based variation in a RSF. In particular, we draw attention to competition and density-dependent habitat selection, the role of predation, longitudinal changes in resource availability and functional responses in resource use.
5.  How best to incorporate governing factors in a RSF is currently in a state of development; however, we see promise in the inclusion of random as well as fixed effects in resource selection models, and matched case–control logistic regression.
6.  Investigating the basis of ecological dynamics in a RSF will allow us to develop more robust models when applied to forecasting the spatial distribution of animals. It may also further our understanding of the relative importance of ecological interactions on the distribution and abundance of species.     

Accuracy of resource selection functions across spatial scales

Resource selection functions (RSFs) can be used to map suitable habitat of a species based on predicted probability of use. The spatial scale may affect accuracy of such predictions. To provide guidance as to which spatial extent or grain is appropriate and most accurate for animals, we used the concept of hierarchical selection orders to dictate extent and grain. We conducted a meta-analysis from 123 RSF studies of 886 species to identify differences in prediction success that might be expected for five selection orders. Many studies do not constrain spatial extent to the grain of the next broader selection order in the hierarchy, mixing scaling effects. Thus, we also compared accuracy of single- vs. multiple-grain RSFs developed at the unconstrained extent of an entire study area. Results suggested that the geographical range of a species was the easiest to predict of the selection orders. At smaller scales within the geographical range, use of a site was easier to predict when environmental variables were measured at a grain equivalent to the home-range size or a microhabitat feature required for reproduction or resting. Selection of patches within home ranges and locations of populations was often more difficult to predict. Multiple-grain RSFs were more predictive than single-grain RSFs when the entire study area was considered available. Models with variables measured at both small and large (> 100 ha) grains were usually most predictive, even for many species with small home ranges. Multiple-grain models may be particularly important for species with moderate dispersal abilities in habitat fragments surrounded by an unsuitable matrix. We recommend studies should no longer address only one grain to map animal species distributions.     

A machine‐learning approach for extending classical wildlife resource selection analyses

Resource selection functions (RSFs) are tremendously valuable for ecologists and resource managers because they quantify spatial patterns in resource utilization by wildlife, thereby facilitating identification of critical habitat areas and characterizing specific habitat features that are selected or avoided. RSFs discriminate between known‐use resource units (e.g., telemetry locations) and available (or randomly selected) resource units based on an array of environmental features, and in their standard form are performed using logistic regression. As generalized linear models, standard RSFs have some notable limitations, such as difficulties in accommodating nonlinear (e.g., humped or threshold) relationships and complex interactions. Increasingly, ecologists are using flexible machine‐learning methods (e.g., random forests, neural networks) to overcome these limitations. Herein, we investigate the seasonal resource selection patterns of mule deer (Odocoileus hemionus) by comparing a logistic regression framework with random forest (RF), a popular machine‐learning algorithm. Random forest (RF) models detected nonlinear relationships (e.g., optimal ranges for slope and elevation) and complex interactions which would have been very challenging to discover and characterize using standard model‐based approaches. Compared with standard RSF models, RF models exhibited improved predictive skill, provided novel insights about resource selection patterns of mule deer, and, when projected across a relevant geographic space, manifested notable differences in predicted habitat suitability. We recommend that wildlife researchers harness the strengths of machine‐learning tools like RF in addition to “classical” tools (e.g., mixed‐effects logistic regression) for evaluating resource selection, especially in cases where extensive telemetry data sets are available.     

蓝冠噪鹛繁殖期生境选择特征分析

2013年至2015年每年4—7月,在江西婺源境内对蓝冠噪鹛繁殖小群进行调查。观察并测量其繁殖地斑块海拔,距山地、水源及干扰源的距离,计算斑块面积、周长及形状指数,并在每个繁殖斑块的4个方向5km以外选取同样植被类型的对照斑块,比较繁殖斑块与对照斑块在以上7个因子的差异。结果表明繁殖斑块海拔,距山地距离和距干扰距离显著小于对照斑块。说明在斑块尺度上,蓝冠噪鹛繁殖期倾向于选择低海拔阔叶林,且在离山地更近的村庄附近繁殖,这可能与食物丰富和天敌较少有关。在微生境尺度,选择繁殖点B在巢区及同一片阔叶林中无噪鹛筑巢的对照区进行10个生态因子的测量,并用资源选择函数以及Vanderploeg和Scavia选择系数进行分析。资源选择函数结果表明草本密度、草本高度在微生境尺度对蓝冠噪鹛生境选择贡献最大;而Vanderploeg和Scavia选择系数结果表明蓝冠噪鹛喜在胸径较粗(40—80cm)的朴树、枫杨和枫香3种树上筑巢,筑巢偏好树高20m以上及草本盖度较高(60%—90%)的生境。综合两种分析结果,在微生境尺度蓝冠噪鹛对筑巢树种及高度具有选择性,对巢区隐蔽性有所要求,巢下草本情况可以反映昆虫等食物资源状况,说明蓝冠噪鹛繁殖期偏好在食物相对丰富的区域筑巢。     

Estimating resource selection with count data

Resource selection functions (RSFs) are typically estimated by comparing covariates at a discrete set of “used” locations to those from an “available” set of locations. This RSF approach treats the response as binary and does not account for intensity of use among habitat units where locations were recorded. Advances in global positioning system (GPS) technology allow animal location data to be collected at fine spatiotemporal scales and have increased the size and correlation of data used in RSF analyses. We suggest that a more contemporary approach to analyzing such data is to model intensity of use, which can be estimated for one or more animals by relating the relative frequency of locations in a set of sampling units to the habitat characteristics of those units with count‐based regression and, in particular, negative binomial (NB) regression. We demonstrate this NB RSF approach with location data collected from 10 GPS‐collared Rocky Mountain elk (Cervus elaphus) in the Starkey Experimental Forest and Range enclosure. We discuss modeling assumptions and show how RSF estimation with NB regression can easily accommodate contemporary research needs, including: analysis of large GPS data sets, computational ease, accounting for among‐animal variation, and interpretation of model covariates. We recommend the NB approach because of its conceptual and computational simplicity, and the fact that estimates of intensity of use are unbiased in the face of temporally correlated animal location data.     

Using multilevel models to quantify heterogeneity in resource selection

Models of resource selection are being used increasingly to predict or model the effects of management actions rather than simply quantifying habitat selection. Multilevel, or hierarchical, models are an increasingly popular method to analyze animal resource selection because they impose a relatively weak stochastic constraint to model heterogeneity in habitat use and also account for unequal sample sizes among individuals. However, few studies have used multilevel models to model coefficients as a function of predictors that may influence habitat use at different scales or quantify differences in resource selection among groups. We used an example with white-tailed deer (Odocoileus virginianus) to illustrate how to model resource use as a function of distance to road that varies among deer by road density at the home range scale. We found that deer avoidance of roads decreased as road density increased. Also, we used multilevel models with sika deer (Cervus nippon) and white-tailed deer to examine whether resource selection differed between species. We failed to detect differences in resource use between these two species and showed how information-theoretic and graphical measures can be used to assess how resource use may have differed. Multilevel models can improve our understanding of how resource selection varies among individuals and provides an objective, quantifiable approach to assess differences or changes in resource selection. © 2011 The Wildlife Society.     

Habitat suitability for tsessebe Damaliscus lunatus lunatus

The distribution and numbers of tsessebe (Damaliscus lunatus lunatus) have declined considerably in South Africa, partly due to deteriorating habitat conditions. Identifying important habitat variables will assist in managing the species. The objective of this study was to identify habitat variables important for tsessebe and to develop a predictive model of habitat selection for this species in a savanna biome. The study was conducted in the Nylsvley Nature Reserve over a 2‐year period. A total of eighteen habitat variables were measured in ten plant communities at 200 sites. Logistic regression analyses were used to identify predictor variables and to construct a habitat model. Tsessebe were found <2 km from the nearest source of water, in flat areas with slopes of <3° and with <10% rockiness. Their distribution was not influenced by the woody component. Sites where tsessebe were present had significantly lower grass heights and tuft heights, with a higher grass density compared with areas not utilized by tsessebe. Nitrogen and sodium levels were also higher at present sites. Habitat type and grass height were the most significant predictors of tsessebe presence. The selected model had an overall percentage prediction of 85.0%. The model was subdivided into five vegetation‐specific models and each model was tested with independent data.     

Application of random effects to the study of resource selection by animals

1. Resource selection estimated by logistic regression is used increasingly in studies to identify critical resources for animal populations and to predict species occurrence. 2. Most frequently, individual animals are monitored and pooled to estimate population-level effects without regard to group or individual-level variation. Pooling assumes that both observations and their errors are independent, and resource selection is constant given individual variation in resource availability. 3. Although researchers have identified ways to minimize autocorrelation, variation between individuals caused by differences in selection or available resources, including functional responses in resource selection, have not been well addressed. 4. Here we review random-effects models and their application to resource selection modelling to overcome these common limitations. We present a simple case study of an analysis of resource selection by grizzly bears in the foothills of the Canadian Rocky Mountains with and without random effects. 5. Both categorical and continuous variables in the grizzly bear model differed in interpretation, both in statistical significance and coefficient sign, depending on how a random effect was included. We used a simulation approach to clarify the application of random effects under three common situations for telemetry studies: (a) discrepancies in sample sizes among individuals; (b) differences among individuals in selection where availability is constant; and (c) differences in availability with and without a functional response in resource selection. 6. We found that random intercepts accounted for unbalanced sample designs, and models with random intercepts and coefficients improved model fit given the variation in selection among individuals and functional responses in selection. Our empirical example and simulations demonstrate how including random effects in resource selection models can aid interpretation and address difficult assumptions limiting their generality. This approach will allow researchers to appropriately estimate marginal (population) and conditional (individual) responses, and account for complex grouping, unbalanced sample designs and autocorrelation.     

Validation of elk resource selection models with spatially independent data

Knowledge of how landscape features affect wildlife resource use is essential for informed management. Resource selection functions often are used to make and validate predictions about landscape use; however, resource selection functions are rarely validated with data from landscapes independent of those from which the models were built. This problem has severely limited the application of resource selection functions over larger geographic areas for widely distributed species. North American elk (Cervus elaphus) is an example of a widely-distributed species of keen interest to managers and for which validation of resource selection functions over large geographic areas is important. We evaluated the performance of resource selection functions developed for elk on one landscape in northeast Oregon with independent data from a different landscape in the same region. We compared predicted versus observed elk resource use for 9 monthly or seasonal periods across 3 yr. Results showed strong, positive agreement between predicted and observed use for 2 spring and 3 late summer-early fall models (3-yr r = 0.81–0.95). Predicted versus observed use was negatively or weakly positively correlated for 3 summer models and 1 mid-fall model (3-yr r = −0.57–0.14). Predicted and observed use correlated well when forage was limited (spring and late summer or early fall), corresponding to important biological stages for elk (parturition and breeding seasons). For these seasonal periods, model covariates such as rate of motorized traffic and canopy closure often were effective predictors of elk resource selection. The models we validated for spring and late summer-early fall may be used to evaluate management activities in areas with similar landscape characteristics. © 2010 The Wildlife Society.     

Nomograms Aid Interpretation of Complex Regression Models

ABSTRACT Ecologists often develop complex regression models that include multiple categorical and continuous variables, interactions among predictors, and nonlinear relationships between the response and predictor variables. Nomograms, which are graphical devices for presenting mathematical functions and calculating output values, can aid biologists in interpreting and presenting these complex models. To illustrate benefits of nomograms, we developed a logistic regression model of elk (Cervus elaphus) resource selection. With this model, we demonstrated how a nomogram helps scientists and managers interpret interactions among variables, compare the relative biological importance of variables, and examine predicted shapes of relationships (e.g., linear vs. nonlinear) between response and predictor variables. Although our example focused on logistic regression, nomograms are equally useful for other linear and nonlinear models. Regardless of the approach used for model development, nomograms and other graphical summaries can help scientists and managers develop, interpret, and apply statistical models.     

Seasonal Resource Selection of Canada Lynx in Managed Forests of the Northern Rocky Mountains

ABSTRACT We investigated seasonal patterns in resource selection of Canada lynx (Lynx canadensis) in the northern Rockies (western MT, USA) from 1998 to 2002 based on backtracking in winter (577 km; 10 M, 7 F) and radiotelemetry (630 locations; 16 M, 11 F) in summer. During winter, lynx preferentially foraged in mature, multilayer forests with Engelmann spruce (Picea engelmannii) and subalpine fir (Abies lasiocarpa) in the overstory and midstory. Forests used during winter were composed of larger diameter trees with higher horizontal cover, more abundant snowshoe hares (Lepus americanus), and deeper snow compared to random availability; multilayer, spruce-fir forests provided high horizontal cover with tree branching that touched the snow surface. During winter, lynx killed prey at sites with higher horizontal cover than that along foraging paths. Lynx were insensitive to snow depth or penetrability in determining where they killed prey. During summer, lynx broadened their resource use to select younger forests with high horizontal cover, abundant total shrubs, abundant small-diameter trees, and dense saplings, especially spruce-fir saplings. Based on multivariate logistic-regression models, resource selection occurred primarily at a fine spatial scale as was consistent with a sight-hunting predator in dense forests. However, univariate comparisons of patch-level metrics indicated that lynx selected homogenous spruce-fir patches, and avoided recent clear-cuts or other open patches. Given that lynx in Montana exhibit seasonal differences in resource selection, we encourage managers to maintain habitat mosaics. Because winter habitat may be most limiting for lynx, these mosaics should include abundant multistory, mature spruce-fir forests with high horizontal cover that are spatially well-distributed.     

Spatial heterogeneity in habitat selection: Nest site selection by greater prairie-chickens

Ecological relationships of animals and their environments are known to vary spatially and temporally across scales. However, common approaches for evaluating resource selection by animals assume that the processes of habitat selection are stationary across space. The assumption that habitat selection is spatially homogeneous may lead to biased inference and ineffective management. We present the first application of geographically weighted logistic regression to habitat selection by a wildlife species. As a case study, we examined nest site selection by greater prairie-chickens at 3 sites with different ecological conditions in Kansas to assess whether the relative importance of habitat features varied across space. We found that 1) nest sites were associated with habitat conditions at multiple spatial scales, 2) habitat associations across spatial scales were correlated, and 3) the influence of habitat conditions on nest site selection was spatially explicit. Post hoc analyses revealed that much of the spatial variability in habitat selection processes was explained at a regional scale. Moreover, habitat features at local spatial scales were more strongly associated with nest site selection in unfragmented grasslands managed intensively for cattle production than they were in fragmented grasslands within a matrix of farmland. Female prairie-chickens exhibited spatial variability in nest site selection at multiple spatial scales, suggesting plasticity in habitat selection behavior. Our results highlight the importance of accounting for spatial heterogeneity when evaluating the ecological effects of habitat components. © 2013 The Wildlife Society.