Kathryn M. Irvine

Wildlife contact analysis: emerging methods, questions, and challenges

Recent technological advances, such as proximity loggers, allow researchers to collect complete interaction histories, day and night, among sampled individuals over several months to years. Social network analyses are an obvious approach to analyzing interaction data because of their flexibility for fitting many different social structures as well as the ability to assess both direct contacts and indirect associations via intermediaries. For many network properties, however, it is not clear whether estimates based upon a sample of the network are reflective of the entire network. In wildlife applications, networks may be poorly sampled and boundary effects will be common. We present an alternative approach that utilizes a hierarchical modeling framework to assess the individual, dyadic, and environmental factors contributing to variation in the interaction rates and allows us to estimate the underlying process variation in each. In a disease control context, this approach will allow managers to focus efforts on those types of individuals and environments that contribute the most toward super-spreading events. We account for the sampling distribution of proximity loggers and the non-independence of contacts among groups by only using contact data within a group during days when the group membership of proximity loggers was known. This allows us to separate the two mechanisms responsible for a pair not contacting one another: they were not in the same group or they were in the same group but did not come within the specified contact distance. We illustrate our approach with an example dataset of female elk from northwestern Wyoming and conclude with a number of important future research directions.

Female elk contacts are neither frequency nor density dependent

Identifying drivers of contact rates among individuals is critical to understanding disease dynamics and implementing targeted control measures. We studied the interaction patterns of 149 female elk (Cervus canadensis) distributed across five different regions of western Wyoming over three years, defining a contact as an approach within one body length (-2 min). Using hierarchical models that account for correlations within individuals, pairs, and groups, we found that pairwise contact rates within a group declined by a factor of three as group sizes increased 33-fold. Per capita contact rates, however, increased with group size according to a power function, such that female elk contact rates fell in between the predictions of density- or frequency-dependent disease models. We found similar patterns for the duration of contacts. Our results suggest that larger elk groups are likely to play a disproportionate role in the disease dynamics of directly transmitted infections in elk. Supplemental feeding of elk had a limited impact on pairwise interaction rates and durations, but per capita rates were more than two times higher on feeding grounds. Our statistical approach decomposes the variation in contact rate into individual, dyadic, and environmental effects, and provides insight into factors that may be targeted by disease control programs. In particular, female elk contact patterns were driven more by environmental factors such as group size than by either individual or dyad effects.

Spatial Designs and Properties of Spatial Correlation: Effects on Covariance Estimation

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the influence of the strength of spatial dependence on maximum likelihood (ML) and restricted maximum likelihood (REML) estimates of covariance parameters in an exponential-with-nugget model, and we also examine these influences under different sampling designs—specifically, lattice designs and more realistic random and cluster designs—at differing intensities of sampling (n=144 and 361). We find that neither ML nor REML estimates perform well when the range parameter and/or the nugget-to-sill ratio is large—ML tends to underestimate the autocorrelation function and REML produces highly variable estimates of the autocorrelation function. The best estimates of both the covariance parameters and the autocorrelation function come under the cluster sampling design and large sample sizes. As a motivating example, we consider a spatial model for stream sulfate concentration.

A Practical Sampling Design for Acoustic Surveys of Bats

ABSTRACT Acoustic surveys are widely used for describing bat occurrence and activity patterns and are increasingly important for addressing concerns for habitat management, wind energy, and disease on bat populations. Designing these surveys presents unique challenges, particularly when a probabilistic sample is required for drawing inference to unsampled areas. Sampling frame errors and other logistical constraints often require survey sites to be dropped from the sample and new sites added. Maintaining spatial balance and representativeness of the sample when these changes are made can be problematic. Spatially balanced sampling designs recently developed to support aquatic surveys along rivers provide solutions to a number of practical challenges faced by bat researchers and allow for sample site additions and deletions, support unequal-probability selection of sites, and provide an approximately unbiased local neighborhood-weighted variance estimator that is efficient for spatially structured populations such as is typical for bats. We implemented a spatially balanced design to survey canyon bat (Parastrellus hesperus) activity along a stream network. The spatially balanced design accommodated typical logistical challenges and yielded a 25% smaller estimated standard error for the mean activity level than the usual simple random sampling estimator. Spatially balanced designs have broad application to bat research and monitoring programs and will improve studies relying on model-based inference (e.g., occupancy models) by providing flexibility and protection against violations of the independence assumption, even if design-based estimators are not used. Our approach is scalable and can be used for pre- and post-construction surveys along wind turbine arrays and for regional monitoring programs.

Assessing the status and trend of bat populations across broad geographic regions with dynamic distribution models

Bats face unprecedented threats from habitat loss, climate change, disease, and wind power development, and populations of many species are in decline. A better ability to quantify bat population status and trend is urgently needed in order to develop effective conservation strategies. We used a Bayesian autoregressive approach to develop dynamic distribution models for Myotis lucifugus, the little brown bat, across a large portion of northwestern USA, using a four-year detection history matrix obtained from a regional monitoring program. This widespread and abundant species has experienced precipitous local population declines in northeastern USA resulting from the novel disease white-nose syndrome, and is facing likely range-wide declines. Our models were temporally dynamic and accounted for imperfect detection. Drawing on species-energy theory, we included measures of net primary productivity (NPP) and forest cover in models, predicting that M. lucifugus occurrence probabilities would covary positively along those gradients. Despite its common status, M. lucifugus was only detected during -50% of the surveys in occupied sample units. The overall naive estimate for the proportion of the study region occupied by the species was 0.69, but after accounting for imperfect detection, this increased to -0.90. Our models provide evidence of an association between NPP and forest cover and M. lucifugus distribution, with implications for the projected effects of accelerated climate change in the region, which include net aridification as snowpack and stream flows decline. Annual turnover, the probability that an occupied sample unit was a newly occupied one, was estimated to be low (-0.04-0.14), resulting in flat trend estimated with relatively high precision (SD = 0.04). We mapped the variation in predicted occurrence probabilities and corresponding prediction uncertainty along the productivity gradient. Our results provide a much needed baseline against which future anticipated declines in M. lucifugus occurrence can be measured. The dynamic distribution modeling approach has broad applicability to regional bat monitoring efforts now underway in several countries and we suggest ways to improve and expand our grid-based monitoring program to gain robust insights into bat population status and trend across large portions of North America.

Predicting foundation bunchgrass species abundances: model-assisted decision-making in protected-area sagebrush steppe

Foundation species are structurally dominant members of ecological communities that can stabilize ecological processes and influence resilience to disturbance and resistance to invasion. Being common, they are often overlooked for conservation but are increasingly threatened from land use change, biological invasions, and over-exploitation. The pattern of foundation species abundances over space and time may be used to guide decision-making, particularly in protected areas for which they are iconic. We used ordinal logistic regression to identify the important environmental influences on the abundance patterns of bluebunch wheatgrass (Pseudoroegneria spicata), Thurbers needlegrass (Achnatherum thurberianum), and Sandberg bluegrass (Poa secunda) in protected-area sagebrush steppe. We then predicted bunchgrass abundances along gradients of topography, disturbance, and invasive annual grass abundance. We used model predictions to prioritize the landscape for implementation of a management and restoration decision-support tool. Models were fit to categorical estimates of grass cover obtained from an extensive ground-based monitoring dataset. We found that remnant stands of abundant wheatgrass and bluegrass were associated with steep north-facing slopes in higher and more remote portions of the landscape outside of recently burned areas where invasive annual grasses were less abundant. These areas represented only 25% of the landscape and were prioritized for protection efforts. Needlegrass was associated with south-facing slopes, but in low abundance and in association with invasive cheatgrass (Bromus tectorum). Abundances of all three species were strongly negatively correlated with occurrence of another invasive annual grass, medusahead (Taeniatherum caput-medusae). The rarity of priority bunchgrass stands underscored the extent of degradation and the need for prioritization. We found no evidence that insularity reduced invasibility; annual grass invasion represents a serious threat to protected-area bunchgrass communities. Our study area was entirely within the Wyoming big sagebrush ecological zone, understood to have inherently low resilience to disturbance and resistance to weed invasion. However, our study revealed important variation in abundance of the foundation species associated with resilience and resistance along the topographic-soil moisture gradient within this zone, providing an important foothold for conservation decision-making in these steppe ecosystems. We found the foundation species focus a parsimonious strategy linking monitoring to decision-making via biogeographic modeling.

A power analysis for multivariate tests of temporal trend in species composition

Long-term monitoring programs emphasize power analysis as a tool to determine the sampling effort necessary to effectively document ecologically significant changes in ecosystems. Programs that monitor entire multispecies assemblages require a method for determining the power of multivariate statistical models to detect trend. We provide a method to simulate presence-absence species assemblage data that are consistent with increasing or decreasing directional change in species composition within multiple sites. This step is the foundation for using Monte Carlo methods to approximate the power of any multivariate method for detecting temporal trends. We focus on comparing the power of the Mantel test, permutational multivariate analysis of variance, and constrained analysis of principal coordinates. We find that the power of the various methods we investigate is sensitive to the number of species in the community, univariate species patterns, and the number of sites sampled over time. For increasing directional change scenarios, constrained analysis of principal coordinates was as or more powerful than permutational multivariate analysis of variance, the Mantel test was the least powerful. However, in our investigation of decreasing directional change, the Mantel test was typically as or more powerful than the other models.

A goodness‐of‐fit test for occupancy models with correlated within‐season revisits

Abstract Occupancy modeling is important for exploring species distribution patterns and for conservation monitoring. Within this framework, explicit attention is given to species detection probabilities estimated from replicate surveys to sample units. A central assumption is that replicate surveys are independent Bernoulli trials, but this assumption becomes untenable when ecologists serially deploy remote cameras and acoustic recording devices over days and weeks to survey rare and elusive animals. Proposed solutions involve modifying the detection‐level component of the model (e.g., first‐order Markov covariate). Evaluating whether a model sufficiently accounts for correlation is imperative, but clear guidance for practitioners is lacking. Currently, an omnibus goodness‐of‐fit test using a chi‐square discrepancy measure on unique detection histories is available for occupancy models (MacKenzie and Bailey, Journal of Agricultural, Biological, and Environmental Statistics, 9, 2004, 300; hereafter, MacKenzie–Bailey test). We propose a join count summary measure adapted from spatial statistics to directly assess correlation after fitting a model. We motivate our work with a dataset of multinight bat call recordings from a pilot study for the North American Bat Monitoring Program. We found in simulations that our join count test was more reliable than the MacKenzie–Bailey test for detecting inadequacy of a model that assumed independence, particularly when serial correlation was low to moderate. A model that included a Markov‐structured detection‐level covariate produced unbiased occupancy estimates except in the presence of strong serial correlation and a revisit design consisting only of temporal replicates. When applied to two common bat species, our approach illustrates that sophisticated models do not guarantee adequate fit to real data, underscoring the importance of model assessment. Our join count test provides a widely applicable goodness‐of‐fit test and specifically evaluates occupancy model lack of fit related to correlation among detections within a sample unit. Our diagnostic tool is available for practitioners that serially deploy survey equipment as a way to achieve cost savings.

Comparison of Transect-Based Standard and Adaptive Sampling Methods for Invasive Plant Species

Abstract Early detection of an invading nonindigenous plant species (NIS) may be critical for efficient and effective management. Adaptive survey sampling methods may provide unbiased sampling for best estimates of distribution of rare and spatially clustered populations of plants in the early stages of invasion. However, there are few examples of these methods being used for nonnative plant surveys in which travelling distances away from an initial or source patch, or away from a road or trail, can be time consuming due to the topography and vegetation. Nor is there guidance as to which of the many adaptive methods would be most appropriate as a basis for invasive plant mapping and subsequent management. Here we used an empirical complete census of four invader species in early to middle stages of invasion in a management area to assess the effectiveness and efficiency of three nonadaptive methods, four adaptive cluster methods, and four adaptive web sampling methods that all originated from transects. The adaptive methods generally sampled more NIS-occupied cells and patches than standard transect approaches. Sampling along roads only was time-efficient and effective, but only for species with restricted distribution along the roads. When populations were more patchy and dispersed over the landscape the adaptive cluster starting at the road generally proved to be the most time-efficient and effective NIS detection method. Management Implications: It is often not possible or cost-effective to conduct a complete inventory of potentially invasive plant species in large management areas, particularly at the early stages of invasion when populations may be infrequent and dispersed on the landscape. Detection at the early stages of invasion may be crucial for effective and cost-effective management. Thus managers must have survey methods that are effective and efficient for estimating the distribution of invading species. To accomplish different survey goals, which may include finding early invading populations, locating many different invasive plant species, finding the most populations of a single species, or collecting information to characterize species distributions, knowing which survey technique to use is critical. We tested three standard and eight adaptive survey methods on a virtual landscape populated with four empirically censused invasive plant species: Canada thistle, Dalmatian toadflax, smooth brome, and common St. Johnswort. The species exhibited somewhat different growth forms, reproductive patterns, and seed dispersal distances and were in different stages of invasion. Random transects with adaptive cluster sampling generally performed best when the survey goal was to find the largest number of populations in the shortest amount of time for species that were well established and occupied areas away from the road. If the species was in the early stages of invasion and only occupied roadside habitat, surveying along roads performed best. When the survey goal was to accurately assess the proportion of the landscape infested by each species, stratified random targeted transects without adaptive sampling performed best for all species. However, managers should be aware that adaptive sampling methods overestimate infested area. This study indicates that adaptive sampling methods can improve nonindigenous species patch detection for management, but regardless of the sampling method, detection remains relative low (maximum of 33% of patches) with typical management constraints and therefore seriously challenges the concept of early detection and rapid response.

Estimating Temporal Trend in the Presence of Spatial Complexity: A Bayesian Hierarchical Model for a Wetland Plant Population Undergoing Restoration

Monitoring programs that evaluate restoration and inform adaptive management are important for addressing environmental degradation. These efforts may be well served by spatially explicit hierarchical approaches to modeling because of unavoidable spatial structure inherited from past land use patterns and other factors. We developed Bayesian hierarchical models to estimate trends from annual density counts observed in a spatially structured wetland forb (Camassia quamash [camas]) population following the cessation of grazing and mowing on the study area, and in a separate reference population of camas. The restoration site was bisected by roads and drainage ditches, resulting in distinct subpopulations (“zones”) with different land use histories. We modeled this spatial structure by fitting zone-specific intercepts and slopes. We allowed spatial covariance parameters in the model to vary by zone, as in stratified kriging, accommodating anisotropy and improving computation and biological interpretation. Trend estimates provided evidence of a positive effect of passive restoration, and the strength of evidence was influenced by the amount of spatial structure in the model. Allowing trends to vary among zones and accounting for topographic heterogeneity increased precision of trend estimates. Accounting for spatial autocorrelation shifted parameter coefficients in ways that varied among zones depending on strength of statistical shrinkage, autocorrelation and topographic heterogeneity—a phenomenon not widely described. Spatially explicit estimates of trend from hierarchical models will generally be more useful to land managers than pooled regional estimates and provide more realistic assessments of uncertainty. The ability to grapple with historical contingency is an appealing benefit of this approach.