Perry J. Williams

The basis function approach for modeling autocorrelation in ecological data

Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many seemingly disparate statistical methods used to account for autocorrelation can be expressed as regression models that include basis functions. Basis functions also enable ecologists to modify a wide range of existing ecological models in order to account for autocorrelation, which can improve inference and predictive accuracy. Furthermore, understanding the properties of basis functions is essential for evaluating the fit of spatial or time-series models, detecting a hidden form of collinearity, and analyzing large data sets. We present important concepts and properties related to basis functions and illustrate several tools and techniques ecologists can use when modeling autocorrelation in ecological data.

Primates and Cameras

Field-based primate studies often make population inferences using count-based indices (e.g., individuals/plot) or distance sampling; the first does not account for the probability of detection and thus can be biased, while the second requires large sample sizes to obtain precise estimates, which is difficult for many primate studies. We discuss photographic sampling and occupancy modeling to correct for imperfect detection when estimating system states and dynamics at the landscape level, specifically in relation to primate ecology. We highlight the flexibility of the occupancy framework and its many applications to studying low-density primate populations or species that are difficult to detect. We discuss relevant sampling and estimation procedures with special attention to data collection via photographic sampling. To provide tangible meaning to terminology and clarify subtleties, we use illustrative examples. Photographic sampling can have many advantages over observer-based sampling, especially when studying rare or elusive species. Combining photographic sampling with an occupancy framework allows inference to larger scales than is common in primate studies, addresses uncertainty due to the observation process, and allows researchers to examine questions of how landscape-level anthropogenic changes affect primate distributions.

An integrated data model to estimate spatiotemporal occupancy, abundance, and colonization dynamics

Ecological invasions and colonizations occur dynamically through space and time. Estimating the distribution and abundance of colonizing species is critical for efficient management or conservation. We describe a statistical framework for simultaneously estimating spatiotemporal occupancy and abundance dynamics of a colonizing species. Our method accounts for several issues that are common when modeling spatiotemporal ecological data including multiple levels of detection probability, multiple data sources, and computational limitations that occur when making fine-scale inference over a large spatiotemporal domain. We apply the model to estimate the colonization dynamics of sea otters (Enhydra lutris) in Glacier Bay, in southeastern Alaska.

Surveying a Threatened Amphibian Species through a Narrow Detection Window

Crawfish Frogs (Lithobates areolatus) are a relatively widespread but understudied North American species suspected to be in steep decline. Discussions to petition this species for federal listing have begun and therefore effective techniques to survey and monitor populations must be developed. Crawfish Frogs produce unusually loud breeding calls, making call surveys the most efficient way to assess populations; however, their peak breeding period lasts for only a few nights, sometimes for only one night. We used automated calling survey techniques at two wetlands where the numbers of Crawfish Frog males present were known (±1%) for the entire length of the breeding season to examine detection probabilities in relation to season, time of day, weather variables, survey duration, and the numbers of males present. We then used these data to ask three simple but important questions: 1) When should researchers listen—that is, what times and under what environmental conditions should surveys for Crawfish Frogs take place? 2) How long should surveys last? and 3) What can call surveys tell us about the size of a population? The most supported model for detection included the quadratic relationship of time and date, a positive linear relationship with temperature, and a negative linear relationship with recent rain, while the most supported model for estimating abundance included the quadratic relationship of time and date, and call rate. Five-minute surveys should suffice during peak breeding for known large populations; 15-minute surveys with repeat visits should be used for small populations or when sampling new areas. These findings should improve manually collected (auditory) call survey efficiencies for Crawfish Frogs, surveys that are being organized to provide the first objective data on the status of this species across its range.

Habitat Selection by Crawfish Frogs (Lithobates areolatus) in a Large Mixed Grassland/Forest Habitat

Abstract Our objective was to examine breeding dispersal, burrow-use characteristics, and burrow habitat selection by Crawfish Frogs (Lithobates areolatus) in two distinct vegetation types (open grasslands and a mosaic of forest and transitioning grasslands) in southeastern Indiana, from March to August 2009 and 2010. We captured 14 frogs at their breeding ponds and tracked them to their burrows using radio telemetry. Once we identified their burrows, we compared habitat metrics at the burrows to random locations. We used an information-theoretic model selection approach to approximate the parsimony of logistic regression models comparing the habitat features of burrows to random, available sites. Frogs dispersed a straight-line average distance of 215 m and used an average of four burrows. They generally did not change burrows after June. Our top model included covariates for the number of burrows, canopy cover, and a site covariate. Our results suggested that habitat selection by Crawfish Frogs occurred hierarchically; in mixed grassland/forest habitats, they first selected areas with low canopy cover, and then selected areas with many available burrows. To manage habitat for Crawfish Frogs, we recommend preventing woody encroachment and reducing canopy cover in grassland areas occupied by Crawfish Frogs. Additionally, areas with a large number of burrows appear to provide the most suitable Crawfish Frog habitat.

Estimating occupancy and abundance using aerial images with imperfect detection

Summary 1.Species distribution and abundance are critical population characteristics for efficient management, conservation, and ecological insight. Point process models are a powerful tool for modeling distribution and abundance, and can incorporate many data types, including count data, presence-absence data, and presence-only data. Aerial photographic images are a natural tool for collecting data to fit point process models, but aerial images do not always capture all animals that are present at a site. Methods for estimating detection probability for aerial surveys usually include collecting auxiliary data to estimate the proportion of time animals are available to be detected. 2.We developed an approach for fitting point process models using an N-mixture model framework to estimate detection probability for aerial occupancy and abundance surveys. Our method uses multiple aerial images taken of animals at the same spatial location to provide temporal replication of sample sites. The intersection of the images provide multiple counts of individuals at different times. We examined this approach using both simulated and real data of sea otters (Enhydra lutris kenyoni) in Glacier Bay National Park, southeastern Alaska. 3.Using our proposed methods, we estimated detection probability of sea otters to be 0.76, the same as visual aerial surveys that have been used in the past. Further, simulations demonstrated that our approach is a promising tool for estimating occupancy, abundance, and detection probability from aerial photographic surveys. 4.Our methods can be readily extended to data collected using unmanned aerial vehicles, as technology and regulations permit. The generality of our methods for other aerial surveys depends on how well surveys can be designed to meet the assumptions of N-mixture models. This article is protected by copyright. All rights reserved.

Factors affecting nest survival of Henslow's Sparrows (Ammodramus henslowii) in southern Indiana

ABSTRACT Populations of Henslow’s Sparrows have declined dramatically in recent decades, coinciding with widespread loss of native grassland habitat. Prescribed burning is a primary tool for maintaining grassland patches, but its effects on nest survival of Henslow’s Sparrows remains largely unknown, especially in conjunction with other factors. We monitored 135 nests of Henslow’s Sparrows at Big Oaks National Wildlife Refuge in southern Indiana from 1998–2001 in an effort to understand factors influencing nest survival, including prescribed burning of habitat. We used a mixed-effects implementation of the logistic exposure model to predict daily nest survival in an information theoretic framework. We found that daily survival declined near the onset of hatching and increased with the height of standing dead vegetation, although this relationship was weak. We found only nominal support to suggest that time since burn influenced nest survival. Overall, nest age was the most important factor in estimating daily nest survival rates. Our daily survival estimate from our marginal model (0.937) was similar to that derived from the Mayfield method (0.944) suggesting that our results are comparable to previous studies using the Mayfield approach. Our results indicate that frequent burning to limit woody encroachment into grassland habitats might benefit Henslow’s Sparrow, but that a variety of factors ultimately influence daily nest survival. However, we note that burning too frequently can also limit occupancy by Henslow’s Sparrows. We suggest that additional research is needed to determine the population-level consequences of habitat alteration and if other extrinsic factors influence demographics of Henslow’s Sparrows.