• Robert M. Dorazio
• Alan E. Gelfand
• Alix Gitelman
• Geof H. Givens
• Gurutzeta Guillera-Arroita
• Matthew Heaton
• Megan Higgs
• Jennifer Hoeting
• Mevin B. Hooten
• J.B. Illian
• Devin Johnson
• Roland Langrock
• Lisa Madsen
• Juan Manuel Morales
• Brian Reich
• J. Andrew Royle
• David I. Warton
• Dale Zimmerman

• Matthew E. Aiello-Lammens
• Ignacio Alvarez
• Maeregu Arisido
• Ben Brintz
• Kristin M. Broms
• Brian M. Brost
• Frances E. Buderman
• Joshua Goldstein
• Daniel Heersink
• Juha Heikkinen
• Andrew Hoegh
• Whitney Huang
• Christopher Ilori
• Nels G. Johnson
• José J. Lahoz-Monfort
• Clint Leach
• V. Leos Barajas
• Joe Maurer
• Joseph M. Northrup
• Viviana Ruiz-Gutiérrez
• Erin Schliep
• Letícia Soares
• Jared Stabach
• Chris Sutherland
• John Tipton
• Bradley J. Tomasek
• Lynn Waterhouse
• Christopher Wolf
• Robert Yuen

Survival models without mortality: casting closed-population wildlife survey models as survival or recurrent event models

David Borchers, Roland Langrock, Darren Kidney, Greg Distiller and Ben Stevenson

One can formulate closed-population wildlife surveys as survival models (in which individuals "survive" detection for some time) or recurrent event models (in which the events are detections). These models are characterized by the fact that they invariably have a spatial component, and therefore (a) mortality or event hazard rates depend on spatial covariates, and (b) they require a spatial model for individuals' locations in space, and when individual locations are not observed the spatial model acts as a latent variable distribution.

In this talk I develop a general model for wildlife surveys as survival or recurrent event models, consider some widely-used closed-population wildlife survey models from this perspective. I illustrate some of the advantages of formulating models in this way, using case studies that include aerial surveys of seabirds with high-definition video cameras, visual line transect surveys of marine mammals, camera-trap surveys of large cats and acoustic surveys of gibbons.

Unifying species diversity, phylogenetic diversity, functional diversity and related similarity/differentiation measures through Hill numbers

Anne Chao, C.-H. Chiu and Lou Jost

Hill numbers or the "effective number of species" are increasingly used to quantify species diversity of an assemblage. In this talk, I review Hill numbers and the advantages of using Hill numbers to quantify diversities. Hill numbers were recently extended to phylogenetic diversity, which incorporates species evolutionary history, and also to functional diversity, which considers the differences among species traits. I also review these extensions and integrate them into a framework of "attribute diversity" (or the "effective total attribute value") based on Hill numbers. This framework unifies ecologists' measures of species diversity, phylogenetic diversity, and functional diversity. It also provides a unified method of decomposing these diversities and constructing normalized taxonomic, phylogenetic, and functional similarity and differentiation measures, including N-assemblage phylogenetic or functional generalizations of the classic Jaccard, Sørensen, Horn and Morisita-Horn indices. A real example shows how this framework extracts ecological meaning from complex data. (This is a joint work with C.-H. Chiu and Lou

Forecasting the forest and the trees: climate interactions from individual to community

James S. Clark, Bradley Tomasek, Chris Woodall, Kai Zhu

Is the study of individuals sufficient to predict changing distribution and abundance of species? Alternatively, can the dynamics of interacting species be explained without knowledge of individual responses? From population viability to global warming, biodiversity predictions of change and vulnerability come from one scale or the other, but do not combine them.

Individual-scale models include matrix projection models (MPMs), integral projection models (IPMs), and partial differential equations (PDEs). These methods have in common a reliance on parameters estimated for independent responses (growth, survival, fecundity) of independent individuals. More aggregated models are spatially coarse and include species distribution models (SDMs). SDMs implement independent models for each species or functional type, then add them together to predict diversity and productivity. Neither approach is designed to address four-dimensional population structure across size, species, space, and time, where individuals and species respond to the environment as a joint distribution. Here I discuss how to combine data and processes across these scales to provide inference on the joint distribution of species in space, time, and size structure. The model can be viewed as a PDE, a MPM, or an IPM, but at the population, rather than individual scale. It is also a SMD, but implemented jointly over time, a dynamic joint species distribution model. A single model helps address long-standing questions concerning the demographic processes that determine species range limits, how distribution and abundance can change with climate, and how competition and climate interact to affect distributions of species. With an application to long-term and spatially extensive forest plots in eastern North America we show which species respond most to climate, the extent to which local moisture gradients can alleviate negative impacts of increasing aridity, and how competition exacerbates effects of climate change in different ways for different species.

The Hidden Costs of Multimodel Inference

Jay M. Ver Hoef, Peter L. Boveng

Multimodel inference accommodates uncertainty when selecting or averaging models, which seems logical and natural. However, there are costs associated with multimodel inferences, so they are not always appropriate or desirable. First, we present statistical inference in the big picture of data analysis and the deductive-inductive process of scientific discovery. Against this backdrop, some statistical models are presented as being correct and some others as incorrect but useful. Multimodel inference is used primarily when modeling processes of nature, when there is no hope of knowing the true model, so a useful one is used. However, even in these cases, a single model to meet an objective may be better. Additionally, researchers should consider model diagnostics when using multiple models. Some of the costs of multimodel inference include 1) developing competency in multimodel inference procedures and the models that compose them, 2) coding time, 3) computing time, and 4) contemplation time. An optimal strategy, when cost is included, may often be a single model. We recommend that researchers and managers carefully examine objectives and cost when considering multimodel inference methods.

Statistical Methods for Spatial Categorical Data Analysis in Ecology

Jun Zhu

Modeling spatial categorical data in ecology and drawing statistical inference can be challenging when the number of categories is large and/or size of the sample is big.  The motivating examples include data derived from the Public Land Survey System (PLSS) records in various parts of the United States, which require statistical methods for data analysis that balance modeling complexity, statistical efficiency, and computational feasibility.  In this talk, some of the existing methodology for spatial categorical data is reviewed and new approaches are proposed.  In particular, models for spatial ordinal data and spatial nominal data are described and both frequentist and Bayesian inference are considered. Comparisons and connections will be drawn between different data types and different modeling approaches. For illustration, the methods are applied to analyze PLSS forest cover data for mapping and inferring about the forest landscape structures.

Accounting for Imperfect Detection in Statistical Analysis of Presence-only Data

During the past decade ecologists have attempted to estimate the parameters of species distribution models by combining species presence locations observed in opportunistic surveys with spatially referenced covariates of occurrence. Several statistical models have been proposed for the analysis of presence-only data, but these models have largely ignored the effects of imperfect detectability, which can bias the predicted distribution of a species. In this paper I describe a model-based approach for the analysis of presence-only data that accounts for errors in detection of individuals.

I develop a hierarchical, statistical model that allows presence-only data to be analyzed in conjunction with data acquired independently in bona fide surveys. One component of the model specifies the spatial distribution of individuals within a bounded, geographic region as a realization of a spatial point process. A second component of the model specifies two kinds of observations, the detections of individuals encountered during opportunistic surveys and the detections of individuals encountered during planned surveys.

Using mathematical proof and simulation-based comparisons, I demonstrate that biases induced by imperfect detectability can be reduced or eliminated by using this model to analyze presence-only data in conjunction with counts observed in planned surveys. I show that a relatively small amount of high-quality data (from planned surveys) can be used to leverage the information in presence-only observations, which usually have broad spatial coverage but may not be informative of both occurrence and detectability of individuals. Because a variety of sampling protocols can be used in planned surveys, this approach to the analysis of presence-only data is widely applicable. In addition, since the point-process model is formulated at the level of an individual, it can be extended to account for biological interactions between individuals and temporal changes in their spatial distributions.

Stochastic Modeling for Climate Change Velocities

Alan E. Gelfand, Erin Schliep

The ranges of plants and animals are moving in response to change in climate. In particular, if temperatures rise, some species will have to move their range. On a fine spatial scale, this may mean moving up in elevation; on a larger spatial scale, this may result in a latitudinal change. In this regard, the notion of velocity of climate change has been introduced to reflect change in location corresponding to change in temperature. If location is viewed as one dimensional, say x and time is denoted by t, the velocity becomes dx/dt. In the crudest form, given a relationship between temperature (Temp) and time as well as a relationship between Temp and location, we would have dx/dt=[dTemp/dt]/[Temp/dx].

The contribution here is to extend this simple definition to more realistic models, models incorporating more sophisticated explanations of temperature, models introducing spatial locations, and, most importantly, models that are stochastic over space and time. With such model components, we can learn about directional velocities, with uncertainty. We can capture spatial structure in velocities. We can assess whether velocities tend to be positive or negative, and in fact, whether and where they tend to be significantly different from 0. Extension of the model development can be envisioned to the species level, i.e., to species-
specific velocities. Here, we replace a temperature model as the driver with presence-only or presence/absence models. We can make attractive connections to customary advection and diffusion specifications through partial differential equations.

We illustrate with 118 years of data at 10km resolution (resulting in more than 21, 000 cells) for the eastern United States. We adopt a Bayesian framework and can obtain posterior distributions of directional velocities at arbitrary spatial locations and times. This is joint work with Erin Schliep.

Model Selection for Ecosystem Disturbance Pathways

Alix Gitelman, Kathryn M. Irvine

Applications of causal analysis are becoming more common in both aquatic and terrestrial ecosystems as scientists try to understand pathways of ecosystem disturbance. This approach requires synthesizing current scientific knowledge such that connections among ecological indicators and key ecosystem states or processes can be conveyed using a directed acyclic graph. Measured variables are represented as nodes in these graphs, and edges between nodes can be direct (suggesting possible cause-effect relationships) or indirect (suggesting more complicated, or mediated, cause-effect relationships.) Together, these pathways can provide a nuanced understanding of ecological mechanisms by harnessing a ``network of predictors.'' We describe several methods for model comparison in this context---where the question isn't about discovering edges, but rather about deciding between different ecologically plausible pathways. This work is motivated by recent interest in how climate drivers (e.g., drought, reduced snowpack) may effect intermediate stressors (e.g., disease, insect outbreaks, invasive species) which in turn impact species or biological communities of interest. Alternatively, the primary drivers effecting stressors and ultimately biota may be nthropogenic (e.g., land use change, urbanization, deforestation). We describe several methods for model comparison in this context---where the question isn't about discovering edges, but rather about deciding between different ecologically plausible pathways.

We examine the use of an unusual Horvitz-Thompson type estimator developed for the estimation of total population abundance of the Bering-Chukchi-Beaufort Seas population of bowhead whales in 2011 based on visual sightings and acoustic locations obtained from ice-based visual observation stations and submersed marine acoustical units. What makes this analysis unique is the derivation of three estimated correction factors required to account for complexities presented by the survey protocol and resulting features of the dataset. The first factor adjusts for detectability using uncertain recapture data to estimate detection probabilities and their dependence on offshore distance, ice condition, and whale group size. The second correction adjusts for availability using the acoustic location data to estimate a time-varying smooth function of the probability that animals pass within visual range of the observation stations. The third correction accounts for missed visual watch effort. Uncertainty in the estimates of these corrections is propagated into the final abundance estimate and an associated estimate of population trend that incorporates a time series of past estimates. Although some of the particulars of the approach are closely connected to the bowhead application, adjustments for detection, availability and effort are common and some of the methods discussed here could be adapted for abundance surveys facing similar challenges.

Gurutzeta Guillera-Arroita

It has long been recognized that field detection is often imperfect in wildlife surveys, and that this can bias the estimators of ecologically relevant state variables. In recognition of this problem, models that are developed in statistical ecology often include the description of two distinct processes: a system process that describes the biological system and an observation process that reflects the characteristics of data collection. Examples based on this general structure include models that estimate demographic parameters or abundance from capture- recapture data, and the estimation of abundance from distance-sampling records.

The last decade has seen particularly rapid development of models aimed at estimating species occupancy probability while accounting for imperfect detection. Whilst initially developed for wildlife monitoring applications, these models are starting to be recognized as relevant tools for species distribution modelling too. However, even as the interest in "detectability-aware" occupancy methods and their application continues to rise, there has been recently published work questioning their utility. These include suggestions that these models only provide very modest performance improvement (Rota et al. 2011), as well as stronger criticisms claiming that the models are difficult to fit and that disregarding detectability can be better than trying to adjust for it, with authors even concluding that adjusting for non-detection "is simply not worthwhile" (Welsh et al. 2013).

In this talk, I will explain why I think that these conclusions and related recommendation are not well founded and may have a negative impact on the quality of statistical inference in ecology. In particular, I will show how it is the choice of specific scenarios used to support these negative claims (Guillera-Arroita et al., in review), as well as confusion regarding how to assess the predictive performance of the models (Lahoz-Monfort et al. 2014), that provides a distorted picture of the true value of accounting for detectability.

Resource selection by scientists: Navigating the model selection and multi-model landscape toward question-focused modeling

Megan Higgs

Ecological researchers are often faced with navigating the myriad of potential statistical methods and models, and in recent history have gravitated toward model or variable selection techniques to address a huge variety of research questions.  For many, this has become a default choice, with little explicit justification based on research questions and study design.  Here, we appeal to the basic foundations of regression to demonstrate potential mismatches between questions of interest and the use of selection techniques. We explore differences between variable selection and model selection, the common fear of multicollinearity, and connections between multi-model inference and regularization techniques such as the adaptive lasso.  We offer practical strategies to aid researchers in deciding whether techniques are appropriate for their scientific questions and study design.  For example, we propose a graphical method for assessing whether model averaged regression coefficients are practically meaningful for a particular study. These investigations do not criticize particular methods, but instead present work meant to help researchers implement a more question-focused, rather than method-focused, approach to carrying out statistical inference.

Jennifer Hoeting, Nick Cummings, Mary Meyer

We propose a constrained, non-parametric, stationary, isotropic, spatial covariance model. The model allows for greater flexibility than parametric models, makes fewer assumptions, and is relatively easy to fit. The model is based on reversed C-spline basis functions which are calculated in closed form. The log likelihood of the data model is maximized using constrained optimization to find the coefficients of the basis functions that best fit the covariogram curve.  This fit, in turn, determines the covariance matrix. We demonstrate the efficiency and effectiveness of this method via simulation study and an example. This is joint work with Nick Cummings
and Mary Meyer.

Linking long-distance animal movement behavior and landscapes using multiscale functional models

Mevin B. Hooten

Advances in animal telemetry data collection techniques have served as a catalyst for the creation of statistical methodology for analyzing animal movement data.  Such data and methodology have provided a wealth of information about animal space use and the investigation of animal-environment relationships.  While the technology for data collection is improving dramatically over time, we are left with massive archives of historical animal telemetry data of varying quality.  However, many contemporary statistical approaches for inferring movement behavior are designed for newer data that are very accurate and high-resolution.  From a scientific perspective, the behaviors we are interested in learning about may be nonstationary and occur across multiple scales.  We describe a statistical modeling approach that uses multiple historical data sources in an explicitly multiscale framework to better understand animal spatial behavior. The models we describe are fast to implement, accessible to ecologists, easily generalized, and properly account for the uncertainty associated with telemetry data and the movement process. We apply this methodology to the study of Colorado predators for the identification of corridors and barriers to long-distance movement events.

Advancements in Sample Data Augmentation

J.B. Illian, , T.G. Martins, A. Riebler, H. Rue, D. Simpson, S.H. Sørbye

In a Bayesian context, choosing an appropriate prior distribution should ideally form an integral part of the modelling process. The prior distribution should encode prior knowledge about the parameters; however translating existing prior knowledge into a prior distribution often seems to be unattainable in practice. As a result, users resort to a "default" prior without explicitly discussing its choice.

At the same time, models typically rely on a number of distributional assumptions, which might or might not be met in practice - with all the implications on the validity of the conclusions drawn from the model. This is particularly relevant in ecology; however surprisingly few flexible methods are available that are directly linked to a standard model. The approach we discuss here addresses both the issue of prior choice and that of deviation from a standard model by explicitly incorporating deviation from a standard model into the modelling process. This is done within an extended family of models that has a basic standard model at is centre.

This family is constructed by introducing an additional flexibility parameter that controls the deviation from the basic model. Instead of parameterising the flexibility parameters directly, we base the distance between the base and the flexible model. Based on this distance we derive meaningful prior distributions for the flexibility parameters. These allow us to interpret the flexible model as a flexible version of the basic model. Shrinkage to the base model is warranted when supported by the data, but moderate deviations from the base model are properly captured if required.

Further, the approach can directly be integrated into the R-INLA software. Hence we are able to work with more flexible models without loosing the usual benefits of integrated nested Laplace approximation (INLA; Rue et al. 2009), i.e. short computation times and high accuracy. This extends the toolbox of models available in R-INLA and makes these models accessible to a wide audience of users. We illustrate the methodology with a number of relevant ecological examples primarily discussing the approach in the context of complex spatial models.

Estimating animal resource selection from telemetry data using point process models

Devin Johnson

Analyses of animal resource selection functions (RSF) using data collected from relocations of individuals via remote telemetry devices have become commonplace. Increasing technological advances, however, have produced statistical challenges in analysing such highly autocorrelated data. Weighted distribution methods have been proposed for analysing RSFs with telemetry data. However, they can be computationally challenging and cannot be aggregated (i.e. collapsed) over time to make space-only inference. We take a conceptually different approach to modeling animal telemetry data for making RSF inference by considering the telemetry data to be a realization of a space¡Vtime point process. Under the point process paradigm, the times of the relocations are also considered to be random rather than fixed. We show the point process models we propose are a generalization of the weighted distribution telemetry models. By generalizing the weighted model, we can access several numerical techniques for evaluating point process likelihoods that make use of common statistical software. Thus, the analysis methods can be readily implemented by animal ecologists. In addition to ease of computation, the point process models can be aggregated over time by marginalizing over the temporal component of the model. This allows a full range of models to be constructed for RSF analysis at the individual movement level up to the study area level.

Nonparametric inference in ecological latent-state models

Roland Langrock

Latent-state models typically comprise two stochastic processes, only one of which is observed. The observed process is in some way driven by the unobserved process, and the latter exhibits temporal correlation. Corresponding models, such as hidden Markov models, general state-space models or Markov-modulated Poisson processes, have many applications in ecology, where the unobserved process might correspond, for example, to the behavioural state of an animal, to an animal's condition or to the not directly observable size of an animal population. In these modelling classes even parametric inference is often challenging, since the likelihood involves either a summation or an integration over all possible values of the unobserved process, which can render its evaluation very computationally demanding. Nonparametric techniques for flexible modelling, which are nowadays routinely used for example in regression models or in density estimation, have hardly ever been incorporated in latent-state models. In this talk, I will first demonstrate how the relatively simple yet very powerful hidden Markov model machinery can be exploited in different ecological latent-state models. I will then show how the corresponding techniques can be combined with the general advantages of spline-based modelling to allow for nonparametric inference. The methods are applied to animal movement and capture-recapture data.

Simulating Realistic Spatial Count Data

Lisa Madsen

I will present a method to simulate count-valued dependent random variables that mimic an observed data set consisting of weed counts observed in a field. The method simulates a correlated normal random vector, then transforms to the desired marginal distributions. The difficulty is in characterizing the desired dependence and determining the normal correlations that lead to this dependence. I argue that Spearman's rank correlation is an appropriate characterization and show how to determine the normal correlation matrix that will lead to the specified Spearman correlation matrix.

Towards more realistic movement models: comparing simulated and observed movement

Juan Manuel Morales

Computer intensive methods are allowing us to fit increasingly detailed movement models to data. These models usually include the effects of habitat features and even past experiences on movement decisions. However, once the fitted models are simulated (if this is done at all), the trajectories produced by the models rarely look like the observed ones. Here I argue that this problem is mainly due to current models paying too much attention to small-scale features of movement trajectories. A possible way around this issue is for researchers to first define what features of movement they wish to capture and then use posterior predictive checks on such features to assess model performance. Alternatively, Approximate Bayesian Computation based on selected movement features can be used from the outset. I will illustrate these ideas highlighting their potential, challenges and limitations.

Policy optimization for dynamic spatiotemporal systems

Brian Reich

Interventions performed in space and time subject to resource constraints are common in ecology and many other fields.  For example, we consider intervention strategies to slow the spread of white nose syndrome (WNS) in hibernating bats.  WNS has dire consequences for both the bat population and agriculture production in affected areas.  A policy is required to determine where and when interventions such as cave closings should be implemented.  Finding an optimal policy in this case is challenging because data are sparse, disease dynamics are complex, and the state and action spaces are extremely high dimensional.  We propose a general framework for policy optimization in dynamic spatiotemporal systems.  The key features of our approach are that it ensures an interpretable policy, exploits scientific knowledge of the disease, adapts to changes in the system, properly accounts for many sources of uncertainty, and can be applied to high-dimensional problems.  In our analysis of WNS, we show that the proposed approach can lead to substantial improvements over competing methods.

Spatial Capture-Recapture Models Allowing Transience or Dispersal

J. Andrew Royle, Angela K. Fuller,Christopher Sutherland

Spatial capture-recapture (SCR) models are a relatively new development in ecological statistics, and they show promise in addressing a large number of ecological modeling problems related to spatial ecology, including studying movement and dispersal, resource selection and landscape connectivity from ordinary encounter history data.  SCR models hypothesize that space usage in the vicinity of an animal's home range is concentrated around a stationary point, its home range or activity center.  A prominent assumption is stationarity of these individual activity centers. While this may be reasonable for territorial animals, especially over short time periods, it is not always true.  Indeed, many biologists are skeptical of the relevance of SCR models for species that are distinctly non-territorial, or in situations when it is difficult to determine the exact timing of dispersal and subsequent territory establishment.

The purpose of this paper is to evaluate the robustness of estimators of abundance and density using closed population SCR models in the presence of transience and dispersal. To do this we devise a simulation study based on several forms of random and Markovian movement, in which the activity center of an individual potentially changes between each sampling occasion. We fit ordinary SCR models to the resulting data, and summarize the bias of the MLEs of model parameters. While our main objective was to evaluate robustness under non-stationarity regimes, we also demonstrate it is possible to fit Markovian models of transience in which the activity center changes during each sample occasion. We fit such models using the JAGS software, and we provide an example using data from a black bear study conducted on Fort Drum, NY.

Dealing with incomplete data in capture-recapture studies

Carl James Schwarz

The raison d'être of Capture-recapture studies have always been to
deal with detection probabilities less than 1. However, capture-recapture studies increasingly deal with incomplete information on other dimensions. For example, populations may be stratified by sex, but not all animals captured can be sexed because the process of sexing is too costly (e.g. animal must be sacrificed or require specialized expertise). Surveys that  that deliberately only measure a subset  of attributes on a segment of the animals handled may be more cost efficient and actually have better precision than surveys that measure all attributes on all animals. This type of problem is strongly related to missing data problems encountered in many  statistical settings.

Valid community-level inferences from multivariate abundance data

David I. Warton, Yi A. Wang

Multivariate abundance data are commonly and often erroneously analysed using distance-based algorithms (and  techniques related to correspondence analysis), which typically cannot be used to make valid inferences concerning changes in community composition, nor concerning interactions between environmental predictors in their effects on communities.  Model-based approaches provide a way forward, but a key challenge is to account for correlation between different taxa, made difficult because there are typically many more possible pairwise inter-species correlations than there are observations that could be used to estimate them.  We describe a design-based inferential tool which circumvents the issue, by block-resampling residuals constructed via the probability integral transform (which we call a "PIT-trap").  This approach can ensure valid inference even when the species correlation model has been misspecified.  Time-willing we will also discuss model-based inferential tools currently under development, via more parsimonious covariance model specifications, including factor analytic approaches and graphical modelling.  Methods will be illustrated by example, including a study of how species traits mediate changes in environmental response across species (the "fourth corner problem").

Accounting for Flow Volume in the Estimation of Spatial Dependence on Stream Networks

Dale L. Zimmerman

Statistical methods for spatial prediction have long been available for environmental variables on Euclidean domains.  A key precursor to prediction of such a variable is the characterization of the statistical dependence among observed values of the variable over space.  The most celebrated and important tool for this purpose is the sample semivariogram.  Recently, ecologists have begun applying similar methods to variables on non-Euclidean domains, including stream networks.  The Torgegram has been proposed as an analogue of the Euclidean sample semivariogram for characterizing spatial dependence on stream networks.  However, it does not account for flow volume, which, if unequal across tributaries, leads to biased estimation of spatial dependence and makes the nugget and range difficult to discern.  I propose modifications to the Torgegram that adjust for flow volume and essentially eliminate this bias.  An example illustrates the methodology.

Processes of community composition in an environmentally heterogeneous, high biodiversity region

Examining trait by environment relationships can help elucidate the environmental filters that permit some species to establish and persist in a community, while preventing others. These approaches generally involve analysis of data from a single time point or aggregation over multiple years. This form of aggregation can mask important differences in species responses to environmental conditions, and in some cases suggest that neutral processes largely determine community composition. Using functional trait analysis approaches with multi-year multi-site biodiversity inventory data can provide deeper insights into the processes affecting community assembly. We examined associations between community composition, species functional traits, and environmental conditions for plant communities in, and around, the Baviaanskloof Mega-reserve, a protected area within South Africa’s Cape Floristic Region (CFR). Our study area encompasses ~2500 km2 and contains extreme gradients in climatic conditions, is heterogeneous for other environmental conditions (e.g., edaphic features, topographic variation, fire history, etc.), and includes vegetation from four of the five major biome types within the CFR, resulting in both high alpha and beta diversity. During two study years (1992 and 2011), we observed ~600 species in 120 5 x 10 m vegetation plots, with a mean number of species per plot varying from 23 to 32, depending on survey year. Given these characteristics, the Baviaanskloof area represents an ideal location to examine trait by environment relationships and the role of environmental filtering on plant community composition. Integration of functional trait measurements for greater then 350 species with community relevé data allowed us to use community aggregated trait – redundancy analysis and non-parametric randomization methods to examine trait by environment relationships, and determine if environmental filtering plays a major role in structuring these communities. Environmental variables included multiple measures of mean and extreme monthly precipitation and temperature, solar radiation, elevation, slope, aspect, and time since last fire. Examining single year observations, we found functional trait values were weakly associated with environmental gradients with the exception of time since last fire, suggesting that environmental filtering plays a limited role in structuring community composition. However, an examination of changes in community aggregated traits through time shows that communities are functionally more similar than predicted by neutral processes, demonstrating that some filtering processes are in effect. Ultimately, while community-structuring processes appear to be weak within vegetation types, there is evidence for clear functional distinctions between vegetation types, most likely driven by fire dynamics.

Oregon Slender Salamander Occupancy in the Cascade Range:
A Unit and Sub-unit Sample Size Study

The Oregon Slender Salamander, a species of salamander endemic to the Northwestern United States, is vulnerable to habitat loss due to anthropogenic disturbances. Weyerhaeuser, a company that makes tree products by growing and harvesting trees in renewable cycles, would like to better understand the effect of tree harvest on the occupancy rate of the Oregon Slender Salamander in second growth commercial forests in Oregon’s Cascade Range. As a supplement to the Weyerhauser Company’s before-after control-impact study intended to determine the harvesting effect on the salamander’s occupancy in the treated areas, we conduct a sample size study. The goal is to maximize the precision and reduce bias of the estimate of the harvest effect on occupancy.
Because the data collection process for observing the Oregon Slender Salamander is costly, Weyerhauser wants to minimize the sample size but still precisely determine the harvesting effect on salamander occupancy over time. As the cost of travelling between stands is greater than the cost of searching more sub-plots within a stand, Weyerhaeuser specifically wants to determine whether more subplots increases precision enough to allow the use of fewer tree stands. Our sample size study involves simulation of salamander occupancy across different sample sizes followed by estimation of the harvest effect using the Gibbs Sampler implemented in JAGS (Just Another Gibbs Sampler).
With the simulated data, we used a statistical model in JAGS to estimate the harvest effect under various size settings to determine the settings’ effect on bias and precision.  The unit (stand) and sub-unit (sub-plot) sample size study simplifies the BACI study’s structure by simulating data for all three visits regardless of a sighting and determining its effect on only one year post-treatment.  We made various assignments for number of stands and number of sub-plots per stand while additionally accounting for different detection probabilities and post treatment occupancy probabilities. We fixed number of visits (three), number of years (two), the control or pre-treatment occupancy probability (95%), and the probability of sub-plot occupancy (50%). As one of the world’s largest private owners of timerlands, Weyerhaeuser is able to utilitize 60 stands in their study, but wanted the simulation results to apply to future studies implemented using a smaller framework in addition to their own study. As such, we simulated data using twenty, thirty, forty, fifty, and sixty tree stands and five, seven, and nine subplots in each stand. The various settings Weyerhaeuser selected for detection probability are 15% and 30% and 50% for each visit and a post treatment occupancy of 30% and 60%.
Given that the study’s model depends on binary responses based on occupancy, these selected probabilities were transformed to relative values on logit or log odds scale. The simulation is conducted top-down, i.e, stand occupancy is determined, followed by sub-plot occupancy dependent on whether or not a sub-plot’s stand was occupied, and finally visit-level occupancy based on detection probabilities dependent on the occupancy of its sub-plot being occupied. Once the occupancies are determined in the form of arrays containing 1’s and 0’s, we modeled the treatment effect for each group of simulations.
Using JAGS’s model output, we determined the average precision and bias of the estimates on the treatment effect across settings. We found that the precision of the estimate improved on average as number of stands increased as well as when the number of subplots increased. However, we noted that within a specific number of stands, the precision does not consistently improve as the number of subplots increases. We did not observe a consistent improvement in bias as the number of stands increased but did with an increase in number of subplots on average. However, this improvement is not consistently evident within a specific number of stands.

The occupancy model is a zero-inflated binomial regression model that has recently become the primary tool in the analysis of ecological presence-absence data as it accounts for the possibility of nondetection when a site is actually occupied.  We generalized the standard occupancy model to incorporate explicit spatial and temporal structure that is appropriate for data collected on areal units over multiple surveys.  Intrinsic conditional autoregressive (ICAR) models have become popular for adding spatial structure but possess potential confounding that can affect first-order inference.  We used a modification of the ICAR, known as a restricted spatial regression, to account for the spatial dependence between neighboring sites while retaining desirable first-order inference properties.  To model the changes in occupancy over time, we used a probabilistic cellular automata model to account for species’ spread with an additional long-distance component to account for the chance of colonization of a site lacking occupied neighbors.  We applied the model to the common myna (Acridotheres tristis), an invasive species in South Africa whose range has been expanding in recent decades, using data from the Southern African Bird Atlas Project (SABAP). The model fit suggests that myna occurrences are associated with high human population densities and that the range of the myna is expanding at a rate of approximately 3% a year, with the thrust of this expansion occurring along South Africa’s eastern coast and northward into Zimbabwe.  Furthermore, most of the myna's range expansion is through its neighborhood dispersals.  The spatio-temporal occupancy model we present is extremely flexible and can easily be adapted for more complicated long distance dispersal and persistence mechanisms.

Flying foxes (genus Pteropus) are natural reservoirs for viruses, contribute to maintaining biodiversity through pollination, and are also of interest for conservation. In Australia, the grey-headed flying fox (P. poliocephalus) and the spectacled flying fox (P. conspicillatus) are currently listed as vulnerable. Due to this listing, a spectacled flying fox monitoring program has been running in northern Queensland for several years and a national monitoring program intended to assess the population trends of all flying fox species commenced in February 2013. Both monitoring programs utilize monthly or quarterly counts of flying fox communities termed camps. These camp counts are a complete census or an estimate from a sub-sampling routine such as distance sampling. Adding to the challenge, not all camps will be located during surveying efforts. The challenge of such a surveying effort is in incorporating these different counting methods, accounting for their associated errors, into one cohesive estimate of the total population.
We develop a state-space model of spectacled flying fox population that addresses multiple population dynamics concerns such as seasonal proportions of flying foxes in camps, major weather events such as tropical cyclones and heat waves, and uncounted or unknown camps. Particle Markov Chain Monte Carlo methods are used to estimate total and in-camp populations. The observation error was estimated to be approximately 35%, or a coefficient of variation of approximately 65%. This estimate is reasonable given the difficulty of flying fox counting. Model estimates provide evidence that such a modelling approach can improve on raw counts from surveys.

Testing hypotheses on shape and distribution of ecological response curves

Niche theory with hypotheses on shape and distribution of ecological response curves is widely used in the studies of resource sharing of competing plant species. In the context of a study of response curves along a resource gradient in boreal forests, we developed bootstrap methods that allow for realistic testing of such hypotheses (Heikkinen & Mäkipää, Ecol. Mod. 221). In particular, our approach deals with unavoidable deficiencies in the estimated response curves caused by typical problematic features in vegetation data.
Our data originated from Finnish nation-wide soil and vegetation inventory. It contains both soil analyses and visual estimates of percentage cover of all vascular plants, bryophytes, and lichens from 455 inventory plots. Species response curves along a soil fertility gradient (in terms of C/N ratio) were estimated for 51 major species of the field layer vegetation using generalized additive models. The null hypotheses considered were: (1) species optima are uniformly distributed along the gradient, (2) niche width does not depend on the location of a species’ optimum, and (3) skewness of the response curve does not depend on the location of the optimum.
Estimation of species’ optima and, especially, niche width is affected by uneven distribution of observations along the gradient and by ‘censored’ responses of those species whose niche extends beyond the observed part of the gradient. In our bootstrap tests, the response curves estimated from the observed data are compared with those estimated in exactly the same manner from the resampled data, which is simulated according to the null hypothesis and has the same problematic features as the original data. For example, the estimate of the niche width may be unstable if the response curve is severely censored, but this will be accounted for by a large variance in its resampling distribution. The bootstrap approach also enables flexible handling of the distribution of abundance values, which is highly skewed non-negative and continuous with a substantial point mass at 0.

Spatio-Temporal Distribution of Two Eendemic Bird Species Based on Species Distribution Model

Christopher Ilori

Species distributions models (SDMs) have become a dominant paradigm for quantifying species-environment relationships, and their application has witnessed a dramatic growth in ecological research in recent decades. In Africa, however, few studies have used these models to study the distribution of endemic bird species. Species distribution models relate a set of recorded occurrences of a species to environmental variables believed to be important in determining the distribution of species, in order to predict where species will be found throughout a geographical space.
This study produces habitat suitability maps of the distributions of two endemic bird species in the Upper Guinea forest of West Africa using MaxEnt, a presence-only SDM algorithm. For current distributions, climate data spanning 50 years (1950 – 200) were obtained from WorldClim’s data portal. Models were developed for future distributions (2020 and 2050) from the Intergovernmental Panel for Climate Change’s (IPCC) HadCM3 climate model. Environmental layers were also obtained from different sources to examine the effects of different predictors. Environmental variables employed include elevation, slope, aspect, soil, vegetation, normalized difference vegetation index (NDVI) and Leaf Area Index (LAI). Nineteen bioclimatic variables representing 2020 and 2050 climates were also included. We used both large and few samples in modeling the two species to test the effect of sample size on the distribution of species.
While we identified future areas that might be designated as Important Bird Areas (IBAs) for protection of threatened species, we also determined the accuracy of SDMs predictions in a poorly studied region with few sample size. From the Jack-knife test results, NDVI had the highest training gain when used in isolation, and when excluded from the model, there was a decrease in mode gain. This implies that NDVI has the most useful information for predicting distributions by itself, and also has the most useful information that is not present in other variables. Based on our findings, there will be a decrease in species’ suitable areas by 2050 for the two species and the core areas will remain the most suitable habitats.
Finally, we showed that SDMs can be used to obtain information about environmental requirements of a species and can also assist in deploring resources to specific areas of interest.
Evidence from this study supports the demonstration in the literature that species with restricted geographical range produce better models than species with larger distributions. Future studies should account for biotic interaction, which is also an important factor for the distributions of species.

Traditional relationships between species and communities are difficult to apply to microbial communities. For example, rarefaction makes species richness an uninteresting measure of microbial diversity. Further, in DNA systems with multiple PCR primers employed to measure microbial communities, new models for handling multiple primers are necessary for use of non-richness-based diversity measures.  Methanotrophic bacteria are such a DNA system with multiple primers. We introduce a community model for multiple primer DNA-systems and apply it to communities of methanotrophic bacteria from across the Great Plains of the United States of America.
Additionally, we use the new estimates of community composition to compute the Shannon-Weiner diversity. We then take an information-theoretic approach to identify useful models for describing diversity across an environmental gradient. Models based on soil water content and soil texture (i.e., silt, sand, and clay content) work best.

The collapse of the cod fishery on the Scotian Shelf in the early 1990s led to a dramatic and persistent decline in the abundance and body size of predator fish over the last two decades. Hypotheses for the inability of these large predators to recover include predator-prey role reversal, wherein numerically dominant fish at lower trophic levels (forage fish) prey upon the early life stages of large predator fish, and intensified competition between these forage fish and small-bodied predators . Though there is correlative evidence for these hypotheses, here we explore their role more explicitly through the use of mechanistic, size-structured partial differential equation models. These models account for intraspecific variability in body size and diet by using species traits and individual physiology to track the flow of biomass through time and along a size spectrum (i.e. from small prey to larger predators). In order to evaluate the role of the above mechanisms in preventing the recovery of large predators, we develop a hierarchical Bayesian framework for such a size-structured food web model and apply it to 33 years of abundance-at-length estimates from 13 species from the Scotian Shelf. The size-structured food web model is generally successful in capturing the dynamics and structure of the Scotian Shelf fish community following the collapse of the cod fishery, though food web coupling strengths do not seem to be well-identified, making it difficult to detect a signal of predator-prey role reversal. Nonetheless, this work still offers mechanistic insight into the processes structuring the Scotian Shelf fish community and has the potential to inform management policies that facilitate recovery and prevent such dramatic collapses from occurring elsewhere. In addition, this work provides the foundation for future work that explores more broadly the trait diversity and food web mechanisms required to effectively model the dynamics of real marine communities.

A year-long for-hire study conducted by the National Marine Fisheries Service of catch by charter boats in the Gulf of Mexico allowed for estimation of expected Red Snapper harvest from two data sources: logbook and dockside reports. The former contained information reported directly by vessel captains and the latter required hiring port officials to verify catch quantities. We defined an estimator for expected harvest, tau, where tau is a function of the expected number of trips , expected effort psi in hours spent fishing, and the expected catch per unit of effort (cpue) lambda in numbers. We employed a Bayesian approach to estimate tau and obtained 95% credible intervals directly from the quantiles of the posterior distribution. A posterior predictive distribution of tau was computed by multiplying samples from posterior predictive distributions of expected cpue, expected effort, and expected number of trips. Selecting a distributional form for effort was complicated by the presence of extreme values while the distributional form for cpue was complicated by a high peak in the data with scattered larger values present. Additional verication sampling was conducted to estimate the percentage of compliance for estimation of expected number of trips. Credible intervals of weekly and cumulative expected harvest during the Red Snapper harvest season, June 1-July 18 , 2011, from logbook reports and dockside reports largely overlapped. Overall, logbook reports provided comparable results and narrower credible intervals to the more reliable dockside reports.

Joe Maurer, Dan Dalthorp and Manuela Huso

In estimating fatality at wind power facilities, we generally focus on two primary sources of imperfect detection: 1) carcasses are removed before sampling, and 2) carcasses present in the searched area are missed by observers. A third source that is often overlooked is that carcasses land in unsearched areas. We focus on this aspect to evaluate the potential for estimating total site fatality from carcasses observed on roads and pads. We consider three estimators: a ratio estimator (ratio), parametric model estimator (glm), and an empirical method (cake), all of which have been suggested in reports or in the peer-reviewed literature. Comparisons are made considering different (1) per-turbine fatality rates, (2) distance distribution functions, and (3) anisotropic conditions. Preliminary results suggest the cake and glm methods may be preferred when rates are low as the ratio methods is biased and has relatively more variation. However, the ratio estimator may be preferred when rates are high and anisotropy is present but unaccounted for by the other methods.  We discuss potential approaches to account for anisotropy in the three methods.

Joseph M. Northrup, Charles R. Anderson Jr., George Wittemyer

The field of animal movement has advanced rapidly over the last decade. Improvements in collar technology allow the collection of highly detailed and accurate location data that can now be paired with behavioral or physiological data such as heart rates and diving depths of marine mammals. Concurrent advances in statistical and mathematical methods provide insight into an array of complicated ecological processes including the environmental drivers of habitat selection, and the location and timing of different behavioral modes. These advances have provided a means to answer important questions in ecology and evolution with substantial implications for the conservation and management of species. Indeed, the field of animal movement is a natural fit for understanding how changing environmental and anthropogenic stressors can influence the behavior, and ultimately population dynamics of wildlife. However, due to the substantial need for methodological development in this field there has been relatively little application to pressing conservation or management issues particularly in the terrestrial environment. Here we use statistical models for animal movement to understand optimal foraging patterns of mule deer and the potential influence of environmental and anthropogenic stressors on these patterns. We captured adult (>1 year old) female mule deer in the Piceance Basin of Colorado between 2010 and 2013 and fit them with global positioning system (GPS) radio collars set to obtain fixes once every hour or once every 30 minutes. We fit a latent state mixture model to the resulting data in a Bayesian framework.

Ground level ozone is a harmful pollutant that negatively affects people as well as plant species, and these negative effects are intensified when ozone is at its most extreme levels. This project aims to increase understanding of the meteorological conditions which lead to extreme ozone levels. Our approach differs from previous methods in that it focuses only on the tail behavior by utilizing the framework of regular variation. Our approach has two parts. The first is an optimization problem: given a set of continuous meteorological covariates, we aim to find the linear combination of these covariates which has the highest degree of tail dependence with ozone. The second is a data mining problem: given a long list of possible meteorological covariates, we seek to find the ones which are linked to extreme ozone.
To find the linear combination of covariates which optimizes tail dependence with ozone, we use a constrained optimization procedure which maximizes a measure of tail dependence and whose constraint enforces a requirement on the marginal distribution. Our optimization procedure requires that we consider tail dependence estimators with a smooth threshold, rather than the hard threshold typical of extremes, and we consider the consistency of estimators with smoothed thresholds. We quantify uncertaintly in our parameter estimates using the nonparametric bootstrap. To find the subset of covariates that are most strongly associated with extreme ozone, we search the model space using a simulated annealing algorithm. In this data mining procedure, we use a model comparison criterion based on cross-validation. We present a simulation study which shows that the method can detect complicated conditions leading to extreme responses. We apply the data mining method to ozone data for Atlanta and Charlotte and find similar meteorological drivers for these two Southeastern US cities. While several of these meteorological covariates are known to be linked to ozone concentrations, our procedure suggests some additional covariates which may influence extreme ozone levels.
Our results show that covariates such as air temperature, wind speed, and downward short wave radiation flux are influential in producing extreme ozone events. More importantly, our analysis shows that other covariates such as the height of the planetary boundary layer and relative humidity may also be important for creating the conditions which lead to extreme ozone levels.
Precipitation has been a curious covariate. The fact that it is not continuous has necessitated its inclusion as an indicator variable, which has required an adjustment to our model fitting procedure. Jacob and Winner (2009) show that precipitation has little effect on ground level ozone pollution. However, our data mining procedure finds precipitation to be an important covariate in terms of extreme ozone events.
The results of the data mining procedure suggest a group of meteorological covariates to be included when studying extreme ozone. We would like to investigate a spatial extension of our model to reduce uncertainty and provide additional understanding of how the meteorological drivers of extreme ozone differ over a larger spatial domain. To this end, we are currently analyzing multiple locations within EPA regions 3 and 4. Preliminary results suggest that the drivers of extreme ozone vary over this spatial domain. For example, we find that cloud cover and wind speed seem to vary in importance throughout the region. We are currently working towards using this knowledge to assist us in modeling the parameters in our method spatially.

Tree growth estimation is a challenging task as difficulties associated with data collection and inference often result in inaccurate estimates. Two main methods for tree growth estimation are diameter tape measurements and increment cores. The former involves repeatedly measuring tree diameters with a cloth or metal tape whose scale has been adjusted to give diameter readings directly. This approach has the advantage that diameters can be measured rapidly. However, due to the substantial error involved during tape measurements, negative diameter increments are often observed. Alternatively, annual radius increment data can be obtained by taking tree cores and averaging repeated measurements of the ring widths. However, acquiring and analyzing tree cores is a time consuming process, and taking multiple cores may have negative effects on tree health. Therefore, radius increment data is typically only available for a subset of trees within a stand.
We offer a fusion of the data sources which enables us to accommodate missingness and to borrow strength across individuals. It enables individual tree level inference as well as average or stand level inference. We apply our modeling to a fairly large dataset taken from two forest stands in Duke Forest, Durham, North Carolina, collected from 1991 to 2011. 

Mechanisms shaping occupancy-abundance relationships of avian malaria parasites in the Lesser Antilles

Letícia Soares, Robert Ricklefs

The positive correlation between local population abundances and geographic distribution is among the few universal laws in ecology. In the archipelago of the Lesser Antilles, avian malaria parasites (order Haemosporida: Plasmodium and Haemoproteus) show such correlation: the number of islands a lineage occupies is directly proportional to its average prevalence. Interestingly, avian host species are also distributed in the archipelago in a way that their abundances have a positive correspondence with the number of islands where they are found. We are interested in estimating host individual-related infection probabilities, for individual parasite lineages. We hypothesize that individual infection probabilities, on islands and in island host populations, are a function of host relative abundances, host community composition, and the presence of other parasites. Here, we introduce an individual-based model that estimates the probability of infection with a host-generalist and geographically widespread parasite lineage.
We use ideas from the hypothesis of core-satellite species to build the individual-based models presented here. Hanki’s core-satellite hypothesis predicts that the occurrence of core species across the space is more or less constant over the time, and that competition is the main force determining their abundances, which can be seen through little or non resource use overlap by these species. On the other hand, satellite species tend to have some considerable resource use overlap, and high geographic and temporal turnover. In the West Indies, we have two evidences to believe that avian malaria lineages behave in metapopulation dynamics of core and satellite lineages occupying ‘host population patches’ in space. The first evidence is the previously mentioned positive prevalence-occupancy relationship, and the second evidence is the turnover across host populations, of widespread and highly prevalent pathogen lineages. As an example, populations the bananaquit (Coereba flaveola) are mainly infected by two lineages: one host-specialist (LA 07), and one host-generalist (OZ 21). These lineages shift dominance across the islands, in a way that they are never concomitantly found in high frequencies in the same population.

Tree recruitment at range limits: too hot, too cold, or competition?

Bradley J. Tomasek, Matt Kwit, James S. Clark, Jerry Mellilo, & Jaqueline Mohan

If sensitivity to environmental factors differs among tree species, climate change could change the composition of forests ecosystems through species migration. The sensitivity of recruitment is especially important, as seedlings must germinate and survive outside of the current ranges of adults in order to migrate. As a result, factors controlling current range limits are important for understanding future impacts of climate change on our forests. Physiological stress caused by cooler climates is often expected to have the greatest impact at northern range limits, while competition is expected to be more limiting at southern range limits (the climate-competition hypothesis).
We tested the climate-competition hypothesis on recruitment by combining data of germination and survival for common eastern temperate tree species grown from both experimentally heated open-air plots and natural observational plots. Experimental treatments were implemented in a factorial design, with two light treatments (gap or understory) and three temperatures (ambient, +3C, +5C), to determine the relative importance of climate and competition for recruitment at both the Duke and Harvest Forests. We utilized a zero-inflated binomial Bayesian modeling approach to quantify the effects of environmental variability on germination of tree seeds. The model framework is robust enough to account for the substantial number of cases where no seedlings in a cohort will germinate, and flexible enough to coherently integrate germination data derived from both experimental and observational field studies. Regular censuses in the experimental plots allowed us to track the summer and winter survival of individual seedlings, which we quantified using species-specific logistic regressions.
Results were opposed to the predictions from the climate-competition hypothesis for range limits. The largest climatic effect on survival was summer temperatures, which decreased survival for most species. Despite anomalously cold years during the study, winter temperatures did not show the expected effect on survival. Competition with the canopy for light and moisture had a large impact on germination and survival of all species. Positive interactions between light levels and summer temperatures were observed for 25% of species. In contrast, the gap treatment did not have significant effects on winter survival. Germination showed similar patterns of decline with increasing temperatures. Overall, summer temperatures exerted a stronger regulation of recruitment than winter temperatures by decreasing both germination and survival rates. Further, competition for light and moisture may be equally important in regulating recruitment at both northern and southern boundaries.

Reconstructing population trends using a state space model based on an in situ mark-resighting method to assess the abundance of spawners at fish spawning aggregation

Lynn Waterhouse, Brice X. Semmens, Phillipe Bush, Scott A. Heppell, Christy Pattengill-Semmens, Croy McCoy, Bradley Johson

This study presents a reconstruction of the abundance of an endangered species, the Nassau grouper, at a spawning aggregation sight in Little Cayman Island, Cayman Islands.  An in situ visual mark-resighting design is described which can be used to estimate total abundance of spawners at the aggregation site. Mark-resight data can be used to estimate the population size during each spawning aggregation, which in turn can be fit using a state space model to obtain an estimate the population growth rate. 
Nassau grouper form large reproductive aggregations at highly predictable times (winter full moons) and locations throughout their range. Once aggregations of the species are discovered, they are typically fished intensively each winter; many such aggregations have ultimately been fished to the point where fish apparently cease to aggregate.  Management actions in the Cayman Islands include seasonal closures during spawning and marine protected areas at aggregation sites.  A main goal is to evaluate the effectiveness of such restrictions placed on the Nassau grouper fishery in the hopes of rebuilding and protecting the population.  The data were collected as part of the Grouper Moon program, a collaborative research program between Reef Environmental Education Foundation (REEF), Cayman Islands Department of Environment, Oregon State University, and Scripps Institution of Oceanography, aimed at documenting the success of management actions established in order to protect Nassau grouper.
The mark-resight method takes advantage of the high density and approachability of aggregating grouper by SCUBA divers in order to tag a subset of aggregating Nassau grouper, and subsequently generate surveys of the proportion of tagged individuals in discrete counts. These proportions are subsequently used to estimate total population size. For a variety of reasons, including minimizing harm to the animals (i.e., short and long term tag induced mortality or tagging related changes to reproductive success), it is necessary to balance the trade-off between number of tagged individuals and accuracy of population estimates based on resightings data. Simulation methods can be used to identify trade-offs between number of individuals tagged and number of subsequent surveys required in order to meet an acceptable level of uncertainty in population estimates. When estimating the total population size, the inclusion of covariates such as observer, date, and time can be evaluated.
In addition to the use of seven years of in situ (Floytag) visual mark-resighting data, video analysis can be used to estimate population abundance.  Two different types of video are recorded during each field season: video pans are taken to aid in estimating total population and a custom video recorder with parallel-mounted lasers is used to collect size frequency data.  Video pans are dependent on fish behaviors and may not be possible when aggregations are too dense or over dispersed; however, at times they can be used for collecting mark-resight data.  The laser video for size frequency distribution captures a much smaller total number of fish but enables one to collect an additional source of mark-resight data.  Combining all three types of data increases the sample size used to estimate overall abundance. An estimate of the growth rate is found by fitting a state space model to the posterior distributions of Bayesian estimates for population abundance over time.  When combined with the size-frequency data, the estimates of population growth rate and abundance provide more information on the status of the Nassau grouper.  Ideally, an increase in population size would be coupled with an increase in smaller sizes, indicating recruitment to the spawning aggregation.