On thinning of chains in MCMC

1. Markov chain Monte Carlo (MCMC) is a simulation technique that has revolutionised the analysis of ecological data, allowing the fitting of complex models in a Bayesian framework. Since 2001, there have been nearly 200 papers using MCMC in publications of the Ecological Society of America and the British Ecological Society, including more than 75 in the journal Ecology and 35 in the Journal of Applied Ecology. 2. We have noted that many authors routinely ‘thin’ their simulations, discarding all but every kth sampled value; of the studies we surveyed with details on MCMC implementation, 40% reported thinning. 3. Thinning is often unnecessary and always inefficient, reducing the precision with which features of the Markov chain are summarised. The inefficiency of thinning MCMC output has been known since the early 1990’s, long before MCMC appeared in ecological publications. 4. We discuss the background and prevalence of thinning, illustrate its consequences, discuss circumstances when it might be regarded as a reasonable option and recommend against routine thinning of chains unless necessitated by computer memory limitations

Estimating age from recapture data: integrating incremental growth measures with ancillary data to infer age-at-length

Estimating the age of individuals in wild populations can be of fundamental importance for answering ecological questions, modeling population demographics, and managing exploited or threatened species. Significant effort has been devoted to determining age through the use of growth annuli, secondary physical characteristics related to age, and growth models. Many species, however, either do not exhibit physical characteristics useful for independent age validation or are too rare to justify sacrificing a large number of individuals to establish the relationship between size and age. Length-at-age models are well represented in the fisheries and other wildlife management literature. Many of these models overlook variation in growth rates of individuals and consider growth parameters as population parameters. More recent models have taken advantage of hierarchical structuring of parameters and Bayesian inference methods to allow for variation among individuals as functions of environmental covariates or individual-specific random effects. Here, we describe hierarchical models in which growth curves vary as individual-specific stochastic processes, and we show how these models can be fit using capture–recapture data for animals of unknown age along with data for animals of known age. We combine these independent data sources in a Bayesian analysis, distinguishing natural variation (among and within individuals) from measurement error. We illustrate using data for African dwarf crocodiles, comparing von Bertalanffy and logistic growth models. The analysis provides the means of predicting crocodile age, given a single measurement of head length. The von Bertalanffy was much better supported than the logistic growth model and predicted that dwarf crocodiles grow from 19.4 cm total length at birth to 32.9 cm in the first year and 45.3 cm by the end of their second year. Based on the minimum size of females observed with hatchlings, reproductive maturity was estimated to be at nine years. These size benchmarks are believed to represent thresholds for important demographic parameters; improved estimates of age, therefore, will increase the precision of population projection models. The modeling approach that we present can be applied to other species and offers significant advantages when multiple sources of data are available and traditional aging techniques are not practical

Implementation of an occupancy-based monitoring protocol for a widespread and cryptic species, the New England cottontail (Sylvilagus transitionalis)

Context. Designing effective long-term monitoring strategies is essential for managing wildlife populations. Implementing a cost-effective, practical monitoring program is especially challenging for widespread but locally rare species. Early successional habitat preferred by the New England cottontail (NEC) has become increasingly rare and fragmented, resulting in substantial declines from their peak distribution in the mid-1900s. The introduction of a possible competitor species, the eastern cottontail (EC),may also have played a role. Uncertainty surrounding how these factors have contributed to NEC declines has complicated management and necessitated development of an appropriate monitoring framework to understand possible drivers of distribution and dynamics. Aims. Because estimating species abundance is costly, we designed presence–absence surveys to estimate species distributions, test assumptions about competitive interactions, and improve understanding of demographic processes for eastern cottontails (EC) and New England cottontails (NEC). The survey protocol aimed to balance long-term management objectives with practical considerations associated with monitoring a widespread but uncommon species. Modelling data arising from these observations allow for estimation of covariate relationships between species status and environmental conditions including habitat and competition. The framework also allows inference about species status at unsurveyed locations. Methods. Wedesigned a monitoring protocol to collect data across six north-easternUSAstates and, using data collected from the first year of monitoring, fit a suite of single-season occupancy models to assess how abiotic and biotic factors influence NEC occurrence, correcting for imperfect detectability. Key results. Models did not provide substantial support for competitive interactions between EC and NEC. NEC occurrence patterns appear to be influenced by several remotely sensed habitat covariates (land-cover classes), a habitatsuitability index, and, to a lesser degree, plot-level habitat covariates (understorey density and canopy cover). Conclusions. We recommend continuing presence–absence monitoring and the development of dynamic occupancy models to provide further evidence regarding hypotheses of competitive interactions and habitat influences on the underlying dynamics of NEC occupancy. Implications. State and federal agencies responsible for conserving this and other threatened species can engage with researchers in thoughtful discussions, based on management objectives, regarding appropriate monitoring design to ensure that the allocation of monitoring efforts provides useful inference on population drivers to inform management intervention

Implementation of an occupancy-based monitoring protocol for a widespread and cryptic species, the New England cottontail (Sylvilagus transitionalis)

Context. Designing effective long-term monitoring strategies is essential for managing wildlife populations. Implementing a cost-effective, practical monitoring program is especially challenging for widespread but locally rare species. Early successional habitat preferred by the New England cottontail (NEC) has become increasingly rare and fragmented, resulting in substantial declines from their peak distribution in the mid-1900s. The introduction of a possible competitor species, the eastern cottontail (EC),may also have played a role. Uncertainty surrounding how these factors have contributed to NEC declines has complicated management and necessitated development of an appropriate monitoring framework to understand possible drivers of distribution and dynamics. Aims. Because estimating species abundance is costly, we designed presence–absence surveys to estimate species distributions, test assumptions about competitive interactions, and improve understanding of demographic processes for eastern cottontails (EC) and New England cottontails (NEC). The survey protocol aimed to balance long-term management objectives with practical considerations associated with monitoring a widespread but uncommon species. Modelling data arising from these observations allow for estimation of covariate relationships between species status and environmental conditions including habitat and competition. The framework also allows inference about species status at unsurveyed locations. Methods. Wedesigned a monitoring protocol to collect data across six north-easternUSAstates and, using data collected from the first year of monitoring, fit a suite of single-season occupancy models to assess how abiotic and biotic factors influence NEC occurrence, correcting for imperfect detectability. Key results. Models did not provide substantial support for competitive interactions between EC and NEC. NEC occurrence patterns appear to be influenced by several remotely sensed habitat covariates (land-cover classes), a habitatsuitability index, and, to a lesser degree, plot-level habitat covariates (understorey density and canopy cover). Conclusions. We recommend continuing presence–absence monitoring and the development of dynamic occupancy models to provide further evidence regarding hypotheses of competitive interactions and habitat influences on the underlying dynamics of NEC occupancy. Implications. State and federal agencies responsible for conserving this and other threatened species can engage with researchers in thoughtful discussions, based on management objectives, regarding appropriate monitoring design to ensure that the allocation of monitoring efforts provides useful inference on population drivers to inform management intervention

Implementation of an occupancy-based monitoring protocol for a widespread and cryptic species, the New England cottontail (Sylvilagus transitionalis)

Context. Designing effective long-term monitoring strategies is essential for managing wildlife populations. Implementing a cost-effective, practical monitoring program is especially challenging for widespread but locally rare species. Early successional habitat preferred by the New England cottontail (NEC) has become increasingly rare and fragmented, resulting in substantial declines from their peak distribution in the mid-1900s. The introduction of a possible competitor species, the eastern cottontail (EC),may also have played a role. Uncertainty surrounding how these factors have contributed to NEC declines has complicated management and necessitated development of an appropriate monitoring framework to understand possible drivers of distribution and dynamics. Aims. Because estimating species abundance is costly, we designed presence–absence surveys to estimate species distributions, test assumptions about competitive interactions, and improve understanding of demographic processes for eastern cottontails (EC) and New England cottontails (NEC). The survey protocol aimed to balance long-term management objectives with practical considerations associated with monitoring a widespread but uncommon species. Modelling data arising from these observations allow for estimation of covariate relationships between species status and environmental conditions including habitat and competition. The framework also allows inference about species status at unsurveyed locations. Methods. Wedesigned a monitoring protocol to collect data across six north-easternUSAstates and, using data collected from the first year of monitoring, fit a suite of single-season occupancy models to assess how abiotic and biotic factors influence NEC occurrence, correcting for imperfect detectability. Key results. Models did not provide substantial support for competitive interactions between EC and NEC. NEC occurrence patterns appear to be influenced by several remotely sensed habitat covariates (land-cover classes), a habitatsuitability index, and, to a lesser degree, plot-level habitat covariates (understorey density and canopy cover). Conclusions. We recommend continuing presence–absence monitoring and the development of dynamic occupancy models to provide further evidence regarding hypotheses of competitive interactions and habitat influences on the underlying dynamics of NEC occupancy. Implications. State and federal agencies responsible for conserving this and other threatened species can engage with researchers in thoughtful discussions, based on management objectives, regarding appropriate monitoring design to ensure that the allocation of monitoring efforts provides useful inference on population drivers to inform management intervention

Testing metapopulation concepts: effects of patch characteristics and neighborhood occupancy on the dynamics of an endangered lagomorph

Metapopulation ecology is a field that is richer in theory than in empirical results. Many existing empirical studies use an incidence function approach based on spatial patterns and key assumptions about extinction and colonization rates. Here we recast these assumptions as hypotheses to be tested using 18 years of historic detection survey data combined with four years of data from a new monitoring program for the Lower Keys marsh rabbit. We developed a new model to estimate probabilities of local extinction and colonization in the presence of nondetection, while accounting for estimated occupancy levels of neighboring patches. We used model selection to identify important drivers of population turnover and estimate the effective neighborhood size for this system. Several key relationships related to patch size and isolation that are often assumed in metapopulation models were supported: patch size was negatively related to the probability of extinction and positively related to colonization, and estimated occupancy of neighboring patches was positively related to colonization and negatively related to extinction probabilities. This latter relationship suggested the existence of rescue effects. In our study system, we inferred that coastal patches experienced higher probabilities of extinction and colonization than interior patches. Interior patches exhibited higher occupancy probabilities and may serve as refugia, permitting colonization of coastal patches following disturbances such as hurricanes and storm surges. Our modeling approach should be useful for incorporating neighbor occupancy into future metapopulation analyses and in dealing with other historic occupancy surveys that may not include the recommended levels of sampling replication

Testing metapopulation concepts: effects of patch characteristics and neighborhood occupancy on the dynamics of an endangered lagomorph

Metapopulation ecology is a field that is richer in theory than in empirical results. Many existing empirical studies use an incidence function approach based on spatial patterns and key assumptions about extinction and colonization rates. Here we recast these assumptions as hypotheses to be tested using 18 years of historic detection survey data combined with four years of data from a new monitoring program for the Lower Keys marsh rabbit. We developed a new model to estimate probabilities of local extinction and colonization in the presence of nondetection, while accounting for estimated occupancy levels of neighboring patches. We used model selection to identify important drivers of population turnover and estimate the effective neighborhood size for this system. Several key relationships related to patch size and isolation that are often assumed in metapopulation models were supported: patch size was negatively related to the probability of extinction and positively related to colonization, and estimated occupancy of neighboring patches was positively related to colonization and negatively related to extinction probabilities. This latter relationship suggested the existence of rescue effects. In our study system, we inferred that coastal patches experienced higher probabilities of extinction and colonization than interior patches. Interior patches exhibited higher occupancy probabilities and may serve as refugia, permitting colonization of coastal patches following disturbances such as hurricanes and storm surges. Our modeling approach should be useful for incorporating neighbor occupancy into future metapopulation analyses and in dealing with other historic occupancy surveys that may not include the recommended levels of sampling replication

Spatial Patch Occupancy Patterns of the Lower Keys Marsh Rabbit

Reliable estimates of presence or absence of a species can provide substantial information on management questions related to distribution and habitat use but should incorporate the probability of detection to reduce bias. We surveyed for the endangered Lower Keys marsh rabbit (Sylvilagus palustris hefneri) in habitat patches on 5 Florida Key islands, USA, to estimate occupancy and detection probabilities. We derived detection probabilities using spatial replication of plots and evaluated hypotheses that patch location (coastal or interior) and patch size influence occupancy and detection. Results demonstrate that detection probability, given rabbits were present, was \u3c0.5 and suggest that naı¨ve estimates (i.e., estimates without consideration of imperfect detection) of patch occupancy are negatively biased. We found that patch size and location influenced probability of occupancy but not detection. Our findings will be used by Refuge managers to evaluate population trends of Lower Keys marsh rabbits from historical data and to guide management decisions for species recovery. The sampling and analytical methods we used may be useful for researchers and managers of other endangered lagomorphs and cryptic or fossorial animals occupying diverse habitats

Global change and conservation triage on National Wildlife Refuges

National Wildlife Refuges (NWRs) in the United States play an important role in the adaptation of social-ecological systems to climate change, land-use change, and other global-change processes. Coastal refuges are already experiencing threats from sea-level rise and other change processes that are largely beyond their ability to influence, while at the same time facing tighter budgets and reduced staff. We engaged in workshops with NWR managers along the U.S. Atlantic coast to understand the problems they face from global-change processes and began a multidisciplinary collaboration to use decision science to help address them. We are applying a values-focused approach to base management decisions on the resource objectives of land managers, as well as those of stakeholders who may benefit from the goods and services produced by a refuge. Two insights that emerged from our workshops were a conspicuous mismatch between the scale at which management can influence outcomes and the scale of environmental processes, and the need to consider objectives related to ecosystem goods and services that traditionally have not been explicitly considered by refuges (e.g., protection from storm surge). The broadening of objectives complicates the decision-making process, but also provides opportunities for collaboration with stakeholders who may have agendas different from those of the refuge, as well as an opportunity for addressing problems across scales. From a practical perspective, we recognized the need to (1) efficiently allocate limited staff time and budgets for short-term management of existing programs and resources under the current refuge design and (2) develop long-term priorities for acquiring or protecting new land/habitat to supplement or replace the existing refuge footprint and thus sustain refuge values as the system evolves over time. Structuring the decision-making problem in this manner facilitated a better understanding of the issues of scale and suggested that a long-term solution will require a significant reassessment of objectives to better reflect the comprehensive values of refuges to society. We discuss some future considerations to integrate these two problems into a single framework by developing novel optimization approaches for dynamic problems that account for uncertainty in future conditions