Persistence for ecosystem microcosm models

A qualitative analysis of a system of autonomous differential equations modelling an ecosystem microcosm is carried out from the point of view of persistence. Necessary and sufficient conditions are given that no trajectory with positive initial conditions has a component that tends to zero asymptotically or reaches zero in finite time. The results are stated in terms of threshold levels for the input nutrient parameter in the system.     

Age-dependent survival analyzed with Bayesian models of mark-recapture data

We describe a Bayesian random effects model of mark-recapture data that accounts for age-dependence in survival and individual heterogeneity in capture probabilities and survival. The model is applied to data on the Glanville fritillary butterfly (Melitaea cinxia) collected from a population enclosed in a large cage in the field. The cage population consisted of a mixture of butterflies originating from newly established and old populations in a large metapopulation in the Aland Islands in Finland. The explanatory variables in the model included the effects of temperature, sex, and population type (new vs. old) on capture probabilities, and the effects of age, sex, population type, and day vs. night on survival. We found that mortality rate increased with age, that mortality rate was much higher during the day than during the night, and that the life span of females originating from newly established populations was shorter than the life span of females from old populations. Capture probability decreased with increasing temperature and decreased with increasing mobility of individuals.     

Trap mortality in mark-recapture studies

When animals die in traps in a mark-recapture study, straightforward likelihood inferences are possible in a class of models. The class includes M₀, M_t, and M_b as reported by White et al. (Los Alamos National Laboratory, LA-8787-NERP, pp 235, 1982), those that do not involve heterogeneity. We include three Markov chain “persistence” models and show that they provide good fits in a trapping study of deer mice in the Cascade-Siskiyou National Monument of Southern Oregon where trapping mortality was high.

Flexible hierarchical mark-recapture modeling for open populations using WinBUGS

Hierarchical mark-recapture models offer three advantages over classical mark-recapture models: (i) they allow expression of complicated models in terms of simple components; (ii) they provide a convenient way of modeling missing data and latent variables in a way that allows expression of relationships involving latent variables in the model; (iii) they provide a convenient way of introducing parsimony into models involving many nuisance parameters. Expressing models using the complete data likelihood we show how many of the standard mark-recapture models for open populations can be readily fitted using the software WinBUGS. We include examples that illustrate fitting the Cormack–Jolly–Seber model, multi-state and multi-event models, models including auxiliary data, and models including density dependence.

Bayesian methods for analyzing movements in heterogeneous landscapes from mark-recapture data

Spatially referenced mark-recapture data are becoming increasingly available, but the analysis of such data has remained difficult for a variety of reasons. One of the fundamental problems is that it is difficult to disentangle inherent movement behavior from sampling artifacts. For example, in a typical study design, short distances are sampled more frequently than long distances. Here we present a modeling-based alternative that combines a diffusion-based process model with an observation model to infer the inherent movement behavior of the species from the data. The movement model is based on classifying the landscape into a number of habitat types, and assuming habitat-specific diffusion and mortality parameters, and habitat selection at edges between the habitat types. As the problem is computationally highly intensive, we provide software that implements adaptive Bayesian methods for effective sampling of the posterior distribution. We illustrate the modeling framework by analyzing individual mark-recapture data on the Glanville fritillary butterfly (Melitaea cinxia), and by comparing our results with earlier ones derived from the same data using a purely statistical approach. We use simulated data to perform an analysis of statistical power, examining how accuracy in parameter estimates depends on the amount of data and on the study design. Obtaining precise estimates for movement rates and habitat preferences turns out to be especially challenging, as these parameters can be highly correlated in the posterior density. We show that the parameter estimates can be considerably improved by alternative study designs, such as releasing some of the individuals into the unsuitable matrix, or spending part of the recapture effort in the matrix.     

Photographic mark-recapture analysis of local dynamics within an open population of dolphins

Identifying demographic changes is important for understanding population dynamics. However, this requires long-term studies of definable populations of distinct individuals, which can be particularly challenging when studying mobile cetaceans in the marine environment. We collected photo-identification data from 19 years (1992-2010) to assess the dynamics of a population of bottlenose dolphins (Tursiops truncatus) restricted to the shallow (<7 m) waters of Little Bahama Bank, northern Bahamas. This population was known to range beyond our study area, so we adopted a Bayesian mixture modeling approach to mark-recapture to identify clusters of individuals that used the area to different extents, and we specifically estimated trends in survival, recruitment, and abundance of a "resident" population with high probabilities of identification. There was a high probability (p= 0.97) of a long-term decrease in the size of this resident population from a maximum of 47 dolphins (95% highest posterior density intervals, HPDI = 29-61) in 1996 to a minimum of just 24 dolphins (95% HPDI = 14-37) in 2009, a decline of 49% (95% HPDI = approximately 5% to approximately 75%). This was driven by low per capita recruitment (average approximately 0.02) that could not compensate for relatively low apparent survival rates (average approximately 0.94). Notably, there was a significant increase in apparent mortality (approximately 5 apparent mortalities vs. approximately 2 on average) in 1999 when two intense hurricanes passed over the study area, with a high probability (p = 0.83) of a drop below the average survival probability (approximately 0.91 in 1999; approximately 0.94, on average). As such, our mark-recapture approach enabled us to make useful inference about local dynamics within an open population of bottlenose dolphins; this should be applicable to other studies challenged by sampling highly mobile individuals with heterogeneous space use.     

Multiple data sources improve DNA-based mark-recapture population estimates of grizzly bears.

A fundamental challenge to estimating population size with mark-recapture methods is heterogeneous capture probabilities and subsequent bias of population estimates. Confronting this problem usually requires substantial sampling effort that can be difficult to achieve for some species, such as carnivores. We developed a methodology that uses two data sources to deal with heterogeneity and applied this to DNA mark-recapture data from grizzly bears (Ursus arctos). We improved population estimates by incorporating additional DNA "captures" of grizzly bears obtained by collecting hair from unbaited bear rub trees concurrently with baited, grid-based, hair snag sampling. We consider a Lincoln-Petersen estimator with hair snag captures as the initial session and rub tree captures as the recapture session and develop an estimator in program MARK that treats hair snag and rub tree samples as successive sessions. Using empirical data from a large-scale project in the greater Glacier National Park, Montana, USA, area and simulation modeling we evaluate these methods and compare the results to hair-snag-only estimates. Empirical results indicate that, compared with hair-snag-only data, the joint hair-snag-rub-tree methods produce similar but more precise estimates if capture and recapture rates are reasonably high for both methods. Simulation results suggest that estimators are potentially affected by correlation of capture probabilities between sample types in the presence of heterogeneity. Overall, closed population Huggins-Pledger estimators showed the highest precision and were most robust to sparse data, heterogeneity, and capture probability correlation among sampling types. Results also indicate that these estimators can be used when a segment of the population has zero capture probability for one of the methods. We propose that this general methodology may be useful for other species in which mark-recapture data are available from multiple sources.     

Effect of predation threat on repeatability of individual crab behavior revealed by mark-recapture

The persistence of behavioral types in situ and the drivers of persistence are central to predicting the ecological effects of intraspecific behavioral variation. We surveyed individual refuge use of mud crabs (Panopeus herbstii), a behavior related to the strength of a trait-mediated trophic cascade in oyster reefs, in the absence and presence of toadfish (Opsanus tau) predation threat. We then released these crabs into the field and using mark-recapture, measured the repeatability of this behavior in the absence and presence of threat, and how behavioral change was affected by time in the field (a month on average, up to 81 days), crab size, and sex. Because crabs exhibited some evidence of a circatidal rhythm in refuge use, we also tested how tidal height during observation influenced behavioral change. Predation threat increased refuge use, and small crabs used the refuge more than large crabs, particularly under threat. In recaptured crabs, refuge use was more repeatable under threat. Neither time in the field, crab size, crab sex, nor tidal height had any effect on behavioral change. Our results support the non-mutually exclusive hypotheses that (1) prey organisms in the presence, rather than absence, of predation threat should exhibit less behavioral variability because the fear of dying (a severe fitness consequence) should take precedence over less immediately important influences on behavior (e.g., hunger) and that (2) individual behaviors tied to fixed traits (e.g., the body size dependence of refuge use under threat in this study), rather than variable traits, should be more repeatable over time.     

Using multistate mark-recapture methods to model adult salmonid migration in an industrialized river

A multistate mark-recapture (MSMR) model of the adult salmonid migration through the lower Columbia River and into the Snake River was developed, designed for radiotelemetry detections at dams and tributary mouths. The model focuses on upstream-directed travel, with states determined from observed fish movement patterns indicating directed upstream travel, downstream travel (fallback), and use of non-natal tributaries. The model was used to analyze telemetry data from 846 migrating adult spring-summer Chinook salmon (Oncorhynchus tshawytscha) tagged in 1996 at Bonneville Dam on the Columbia River. We used the model to test competing hypotheses regarding delayed effects of fallback at dams and visits to tributaries, and to define and estimate migration summary measures. Tagged fish had an average probability of 0.755 () of ending migration at a tributary or upstream of Lower Granite Dam on the Snake River, and a probability of 0.245 () of unaccountable loss (i.e., mortality or mainstem spawning) between the release site downstream of Bonneville Dam and Lower Granite Dam. The highest probability of unaccountable loss (0.092; ) was in the reach between Bonneville Dam and The Dalles Dam. Study fish used the tributaries primarily as exits from the hydrosystem, and visits to non-natal tributaries had no significant effect on subsequent movement upriver (P = 0.4245). However, fallback behavior had a small effect on subsequent tributary entry and exit (P = 0.0530), with fish using tributaries as resting areas after reascending Bonneville Dam after fallback. The spatial MSMR model developed here can be adapted to address additional questions about the interaction of migrating organisms with their environment, or for the study of migrations in other river systems.     

Photographic mark-recapture analysis of clustered mammal-eating killer whales around the Aleutian Islands and Gulf of Alaska

We used photographic mark-recapture methods to estimate the number of mammal-eating “transient” killer whales using the coastal waters from the central Gulf of Alaska to the central Aleutian Islands, around breeding rookeries of endangered Steller sea lions. We identified 154 individual killer whales from 6,489 photographs collected between July 2001 and August 2003. A Bayesian mixture model estimated seven distinct clusters (95% probability interval = 7–10) of individuals that were differentially covered by 14 boat-based surveys exhibiting varying degrees of association in space and time. Markov Chain Monte Carlo methods were used to sample identification probabilities across the distribution of clusters to estimate a total of 345 identified and undetected whales (95% probability interval = 255–487). Estimates of covariance between surveys, in terms of their coverage of these clusters, indicated spatial population structure and seasonal movements from these near-shore waters, suggesting spatial and temporal variation in the predation pressure on coastal marine mammals.     

Abundance of the New Zealand subantarctic southern right whale population estimated from photo-identification and genotype mark-recapture

The abundance of New Zealand subantarctic southern right whales (Eubalaena australis) was estimated for the first time using mark-recapture methods based on photo-identification and microsatellite genotyping (13 loci). Individual identification photographs of 383 whales and microsatellite genotypes of 235 whales were collected during annual austral winter field surveys from 1995 to 1998. Given the 4-year survey period and lack of geographic and demographic closure, we estimated super-population abundance using the POPAN Jolly-Seber model implemented in the software programme MARK. Models with constant survivorship but time-varying capture probability and probability of entry into the population were the most suitable due to the survey design. This provided estimates of abundance in 1998 of 908 non-calf whales (95% C.L. = 755, 1,123) for the photo-identification and 910 non-calf whales (95% C.L. = 641, 1,354) for the microsatellite genotype data sets. The current estimate of 900 whales may represent less than 5% of the pre-whaling abundance in New Zealand waters.     

A new approach to the "apparent survival" problem: estimating true survival rates from mark-recapture studies

Survival estimates generated from live capture-mark-recapture studies may be negatively biased due to the permanent emigration of marked individuals from the study area. In the absence of a robust analytical solution, researchers typically sidestep this problem by simply reporting estimates using the term "apparent survival." Here, we present a hierarchical Bayesian multistate model designed to estimate true survival by accounting for predicted rates of permanent emigration. Initially we use dispersal kernels to generate spatial projections of dispersal probability around each capture location. From these projections, we estimate emigration probability for each marked individual and use the resulting values to generate bias-adjusted survival estimates from individual capture histories. When tested using simulated data sets featuring variable detection probabilities, survival rates, and dispersal patterns, the model consistently eliminated negative biases shown by apparent survival estimates from standard models. When applied to a case study concerning juvenile survival in the endangered Cape Sable Seaside Sparrow (Ammodramus maritimus mirabilis), bias-adjusted survival estimates increased more than twofold above apparent survival estimates. Our approach is applicable to any capture-mark-recapture study design and should be particularly valuable for organisms with dispersive juvenile life stages.     

Quantifying Plant Population Persistence in Human-Dominated Landscapes

Abstract:  We assessed population performance of rare plants across a gradient from rural to urban landscapes and evaluated 2 hypotheses central to strategic conservation planning: (1) population performance declines with increasing human dominance and (2) small populations perform poorly relative to larger ones. Assessing these hypotheses is critical to strategic conservation planning. The current conservation paradigm adheres to the well-established ecology theory that small isolated populations, particularly those in human-dominated landscapes, are the least likely to succeed over the long term. Consequently, conservation planning has strongly favored large, remote targets for protection. This shift in conservation toward ecosystem-based programs and protection of populations within large, remote systems has been at the expense of protection of the rarest of the rare species, the dominant paradigm for conservation driven by the endangered species act. Yet, avoiding conservation of small populations appears to be based more on theoretical understanding and expert opinion than empiricism. We used Natural Heritage data from California in an assessment of population performance of rare plants across a landscape with an urban-rural gradient. Population performance did not decrease in urban settings or for populations that were initially small. Our results are consistent with a pattern of few species extinctions within these landscapes over the past several decades. We conclude that these populations within compromised landscapes can contribute to overall biodiversity conservation. We further argue that conservation planning for biodiversity preservation should allocate relatively more resources to protecting urban-associated plant taxa because they may provide conservation benefit beyond simply protecting isolated populations; they may be useful in building social interest in conservation.     

Persistence of polychlorinated biphenyls in marine bivalves

Bivalves (Cerastoderma edule and Macoma balthica) which had previously been exposed to Aroclors^® 1242, 1254 and 1260 were able to reduce their tissue burdens of chlorobiphenyls with 2 to 5 chlorine atoms in short-term static assay systems. Elimination rates decreased with increasing chlorination and removal of isomers with more than 5 chlorine atoms was not recorded. Position, in addition to the number, of chlorine atoms influenced the persistence of chlorobiphenyls. Isomers with most ortho-substituted chlorine atoms were least persistent. Experiments with single isomers indicated variation in the elimination of low chlorinated isomers between bivalve species. These biological and chemical influences on tissue residues, together with environmental parameters such as temperature and suspended solids, are considered in relation to the use of bivalves as bio-indicators of marine pollution.     

Time-varying models for extreme values

We propose a new approach for modeling extreme values that are measured in time and space. First we assume that the observations follow a Generalized Extreme Value (GEV) distribution for which the location, scale or shape parameters define the space–time structure. The temporal component is defined through a Dynamic Linear Model (DLM) or state space representation that allows to estimate the trend or seasonality of the data in time. The spatial element is imposed through the evolution matrix of the DLM where we adopt a process convolution form. We show how to produce temporal and spatial estimates of our model via customized Markov Chain Monte Carlo (MCMC) simulation. We illustrate our methodology with extreme values of ozone levels produced daily in the metropolitan area of Mexico City and with rainfall extremes measured at the Caribbean coast of Venezuela.     

A reliability index for models

Since the prediction of environmental changes depends heavily on mathematical models, environmental planners have a definite need for a general test that can be easily applied to determine the reliability of a model or to choose between available models. In this paper a ‘reliability index’ for a model is defined. This index is a number k ? 1 which is determined from a set x₁,x₂,…,x_n of model predictions and a corresponding set y₁,y₂,…,y_n of observations. One interpretation of the index k is that the model predictions agree with observations, in some sense, within a factor of k. The index k is defined using an intuitive, geometric approach and is justified through agreement with another index developed using statistical techniques. Examples are given for a model which predicts the atmospheric movement of radon-222 originating from a concentrated source of radium-226, such as a uranium tailings pile.     

Erlangian models for capture-recapture data

Models for the analysis of capture-recapture data based on Erlangian distributions reflecting assumptions about the times at which individuals enter and leave the population are described. A procedure for fitting such models by the method of maximum likelihood is illustrated.     

Stochastic models for forest fires

A stochastic model for man-caused forest fires is developed for a forest with given environmental conditions which is represented by an index. This model is then generalized to take into account both man-caused and natural fires and the mean and the variance of the number of fires is derived. Fitting procedure for given data is suggested.