Multistate modeling of habitat dynamics: factors affecting Florida scrub transition probabilities

Many ecosystems are influenced by disturbances that create specific successional states and habitat structures that species need to persist. Estimating transition probabilities between habitat states and modeling the factors that influence such transitions have many applications for investigating and managing disturbance-prone ecosystems. We identify the correspondence between multistate capture-recapture models and Markov models of habitat dynamics. We exploit this correspondence by fitting and comparing competing models of different ecological covariates affecting habitat transition probabilities in Florida scrub and flatwoods, a habitat important to many unique plants and animals. We subdivided a large scrub and flatwoods ecosystem along central Florida's Atlantic coast into 10-ha grid cells, which approximated average territory size of the threatened Florida Scrub-Jay (Aphelocoma coerulescens), a management indicator species. We used 1.0-m resolution aerial imagery for 1994, 1999, and 2004 to classify grid cells into four habitat quality states that were directly related to Florida Scrub-Jay source-sink dynamics and management decision making. Results showed that static site features related to fire propagation (vegetation type, edges) and temporally varying disturbances (fires, mechanical cutting) best explained transition probabilities. Results indicated that much of the scrub and flatwoods ecosystem was resistant to moving from a degraded state to a desired state without mechanical cutting, an expensive restoration tool. We used habitat models parameterized with the estimated transition probabilities to investigate the consequences of alternative management scenarios on future habitat dynamics. We recommend this multistate modeling approach as being broadly applicable for studying ecosystem, land cover, or habitat dynamics. The approach provides maximum-likelihood estimates of transition parameters, including precision measures, and can be used to assess evidence among competing ecological models that describe system dynamics.     

Combining multistate capture-recapture data with tag recoveries to estimate demographic parameters

Matrix population models that allow an animal to occupy more than one state over time are important tools for population and evolutionary ecologists. Definition of state can vary, including location for metapopulation models and breeding state for life history models. For populations whose members can be marked and subsequently reencountered, multistate mark-recapture models are available to estimate the survival and transition probabilities needed to construct population models. Multistate models have proved extremely useful in this context, but they often require a substantial amount of data and restrict estimation of transition probabilities to those areas or states subjected to formal sampling effort. At the same time, for many species, there are considerable tag recovery data provided by the public that could be modeled in order to increase precision and to extend inference to a greater number of areas or states. Here we present a statistical model for combining multistate capture-recapture data (e.g., from a breeding ground study) with multistate tag recovery data (e.g., from wintering grounds). We use this method to analyze data from a study of Canada Geese (Branta canadensis) in the Atlantic Flyway of North America. Our analysis produced marginal improvement in precision, due to relatively few recoveries, but we demonstrate how precision could be further improved with increases in the probability that a retrieved tag is reported.     

General methods for sensitivity analysis of equilibrium dynamics in patch occupancy models

Sensitivity analysis is a useful tool for the study of ecological models that has many potential applications for patch occupancy modeling. Drawing from the rich foundation of existing methods for Markov chain models, I demonstrate new methods for sensitivity analysis of the equilibrium state dynamics of occupancy models. Estimates from three previous studies are used to illustrate the utility of the sensitivity calculations: a joint occupancy model for a prey species, its predators, and habitat used by both; occurrence dynamics from a well-known metapopulation study of three butterfly species; and Golden Eagle occupancy and reproductive dynamics. I show how to deal efficiently with multistate models and how to calculate sensitivities involving derived state variables and lower-level parameters. In addition, I extend methods to incorporate environmental variation by allowing for spatial and temporal variability in transition probabilities. The approach used here is concise and general and can fully account for environmental variability in transition parameters. The methods can be used to improve inferences in occupancy studies by quantifying the effects of underlying parameters, aiding prediction of future system states, and identifying priorities for sampling effort.     

Modeling survival and mark loss in molting animals: recapture, dead recoveries, and exuvia recoveries

Capture-mark-recapture (CMR) analyses aim primarily at estimating relevant life history parameters, despite the fact that some individuals are not always recaptured, even if alive on the study site. Applying such approaches to species with a complex life cycle, such as insects, remains challenging because each change of stage tends to cause mark loss through molting. We developed a multistate model based on three exclusive events ("dead", "surviving and molting", and "surviving and staying in the same larval stage") to estimate probabilities of survival and mark loss. Estimates of biologically relevant parameters were derived from those of the probabilities of transition between these states. The model was applied to data from radio-tracking diodes glued on grasshoppers. The estimates of recapture probabilities decreased throughout the season for animals remaining alive, while the detection of dead animals and lost diodes was exhaustive. The survival probability was higher for larvae than for adults (0.98 vs. 0.96), and mark loss was stronger in larvae than in adults (0.09 vs. 0.06). We show that the survival rate of a species with a high rate of mark loss can be estimated using multistate models, provided that marks can be recovered after being lost. These models are flexible enough to test for several effects that potentially affect survival and mark loss probabilities.     

Multinomial mixture model with heterogeneous classification probabilities

Royle and Link (Ecology 86(9):2505?C2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data.     

Multimethod,multistate Bayesian hierarchical modeling approach for use in regional monitoring of wolves

In many cases, the first step in large‐carnivore management is to obtain objective, reliable, and cost‐effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical‐site‐occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost‐effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well‐coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population‐parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population parameters.     

The Reliability of Using Population Viability Analysis for Risk Classification of Species

I examine whether or not it is appropriate to use extinction probabilities generated by population viability analyses, based on best estimates for model parameters, as criteria for listing species in Red Data Book categories as recently proposed by the World Conservation Union. Such extinction probabilities are influenced by how accurately model parameters are estimated and by how accurately the models depict actual population dynamics. I evaluate the effect of uncertainty in parameter estimation through simulations. Simulations based on Steller sea lions were used to evaluate bias and precision in estimates of probability of extinction and to consider the performance of two proposed classification schemes. Extinction time estimates were biased (because of violation of the assumption of stable age distribution) and underestimated the variability of probability of extinction for a given time (primarily because of uncertainty in parameter estimation). Bias and precision in extinction probabilities are important when these probabilities are used to compare the risk of extinction between species. Suggestions are given for population viability analysis techniques that incorporate parameter uncertainty. I conclude that testing classification schemes with simulations using quantitative performance objectives should precede adoption of quantitative listing criteria.     

Effects of surrounding land use and water depth on seagrass dynamics relative to a catastrophic algal bloom

Seagrasses are the foundation of many coastal ecosystems and are in global decline because of anthropogenic impacts. For the Indian River Lagoon (Florida, U.S.A.), we developed competing multistate statistical models to quantify how environmental factors (surrounding land use, water depth, and time [year]) influenced the variability of seagrass state dynamics from 2003 to 2014 while accounting for time‐specific detection probabilities that quantified our ability to determine seagrass state at particular locations and times. We classified seagrass states (presence or absence) at 764 points with geographic information system maps for years when seagrass maps were available and with aerial photographs when seagrass maps were not available. We used 4 categories (all conservation, mostly conservation, mostly urban, urban) to describe surrounding land use within sections of lagoonal waters, usually demarcated by land features that constricted these waters. The best models predicted that surrounding land use, depth, and year would affect transition and detection probabilities. Sections of the lagoon bordered by urban areas had the least stable seagrass beds and lowest detection probabilities, especially after a catastrophic seagrass die‐off linked to an algal bloom. Sections of the lagoon bordered by conservation lands had the most stable seagrass beds, which supports watershed conservation efforts. Our results show that a multistate approach can empirically estimate state‐transition probabilities as functions of environmental factors while accounting for state‐dependent differences in seagrass detection probabilities as part of the overall statistical inference procedure.     

Optimization of capture–recapture monitoring of elusive species illustrated with a threatened grasshopper

Information on population sizes and trends of threatened species is essential for their conservation, but obtaining reliable estimates can be challenging. We devised a method to improve the precision of estimates of population size obtained from capture–recapture studies for species with low capture and recapture probabilities and short seasonal activity, illustrated with population data of an elusive grasshopper (Prionotropis rhodanica). We used data from 5 capture–recapture studies to identify methodological and environmental factors affecting capture and recapture probabilities and estimates of population size. In a simulation, we used the population size and capture and recapture probability estimates obtained from the field studies to identify the minimum number of sampling occasions needed to obtain unbiased and robust estimates of population size. Based on these results we optimized the capture–recapture design, implemented it in 2 additional studies, and compared their precision with those of the nonoptimized studies. Additionally, we simulated scenarios based on thresholds of population size in criteria C and D of the International Union for Conservation of Nature (IUCN) Red List to investigate whether estimates of population size for elusive species can reliably inform red-list assessments. Identifying parameters that affect capture and recapture probabilities (for the grasshopper time since emergence of first adults) and optimizing field protocols based on this information reduced study effort (−6% to −27% sampling occasions) and provided more precise estimates of population size (reduced coefficient of variation) compared with nonoptimized studies. Estimates of population size from the scenarios based on the IUCN thresholds were mostly unbiased and robust (only the combination of very small populations and little study effort produced unreliable estimates), suggesting capture–recapture can be considered reliable for informing red-list assessments. Although capture–recapture remains difficult and costly for elusive species, our optimization procedure can help determine efficient protocols to increase data quality and minimize monitoring effort.     

Lotka-Volterra competition models for sessile organisms

Markov models are widely used to describe the dynamics of communities of sessile organisms, because they are easily fitted to field data and provide a rich set of analytical tools. In typical ecological applications, at any point in time, each point in space is in one of a finite set of states (e.g., species, empty space). The models aim to describe the probabilities of transitions between states. In most Markov models for communities, these transition probabilities are assumed to be independent of state abundances. This assumption is often suspected to be false and is rarely justified explicitly. Here, we start with simple assumptions about the interactions among sessile organisms and derive a model in which transition probabilities depend on the abundance of destination states. This model is formulated in continuous time and is equivalent to a Lotka-Volterra competition model. We fit this model and a variety of alternatives in which transition probabilities do not depend on state abundances to a long-term coral reef data set. The Lotka-Volterra model describes the data much better than all models we consider other than a saturated model (a model with a separate parameter for each transition at each time interval, which by definition fits the data perfectly). Our approach provides a basis for further development of stochastic models of sessile communities, and many of the methods we use are relevant to other types of community. We discuss possible extensions to spatially explicit models.     

Simultaneous-count models to estimate abundance from counts of unmarked individuals with imperfect detection

We developed a method to estimate population abundance from simultaneous counts of unmarked individuals over multiple sites. We considered that at each sampling occasion, individuals in a population could be detected at 1 of the survey sites or remain undetected and used either multinomial or binomial simultaneous-count models to estimate abundance, the latter being equivalent to an N-mixture model with one site. We tested model performance with simulations over a range of detection probabilities, population sizes, growth rates, number of years, sampling occasions, and sites. We then applied our method to 3 critically endangered vulture species in Cambodia to demonstrate the real-world applicability of the model and to provide the first abundance estimates for these species in Cambodia. Our new approach works best when existing methods are expected to perform poorly (i.e., few sites and large variation in abundance among sites) and if individuals may move among sites between sampling occasions. The approach performed better when there were >8 sampling occasions and net probability of detection was high (>0.5). We believe our approach will be useful in particular for simultaneous surveys at aggregation sites, such as roosts. The method complements existing approaches for estimating abundance of unmarked individuals and is the first method designed specifically for simultaneous counts.     

Impact and Dynamics of Disease in Species Threatened by the Amphibian Chytrid Fungus, Batrachochytrium dendrobatidis

Abstract:  Estimating disease-associated mortality and transmission processes is difficult in free-ranging wildlife but important for understanding disease impacts and dynamics and for informing management decisions. In a capture–mark–recapture study, we used a PCR-based diagnostic test in combination with multistate models to provide the first estimates of disease-associated mortality and detection, infection, and recovery rates for frogs endemically infected with the chytrid fungus Batrachochytrium dendrobatidis (Bd), which causes the pandemic amphibian disease chytridiomycosis. We found that endemic chytridiomycosis was associated with a substantial reduction (approximately 38%) in apparent monthly survival of the threatened rainforest treefrog Litoria pearsoniana despite a long period of coexistence (approximately 30 years); detection rate was not influenced by disease status; improved recovery and reduced infection rates correlated with decreased prevalence, which occurred when temperatures increased; and incorporating changes in individuals' infection status through time with multistate models increased effect size and support (98.6% vs. 71% of total support) for the presence of disease-associated mortality when compared with a Cormack–Jolly–Seber model in which infection status was restricted to the time of first capture. Our results indicate that amphibian populations can face significant ongoing pressure from chytridiomycosis long after epidemics associated with initial Bd invasions subside, an important consideration for the long-term conservation of many amphibian species worldwide. Our findings also improve confidence in estimates of disease prevalence in wild amphibians and provide a general framework for estimating parameters in epidemiological models for chytridiomycosis, an important step toward better understanding and management of this disease.     

Determining Optimal Population Monitoring for Rare Butterflies

Abstract: Determining population viability of rare insects depends on precise, unbiased estimates of population size and other demographic parameters. We used data on the endangered St. Francis' satyr butterfly (Neonympha mitchellii francisci) to evaluate 2 approaches (mark–recapture and transect counts) for population analysis of rare butterflies. Mark–recapture analysis provided by far the greatest amount of demographic information, including estimates (and standard errors) of population size, detection, survival, and recruitment probabilities. Mark–recapture analysis can also be used to estimate dispersal and temporal variation in rates, although we did not do this here. Models of seasonal flight phenologies derived from transect counts (Insect Count Analyzer) provided an index of population size and estimates of survival and statistical uncertainty. Pollard–Yates population indices derived from transect counts did not provide estimates of demographic parameters. This index may be highly biased if detection and survival probabilities vary spatially and temporally. In terms of statistical performance, mark–recapture and Pollard–Yates indices were least variable. Mark–recapture estimates were less likely to fail than Insect Count Analyzer, but mark–recapture estimates became less precise as sampling intensity decreased. In general, count‐based approaches are less costly and less likely to cause harm to rare insects than mark–recapture. The optimal monitoring approach must reconcile these trade‐offs. Thus, mark–recapture should be favored when demographic estimates are needed, when financial resources enable frequent sampling, and when marking does not harm the insect populations. The optimal sampling strategy may use 2 sampling methods together in 1 overall sampling plan: limited mark–recapture sampling to estimate survival and detection probabilities and frequent but less expensive transect counts.     

Quantifying parameter uncertainty in a coral reef model using Metropolis-Coupled Markov Chain Monte Carlo

Coral reefs are threatened ecosystems, so it is important to have predictive models of their dynamics. Most current models of coral reefs fall into two categories. The first is simple heuristic models which provide an abstract understanding of the possible behaviour of reefs in general, but do not describe real reefs. The second is complex simulations whose parameters are obtained from a range of sources such as literature estimates. We cannot estimate the parameters of these models from a single data set, and we have little idea of the uncertainty in their predictions.We have developed a compromise between these two extremes, which is complex enough to describe real reef data, but simple enough that we can estimate parameters for a specific reef from a time series. In previous work, we fitted this model to a long-term data set from Heron Island, Australia, using maximum likelihood methods. To evaluate predictions from this model, we need estimates of the uncertainty in our parameters. Here, we obtain such estimates using Bayesian Metropolis-Coupled Markov Chain Monte Carlo. We do this for versions of the model in which corals are aggregated into a single state variable (the three-state model), and in which corals are separated into four state variables (the six-state model), in order to determine the appropriate level of aggregation. We also estimate the posterior distribution of predicted trajectories in each case.In both cases, the fitted trajectories were close to the observed data, but we had doubts about the biological plausibility of some parameter estimates. We suggest that informative prior distributions incorporating expert knowledge may resolve this problem. In the six-state model, the posterior distribution of state frequencies after 40 years contained two divergent community types, one dominated by free space and soft corals, and one dominated by acroporid, pocilloporid, and massive corals. The three-state model predicts only a single community type. We conclude that the three-state model hides too much biological heterogeneity, but we need more data if we are to obtain reliable predictions from the six-state model. It is likely that there will be similarly large, but currently unevaluated, uncertainty in the predictions of other coral reef models, many of which are much more complex and harder to fit to real data.     

Occupancy estimation and modeling with multiple states and state uncertainty

The distribution of a species over space is of central interest in ecology, but species occurrence does not provide all of the information needed to characterize either the well-being of a population or the suitability of occupied habitat. Recent methodological development has focused on drawing inferences about species occurrence in the face of imperfect detection. Here we extend those methods by characterizing occupied locations by some additional state variable (e.g., as producing young or not). Our modeling approach deals with both detection probabilities <1 and uncertainty in state classification. We then use the approach with occupancy and reproductive rate data from California Spotted Owls (Strix occidentalis occidentalis) collected in the central Sierra Nevada during the breeding season of 2004 to illustrate the utility of the modeling approach. Estimates of owl reproductive rate were larger than na?ve estimates, indicating the importance of appropriately accounting for uncertainty in detection and state classification.     

Estimating Population Size of Elusive Animals with DNA from Hunter-Collected Feces: Four Methods for Brown Bears

Abstract:  Noninvasive genetic methods can be used to estimate animal abundances and offer several advantages over conventional methods. Few attempts have been made, however, to evaluate the accuracy and precision of the estimates. We compared four methods of estimating population size based on fecal sampling. Two methods used rarefaction indices and two were based on capture-mark-recapture (CMR) estimators, one combining genetic and field data. Volunteer hunters and others collected 1904 fecal samples over 2 consecutive years in a large area containing a well-studied population of brown bears ( Ursus arctos ). On our 49,000-km² study area in south-central Sweden, population size estimates ranged from 378 to 572 bears in 2001 and 273 to 433 bears in 2002, depending on the method of estimation used. The estimates from the best model in the program MARK appeared to be the most accurate, based on the minimum population size estimate from radio-marked bears in a subsection of our sampling area. In addition, MARK models included heterogeneity and temporal variation in detection probabilities, which appeared to be present in our samples. All methods, though, incorrectly suggested a biased sex ratio, probably because of sex differences in detection probabilities and low overall detection probabilities. The population size of elusive animals can be estimated reliably over large areas with noninvasive genetic methods, but we stress the importance of an adequate and well-distributed sampling effort. In cases of biased sampling, calibration with independent estimates may be necessary. We recommend that this noninvasive genetic approach, using the MARK models, be used in the future in areas where sufficient numbers of volunteers can be mobilized.     

Testing hypotheses in evolutionary ecology with imperfect detection: capture-recapture structural equation modeling

Studying evolutionary mechanisms in natural populations often requires testing multifactorial scenarios of causality involving direct and indirect relationships among individual and environmental variables. It is also essential to account for the imperfect detection of individuals to provide unbiased demographic parameter estimates. To cope with these issues, we developed a new approach combining structural equation models with capture-recapture models (CR-SEM) that allows the investigation of competing hypotheses about individual and environmental variability observed in demographic parameters. We employ Markov chain Monte Carlo sampling in a Bayesian framework to (1) estimate model parameters, (2) implement a model selection procedure to evaluate competing hypotheses about causal mechanisms, and (3) assess the fit of models to data using posterior predictive checks. We illustrate the value of our approach using two case studies on wild bird populations. We first show that CR-SEM can be useful to quantify the action of selection on a set of phenotypic traits with an analysis of selection gradients on morphological traits in Common Blackbirds (Turdus merula). In a second case study on Blue Tits (Cyanistes caeruleus), we illustrate the use of CR-SEM to study evolutionary trade-offs in the wild, while accounting for varying environmental conditions.     

Closed population estimation models and their extensions in Program MARK

Program MARK provides > 65 data types in a common configuration for the estimation of population parameters from mark-encounter data. Encounter information from live captures, live resightings, and dead recoveries can be incorporated to estimate demographic parameters. Available estimates include survival (S or ϕ), rate of population change (λ), transition rates between strata (Ψ), emigration and immigration rates, and population size (N). Although N is the parameter most often desired by biologists, N is one of the most difficult parameters to estimate precisely without bias for a geographically and demographically closed population. The set of closed population estimation models available in Program MARK incorporate time (t) and behavioral (b) variation, and individual heterogeneity (h) in the estimation of capture and recapture probabilities in a likelihood framework. The full range of models from M ₀ (null model with all capture and recapture probabilities equal) to M _tbh are possible, including the ability to include temporal, group, and individual covariates to model capture and recapture probabilities. Both the full likelihood formulation of Otis et al. (1978) and the conditional model formulation of Huggins (1989, 1991) and Alho (1990) are provided in Program MARK, and all of these models are incorporated into the robust design (Kendall et al. 1995, 1997; Kendall and Nichols 1995) and robust-design multistrata (Hestbeck et al. 1991, Brownie et al. 1993) data types. Model selection is performed with AICc (Burnham and Anderson 2002) and model averaging (Burnham and Anderson 2002) is available in Program MARK to provide estimates of N with standard error that reflect model selection uncertainty.     

A hierarchical Bayesian model for forecasting state-level corn yield

Historically, the National Agricultural Statistics Service crop forecasts and estimates have been determined by a group of commodity experts called the Agricultural Statistics Board (ASB). The corn yield forecasts for the “speculative region,” ten states that account for approximately 85 % of corn production, are based on two sets of monthly surveys, a farmer interview survey and a field measurement survey. The members of the ASB subjectively determine a forecast on the basis of a discussion of the survey data and auxiliary information about weather, average planting dates, and crop maturity. The ASB uses an iterative procedure, where initial state estimates are adjusted so that the weighted sum of the final state estimates is equal to a previously-determined estimate for the speculative region. Deficiencies of the highly subjective ASB process are lack of reproducibility and a measure of uncertainty. This paper describes the use of Bayesian methods to model the ASB process in a way that leads to objective forecasts and estimates of the corn yield. First, we use small area estimation techniques to obtain state-level forecasts. Second, we describe a way to adjust the state forecasts so that the weighted sum of the state forecasts is equal to a previously-determined regional forecast. We use several diagnostic techniques to assess the goodness of fit of various models and their competitors. We use Markov chain Monte Carlo methods to fit the models to both historic and current data from the two monthly surveys. Our results show that our methodology can provide reasonable and objective forecasts of corn yields for states in the speculative region.