Use of stochastic patch occupancy models in the California red-legged frog for Bayesian inference regarding past events and future persistence

Assessing causes of population decline is critically important to management of threatened species. Stochastic patch occupancy models (SPOMs) are popular tools for examining spatial and temporal dynamics of populations when presence–absence data in multiple habitat patches are available. We developed a Bayesian Markov chain method that extends existing SPOMs by focusing on past environmental changes that may have altered occupancy patterns prior to the beginning of data collection. Using occupancy data from 3 creeks, we applied the method to assess 2 hypothesized causes of population decline—in situ die-off and residual impact of past source population loss—in the California red-legged frog. Despite having no data for the 20–30 years between the hypothetical event leading to population decline and the first data collected, we were able to discriminate among hypotheses, finding evidence that in situ die-off increased in 2 of the creeks. Although the creeks had comparable numbers of occupied segments, owing to different extinction–colonization dynamics, our model predicted an 8-fold difference in persistence probabilities of their populations to 2030. Adding a source population led to a greater predicted persistence probability than did decreasing the in situ die-off, emphasizing that reversing the deleterious impacts of a disturbance may not be the most efficient management strategy. We expect our method will be useful for studying dynamics and evaluating management strategies of many species.     

Landscape history, fragmentation, and patch occupancy: models for a forest bird with limited dispersal.

We developed and tested patch occupancy models for an endemic understory bird with limited dispersal ability, the Chucao Tapaculo (Scelorchilus rubecula), in two South American temperate rain forest landscapes that differed in levels and duration of forest loss. We assessed cover changes since 1961 in each landscape and surveyed patches for Chucao Tapaculo occupancy. We then developed incidence-based predictive models independently for each landscape and tested each model reciprocally in the alternative study area. We thereby assessed the domain of model applicability and identified those predictor variables with general effects and those that varied between the two landscapes. The two models were consistent regarding variable selection, and predictive accuracy of each model was high in the landscape where training data were collected. However, the models differed substantially in the magnitudes of effects related to patch size, with larger unoccupied patches observed in the landscape with the more advanced stage of fragmentation. Due to this discrepancy, each model performed poorly when applied to the alternative landscape, potentially reflecting the contrasting stages of habitat loss. Although it was impossible to dissociate effects of level and duration of forest loss, we viewed the landscapes as representing two extremes along a continuum of fragmentation, providing insights into potential trajectories for portions of the biome where deforestation is occurring. Further, our data suggest that static equilibrium models developed from distribution patterns in recently fragmented landscapes may overestimate persistence when used as a forecasting tool, or when extrapolated to alternative landscapes where fragmentation is more advanced. Thus, we suggest that landscapes used as standards for model building should be selected with caution. We recommend that distribution patterns be obtained from landscapes where fragmentation is advanced, preferably with histories of fragmentation long enough that time-delayed extinctions already would have occurred.     

Statistical selection of perimeter-area models for patch mosaics in multiscale landscape analysis

This paper presents a statistical method for detecting distinct scales of pattern for mosaics of irregular patches, by means of perimeter–area relationships. Krummel et al. (1987) were the first to develop a method for detecting different scaling domains in a landscape of irregular patches, but this method requires investigator judgment and is not completely satisfying. Grossi et al. (2001) suggested a modification of Krummel's method in order to detect objectively the change points between different scaling domains. Their procedure is based on the selection of the best piecewise linear regression model using a set of statistical tests. Even though the change points were estimated, the null distributions used for testing purposes were those appropriate for known change points. The present paper investigates the effect that estimating the change points has on the underlying distribution theory. The procedure we suggest is based on the selection of the best piecewise linear regression model using a likelihood ratio (LR) test. Each segment of the piecewise linear model corresponds to a fractal domain. Breakpoints between different segments are unknown, so the piecewise linear models are non-linear. In this case, the frequency distribution of the LR statistic cannot be approximated by a chi-squared distribution. Instead, Monte Carlo simulation is used to obtain an empirical null distribution of the LR statistic. The suggested method is applied to three patch types (CORINE biotopes) located in the Val Baganza watershed of Italy.     

Using experimental reintroductions to resolve the roles of habitat quality and metapopulation dynamics on patch occupancy in fragmented landscapes

Declines of species in fragmented landscapes can potentially be reversed either by restoring connectivity or restoring local habitat quality. Models fitted to snapshot occupancy data can be used to predict the effectiveness of these actions. However, such inferences can be misleading if the reliability of the habitat and landscape metrics used is unknown. The only way to unambiguously resolve the roles of habitat quality and metapopulation dynamics is to conduct experimental reintroductions to unoccupied patches so that habitat quality can be measured directly from data on vital rates. We, therefore, conducted a 15-year study that involved reintroducing a threatened New Zealand bird to unoccupied forest fragments to obtain reliable data on their habitat quality and reassess initial inferences made by modeling occupancy against habitat and landscape metrics. Although reproductive rates were similar among fragments, subtle differences in adult survival rates resulted in λ (finite rate of increase) estimations of <0.9 for 9 of the 12 fragments that were previously unoccupied. This was the case for only 1 of 14 naturally occupied fragments. This variation in λ largely explained the original occupancy pattern, reversing our original conclusion from occupancy modeling that this occupancy pattern was isolation driven and suggesting that it would be detrimental to increase connectivity without improving local habitat quality. These results illustrate that inferences from snapshot occupancy should be treated with caution and subjected to testing through experimental reintroductions in selected model systems.     

Using global sensitivity analysis of demographic models for ecological impact assessment

Population viability analysis (PVA) is widely used to assess population‐level impacts of environmental changes on species. When combined with sensitivity analysis, PVA yields insights into the effects of parameter and model structure uncertainty. This helps researchers prioritize efforts for further data collection so that model improvements are efficient and helps managers prioritize conservation and management actions. Usually, sensitivity is analyzed by varying one input parameter at a time and observing the influence that variation has over model outcomes. This approach does not account for interactions among parameters. Global sensitivity analysis (GSA) overcomes this limitation by varying several model inputs simultaneously. Then, regression techniques allow measuring the importance of input‐parameter uncertainties. In many conservation applications, the goal of demographic modeling is to assess how different scenarios of impact or management cause changes in a population. This is challenging because the uncertainty of input‐parameter values can be confounded with the effect of impacts and management actions. We developed a GSA method that separates model outcome uncertainty resulting from parameter uncertainty from that resulting from projected ecological impacts or simulated management actions, effectively separating the 2 main questions that sensitivity analysis asks. We applied this method to assess the effects of predicted sea‐level rise on Snowy Plover (Charadrius nivosus). A relatively small number of replicate models (approximately 100) resulted in consistent measures of variable importance when not trying to separate the effects of ecological impacts from parameter uncertainty. However, many more replicate models (approximately 500) were required to separate these effects. These differences are important to consider when using demographic models to estimate ecological impacts of management actions.     

A Bayesian state-space formulation of dynamic occupancy models

Species occurrence and its dynamic components, extinction and colonization probabilities, are focal quantities in biogeography and metapopulation biology, and for species conservation assessments. It has been increasingly appreciated that these parameters must be estimated separately from detection probability to avoid the biases induced by non-detection error. Hence, there is now considerable theoretical and practical interest in dynamic occupancy models that contain explicit representations of metapopulation dynamics such as extinction, colonization, and turnover as well as growth rates. We describe a hierarchical parameterization of these models that is analogous to the state-space formulation of models in time series, where the model is represented by two components, one for the partially observable occupancy process and another for the observations conditional on that process. This parameterization naturally allows estimation of all parameters of the conventional approach to occupancy models, but in addition, yields great flexibility and extensibility, e.g., to modeling heterogeneity or latent structure in model parameters. We also highlight the important distinction between population and finite sample inference; the latter yields much more precise estimates for the particular sample at hand. Finite sample estimates can easily be obtained using the state-space representation of the model but are difficult to obtain under the conventional approach of likelihood-based estimation. We use R and WinBUGS to apply the model to two examples. In a standard analysis for the European Crossbill in a large Swiss monitoring program, we fit a model with year-specific parameters. Estimates of the dynamic parameters varied greatly among years, highlighting the irruptive population dynamics of that species. In the second example, we analyze route occupancy of Cerulean Warblers in the North American Breeding Bird Survey (BBS) using a model allowing for site-specific heterogeneity in model parameters. The results indicate relatively low turnover and a stable distribution of Cerulean Warblers which is in contrast to analyses of counts of individuals from the same survey that indicate important declines. This discrepancy illustrates the inertia in occupancy relative to actual abundance. Furthermore, the model reveals a declining patch survival probability, and increasing turnover, toward the edge of the range of the species, which is consistent with metapopulation perspectives on the genesis of range edges. Given detection/non-detection data, dynamic occupancy models as described here have considerable potential for the study of distributions and range dynamics.     

Multiplicative sensitivity analysis and its role in development of simulation models

A procedure of extended sensitivity analysis for simulation models is developed which is applicable to the situation in which input uncertainties are specified in a multiplicative (rather than an additive) way. This type of specification usually occurs when error estimates are large relative to the parameter values. The input parameter errors are assumed to have log-normal distributions and the basis for this assumption is explained along with the advantages it provides. The new procedure, multiplicative sensitivity analysis, is developed for the purposes of internal model validation and identification of priorities for specific experimental and theoretical studies needed for a particular system being modelled. The applicability of the procedure in the very early stages of a research program is its main advantage and further expands the rôle of simulation models.     

Generalized site occupancy models allowing for false positive and false negative errors

Site occupancy models have been developed that allow for imperfect species detection or "false negative" observations. Such models have become widely adopted in surveys of many taxa. The most fundamental assumption underlying these models is that "false positive" errors are not possible. That is, one cannot detect a species where it does not occur. However, such errors are possible in many sampling situations for a number of reasons, and even low false positive error rates can induce extreme bias in estimates of site occupancy when they are not accounted for. In this paper, we develop a model for site occupancy that allows for both false negative and false positive error rates. This model can be represented as a two-component finite mixture model and can be easily fitted using freely available software. We provide an analysis of avian survey data using the proposed model and present results of a brief simulation study evaluating the performance of the maximum-likelihood estimator and the naive estimator in the presence of false positive errors.     

Selecting parameters for calibration via sensitivity analysis: An individual-based model of mosquitofish population dynamics

A stochastic individual-based model (IBM) of mosquitofish population dynamics in experimental ponds was constructed in order to increase, virtually, the number of replicates of control populations in an ecotoxicology trial, and thus to increase the statistical power of the experiments. In this context, great importance had to be paid to model calibration as this conditions the use of the model as a reference for statistical comparisons. Accordingly, model calibration required that both mean behaviour and variability behaviour of the model were in accordance with real data. Currently, identifying parameter values from observed data is still an open issue for IBMs, especially when the parameter space is large. Our model included 41 parameters: 30 driving the model expectancy and 11 driving the model variability. Under these conditions, the use of “Latin hypercube” sampling would most probably have “missed” some important combinations of parameter values. Therefore, complete factorial design was preferred. Unfortunately, due to the constraints of the computational capacity, cost-acceptable “complete designs” were limited to no more than nine parameters, the calibration question becoming a parameter selection question. In this study, successive “complete designs” were conducted with different sets of parameters and different parameter values, in order to progressively narrow the parameter space. For each “complete design”, the selection of a maximum of nine parameters and their respective n values was carefully guided by sensitivity analysis. Sensitivity analysis was decisive in selecting parameters that were both influential and likely to have strong interactions. According to this strategy, the model of mosquitofish population dynamics was calibrated on real data from two different years of experiments, and validated on real data from another independent year. This model includes two categories of agents; fish and their living environment. Fish agents have four main processes: growth, survival, puberty and reproduction. The outputs of the model are the length frequency distribution of the population and the 16 scalar variables describing the fish populations. In this study, the length frequency distribution was parameterized by 10 scalars in order to be able to perform calibration. The recently suggested notion of “probabilistic distribution of the distributions” was also applied to our case study, and was shown to be very promising for comparing length frequency distributions (as such).     

Estimation methods for nonlinear state-space models in ecology

The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance for all three methods was largely identical, however with BUGS providing overall wider credible intervals for parameters than HMM and ADMB confidence intervals.     

Hidden process models for animal population dynamics.

Hidden process models are a conceptually useful and practical way to simultaneously account for process variation in animal population dynamics and measurement errors in observations and estimates made on the population. Process variation, which can be both demographic and environmental, is modeled by linking a series of stochastic and deterministic subprocesses that characterize processes such as birth, survival, maturation, and movement. Observations of the population can be modeled as functions of true abundance with realistic probability distributions to describe observation or estimation error. Computer-intensive procedures, such as sequential Monte Carlo methods or Markov chain Monte Carlo, condition on the observed data to yield estimates of both the underlying true population abundances and the unknown population dynamics parameters. Formulation and fitting of a hidden process model are demonstrated for Sacramento River winter-run chinook salmon (Oncorhynchus tshawytsha).     

Switching state-space models for modeling penguin population dynamics

Environmental and Ecological Statistics - Tracking individual animals through time using mark-recapture methods is the gold standard for understanding how environmental conditions influence...     

Metapopulation dynamics in the butterfly Hipparchia semele changed decades before occupancy declined in The Netherlands

The survival of many species in human-dominated, fragmented landscapes depends on metapopulation dynamics, i.e., on a dynamic equilibrium of extinctions and colonizations in patches of suitable habitat. To understand and predict distributional changes, knowledge of these dynamics can be essential, and for this, metapopulation studies are preferably based on long-time-series data from many sites. Alas, such data are very scarce. An alternative is to use opportunistic data (i.e., collected without applying standardized field methods), but these data suffer from large variations in field methods and search intensity between sites and years. Dynamic site-occupancy models offer a general approach to adjust for variable survey effort. These models extend classical metapopulation models to account for imperfect detection of species and yield estimates of the probabilities of occupancy, colonization, and survival of species at sites. By accounting for detection, they fully correct for among-year variability in search effort. As an illustration, we fitted a dynamic site-occupancy model to 60 years of presence-absence data (more precisely, detection-nondetection) of the heathland butterfly Hipparchia semele in The Netherlands. Detection records were obtained from a database containing volunteer-based data from 1950-2009, and nondetection records were deduced from database records of other butterfly species. Our model revealed that metapopulation dynamics of Hipparchia had changed decades before the species' distribution began to contract. Colonization probability had already started to decline from 1950 onward, but this was counterbalanced by an increase in the survival of existing populations, the result of which was a stable distribution. Only from 1990 onward was survival not sufficient to compensate for the further decrease of colonization, and occupancy started to decline. Hence, it appears that factors acting many decades ago triggered a change in the metapopulation dynamics of this species, which ultimately led to a severe decline in occupancy that only became apparent much later. Our study emphasizes the importance of knowledge of changes in survival and colonization of species in modern landscapes over a very long time scale. It also demonstrates the power of site-occupancy modeling to obtain important population dynamics information from databases containing opportunistic sighting records.     

Definition and properties of a coefficient of sensitivity for mathematical models

This paper contains a definition of a measure of the uncertainty inherent in the output of a mathematical model. The definition is essentially a formalisation of the kind of uncertainty measures that have been previously used in various modelling applications in many disciplines. The characteristics of the measure are described, and an example is given of its use with a particular mathematical model.     

Individual-based modelling of carbon and nitrogen dynamics in soils: Parameterization and sensitivity analysis of microbial components

The fate of soil carbon and nitrogen compounds in soils in response to climate change is currently the object of significant research. In particular, there is much interest in the development of a new generation of micro-scale models of soil ecosystems processes. Crucial to the elaboration of such models is the ability to describe the growth and metabolism of small numbers of individual microorganisms, distributed in a highly heterogeneous environment. In this context, the key objective of the research described in this article was to further develop an individual-based soil organic matter model, INDISIM-SOM, first proposed a few years ago, and to assess its performance with a broader experimental data set than previously considered. INDISIM-SOM models the dynamics and evolution of carbon and nitrogen associated with organic matter in soils. The model involves a number of state variables and parameters related to soil organic matter and microbial activity, including growth and decay of microbial biomass, temporal evolutions of easily hydrolysable N, mineral N in ammonium and nitrate, CO₂ and O₂. The present article concentrates on the biotic components of the model. Simulation results demonstrate that the model can be calibrated to provide good fit to experimental data from laboratory incubation experiments performed on three different types of Mediterranean soils. In addition, analysis of the sensitivity toward its biotic parameters shows that the model is far more sensitive to some parameters, i.e., the microbial maintenance energy and the probability of random microbial death, than to others. These results suggest that, in the future, research should focus on securing better measurements of these parameters, on environmental determinants of the switch from active to dormant states, and on the causes of random cell death in soil ecosystems.     

Old models explain new observations of butterfly movement at patch edges

Understanding movement in heterogeneous environments is central to predicting how landscape changes affect animal populations. Several recent studies point out an intriguing and distinctive looping behavior by butterflies at habitat patch edges and hypothesize that this behavior requires a new framework for analyzing animal movement. We show that this looping behavior could be caused by a longstanding movement model, biased correlated random walk, with bias toward habitat patches. The ability of this longstanding model to explain recent observations reinforces the point that butterflies respond to habitat heterogeneity and do not move randomly through heterogeneous environments. We discuss the implications of different movement models for predicting butterfly responses to landscape change, and our rationale for retaining longstanding movement models, rather than developing new modeling frameworks for looping behavior at patch edges.     

Comparative analysis of impact of human occupancy on indoor microbiomes

• Exposure to indoor microbiomes is a public health concern in educational facilities. • Indoor microbiomes were characterized in two multifunctional university buildings. • Human occupancy had significant impact on the composition of indoor microbiomes. • The skin microbiota of occupants represented important sources of indoor microbiomes. Educational facilities serve as community hubs and consequently hotspots for exposure to pathogenic microorganisms. Therefore, it is of critical importance to understand processes shaping the indoor microbiomes in educational facilities to protect public health by reducing potential exposure risks of students and the broader community. In this study, the indoor surface bacterial microbiomes were characterized in two multifunctional university buildings with contrasting levels of human occupancy, of which one was recently constructed with minimal human occupancy while the other had been in full operation for six years. Higher levels of human occupancy in the older building were shown to result in greater microbial abundance in the indoor environment and greater proportion of the indoor surface bacterial microbiomes contributed from human-associated microbiota, particularly the skin microbiota. It was further revealed that human-associated microbiota had greater influence on the indoor surface bacterial microbiomes in areas of high occupancy than areas of low occupancy. Consistent with minimal impact from human occupancy in a new construction, the indoor microbiomes in the new building exhibited significantly lower influence from human-associated microbiota than in the older building, with microbial taxa originating from soil and plants representing the dominant constituents of the indoor surface bacterial microbiomes. In contrast, microbial taxa in the older building with extensive human occupancy were represented by constituents of the human microbiota, likely from occupants. These findings provide insights into processes shaping the indoor microbiomes which will aid the development of effective strategies to control microbial exposure risks of occupants in educational facilities.     

Estimating population impacts via dynamic occupancy analysis of Before-After Control-Impact studies

Estimating environmental impacts on populations is one of the main goals of wildlife monitoring programs, which are often conducted in conjunction with management actions or following natural disturbances. In this study we investigate the statistical power of dynamic occupancy models to detect changes in local survival and colonization from detection-nondetection data, while accounting for imperfect detection probability, in a Before-After Control-Impact (BACI) framework. We simulated impacts on local survival and/or detection probabilities, and asked questions related to: (1) costs and benefits of different analysis models, (2) confounding changes in detection with changes in local survival, (3) sampling design trade-offs, and (4) species with low vs. high rates of turnover. Estimating seasonal effects on local survival and colonization, as opposed to estimating Before-After effects, had little effect on the power to detect changes in local survival. Estimating a parameter that accounted for pretreatment differences in local survival between Control and Impact sites decreased power by 50%, but it was critical to include when such differences existed. When the experimental treatment had a negative impact on species detectability but analysis assumed constant detection, the Type I error rates were dramatically inflated (0.20 0.33). In general, there was low power (< 0.5) to detect a 50% decrease in local survival for all combinations of sites (N = 50 vs. 100), seasons sampled (8 vs. 12), and visits per site per season (4 vs. 6). Unbalanced designs performed worse than balanced designs, with the exception of the case of treatments being implemented in different seasons at different sites. Adding more control sites improved the ability to detect changes in local survival. Surveying more seasons after impact resulted in modest power gains, but at least three seasons before impact were required to successfully implement BACI occupancy studies. Turnover rates had a low impact on power. Occupancy studies conducted in a BACI design offer the opportunity to detect environmental impacts on wildlife populations without the costs of intensive studies. However, given the low power to detect small changes (20%) in local survival, these studies should be used when researchers are confident that major treatment impacts will occur or very large sample sizes are obtainable.     

Kinetic and equilibrium models for the biosorption of Cr(III) on Streptomyces rimosus

This study focused on the biosorption of trivalent chromium onto mycelial bacterium (Streptomyces rimosus) biomass from effluent of tannery. The biomass was prepared by treatment with alkali. Fourier transforms-infra red analysis of the mycelial bacterial revealed the presence of carboxyl groups as possible binding sites. Experimental parameters affecting biosorption processes such as pH contact time were studied. Langmuir, Freundlich, and Temkin models were applied to describe the biosorption isotherms. The Langmuir model fitted the equilibrium data better than the Freundlich isotherm. The biosorption capacity of S. rimosus biomass for trivalent chromium was found to be 83 mg g^?1 at pH 4.8 and 3 g L^?1 biomass dosage, 300 min equilibrium time and 20°C. Kinetic evaluation of experimental data showed that the biosorption processes of trivalent chromium followed pseudo-second-order kinetics well.