Traditional occupancy–abundance models are inadequate for zero-inflated ecological count data

Traditional occupancy–abundance and abundance–variance–occupancy models do not take into account zero-inflation, which occurs when sampling rare species or in correlated counts arising from repeated measures. In this paper we propose a novel approach extending occupancy–abundance relationships to zero-inflated count data. This approach involves three steps: (1) selecting distributional assumptions and parsimonious models for the count data, (2) estimating abundance, occupancy and variance parameters as functions of site- and/or time-specific covariates, and (3) modelling the occupancy–abundance relationship using the parameters estimated in step 2. Five count datasets were used for comparing standard Poisson and negative binomial distribution (NBD) occupancy–abundance models. Zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) occupancy–abundance models were introduced for the first time, and these were compared with the Poisson, NBD, He and Gaston's and Wilson and Room's abundance–variance–occupancy models. The percentage of zero counts ranged from 45 to 80% in the datasets analysed. For most of the datasets, the ZINB occupancy–abundance model performed better than the traditional Poisson, NBD and Wilson and Room's model. He and Gaston's model performed better than the ZINB in two out of the five datasets. However, the occupancy predicted by all models increased faster than the observed as density increased resulting in significant mismatch at the highest densities. Limitations of the various models are discussed, and the need for careful choice of count distributions and predictors in estimating abundance and occupancy parameter are indicated.     

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.     

Improving effectiveness of systematic conservation planning with density data

Systematic conservation planning aims to design networks of protected areas that meet conservation goals across large landscapes. The optimal design of these conservation networks is most frequently based on the modeled habitat suitability or probability of occurrence of species, despite evidence that model predictions may not be highly correlated with species density. We hypothesized that conservation networks designed using species density distributions more efficiently conserve populations of all species considered than networks designed using probability of occurrence models. To test this hypothesis, we used the Zonation conservation prioritization algorithm to evaluate conservation network designs based on probability of occurrence versus density models for 26 land bird species in the U.S. Pacific Northwest. We assessed the efficacy of each conservation network based on predicted species densities and predicted species diversity. High‐density model Zonation rankings protected more individuals per species when networks protected the highest priority 10‐40% of the landscape. Compared with density‐based models, the occurrence‐based models protected more individuals in the lowest 50% priority areas of the landscape. The 2 approaches conserved species diversity in similar ways: predicted diversity was higher in higher priority locations in both conservation networks. We conclude that both density and probability of occurrence models can be useful for setting conservation priorities but that density‐based models are best suited for identifying the highest priority areas. Developing methods to aggregate species count data from unrelated monitoring efforts and making these data widely available through ecoinformatics portals such as the Avian Knowledge Network will enable species count data to be more widely incorporated into systematic conservation planning efforts.     

Estimation of abundance from presence–absence maps using cluster models

A presence–absence map consists of indicators of the occurrence or nonoccurrence of a given species in each cell over a grid, without counting the number of individuals in a cell once it is known it is occupied. They are commonly used to estimate the distribution of a species, but our interest is in using these data to estimate the abundance of the species. In practice, certain types of species (in particular flora types) may be spatially clustered. For example, some plant communities will naturally group together according to similar environmental characteristics within a given area. To estimate abundance, we develop an approach based on clustered negative binomial models with unknown cluster sizes. Our approach uses working clusters of cells to construct an estimator which we show is consistent. We also introduce a new concept called super-clustering used to estimate components of the standard errors and interval estimators. A simulation study is conducted to examine the performance of the estimators and they are applied to real data.     

On the choice of statistical models for estimating occurrence and extinction from animal surveys

In surveys of natural animal populations the number of animals that are present and available to be detected at a sample location is often low, resulting in few or no detections. Low detection frequencies are especially common in surveys of imperiled species; however, the choice of sampling method and protocol also may influence the size of the population that is vulnerable to detection. In these circumstances, probabilities of animal occurrence and extinction will generally be estimated more accurately if the models used in data analysis account for differences in abundance among sample locations and for the dependence between site-specific abundance and detection. Simulation experiments are used to illustrate conditions wherein these types of models can be expected to outperform alternative estimators of population site occupancy and extinction.     

Estimating the complexity of bird song by using capture-recapture approaches from community ecology

Repertoire size, the number of unique song or syllable types in the repertoire, is a widely used measure of song complexity in birds, but it is difficult to calculate this exactly in species with large repertoires. A new method of repertoire size estimation applies species richness estimation procedures from community ecology, but such capture-recapture approaches have not been much tested. Here, we establish standardized sampling schemes and estimation procedures using capture-recapture models for syllable repertoires from 18 bird species, and suggest how these may be used to tackle problems of repertoire estimation. Different models, with different assumptions regarding the heterogeneity of the use of syllable types, performed best for different species with different song organizations. For most species, models assuming heterogeneous probability of occurrence of syllables (so-called detection probability) were selected due to the presence of both rare and frequent syllables. Capture-recapture estimates of syllable repertoire size from our small sample did not differ significantly from previous estimates using larger samples of count data. However, the enumeration of syllables in 15 songs yielded significantly lower estimates than previous reports. Hence, heterogeneity in detection probability of syllables should be addressed when estimating repertoire size. This is neglected using simple enumeration procedures, but is taken into account when repertoire size is estimated by appropriate capture-recapture models adjusted for species-specific song organization characteristics. We suggest that such approaches, in combination with standardized sampling, should be applied in species with potentially large repertoire size. On the other hand, in species with small repertoire size and homogenous syllable usage, enumerations may be satisfactory. Although researchers often use repertoire size as a measure of song complexity, listeners to songs are unlikely to count entire repertoires and they may rely on other cues, such as syllable detection probability.Communicated by A. Cockburn     

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.     

Despotic, high-impact species and the subcontinental scale control of avian assemblage structure

Some species have disproportionate influence on assemblage structure, given their numbers or biomass. Most examples of such "strong interactors" come from small-scale experiments or from observations of the effects of invasive species. There is evidence that entire avian assemblages in open woodlands can be influenced strongly by individual species over very large areas in eastern Australia, with small-bodied species (< 50 g) being adversely affected. We used data from repeated surveys in 371 sites in seven districts across a region from Victoria to Queensland (> 2000 km). A series of linked Bayesian models was used to identify large-bodied (> or = 50 g) bird species that were associated with changes in occurrence and abundance of small-bodied species. One native species, the Noisy Miner (Manorina melanocephala; family Meliphagidae), was objectively identified as the sole large-bodied species having similar detrimental effects in all districts, depressing occurrence of 57 of 71 small-bodied species. Adverse effects on abundances of small-bodied species were profound when the Noisy Miner occurred with mean site abundances > or = 1.6 birds/2 ha. The Noisy Miner may be the first species to have been shown to influence whole-of-avifauna assemblage structure through despotic aggressiveness over subcontinental scales. These substantial shifts in occurrence rates and abundances of small-bodied species flow on to alter species abundance distributions of entire assemblages over much of eastern Australia.     

Detecting Population Declines over Large Areas with Presence-Absence, Time-to-Encounter, and Count Survey Methods

Abstract:  Ecologists often discount presence-absence surveys as a poor way to gain insight into population dynamics, in part because these surveys are not amenable to many standard statistical tests. Still, presence-absence surveys are sometimes the only feasible alternative for monitoring large areas when funds are limited, especially for sparse or difficult-to-detect species. I undertook a detailed simulation study to compare the power of presence-absence, count, and time-to-encounter surveys to detect regional declines in a population. I used a modeling approach that simulates both population numbers and the monitoring process, accounting for observation and other measurement errors. In gauging the efficacy of presence-absence surveys versus other approaches, I varied the number of survey sites, the spatial variation in encounter rate, the mean encounter rate, and the type of population loss. My results showed that presence-absence data can be as or more powerful than count data in many cases. Quantitative guidelines for choosing between presence-absence surveys and count surveys depend on the biological and logistical constraints governing a conservation monitoring situation. Generally, presence-absence surveys work best when there is little variability in abundance among the survey sites, the organism is rare, and the species is difficult to detect so that the time spent getting to each survey site is less than or equal to the time spent surveying each site. Count surveys work best otherwise. I present a case study with count data on the Northern Flicker ( Colaptes auratus ) from the North American Breeding Bird Survey to illustrate how the method might be used with field-survey data. The case study demonstrates that a count survey would be the most cost-effective design but would entail reduction in the number of sites. If this site reduction is not desirable, a presence-absence survey would be the most cost-effective survey.     

Zero-inflated models with application to spatial count data

Count data arises in many contexts. Here our concern is with spatial count data which exhibit an excessive number of zeros. Using the class of zero-inflated count models provides a flexible way to address this problem. Available covariate information suggests formulation of such modeling within a regression framework. We employ zero-inflated Poisson regression models. Spatial association is introduced through suitable random effects yielding a hierarchical model. We propose fitting this model within a Bayesian framework considering issues of posterior propriety, informative prior specification and well-behaved simulation based model fitting. Finally, we illustrate the model fitting with a data set involving counts of isopod nest burrows for 1649 pixels over a portion of the Negev desert in Israel.     

Improving occupancy estimation when two types of observational error occur: non-detection and species misidentification

Efforts to draw inferences about species occurrence frequently account for false negatives, the common situation when individuals of a species are not detected even when a site is occupied. However, recent studies suggest the need to also deal with false positives, which occur when species are misidentified so that a species is recorded as detected when a site is unoccupied. Bias in estimators of occupancy, colonization, and extinction can be severe when false positives occur. Accordingly, we propose models that simultaneously account for both types of error. Our approach can be used to improve estimates of occupancy for study designs where a subset of detections is of a type or method for which false positives can be assumed to not occur. We illustrate properties of the estimators with simulations and data for three species of frogs. We show that models that account for possible misidentification have greater support (lower AIC for two species) and can yield substantially different occupancy estimates than those that do not. When the potential for misidentification exists, researchers should consider analytical techniques that can account for this source of error, such as those presented here.     

Use of Community‐Composition Data to Predict the Fecundity and Abundance of Species

Abstract: Species distribution models are critical tools for the prediction of invasive species spread and conservation of biodiversity. The majority of species distribution models have been built with environmental data. Community ecology theory suggests that species co‐occurrence data could also be used to predict current and potential distributions of species. Species assemblages are the products of biotic and environmental constraints on the distribution of individual species and as a result may contain valuable information for niche modeling. We compared the predictive ability of distribution models of annual grassland plants derived from either environmental or community‐composition data. Composition‐based models were built with the presence or absence of species at a site as predictors of site quality, whereas environment‐based models were built with soil chemistry, moisture content, above‐ground biomass, and solar radiation as predictors. The reproductive output of experimentally seeded individuals of 4 species and the abundance of 100 species were used to evaluate the resulting models. Community‐composition data were the best predictors of both the site‐specific reproductive output of sown individuals and the site‐specific abundance of existing populations. Successful community‐based models were robust to omission of data on the occurrence of rare species, which suggests that even very basic survey data on the occurrence of common species may be adequate for generating such models. Our results highlight the need for increased public availability of ecological survey data to facilitate community‐based modeling at scales relevant to conservation.     

Shifting elasmobranch community assemblage at Cocos Island—an isolated marine protected area

Fishing pressure has increased the extinction risk of many elasmobranch (shark and ray) species. Although many countries have established no‐take marine reserves, a paucity of monitoring data means it is still unclear if reserves are effectively protecting these species. We examined data collected by a small group of divers over the past 21 years at one of the world's oldest marine protected areas (MPAs), Cocos Island National Park, Costa Rica. We used mixed effects models to determine trends in relative abundance, or probability of occurrence, of 12 monitored elasmobranch species while accounting for variation among observers and from abiotic factors. Eight of 12 species declined significantly over the past 2 decades. We documented decreases in relative abundance for 6 species, including the iconic scalloped hammerhead shark (Sphyrna lewini) (?45%), whitetip reef shark (Triaenodon obesus) (?77%), mobula ray (Mobula spp.) (?78%), and manta ray (Manta birostris) (?89%), and decreases in the probability of occurrence for 2 other species. Several of these species have small home ranges and should be better protected by an MPA, which underscores the notion that declines of marine megafauna will continue unabated in MPAs unless there is adequate enforcement effort to control fishing. In addition, probability of occurrence at Cocos Island of tiger (Galeocerdo cuvier), Galapagos (Carcharhinus galapagensis), blacktip (Carcharhinus limbatus), and whale (Rhincodon typus) sharks increased significantly. The effectiveness of MPAs cannot be evaluated by examining single species because population responses can vary depending on life history traits and vulnerability to fishing pressure.     

Declines in Common, Widespread Butterflies in a Landscape under Intense Human Use

Abstract:  Analyses of species' population losses typically show a dichotomy between strongly affected, rare, and localized species and apparently unaffected, common, and widespread species. We analyzed 16 years (1992–2007) of butterfly transect count data from The Netherlands in a reevaluation of the trends of common, widespread species. Fifty-five percent (11 of 20 species) of these species suffered severe declines in distribution and abundance. Overall, cumulative butterfly abundance declined by around 30%. Some of the species in decline used to be omnipresent in gardens and parks, and 2 of the species were previously considered agricultural pests. Based on their declines over the last 16 years, 2 of the 20 species ( Lasiommata megera and Gonepteryx rhamni ) reached endangered status in The Netherlands under the IUCN (International Union for Conservation of Nature) population-decline criterion, and 2 species ( Inachis io and Thymelicus lineola ) met vulnerable criterion. Butterflies in farmland, urban, and particularly woodland areas showed the largest decline in species abundance. The abundance of species associated with vegetation types found mainly in nature reserves (dunes, heathland, and, to a lesser extent, seminatural grassland) increased or remained stable. The decline of widespread species requires additional conservation strategies in the wider landscape.     

Comparing species abundance models

Five regression models (Poisson, negative binomial, quasi-Poisson, the hurdle model and the zero-inflated Poisson) were used to assess the relationship between the abundance of a vulnerable plant species, Leionema ralstonii, and the environment. The methods differed in their capacity to deal with common properties of ecological data. They were assessed theoretically, and their predictive performance was evaluated with correlation, calibration and error statistics calculated within a bootstrap evaluation procedure that simulated performance for independent data.     

A spatial scan statistic for zero-inflated Poisson process

The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to do with zero excess. Some studies point out that when applied to data with excess zeros, the spatial scan statistic may produce biased inferences. In this work, we develop a closed-form scan statistic for cluster detection of spatial zero-inflated count data. We apply our methodology to simulated and real data. Our simulations revealed that the Scan-Poisson statistic steadily deteriorates as the number of zeros increases, producing biased inferences. On the other hand, our proposed Scan-ZIP and Scan-ZIP+EM statistics are, most of the time, either superior or comparable to the Scan-Poisson statistic.     

Invasive species distribution modeling (iSDM): Are absence data and dispersal constraints needed to predict actual distributions?

Species distribution models (SDMs) based on statistical relationships between occurrence data and underlying environmental conditions are increasingly used to predict spatial patterns of biological invasions and prioritize locations for early detection and control of invasion outbreaks. However, invasive species distribution models (iSDMs) face special challenges because (i) they typically violate SDM's assumption that the organism is in equilibrium with its environment, and (ii) species absence data are often unavailable or believed to be too difficult to interpret. This often leads researchers to generate pseudo-absences for model training or utilize presence-only methods, and to confuse the distinction between predictions of potential vs. actual distribution. We examined the hypothesis that true-absence data, when accompanied by dispersal constraints, improve prediction accuracy and ecological understanding of iSDMs that aim to predict the actual distribution of biological invasions. We evaluated the impact of presence-only, true-absence and pseudo-absence data on model accuracy using an extensive dataset on the distribution of the invasive forest pathogen Phytophthora ramorum in California. Two traditional presence/absence models (generalized linear model and classification trees) and two alternative presence-only models (ecological niche factor analysis and maximum entropy) were developed based on 890 field plots of pathogen occurrence and several climatic, topographic, host vegetation and dispersal variables. The effects of all three possible types of occurrence data on model performance were evaluated with receiver operating characteristic (ROC) and omission/commission error rates. Results show that prediction of actual distribution was less accurate when we ignored true-absences and dispersal constraints. Presence-only models and models without dispersal information tended to over-predict the actual range of invasions. Models based on pseudo-absence data exhibited similar accuracies as presence-only models but produced spatially less feasible predictions. We suggest that true-absence data are a critical ingredient not only for accurate calibration but also for ecologically meaningful assessment of iSDMs that focus on predictions of actual distributions.     

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.     

Integrated models to support multiobjective ecological restoration decisions

Many objectives motivate ecological restoration, including improving vegetation condition, increasing the range and abundance of threatened species, and improving species richness and diversity. Although models have been used to examine the outcomes of ecological restoration, few researchers have attempted to develop models to account for multiple, potentially competing objectives. We developed a combined state‐and‐transition, species‐distribution model to predict the effects of restoration actions on vegetation condition and extent, bird diversity, and the distribution of several bird species in southeastern Australian woodlands. The actions reflected several management objectives. We then validated the models against an independent data set and investigated how the best management decision might change when objectives were valued differently. We also used model results to identify effective restoration options for vegetation and bird species under a constrained budget. In the examples we evaluated, no one action (improving vegetation condition and extent, increasing bird diversity, or increasing the probability of occurrence for threatened species) provided the best outcome across all objectives. In agricultural lands, the optimal management actions for promoting the occurrence of the Brown Treecreeper (Climacteris picumnus), an iconic threatened species, resulted in little improvement in the extent of the vegetation and a high probability of decreased vegetation condition. This result highlights that the best management action in any situation depends on how much the different objectives are valued. In our example scenario, no management or weed control were most likely to be the best management options to satisfy multiple restoration objectives. Our approach to exploring trade‐offs in management outcomes through integrated modeling and structured decision‐support approaches has wide application for situations in which trade‐offs exist between competing conservation objectives.     

Interactive effects of multiscale diversification practices on farmland bird stress

Farmland diversification practices (i.e., methods used to produce food sustainably by enhancing biodiversity in cropping systems) are sometimes considered beneficial to both agriculture and biodiversity, but most studies of these practices rely on species richness, diversity, or abundance as a proxy for habitat quality. Biodiversity assessments may miss early clues that populations are imperiled when species presence does not imply persistence. Physiological stress indicators may help identify low-quality habitats before population declines occur. We explored how avian stress indicators respond to on-farm management practices and surrounding seminatural area (1-km radius) across 21 California strawberry farms. We examined whether commonly used biodiversity metrics correlate with stress responses in wild birds. We used ∼1000 blood and feather samples and body mass and wing chord measurements, mostly from passerines, to test the effects of diversification practices on four physiological stress indicators: heterophil to lymphocyte ratios (H:L), body condition, hematocrit values, and feather growth rates of individual birds. We then tested the relationship between physiological stress indicators and species richness, abundance, occurrence, and diversity derived from 285 bird point count surveys. After accounting for other biological drivers, landscape context mediated the effect of local farm management on H:L and body condition. Local diversification practices were associated with reduced individual stress in intensive agricultural landscapes but increased it in landscapes surrounded by relatively more seminatural area. Feathers grew more slowly in landscapes dominated by strawberry production, suggesting that nutritional condition was lower here than in landscapes with more crop types and seminatural areas. We found scant evidence that species richness, abundance, occurrence, or diversity metrics were correlated with the individual's physiological stress, suggesting that reliance on these metrics may obscure the impacts of management on species persistence. Our findings underscore the importance of considering landscape context when designing local management strategies to promote wildlife conservation.