Joint Modeling of Climate Niches for Adult and Juvenile Trees

Typical ecological gradient analysis for plant species considers variation in the response along a gradient of covariate values, for example, temperature or precipitation. Response is customarily modeled through the presence/absence or a suitable measure of abundance or both. Such analysis enables the creation of a climate niche or range limits for the species using this covariate. Interest often extends to two climate covariates, thus seeking a climate niche in two-dimensional space. It also seeks to learn whether the niche changes over life stages of the species. For instance, is the niche for juveniles different from that for adults? Across the climate domain, where are seedlings relatively more or less abundant than adults? Adult abundance is measured through basal area, juvenile abundance through seedling counts. Our contribution is to describe a coherent modeling approach to address the foregoing objectives. We construct a hierarchical stochastic specification that jointly models juveniles and adults with regard to their two-dimensional climate niches. Joint modeling of the abundance response surfaces is proposed because seedlings and adults are living jointly, competitively and is justified through exploratory analysis. Joint modeling can be challenging when one response is counts and the other is area. We model adult abundance and then juvenile abundance driven by adult abundance. Due to excess zeroes over our study plots, we employ zero-inflated models for both adult and seedling abundance. We demonstrate the benefits of the joint modeling through out-of-sample predictive performance. Our abundance data come from the USDA Forest Service’s Forest Inventory and Analysis dataset. Our climate data come from the 800 m resolution Parameter-elevation Regressions on Independent Slopes Model dataset. In order to extract a response to climate, we aggregate FIA plots to ecological subsections. At plot scale, micro-scale covariates explain variation in abundance; at a larger spatial scale, climate covariates can explain variation in abundance.     

Confidence intervals for expected abundance of rare species

In many ecological research studies, abundance data are skewed and contain more zeros than might be expected. Often, the aim is to model abundance in terms of covariates, and to estimate expected abundance for a given set of covariate values. An approach that has been advocated recently involves the use of a conditional model. This allows one to separately model presence and abundance given presence, which should lead to a more complete understanding as to how the covariates influence abundance. The focus of this article is on the calculation of confidence intervals for expected abundance given particular values of the covariates. The standard Wald confidence interval is symmetric, and therefore unlikely to be of much use for skewed data, where reliable confidence intervals for abundance will generally be asymmetric. The purpose of this article is to show how to calculate a profile likelihood confidence interval for expected abundance using a conditional model.     

Habitat selection by the common wombat (Vombatus ursinus) in disturbed environments: Implications for the conservation of a ‘common’ species

The construction of habitat models is a repeatable technique for describing and mapping species distributions, the utility of which lies in enabling management to predict where a species is likely to occur within a landscape. Typically, habitat models have been used to establish habitat requirements for threatened species; however they have equal applicability for modelling local populations of common species. Often, few data exist on local populations of common species, and issues of abundance and habitat selection at varying scales are rarely addressed. We provide a habitat suitability model for the common wombat (Vombatus ursinus) in southern New South Wales. This species is currently perceived as abundant throughout its extensive range across temperate regions of eastern Australia, yet little factual survey data exist and populations appear under threat. We use wombat burrows to reflect habitat selection and as our basis for ecological modelling. We found that environmental variables representing proximity to cover, measures of vegetation and proximity to watercourses are important predictors of burrow presence. Extrapolation of habitat models identified an abundance of habitat suitable for burrows. However, burrows in many suitable areas were abandoned. Our estimate of the population size was similar to the total annual mortality associated with road-kill. Theoretically, given the availability of suitable habitat, common wombat populations in the region should be thriving. It seems likely that this area once supported a much higher number of wombats; however limiting factors such as road mortality and disease have reduced the populations. The persistence of wombats in the study region must be supported by migration from other populations. Our findings challenge the perception that wombats are currently common and not in need of monitoring, suggesting that perceptions of abundance are often clouded by socio-political motives rather than informed by biological and ecological factors.     

Genetic Introgression and the Survival of Florida Panther Kittens

Estimates of survival for the young of a species are critical for population models. These models can often be improved by determining the effects of management actions and population abundance on this demographic parameter. We used multiple sources of data collected during 1982-2008 and a live-recapture dead-recovery modeling framework to estimate and model survival of Florida panther (Puma concolor coryi) kittens (age 0-1 year). Overall, annual survival of Florida panther kittens was 0.323 ± 0.071 (SE), which was lower than estimates used in previous population models. In 1995, female pumas from Texas (P. c. stanleyana) were released into occupied panther range as part of an intentional introgression program to restore genetic variability. We found that kitten survival generally increased with degree of admixture: F₁ admixed and backcrossed to Texas kittens survived better than canonical Florida panther and backcrossed to canonical kittens. Average heterozygosity positively influenced kitten and older panther survival, whereas index of panther abundance negatively influenced kitten survival. Our results provide strong evidence for the positive population-level impact of genetic introgression on Florida panthers. Our approach to integrate data from multiple sources was effective at improving robustness as well as precision of estimates of Florida panther kitten survival, and can be useful in estimating vital rates for other elusive species with sparse data.     

Joint Modeling of Spatial Variability and Within-Row Interplot Competition to Increase the Efficiency of Plant Improvement

Trials in the early stages of selection are often subject to variation arising from spatial variability and interplot competition, which can seriously bias the assessment of varietal performance and reduce genetic progress. An approach to jointly model both sources of bias is presented. It models genotypic and residual competition and also global and extraneous spatial variation. Variety effects were considered random and residual maximum likelihood was used for parameter estimation. Competition at the residual level was examined using two special simultaneous autoregressive models. An equal-roots second-order autoregressive (EAR(2)) model is proposed for trials where competition is dominant. An equal-roots third-order autoregressive (EAR(3)) model allows for competition and spatial variability. These models are applied to two yield data sets from an Australian sugarcane selection program. One data set is in the paper and the other is in supplementary material available online. To determine the effect of simultaneously adjusting for spatial variability and interplot competition on selection, the percentages of superior varieties in common in the top 15% for the joint model and classical approaches were compared. Agreement between the two approaches was 45 and 84%. Hence, for some trials there are large differences in varieties advanced to the next stage of selection.     

A nine-year study of successful breeding in a Bonelli’s eagle population in southeast Spain: a basis for conservation

We analyse the factors influencing breeding success in a healthy population of Bonelli’s eagle (Hieraaetus fasciatus) from south-east Spain, a raptor that has suffered a serious decline in Europe. Between 18 and 33 pairs were annually monitored during the period 1994-2002. Several factors that may affect four breeding parameters were studied, namely human presence, vegetation, relief, climatic factors, intra- and inter-specific relationships, diet, prey abundance, nest building, adult mortality and age of reproduction. A consistently high breeding success was registered during the study period (productivity=1.43, SD=0.11), which was probably the result of high adult survival, adequate prey availability and mild weather conditions. However, a certain vulnerability to the presence of golden eagles (Aquila chrysaetos) and to human disturbance was observed. One interesting result was the reduced survival of young chicks on north-facing cliffs owing to colder conditions, which may partially explain the decline of the Bonelli’s eagle populations along its European distribution limits. We discuss the role of this healthy subpopulation in an Iberian metapopulation context, and propose that the potential interference of golden eagles should be taken into account when designing management strategies for Bonelli’s eagles. Finally, we pinpoint some conservation priorities and the importance of reducing the main causes of adult mortality (i.e. shooting and electrocution) to assure successful reproduction and survival of this species.     

Modelling populations of long-lived birds of prey for conservation: A study of imperial eagles (Aquila heliaca) in Kazakhstan

Eagle populations worldwide are in decline and their demography is generally poorly understood. We use novel sensitivity analysis of stochastic simulation models to analyse the demography of the worlds highest-density and longest-studied population of eastern imperial eagles (Aquila heliaca), at the Naurzum National Nature Reserve in Kazakhstan. Single variable perturbation (a simple elasticity-type analysis) showed that population growth was most sensitive to changes in adult survival but provided no information on how interactions between parameters may influence population growth. Multiple-variable perturbations (a more comprehensive elasticity-type analysis) suggested that population growth is relatively more sensitive to adult survival than is indicated by single-variable perturbation but also that when adult survival is within a biologically reasonable range, other parameters are still highly consequential to model outputs. For Naurzum’s imperial eagles, and for other structured populations of vertebrates, effective conservation and management likely requires an approach that addresses the importance of simultaneous variation in multiple vital rates including both survivorship and reproductive output.     

A quantitative framework to evaluate incidental take and endangered species population viability

Incidental take is the permitted unintended or collateral killing, harassment, or habitat destruction of a protected species under endangered species law and is permissible as long as the take does not jeopardize the species’ persistence in the wild. However, take is seldom addressed in a quantitative or population modeling context and the criterion of “jeopardy” has no universal, quantitative definition. To model the effect of incidental take on population viability, we modified an existing population model and simulated abundance, population growth, and quasi-extinction probability (the probability of falling below a predetermined abundance threshold) for Piping Plovers (Charadrius melodus) in the Great Plains, USA. The model incorporated environmental stochasticity and variation due to sampling variance. Eggs and chicks were taken out of the population as a “harvest” to simulate incidental take that currently occurs in the Missouri River system. We used least-squares regression and an AIC model selection approach to evaluate the population’s elasticity to incidental take covariates. Even in the absence of take the population declined by 7.5% annually. Population growth and final abundance were reduced and the probability of quasi-extinction was increased in simulations where egg take and chick take were applied. The model selection analysis indicated that incidental take of eggs and chicks depresses population viability and the probability of recovery of Piping Plovers in the Great Plains. Though the model was useful in putting take and jeopardy in a quantitative setting, the question remains as to whether permitted levels of take causes jeopardy for Piping Plovers since there are no decision standards defined by the USFWS. However, evaluating take in a quantitative framework, as we have, will make jeopardy decisions more explicit in terms of viability and recovery metrics.     

A Bayesian Approach to Fitting Gibbs Processes with Temporal Random Effects

We consider spatial point pattern data that have been observed repeatedly over a period of time in an inhomogeneous environment. Each spatial point pattern can be regarded as a ??snapshot?? of the underlying point process at a series of times. Thus, the number of points and corresponding locations of points differ for each snapshot. Each snapshot can be analyzed independently, but in many cases there may be little information in the data relating to model parameters, particularly parameters relating to the interaction between points. Thus, we develop an integrated approach, simultaneously analyzing all snapshots within a single robust and consistent analysis. We assume that sufficient time has passed between observation dates so that the spatial point patterns can be regarded as independent replicates, given spatial covariates. We develop a joint mixed effects Gibbs point process model for the replicates of spatial point patterns by considering environmental covariates in the analysis as fixed effects, to model the heterogeneous environment, with a random effects (or hierarchical) component to account for the different observation days for the intensity function. We demonstrate how the model can be fitted within a Bayesian framework using an auxiliary variable approach to deal with the issue of the random effects component. We apply the methods to a data set of musk oxen herds and demonstrate the increased precision of the parameter estimates when considering all available data within a single integrated analysis.     

Overcoming the rare species modelling paradox: A novel hierarchical framework applied to an Iberian endemic plant

Rare species have restricted geographic ranges, habitat specialization, and/or small population sizes. Datasets on rare species distribution usually have few observations, limited spatial accuracy and lack of valid absences; conversely they provide comprehensive views of species distributions allowing to realistically capture most of their realized environmental niche. Rare species are the most in need of predictive distribution modelling but also the most difficult to model. We refer to this contrast as the “rare species modelling paradox” and propose as a solution developing modelling approaches that deal with a sufficiently large set of predictors, ensuring that statistical models are not over-fitted. Our novel approach fulfils this condition by fitting a large number of bivariate models and averaging them with a weighted ensemble approach. We further propose that this ensemble forecasting is conducted within a hierarchic multi-scale framework. We present two ensemble models for a test species, one at regional and one at local scale, each based on the combination of 630 models. In both cases, we obtained excellent spatial projections, unusual when modelling rare species. Model results highlight, from a statistically sound approach, the effects of multiple drivers in a same modelling framework and at two distinct scales. From this added information, regional models can support accurate forecasts of range dynamics under climate change scenarios, whereas local models allow the assessment of isolated or synergistic impacts of changes in multiple predictors. This novel framework provides a baseline for adaptive conservation, management and monitoring of rare species at distinct spatial and temporal scales.     

A conservation framework for the golden eagle in Scotland: Refining condition targets and assessment of constraint influences

Conservation strategies have three elements: species protection, site protection and, the most challenging component, conservation in the wider environment. Watson and Whitfield [Watson, J., Whitfield, P., 2002. A conservation framework for the golden eagle Aquila chrysaetos in Scotland. Journal of Raptor Research 36(1 Suppl.), 41-49.] proposed a conservation framework for the golden eagle in Scotland whose main innovation, taking a lead from EU conservation Directives, was to incorporate the concept of favourable condition and its maintenance by implementing conservation policies that are regionally targeted at known constraints in the wider environment. Three criteria were suggested to judge favourable condition: a national abundance target of breeding pairs, national and regional targets for breeding productivity, and regional targets for the extent of suitable habitat which is occupied by breeding pairs. Here we refine these criteria, first to take the national abundance target and use it to set regional targets. Distribution targets were implicitly incorporated by this process because abundance targets were set regionally, with regard to the proportion of known territories which should be occupied. This allowed us to dispense with the distribution criterion as originally proposed. Our next refinement was to base regional demographic targets not only on breeding productivity, but also on indirect measures of survival (which are likely to have more influence on population dynamics). Despite apparent overall population stability over the last 20 years, the national golden eagle population failed to meet the abundance target and only 3 of 16 regions where eagles have occupied territories since 1982 were considered to be in favourable condition. The key constraint preventing favourable condition being met was persecution, predominantly in some areas managed for grouse shooting. The advantages of a conservation framework over similar approaches, such as species action plans, are highlighted.     

Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution

Ecological abundance data are often recorded on an ordinal scale in which the lowest category represents species absence. One common example is when plant species cover is visually assessed within bounded quadrats and then assigned to pre-defined cover class categories. We present an ordinal beta hurdle model that directly models ordinal category probabilities with a biologically realistic beta-distributed latent variable. A hurdle-at-zero model allows ecologists to explore distribution (absence) and abundance processes in an integrated framework. This provides an alternative to cumulative link models when data are inconsistent with the assumption that the odds of moving into a higher category are the same for all categories (proportional odds). Graphical tools and a deviance information criterion were developed to assess whether a hurdle-at-zero model should be used for inferences rather than standard ordinal methods. Hurdle-at-zero and non-hurdle ordinal models fit to vegetation cover class data produced substantially different conclusions. The ordinal beta hurdle model yielded more precise parameter estimates than cumulative logit models, although out-of-sample predictions were similar. The ordinal beta hurdle model provides inferences directly on the latent biological variable of interest, percent cover, and supports exploration of more realistic ecological patterns and processes through the hurdle-at-zero or two-part specification. We provide JAGS code as an on-line supplement. Supplementary materials accompanying this paper appear on-line.     

Detecting amphibian population cycles: The importance of appropriate statistical analyses

Amphibian populations are declining worldwide and understanding their temporal dynamics should be important to separate declines from natural fluctuations. In this study sixteen long-term amphibian time series, lasting 15 years or more, were analysed by means of conventional methods of time series analysis to evaluate the relative importance of exogenous and endogenous factors controlling population dynamics, and in particular to assess the existence of population cycles. There was significant autocorrelation in seven time series, and the autocorrelation function showed no signs of statistical cyclicity, but in one case there was some evidence for weak periodicity. In 12 populations the partial rate correlation function suggested the presence of direct density dependence, while there was no evidence for delayed density dependent regulation. In all time series the global Lyapunov exponent, a statistic that characterises the predictability of a dynamic system, indicated that the population trajectories had a tendency to converge towards a stable dynamics. These results may have conservation implications, because populations with direct density dependence possess high capacity of returning to equilibrium after a perturbation and therefore are less likely to go extinct. In the future, I encourage ecologists to increase the use of statistical time series methods and autoregressive modelling to analyse amphibian population dynamics in the framework of local and global climate variability.     

Agricultural landscape modification increases the abundance of an important food resource: Mistletoes, birds and brigalow

Agricultural landuse alters landscape pattern, with important consequences for native species. Complex responses to changes in landscape pattern may be observed for species with strong inter-specific relationships. We investigate how the abundance of an ecologically important food resource, the grey mistletoe (Amyema quandang), is influenced by the interactive influences of human-modified landscape pattern, bird disperser abundance and host condition. Mistletoe abundance was estimated in brigalow (Acacia harpophylla) dominated remnants in three separate study areas with differing landscape patterns. Negative binomial generalised linear models of mistletoe abundance were tested with combinations of seven explanatory variables: study area, landscape connectivity and edge contrast, patch shape, bird disperser abundance, brigalow foliage cover and basal area of standing dead trees. Ranking of model averaged parameter estimates showed that study area, bird disperser abundance, patch shape, dead trees and connectivity had the strongest influence on A. quandang abundance. Mistletoe abundance apparently increased with landscape modification, particularly in narrow linear patches, but may be limited by the availability of seed dispersers and host condition. Given high landscape modification and ongoing degradation, management should be targeted towards maintaining brigalow remnant condition to ensure bird and mistletoe populations can be supported in the long-term.     

Regional conservation priorities for a large predator: golden eagles (Aquila chrysaetos) in the Alpine range

We compared the density of golden eagles (Aquila chrysaetos) and their nest dispersion, productivity and diet in Alpine and pre-Alpine areas. The comparison was made at two spatial scales: (1) at the territory level within two contiguous populations, and (2) at the population level, using published data for 22 populations scattered across four countries (France, Switzerland, Germany and Italy). Availability of golden eagle's main prey species was higher in Alpine than in pre-Alpine regions. The potential foraging ranges of pairs of eagles in the pre-Alps had larger amounts of woodland and lower amounts of suitable foraging habitat than those of Alpine pairs. At both spatial scales, density and productivity were lower in the pre-Alps. Also, pre-Alpine populations were characterised by a lower percentage of main prey species in the diet, which was significantly correlated with productivity, and by a higher breadth of diet, which was negatively correlated with density. Overall, higher prey availability and habitat suitability in the Alps resulted in higher density and breeding success, in a manner compatible with theoretical metapopulation models. We suggest that priority be given to conservation of eagle populations in high quality Alpine habitat, and that conservation action be carried out by a mixture of site-protection measures and conservation of the wider environment.     

An approach for regional threat assessment under IUCN Red List criteria that is robust to uncertainty: The Fiordland bottlenose dolphins are critically endangered

Numerous globally abundant species are exposed to human impacts that threaten the viability of regional populations. Assessing and characterising the risks faced by these populations can have significant implications for biodiversity conservation, given the ecological importance of many such species. To address these risks, the IUCN is starting to conduct assessments of regional populations in addition to species-level assessments of conservation status. Here, we demonstrate a threat assessment process that is robust to uncertainty, applying the IUCN criteria to a regional population of bottlenose dolphins in Fiordland, New Zealand. We compiled available population-specific information to assess the population under the five Red List criteria. We estimated there were 205 Fiordland bottlenose dolphins (CV = 3.5%), using current estimates of abundance for two sub-populations and stochastic modelling of an earlier estimate for the third sub-population. Population trajectory and extinction risk were assessed using stochastic age-structured Leslie matrix population models. The majority of model runs met the criteria for classification as critically endangered (C1: 67.6% of runs) given the number of mature individuals (123; CV = 6.7%) and the predicted rate of population decline (average decline: 31.4% over one generation). The evidence of isolation of the population confirms this was an appropriate regional classification. This approach provided an assessment that was robust to uncertainty.     

Monitoring distributions using call surveys: estimating site occupancy, detection probabilities and inferring absence

Monitoring programs serve to track changes in the distribution and abundance of species. A major problem with most monitoring programs is that species detection is imperfect and some populations are inevitably missed. Therefore, in most monitoring programs the true distribution of a species will be underestimated. Here, we report a field test of the reliability and performance of a commonly used method to monitor the distribution of amphibians (anuran call surveys). We surveyed the distribution of four anuran species in western Switzerland, and estimated detection probabilities to account for imperfect species detection and used these estimates to adjust our estimate of site occupancy (i.e., distribution). Next, we assessed how detection probabilities were affected by weather and how site occupancy was affected by site specific covariates. For one species (Hyla arborea), call surveys proved efficient in determining the regional distribution with only few site visits because detection probabilities were relatively high. The call surveys apparently missed many populations of another common species (Bufo calamita) because detection probabilities were lower. Two other species (Bombina variegata and Alytes obstetricans) were uncommon and strong inference from the analysis is not possible. Thus, multispecies surveys may be inefficient for rare species. Estimates of detection probabilities were used to calculate how many site visits are necessary to infer the absence of a species with some predetermined statistical certainty. The implications of “false absences” are important in ecology as they are known to bias usual habitat suitability models and overestimate extinction/colonization events in metapopulations. Large-scale monitoring programs would benefit from the application of an estimation-based approach to monitoring the distribution of species.     

Predicting species occurrence using information-theoretic approaches and significance testing: An example of dormouse distribution in Cumbria, UK

Predicting the occurrence of species is an essential part of conservation biology. The range of techniques used to do this has increased in recent years. This has included wider use of information-theoretic approaches; particularly Akaike’s information criteria (AIC). AIC is often used with regression modelling when predicting species distribution. The traditional method of model selection in regression modelling, stepwise significance testing, is also still widely used. This paper compares the two approaches, using the occurrence of the dormouse (Muscardinus avellanarius) in Cumbria, UK as an example. The dormouse is a protected species whose abundance and range have declined nationally. Knowledge of its occurrence in Cumbria is required in order to increase measures for its conservation in the area. The paper uses the habitat features woodland size, altitude, soil type, tree species present, temperature and rainfall as potential predictors. As only presence data was available for dormice in Cumbria, pseudo-absences were generated to allow logistic regression modelling. The use of pseudo-absences was justified using a false record permutation test. Cross-validation allowed the ability of models to predict the data to be assessed. This was judged using ROC plots. The size of the wood, temperature and whether the soil was wet or dry were the best predictors of dormouse incidence in Cumbria. The two approaches produced different models; those from the information-theoretic approach had a better ability to fit the data. The information-theoretic approach also had the advantage of enabling model averaging and provided greater understanding of the system.     

Local linear mixed effect models—Model specification and interpretation in a biological context

Clustered data, either as an explicit part of the study design or due to the natural distribution of habitats, populations, and so on, are frequently encountered by biologists. Mixed effect models provide a framework that can handle clustered data by estimating cluster-specific random effects and introducing correlated residual structures. General parametric models have been shown not to suit all biological problems, resulting in an increased popularity for local regression procedures, such as LOESS and splines. To evaluate similar biological problems for clustered data with cluster-specific random effects and potential dependencies between within-cluster residuals, we suggest a local linear mixed model (LLMM). The LLMM approach is a local version of a linear mixed-effect model (LME), and the LLMM approach produces: (1) local shared predictions, (2) local cluster-specific predictions, and (3) estimates of cluster-specific random effects conditioned on the covariates. Thus, in addition to the local estimates of the expected response, we obtain information about how the cluster-specific random variability depends on the values of the covariate. Ovary data are used to illustrate the flexibility and potential of this procedure in biological contexts.     

Modelling interannual and spatial variability of leaf senescence for three deciduous tree species in France

The annual timing of temperate forest leaf colouring is affected by climate change; to date, its modelling remains a challenge. We take advantage of a ca. 400 leaf colouring observations database acquired in France during the period of 1997–2006 in order to develop a new modelling framework aimed at predicting the spatial and year-to-year variability of leaf colouring in European beech and oak (Fagus sylvatica L., Quercus petraea (Matt.) Liebl. and Quercus robur L.). We postulate colouring to be the outcome of a one-way process triggered by photoperiod and progressing through a photoperiod-sensitive cold-degree day summation procedure. Observations were pooled according to genus for the fitting and ensuing validation procedures. Parameters of the model suggest that colouring processes start earlier, and are sensitive to higher temperatures for Quercus than for Fagus. Errors associated with the modelled predictions are up to 13.0 days in Fagus and 10.3 days in Quercus, which are significantly lower than errors associated with (1) the overall mean (null model) or (2) previously published modelling frameworks. When averaged on a site basis, model predictions reproduced spatial variability of leaf colouring over the French territory with good efficiency (modelling efficiencies: 0.44 for Fagus, 0.45 for Quercus). The interannual variability of leaf colouring over France was fairly reproduced (r² = 0.74 for Fagus, 0.83 for Quercus). On that basis, we claim that the modelling framework developed herein can be efficiently integrated into more general schemes aimed at simulating matter and energy fluxes on a regional scale, and we provide a generic parameterisation of the model to be integrated into such schemes. When used in a prospective analysis, the model predicts a trend towards delay in leaf colouring of 1.4 and 1.7 days per decade in Fagus and Quercus, respectively, over the period of 1951–2099 in France.