Jakub Stoklosa

Model-based thinking for community ecology

In this paper, a case is made for the use of model-based approaches for the analysis of community data. This involves the direct specification of a statistical model for the observed multivariate data. Recent advances in statistical modelling mean that it is now possible to build models that are appropriate for the data which address key ecological questions in a statistically coherent manner. Key advantages of this approach include interpretability, flexibility, and efficiency, which we explain in detail and illustrate by example. The steps in a model-based approach to analysis are outlined, with an emphasis on key features arising in a multivariate context. A key distinction in the model-based approach is the emphasis on diagnostic checking to ensure that the model provides reasonable agreement with the observed data. Two examples are presented that illustrate how the model-based approach can provide insights into ecological problems not previously available. In the first example, we test for a treatment effect in a study where different sites had different sampling intensities, which was handled by adding an offset term to the model. In the second example, we incorporate trait information into a model for ordinal response in order to identify the main reasons why species differ in their environmental response.

A climate of uncertainty: accounting for error in climate variables for species distribution models

Summary Spatial climate variables are routinely used in species distribution models (SDMs) without accounting for the fact that they have been predicted with uncertainty, which can lead to biased estimates, erroneous inference and poor performances when predicting to new settings – for example under climate change scenarios. We show how information on uncertainty associated with spatial climate variables can be obtained from climate data models. We then explain different types of uncertainty (i.e. classical and Berkson error) and use two statistical methods that incorporate uncertainty in climate variables into SDMs by means of (i) hierarchical modelling and (ii) simulation–extrapolation. We used simulation to study the consequences of failure to account for measurement error. When uncertainty in explanatory variables was not accounted for, we found that coefficient estimates were biased and the SDM had a loss of statistical power. Further, this bias led to biased predictions when projecting change in distribution under climate change scenarios. The proposed errors-in-variables methods were less sensitive to these issues. We also fit the proposed models to real data (presence/absence data on the Carolina wren, Thryothorus ludovicianus), as a function of temperature variables. The proposed framework allows for many possible extensions and improvements to SDMs. If information on the uncertainty of spatial climate variables is available to researchers, we recommend the following: (i) first identify the type of uncertainty; (ii) consider whether any spatial autocorrelation or independence assumptions are required; and (iii) attempt to incorporate the uncertainty into the SDM through established statistical methods and their extensions.

Small population size and extremely low levels of genetic diversity in island populations of the platypus, Ornithorhynchus anatinus

Genetic diversity generally underpins population resilience and persistence. Reductions in population size and absence of gene flow can lead to reductions in genetic diversity, reproductive fitness, and a limited ability to adapt to environmental change increasing the risk of extinction. Island populations are typically small and isolated, and as a result, inbreeding and reduced genetic diversity elevate their extinction risk. Two island populations of the platypus, Ornithorhynchus anatinus, exist; a naturally occurring population on King Island in Bass Strait and a recently introduced population on Kangaroo Island off the coast of South Australia. Here we assessed the genetic diversity within these two island populations and contrasted these patterns with genetic diversity estimates in areas from which the populations are likely to have been founded. On Kangaroo Island, we also modeled live capture data to determine estimates of population size. Levels of genetic diversity in King Island platypuses are perilously low, with eight of 13 microsatellite loci fixed, likely reflecting their small population size and prolonged isolation. Estimates of heterozygosity detected by microsatellites (HE= 0.032) are among the lowest level of genetic diversity recorded by this method in a naturally outbreeding vertebrate population. In contrast, estimates of genetic diversity on Kangaroo Island are somewhat higher. However, estimates of small population size and the limited founders combined with genetic isolation are likely to lead to further losses of genetic diversity through time for the Kangaroo Island platypus population. Implications for the future of these and similarly isolated or genetically depauperate populations are discussed.

Conservation of genetic uniqueness of populations may increase extinction likelihood of endangered species: the case of Australian mammals.

BackgroundAs increasingly fragmented and isolated populations of threatened species become subjected to climate change, invasive species and other stressors, there is an urgent need to consider adaptive potential when making conservation decisions rather than focussing on past processes. In many cases, populations identified as unique and currently managed separately suffer increased risk of extinction through demographic and genetic processes. Other populations currently not at risk are likely to be on a trajectory where declines in population size and fitness soon appear inevitable.ResultsUsing datasets from natural Australian mammal populations, we show that drift processes are likely to be driving uniqueness in populations of many threatened species as a result of small population size and fragmentation. Conserving and managing such remnant populations separately will therefore often decrease their adaptive potential and increase species extinction risk.ConclusionsThese results highlight the need for a paradigm shift in conservation biology practise; strategies need to focus on the preservation of genetic diversity at the species level, rather than population, subspecies or evolutionary significant unit. The introduction of new genetic variants into populations through in situ translocation needs to be considered more broadly in conservation programs as a way of decreasing extinction risk by increasing neutral genetic diversity which may increase the adaptive potential of populations if adaptive variation is also increased.

Heterogeneous Capture–Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations

In practice, when analyzing data from a capture-recapture experiment it is tempting to apply modern advanced statistical methods to the observed capture histories. However, unless the analysis takes into account that the data have only been collected from individuals who have been captured at least once, the results may be biased. Without the development of new software packages, methods such as generalized additive models, generalized linear mixed models, and simulation-extrapolation cannot be readily implemented. In contrast, the partial likelihood approach allows the analysis of a capture-recapture experiment to be conducted using commonly available software. Here we examine the efficiency of this approach and apply it to several data sets.

A robust P-spline approach to closed population capture-recapture models with time dependence and heterogeneity

We extend the conditional likelihood approach to the analysis of capture-recapture experiments for closed populations by nonparametrically modeling the relationship between capture probabilities and individual covariates using P-splines. The model allows nonparametric functions of multivariate continuous covariates as well as categorical covariates and time effects, greatly enhancing the techniques available to an analyst. To implement this approach in practice, we found it necessary to develop a robust modification of the Horvitz-Thompson estimator. The method is illustrated on several data sets and a small simulation study is conducted.

Fast forward selection for generalized estimating equations with a large number of predictor variables

We propose a new variable selection criterion designed for use with forward selection algorithms; the score information criterion (SIC). The proposed criterion is based on score statistics which incorporate correlated response data. The main advantage of the SIC is that it is much faster to compute than existing model selection criteria when the number of predictor variables added to a model is large, this is because SIC can be computed for all candidate models without actually fitting them. A second advantage is that it incorporates the correlation between variables into its quasi-likelihood, leading to more desirable properties than competing selection criteria. Consistency and prediction properties are shown for the SIC. We conduct simulation studies to evaluate the selection and prediction performances, and compare these, as well as computational times, with some well-known variable selection criteria. We apply the SIC on a real data set collected on arthropods by considering variable selection on a large number of interactions terms consisting of species traits and environmental covariates.

Graphical diagnostics for occupancy models with imperfect detection

Summary Occupancy-detection models that account for imperfect detection have become widely used in many areas of ecology. As with any modelling exercise, it is important to assess whether the fitted model encapsulates the main sources of variation in the data, yet there have been few methods developed for occupancy-detection models that would allow practitioners to do so. In this paper, a new type of residual for occupancy-detection models is developed according to the method of Dunn & Smyth (Journal of Computational and Graphical Statistics, 5, 1996, 236–244). Residuals are separately constructed to diagnose the occupancy and detection components of the model. Because the residuals are quite noisy, we suggest fitting a smoother through plots of residuals against predictors of fitted values, with 95% confidence bands, to diagnose lack-of-fit. The method is illustrated using Swiss squirrel data, and evaluated using simulations based on that dataset. Plotting residuals against predictors or against fitted values performed reasonably well as methods for diagnosing violations of occupancy-detection model assumptions, particularly plots of residuals against a missing predictor. Relatively high false positive rates were sometimes observed, but this seems to be controlled reasonably well by fitting smoothers to these plots and being guided in interpretation by 95% confidence bands around the smoothers.

Genetic rescue increases fitness and aids rapid recovery of an endangered marsupial population

Genetic rescue has now been attempted in several threatened species, but the contribution of genetics per se to any increase in population health can be hard to identify. Rescue is expected to be particularly useful when individuals are introduced into small isolated populations with low levels of genetic variation. Here we consider such a situation by documenting genetic rescue in the mountain pygmy possum, Burramys parvus. Rapid population recovery occurred in the target population after the introduction of a small number of males from a large genetically diverged population. Initial hybrid fitness was more than two-fold higher than non-hybrids; hybrid animals had a larger body size, and female hybrids produced more pouch young and lived longer. Genetic rescue likely contributed to the largest population size ever being recorded at this site. These data point to genetic rescue as being a potentially useful option for the recovery of small threatened populations.Genetic rescue can be valuable for the conservation of small populations threatened by low genetic diversity, but it carries the perceived risk of outbreeding depression. Here, Weeks et al. report increased hybrid fitness in a rescued population of the mountain pygmy possum, which likely contributed to population growth following genetic rescue.

Cormack–Jolly–Seber model with environmental covariates: A P-spline approach

In capture-recapture models, survival and capture probabilities can be modelled as functions of time-varying covariates, such as temperature or rainfall. The Cormack-Jolly-Seber (CJS) model allows for flexible modelling of these covariates; however, the functional relationship may not be linear. We extend the CJS model by semi-parametrically modelling capture and survival probabilities using a frequentist approach via P-splines techniques. We investigate the performance of the estimators by conducting simulation studies. We also apply and compare these models with known semi-parametric Bayesian approaches on simulated and real data sets.