Integrating correlation between traits improves spatial predictions of plant functional composition

Functional trait composition is increasingly recognized as key to better understand and predict community responses to environmental gradients. Predictive approaches traditionally model the weighted mean trait values of communities (CWMs) as a function of environmental gradients. However, most approaches treat traits as independent regardless of known tradeoffs between them, which could lead to spurious predictions. To address this issue, we suggest jointly modeling a suit of functional traits along environmental gradients while accounting for relationships between traits. We use generalized additive mixed effect models to predict the functional composition of alpine grasslands in the Guisane Valley (France). We demonstrate that, compared to traditional approaches, joint trait models explain considerable amounts of variation in CWMs, yield less uncertainty in trait CWM predictions and provide more realistic spatial projections when extrapolating to novel environmental conditions. Modeling traits and their co‐variation jointly is an alternative and superior approach to predicting traits independently. Additionally, compared to a ‘predict first, assemble later’ approach that estimates trait CWMs post hoc based on stacked species distribution models, our ‘assemble first, predict later’ approach directly models trait‐responses along environmental gradients, and does not require data and models on species’ distributions, but only mean functional trait values per community plot. This highlights the great potential of joint trait modeling approaches in large‐scale mapping applications, such as spatial projections of the functional composition of vegetation and associated ecosystem services as a response to contemporary global change.     

Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture

Shared random effects joint models are becoming increasingly popular for investigating the relationship between longitudinal and time‐to‐event data. Although appealing, such complex models are computationally intensive, and quick, approximate methods may provide a reasonable alternative. In this paper, we first compare the shared random effects model with two approximate approaches: a naïve proportional hazards model with time‐dependent covariate and a two‐stage joint model, which uses plug‐in estimates of the fitted values from a longitudinal analysis as covariates in a survival model. We show that the approximate approaches should be avoided since they can severely underestimate any association between the current underlying longitudinal value and the event hazard. We present classical and Bayesian implementations of the shared random effects model and highlight the advantages of the latter for making predictions. We then apply the models described to a study of abdominal aortic aneurysms (AAA) to investigate the association between AAA diameter and the hazard of AAA rupture. Out‐of‐sample predictions of future AAA growth and hazard of rupture are derived from Bayesian posterior predictive distributions, which are easily calculated within an MCMC framework. Finally, using a multivariate survival sub‐model we show that underlying diameter rather than the rate of growth is the most important predictor of AAA rupture.     

Confronting different models of community structure to species-abundance data: a Bayesian model comparison

Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species‐abundance data that yields a full joint probability distribution of each model's parameters plus a relatively parameter‐independent criterion, the posterior Bayes factor, to compare these models. We illustrate our approach by comparing three classical distributions: the zero‐sum multinomial (ZSM) distribution, based on Hubbell's neutral model, the multivariate Poisson lognormal distribution (MPLN), based on niche arguments, and the discrete broken stick (DBS) distribution, based on MacArthur's broken stick model. We give explicit formulas for the probability of observing a particular species‐abundance data set in each model, and argue that conditioning on both sample size and species count is needed to allow comparisons between the two distributions. We apply our approach to two neotropical communities (trees, fish). We find that DBS is largely inferior to ZSM and MPLN for both communities. The tree data do not allow discrimination between ZSM and MPLN, but for the fish data ZSM (neutral model) overwhelmingly outperforms MPLN (niche model), suggesting that dispersal plays a previously underestimated role in structuring tropical freshwater fish communities. We advocate this approach for identifying the relative importance of dispersal and niche‐partitioning in determining diversity of different ecological groups of species under different environmental conditions.     

Selecting from correlated climate variables: a major source of uncertainty for predicting species distributions under climate change

Correlative species distribution models are frequently used to predict species’ range shifts under climate change. However, climate variables often show high collinearity and most statistical approaches require the selection of one among strongly correlated variables. When causal relationships between species presence and climate parameters are unknown, variable selection is often arbitrary, or based on predictive performance under current conditions. While this should only marginally affect current range predictions, future distributions may vary considerably when climate parameters do not change in concert. We investigated this source of uncertainty using four highly correlated climate variables together with a constant set of landscape variables in order to predict current (2010) and future (2050) distributions of four mountain bird species in central Europe. Simulating different parameterization decisions, we generated a) four models including each of the climate variables singly, b) a model taking advantage of all variables simultaneously and c) an un‐weighted average of the predictions of a). We compared model accuracy under current conditions, predicted distributions under four scenarios of climate change, and – for one species – evaluated back‐projections using historical occurrence data. Although current and future variable‐correlations remained constant, and the models’ accuracy under contemporary conditions did not differ, future range predictions varied considerably in all climate change scenarios. Averaged models and models containing all climate variables simultaneously produced intermediate predictions; the latter, however, performed best in back‐projections. This pattern, consistent across different modelling methods, indicates a benefit from including multiple climate predictors in ambiguous situations. Variable selection proved to be an important source of uncertainty for future range predictions, difficult to control using contemporary information. Small, but diverging changes of climate variables, masked by constant overall correlation patterns, can cause substantial differences between future range predictions which need to be accounted for, particularly when outcomes are intended for conservation decisions.     

Model-based uncertainty in species range prediction

Aim Many attempts to predict the potential range of species rely on environmental niche (or ‘bioclimate envelope’) modelling, yet the effects of using different niche‐based methodologies require further investigation. Here we investigate the impact that the choice of model can have on predictions, identify key reasons why model output may differ and discuss the implications that model uncertainty has for policy‐guiding applications. Location The Western Cape of South Africa. Methods We applied nine of the most widely used modelling techniques to model potential distributions under current and predicted future climate for four species (including two subspecies) of Proteaceae. Each model was built using an identical set of five input variables and distribution data for 3996 sampled sites. We compare model predictions by testing agreement between observed and simulated distributions for the present day (using the area under the receiver operating characteristic curve (AUC) and kappa statistics) and by assessing consistency in predictions of range size changes under future climate (using cluster analysis). Results Our analyses show significant differences between predictions from different models, with predicted changes in range size by 2030 differing in both magnitude and direction (e.g. from 92% loss to 322% gain). We explain differences with reference to two characteristics of the modelling techniques: data input requirements (presence/absence vs. presence‐only approaches) and assumptions made by each algorithm when extrapolating beyond the range of data used to build the model. The effects of these factors should be carefully considered when using this modelling approach to predict species ranges. Main conclusions We highlight an important source of uncertainty in assessments of the impacts of climate change on biodiversity and emphasize that model predictions should be interpreted in policy‐guiding applications along with a full appreciation of uncertainty.     

Uncertainty in assessing the impacts of global change with coupled dynamic species distribution and population models

Concern over rapid global changes and the potential for interactions among multiple threats are prompting scientists to combine multiple modelling approaches to understand impacts on biodiversity. A relatively recent development is the combination of species distribution models, land‐use change predictions, and dynamic population models to predict the relative and combined impacts of climate change, land‐use change, and altered disturbance regimes on species' extinction risk. Each modelling component introduces its own source of uncertainty through different parameters and assumptions, which, when combined, can result in compounded uncertainty that can have major implications for management. Although some uncertainty analyses have been conducted separately on various model components – such as climate predictions, species distribution models, land‐use change predictions, and population models – a unified sensitivity analysis comparing various sources of uncertainty in combined modelling approaches is needed to identify the most influential and problematic assumptions. We estimated the sensitivities of long‐run population predictions to different ecological assumptions and parameter settings for a rare and endangered annual plant species (Acanthomintha ilicifolia, or San Diego thornmint). Uncertainty about habitat suitability predictions, due to the choice of species distribution model, contributed most to variation in predictions about long‐run populations.     

Bayesian inference in ecology

Bayesian inference is an important statistical tool that is increasingly being used by ecologists. In a Bayesian analysis, information available before a study is conducted is summarized in a quantitative model or hypothesis: the prior probability distribution. Bayes’ Theorem uses the prior probability distribution and the likelihood of the data to generate a posterior probability distribution. Posterior probability distributions are an epistemological alternative to P‐values and provide a direct measure of the degree of belief that can be placed on models, hypotheses, or parameter estimates. Moreover, Bayesian information‐theoretic methods provide robust measures of the probability of alternative models, and multiple models can be averaged into a single model that reflects uncertainty in model construction and selection. These methods are demonstrated through a simple worked example. Ecologists are using Bayesian inference in studies that range from predicting single‐species population dynamics to understanding ecosystem processes. Not all ecologists, however, appreciate the philosophical underpinnings of Bayesian inference. In particular, Bayesians and frequentists differ in their definition of probability and in their treatment of model parameters as random variables or estimates of true values. These assumptions must be addressed explicitly before deciding whether or not to use Bayesian methods to analyse ecological data.     

MigClim: Predicting plant distribution and dispersal in a changing climate

Aim Many studies have forecasted the possible impact of climate change on plant distributions using models based on ecological niche theory, but most of them have ignored dispersal‐limitations, assuming dispersal to be either unlimited or null. Depending on the rate of climatic change, the landscape fragmentation and the dispersal capabilities of individual species, these assumptions are likely to prove inaccurate, leading to under‐ or overestimation of future species distributions and yielding large uncertainty between these two extremes. As a result, the concepts of ‘potentially suitable’ and ‘potentially colonizable’ habitat are expected to differ significantly. To quantify to what extent these two concepts can differ, we developed Mig Clim, a model simulating plant dispersal under climate change and landscape fragmentation scenarios. Mig Clim implements various parameters, such as dispersal distance, increase in reproductive potential over time, landscape fragmentation or long‐distance dispersal. Location Western Swiss Alps. Methods Using our Mig Clim model, several simulations were run for two virtual species by varying dispersal distance and other parameters. Each simulation covered the 100‐year period 2001–2100 and three different IPCC‐based temperature warming scenarios were considered. Results of dispersal‐limited projections were compared with unlimited and no‐dispersal projections. Results Our simulations indicate that: (1) using realistic parameter values, the future potential distributions generated using Mig Clim can differ significantly (up to more than 95% difference in colonized surface) from those that ignore dispersal; (2) this divergence increases under more extreme climate warming scenarios and over longer time periods; and (3) the uncertainty associated with the warming scenario can be as large as the one related to dispersal parameters. Main conclusions Accounting for dispersal, even roughly, can importantly reduce uncertainty in projections of species distribution under climate change scenarios.     

Integrating over uncertainty in spatial scale of response within multispecies occupancy models yields more accurate assessments of community composition

Species abundance and community composition are affected not only by the local environment, but also by broader landscape and regional context. Yet, determining the spatial scales at which landscapes affect species remains a persistent challenge, hindering our ability to understand how environmental gradients shape communities. This problem is amplified by rare species and imperfect species detection. Here, we present a Bayesian framework that allows uncertainty surrounding the ‘true’ spatial scale of species’ responses (i.e. changes in presence/absence) to be integrated directly into a community hierarchical model. This scale‐selecting multispecies occupancy model (ssMSOM) estimates the scale of response, and shows high accuracy and correct levels of uncertainty in parameter estimates across a broad range of simulation conditions. An ssMSOM can be run in a matter of minutes, as opposed to the many hours required to run normal multispecies occupancy models at all queried spatial scales, and then conduct model selection – a problem that up to now has prohibited scale of response from being rigorously evaluated in an occupancy framework. Alternatives to the ssMSOM, such as GLM‐based approaches frequently fail to detect the correct spatial scale and magnitude of response, and are often falsely confident by favoring the incorrect parameter estimates, especially as species’ detection probabilities deviate from perfect. We further show how trait information can be leveraged to understand how individual species’ scales of response vary within communities. Integrating spatial scale selection directly into hierarchical community models provides a means of formally testing hypotheses regarding spatial scales of response, and more accurately determining the environmental drivers that shape communities.     

Bayesian model adequacy and choice in phylogenetics

Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global) performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance) of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric bootstrap, accounts for uncertainty in the phylogeny and model parameters.     

Robust dynamics of Amazon dieback to climate change with perturbed ecosystem model parameters

Climate change science is increasingly concerned with methods for managing and integrating sources of uncertainty from emission storylines, climate model projections, and ecosystem model parameterizations. In tropical ecosystems, regional climate projections and modeled ecosystem responses vary greatly, leading to a significant source of uncertainty in global biogeochemical accounting and possible future climate feedbacks. Here, we combine an ensemble of IPCC‐AR4 climate change projections for the Amazon Basin (eight general circulation models) with alternative ecosystem parameter sets for the dynamic global vegetation model, LPJmL. We evaluate LPJmL simulations of carbon stocks and fluxes against flux tower and aboveground biomass datasets for individual sites and the entire basin. Variability in LPJmL model sensitivity to future climate change is primarily related to light and water limitations through biochemical and water‐balance‐related parameters. Temperature‐dependent parameters related to plant respiration and photosynthesis appear to be less important than vegetation dynamics (and their parameters) for determining the magnitude of ecosystem response to climate change. Variance partitioning approaches reveal that relationships between uncertainty from ecosystem dynamics and climate projections are dependent on geographic location and the targeted ecosystem process. Parameter uncertainty from the LPJmL model does not affect the trajectory of ecosystem response for a given climate change scenario and the primary source of uncertainty for Amazon ‘dieback’ results from the uncertainty among climate projections. Our approach for describing uncertainty is applicable for informing and prioritizing policy options related to mitigation and adaptation where long‐term investments are required.     

Evaluation of habitat suitability index models by global sensitivity and uncertainty analyses: a case study for submerged aquatic vegetation

Habitat suitability index (HSI) models are commonly used to predict habitat quality and species distributions and are used to develop biological surveys, assess reserve and management priorities, and anticipate possible change under different management or climate change scenarios. Important management decisions may be based on model results, often without a clear understanding of the level of uncertainty associated with model outputs. We present an integrated methodology to assess the propagation of uncertainty from both inputs and structure of the HSI models on model outputs (uncertainty analysis: UA) and relative importance of uncertain model inputs and their interactions on the model output uncertainty (global sensitivity analysis: GSA). We illustrate the GSA/UA framework using simulated hydrology input data from a hydrodynamic model representing sea level changes and HSI models for two species of submerged aquatic vegetation (SAV) in southwest Everglades National Park: Vallisneria americana (tape grass) and Halodule wrightii (shoal grass). We found considerable spatial variation in uncertainty for both species, but distributions of HSI scores still allowed discrimination of sites with good versus poor conditions. Ranking of input parameter sensitivities also varied spatially for both species, with high habitat quality sites showing higher sensitivity to different parameters than low‐quality sites. HSI models may be especially useful when species distribution data are unavailable, providing means of exploiting widely available environmental datasets to model past, current, and future habitat conditions. The GSA/UA approach provides a general method for better understanding HSI model dynamics, the spatial and temporal variation in uncertainties, and the parameters that contribute most to model uncertainty. Including an uncertainty and sensitivity analysis in modeling efforts as part of the decision‐making framework will result in better‐informed, more robust decisions.     

Bringing metabolic networks to life: integration of kinetic, metabolic, and proteomic data

Background

Translating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made.

Results

We compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogenous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations.

Conclusion

We present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.     

A tutorial on dynamic risk prediction of a binary outcome based on a longitudinal biomarker

Dynamic risk predictions based on all available information are useful in timely identification of high-risk patients. However, in contrast with time to event outcomes, there is still a lack of studies that clearly demonstrate how to obtain and update predictions for a future binary outcome using a repeatedly measured biomarker. The aim of this study is to give an illustrative overview of four approaches to obtain such predictions: likelihood based two-stage method (2SMLE), likelihood based joint model (JMMLE), Bayesian two-stage method (2SB), and Bayesian joint model (JMB). We applied the approaches to provide weekly updated predictions of post–molar gestational trophoblastic neoplasia (GTN) based on age and repeated measurements of human chorionic gonadotropin (hCG). Discrimination and calibration measures were used to compare the accuracy of the weekly predictions. Internal validation of the models was conducted using bootstrapping. The four approaches resulted in the same predictive and discriminative performance in predicting GTN. A simulation study showed that the joint models outperform the two-stage methods when we increase the within- and the between-patients variability of the biomarker. The applicability of these models to produce dynamic predictions has been illustrated through a comprehensive explanation and accompanying syntax (R and SAS^®).     

Implications of uniformly distributed,empirically informed priors for phylogeographical model selection: A reply to Hickerson et al.

Establishing that a set of population‐splitting events occurred at the same time can be a potentially persuasive argument that a common process affected the populations. Recently, Oaks et al. ( 2013 ) assessed the ability of an approximate‐Bayesian model‐choice method (msBayes ) to estimate such a pattern of simultaneous divergence across taxa, to which Hickerson et al. ( 2014 ) responded. Both papers agree that the primary inference enabled by the method is very sensitive to prior assumptions and often erroneously supports shared divergences across taxa when prior uncertainty about divergence times is represented by a uniform distribution. However, the papers differ about the best explanation and solution for this problem. Oaks et al. ( 2013 ) suggested the method's behavior was caused by the strong weight of uniformly distributed priors on divergence times leading to smaller marginal likelihoods (and thus smaller posterior probabilities) of models with more divergence‐time parameters (Hypothesis 1); they proposed alternative prior probability distributions to avoid such strongly weighted posteriors. Hickerson et al. ( 2014 ) suggested numerical‐approximation error causes msBayes analyses to be biased toward models of clustered divergences because the method's rejection algorithm is unable to adequately sample the parameter space of richer models within reasonable computational limits when using broad uniform priors on divergence times (Hypothesis 2). As a potential solution, they proposed a model‐averaging approach that uses narrow, empirically informed uniform priors. Here, we use analyses of simulated and empirical data to demonstrate that the approach of Hickerson et al. ( 2014 ) does not mitigate the method's tendency to erroneously support models of highly clustered divergences, and is dangerous in the sense that the empirically derived uniform priors often exclude from consideration the true values of the divergence‐time parameters. Our results also show that the tendency of msBayes analyses to support models of shared divergences is primarily due to Hypothesis 1, whereas Hypothesis 2 is an untenable explanation for the bias. Overall, this series of papers demonstrates that if our prior assumptions place too much weight in unlikely regions of parameter space such that the exact posterior supports the wrong model of evolutionary history, no amount of computation can rescue our inference. Fortunately, as predicted by fundamental principles of Bayesian model choice, more flexible distributions that accommodate prior uncertainty about parameters without placing excessive weight in vast regions of parameter space with low likelihood increase the method's robustness and power to detect temporal variation in divergences.     

Statistical estimation of statistical mechanical models: helix-coil theory and peptide helicity prediction.

Analysis of biopolymer sequences and structures generally adopts one of two approaches: use of detailed biophysical theoretical models of the system with experimentally-determined parameters, or largely empirical statistical models obtained by extracting parameters from large datasets. In this work, we demonstrate a merger of these two approaches using Bayesian statistics. We adopt a common biophysical model for local protein folding and peptide configuration, the helix-coil model. The parameters of this model are estimated by statistical fitting to a large dataset, using prior distributions based on experimental data. L(1)-norm shrinkage priors are applied to induce sparsity among the estimated parameters, resulting in a significantly simplified model. Formal statistical procedures for evaluating support in the data for previously proposed model extensions are presented. We demonstrate the advantages of this approach including improved prediction accuracy and quantification of prediction uncertainty, and discuss opportunities for statistical design of experiments. Our approach yields a 39% improvement in mean-squared predictive error over the current best algorithm for this problem. In the process we also provide an efficient recursive algorithm for exact calculation of ensemble helicity including sidechain interactions, and derive an explicit relation between homo- and heteropolymer helix-coil theories and Markov chains and (non-standard) hidden Markov models respectively, which has not appeared in the literature previously.     

Predicting invasions in Australia by a Neotropical shrub under climate change: the challenge of novel climates and parameter estimation

Aim  To test how well species distributions and abundance can be predicted following invasion and climate change when using only species distribution and abundance data to estimate parameters.
Location  Models were developed for the species' native range in the Americas and applied to Australia.
Methods  We developed a predictive model for an invasive neotropical shrub ( Parkinsonia aculeata) using a popular ecophysiological bioclimatic modelling technique (CLIMEX) fitted against distribution and abundance data in the Americas. The effect of uncertainty in model parameter estimates on predictions in Australia was tested. Alternative data sources were used when model predictions were sensitive to uncertainty in parameter estimates. The resulting best-fit model was run under two climate change scenarios.
Results  Of the 19 parameters used, 9 could not be fitted using data from the native range. However, only parameters that lowered temperature or increased moisture requirements for growth noticeably altered the model prediction in Australia. Differences in predictions were dramatic, and reflect climates in Australia that were not represented in the Americas (novel climates). However, these poorly fitted parameters could be fitted post hoc using alternative data sources prior to predicting responses to climate change.
Conclusions  Novel climates prevented the development of a predictive model which relied only on native-range distribution and abundance data because certain parameters could not be fitted. In fact, predictions were more sensitive to parameter uncertainty than to climate change scenarios. Where uncertainty in parameter estimates affected predictions, it could be addressed through the inclusion of alternative data sources. However, this may not always be possible, for example in the absence of post-invasion data.     

Simultaneously estimating food web connectance and structure with uncertainty

1. Food web models explain and predict the trophic interactions in a food web, and they can infer missing interactions among the organisms. The allometric diet breadth model (ADBM) is a food web model based on the foraging theory. In the ADBM, the foraging parameters are allometrically scaled to body sizes of predators and prey. In Petchey et al. (Proceedings of the National Academy of Sciences, 2008; 105: 4191), the parameterization of the ADBM had two limitations: (a) the model parameters were point estimates and (b) food web connectance was not estimated.
2. The novelty of our current approach is: (a) We consider multiple predictions from the ADBM by parameterizing it with approximate Bayesian computation, to estimate parameter distributions and not point estimates. (b) Connectance emerges from the parameterization, by measuring model fit using the true skill statistic, which takes into account prediction of both the presences and absences of links.
3. We fit the ADBM using approximate Bayesian computation to 12 observed food webs from a wide variety of ecosystems. Estimated connectance was consistently greater than previously found. In some of the food webs, considerable variation in estimated parameter distributions occurred and resulted in considerable variation (i.e., uncertainty) in predicted food web structure.
4. These results lend weight to the possibility that the observed food web data is missing some trophic links that do actually occur. It also seems likely that the ADBM likely predicts some links that do not exist. The latter could be addressed by accounting in the ADBM for additional traits other than body size. Further work could also address the significance of uncertainty in parameter estimates for predicted food web responses to environmental change.

     

Bayesian Inference for the Spatio-Temporal Invasion of Alien Species

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.