A comparison of statistical approaches for modelling fish species distributions

SUMMARY 1. The prediction of species distributions is of primary importance in ecology and conservation biology. Statistical models play an important role in this regard; however, researchers have little guidance when choosing between competing methodologies because few comparative studies have been conducted. 2. We provide a comprehensive comparison of traditional and alternative techniques for predicting species distributions using logistic regression analysis, linear discriminant analysis, classification trees and artificial neural networks to model: (1) the presence/absence of 27 fish species as a function of habitat conditions in 286 temperate lakes located in south‐central Ontario, Canada and (2) simulated data sets exhibiting deterministic, linear and non‐linear species response curves. 3. Detailed evaluation of model predictive power showed that approaches produced species models that differed in overall correct classification, specificity (i.e. ability to correctly predict species absence) and sensitivity (i.e. ability to correctly predict speciespresence) and in terms of which of the study lakes they correctly classified. Onaverage, neural networks outperformed the other modelling approaches, although all approaches predicted species presence/absence with moderate to excellent success. 4. Based on simulated non‐linear data, classification trees and neural networks greatly outperformed traditional approaches, whereas all approaches exhibited similar correct classification rates when modelling simulated linear data. 5. Detailed evaluation of model explanatory insight showed that the relative importance of the habitat variables in the species models varied among the approaches, where habitat variable importance was similar among approaches for some species and very different for others. 6. In general, differences in predictive power (both correct classification rate and identity of the lakes correctly classified) among the approaches corresponded with differences in habitat variable importance, suggesting that non‐linear modelling approaches (i.e. classification trees and neural networks) are better able to capture and model complex, non‐linear patterns found in ecological data. The results from the comparisons using simulated data further support this notion. 7. By employing parallel modelling approaches with the same set of data and focusing on comparing multiple metrics of predictive performance, researchers can begin to choose predictive models that not only provide the greatest predictive power, but also best fit the proposed application.     

Forecasting species range dynamics with process‐explicit models: matching methods to applications

Knowing where species occur is fundamental to many ecological and environmental applications. Species distribution models (SDMs) are typically based on correlations between species occurrence data and environmental predictors, with ecological processes captured only implicitly. However, there is a growing interest in approaches that explicitly model processes such as physiology, dispersal, demography and biotic interactions. These models are believed to offer more robust predictions, particularly when extrapolating to novel conditions. Many process–explicit approaches are now available, but it is not clear how we can best draw on this expanded modelling toolbox to address ecological problems and inform management decisions. Here, we review a range of process–explicit models to determine their strengths and limitations, as well as their current use. Focusing on four common applications of SDMs – regulatory planning, extinction risk, climate refugia and invasive species – we then explore which models best meet management needs. We identify barriers to more widespread and effective use of process‐explicit models and outline how these might be overcome. As well as technical and data challenges, there is a pressing need for more thorough evaluation of model predictions to guide investment in method development and ensure the promise of these new approaches is fully realised.     

From topography to hydrology—The modifiable area unit problem impacts freshwater species distribution models

Species distribution models (SDMs) are statistical tools to identify potentially suitable habitats for species. For SDMs in river ecosystems, species occurrences and predictor data are often aggregated across subcatchments that serve as modeling units. The level of aggregation (i.e., model resolution) influences the statistical relationships between species occurrences and environmental predictors—a phenomenon known as the modifiable area unit problem (MAUP), making model outputs directly contingent on the model resolution. Here, we test how model performance, predictor importance, and the spatial congruence of species predictions depend on the model resolution (i.e., average subcatchment size) of SDMs. We modeled the potential habitat suitability of 50 native fish species in the upper Danube catchment at 10 different model resolutions. Model resolutions were derived using a 90‐m digital‐elevation model by using the GRASS‐GIS module r.watershed. Here, we decreased the average subcatchment size gradually from 632 to 2 km². We then ran ensemble SDMs based on five algorithms using topographical, climatic, hydrological, and land‐use predictors for each species and resolution. Model evaluation scores were consistently high, as sensitivity and True Skill Statistic values ranged from 86.1–93.2 and 0.61–0.73, respectively. The most contributing predictor changed from topography at coarse, to hydrology at fine resolutions. Climate predictors played an intermediate role for all resolutions, while land use was of little importance. Regarding the predicted habitat suitability, we identified a spatial filtering from coarse to intermediate resolutions. The predicted habitat suitability within a coarse resolution was not ported to all smaller, nested subcatchments, but only to a fraction that held the suitable environmental conditions. Across finer resolutions, the mapped predictions were spatially congruent without such filter effect. We show that freshwater SDM predictions can have consistently high evaluation scores while mapped predictions differ significantly and are highly contingent on the underlying subcatchment size. We encourage building freshwater SDMs across multiple catchment sizes, to assess model variability and uncertainties in model outcomes emerging from the MAUP.     

Testing the accuracy of species distribution models using species records from a new field survey

Species distribution models are a very popular tool in ecology and biogeography and have great potential to help direct conservation efforts. Models are traditionally tested by using half the original species records to build the model and half to evaluate it. However, this can lead to overly optimistic estimates of model accuracy, particularly when there are systematic biases in the data. It is better to evaluate models using independent data. This study used independent species records from a new to survey to provide a more rigorous evaluation of distribution‐model accuracy. Distribution models were built for reptile, amphibian, butterfly and mammal species. The accuracy of these models was evaluated using the traditional approach of partitioning the original species records into model‐building and model‐evaluating datasets, and using independent records collected during a new field survey of 21 previously unvisited sites in diverse habitat types. We tested whether variation in distribution‐model accuracy among species could be explained by species detectability, range size, number of records used to build the models, and body size. Estimates of accuracy derived using the new species records correlated positively with estimates generated using the traditional data‐partitioning approach, but were on average 22% lower. Model accuracy was negatively related to range size and number of records used to build the models, and positively related to the body size of butterflies. There was no clear relationship between species detectability and model accuracy. The field data generally validated the species distribution models. However, there was considerable variation in model accuracy among species, some of which could be explained by the characteristics of species.     

Ecological Niche Models using MaxEnt in Google Earth Engine: Evaluation,guidelines and recommendations

Google Earth Engine (GEE) has revolutionized geospatial analyses by fast-processing formerly demanding analyses from multiple research areas. Recently, maximum entropy (MaxEnt), the most commonly used method in ecological niche models (ENMs), was integrated into GEE. This integration can significantly enhance modeling efficiency and encourage multidisciplinary approaches of ENMs, but an evaluation assessment of MaxEnt in GEE is lacking. Herein, we present the first MaxEnt models in GEE, as well as its first statistical and spatial evaluation. We also identify the limitations of the approach, providing guidelines and recommendations for its easier applicability in GEE.We tested MaxEnt in GEE using 11 case studies. For each case, we used species of different taxa (insects, amphibians, reptiles, birds and mammals) distributed across global and regional extents. Each species occupied habitats with distinct environmental characteristics (nine terrestrial and two marine species) and within divergent ecoregions across five continents. The models were performed in GEE and Maxent software, and both approaches were contrasted for their model discrimination performance (assessed by eight evaluation metrics) and spatial consistency (correlation analyses and two measures of niche overlap/equivalency).MaxEnt in GEE allows setting several parameters, but important analyses and outputs are unavailable, such as automatic selection of background data, model replicates, and analyses of variable importance (concretely, jackknife analyses and response curves). GEE provided MaxEnt models with high discrimination performance (area under the curve mean between all species models of 0.90) and with spatial equivalency in relation to Maxent software outputs (Hellinger's I mean between all species models >0.90).Our work demonstrates the first application and assessment of MaxEnt in GEE at global and regional scales. We conclude that the GEE modeling method provides ENMs with high performance and reliable spatial predictions, comparable to the widely used Maxent software. We also acknowledge important limitations that should be integrated into GEE in the future, particularly those related to the assessment of variable importance. We expect that our guidelines, recommendations and potential solutions to surpass the identified limitations could help researchers easily apply MaxEnt in GEE across different research fields.     

Challenges in the application of geometric constraint models

Discerning the processes influencing geographical patterns of species richness remains one of the central goals of modern ecology. Traditional approaches to exploring these patterns have focused on environmental and ecological correlates of observed species richness. Recently, some have suggested these approaches suffer from the lack of an appropriate null model that accounts for species ranges being constrained to occur within a bounded domain. Proponents of these null geometric constraint models (GCMs), and the mid-domain effect these models produce, argue their utility in identifying meaningful gradients in species richness. This idea has generated substantial debate. Here we discuss what we believe are the three major challenges in the application of GCMs. First, we argue that there are actually two equally valid null models for the random placement of species ranges within a domain, one of which actually predicts a uniform distribution of species richness. Second, we highlight the numerous decisions that must be made to implement a GCM that lead to marked differences in the predictions of the null model. Finally, we discuss challenges in evaluating the importance of GCMs once they have been implemented.     

Breaking out from a restricted range: Alternative habitat models to assess population perspectives

Habitat conservation for restricted-range species should also consider adjacent areas, but the analytical approaches for such assessments (particularly for a future perspective) are constrained by currently observed habitat relationships. We used two conceptually different habitat modelling approaches for analysing habitat distribution for the isolated Estonian population of a species of European conservation concern, the Siberian flying squirrel (Pteromys volans (Linnaeus, 1758)). We expected that the correlative (statistical) approaches based on current location data will increasingly deviate along with the distance from the current range, compared with a mechanistic approach based on limiting factors for the species. For conservation planning, we also investigated how the current protected area network covers quality habitats around the current range. We constructed three alternative correlative models (MaxEnt; Random forest; Generalized Boosted Regression) utilizing remote-sensing (Sentinel-2; LiDAR) and forest inventory data for 1299 occurrences in the currently occupied ca. 1400 km² range. A mechanistic model was constructed as a decision tree that distinguished 11 quality classes of forest land based on the ecological prioritization of limiting factors: site type; forest cover; abundance of key tree species; stand age; patch size; and layer structure. Supporting our expectation, an overall good accordance of habitat predictions of all the correlative models and the mechanistic model (at 30 × 30 m pixel size) declined with the distance from the current range. The MaxEnt model most closely followed the full range of habitat quality classes of the mechanistic model, while the other correlative models emphasized the highest habitat-quality class. Within the current range, both MaxEnt and the mechanistic model similarly revealed habitat quality differences between occupied and unoccupied species protection areas. Delineation of habitat aggregations all over the country based on the mechanistic model revealed habitat loss both within and adjacent to the current range, which sets limits to local population recovery. For analysing wider options, we recommend complementing statistical spatial modelling of current conditions with ecologically sound mechanistic approaches. Based on our specific case, we outline how such model predictions can be assessed for management planning beyond current range.     

Effects of grain size and niche breadth on species distribution modeling

Scale is a vital component to consider in ecological research, and spatial resolution or grain size is one of its key facets. Species distribution models (SDMs) are prime examples of ecological research in which grain size is an important component. Despite this, SDMs rarely explicitly examine the effects of varying the grain size of the predictors for species with different niche breadths. To investigate the effect of grain size and niche breadth on SDMs, we simulated four virtual species with different grain sizes/niche breadths using three environmental predictors (elevation, aspect, and percent forest) across two real landscapes of differing heterogeneity in predictor values. We aggregated these predictors to seven different grain sizes and modeled the distribution of each of our simulated species using MaxEnt and GLM techniques at each grain size. We examined model accuracy using the AUC statistic, Pearson's correlations of predicted suitability with the true suitability, and the binary area of presence determined from suitability above the maximum true skill statistic (TSS) threshold. Habitat specialists were more accurately modeled than generalist species, and the models constructed at the grain size from which a species was derived generally performed the best. The accuracy of models in the homogenous landscape deteriorated with increasing grain size to a greater degree than models in the heterogenous landscape. Variable effects on the model varied with grain size, with elevation increasing in importance as grain size increased while aspect lost importance. The area of predicted presence was drastically affected by grain size, with larger grain sizes over predicting this value by up to a factor of 14. Our results have implications for species distribution modeling and conservation planning, and we suggest more studies include analysis of grain size as part of their protocol.     

Adaptive morphological shifts to novel habitats in marine sculpin fishes

Sculpin fishes of the North American Pacific Coast provide an ideal opportunity to examine whether adaptive morphological character shifts have facilitated occupation of novel habitat types because of their well‐described phylogeny and ecology. In this group, the basal‐rooted species primarily occupy the subtidal habitat, whereas the species in the most distal clades are found in the intertidal. We tested multiple evolutionary models to determine whether changes in body size and changes in number of scales are adaptive for habitat use in sculpins. Based on a statistically robust, highly resolved molecular phylogeny of 26 species of sculpins, in combination with morphometric and habitat affinity data, our analyses show that an adaptive model based on habitat use best explains changes in body size and number of scales. The habitat model was statistically supported over models of neutral evolution, stabilizing selection across all habitats, and three clade‐based models. We suggest that loss of scales and reduction of body size in the intertidal may facilitate cutaneous breathing in air when tidepools become hypoxic during low tides. This study demonstrates how the combined use of phylogenetic, ecological and statistical approaches helps to identify traits that are likely adaptive to novel habitats.     

Community‐level vs species‐specific approaches to model selection

A topic of particular current interest is community‐level approaches to species distribution modelling (SDM), i.e. approaches that simultaneously analyse distributional data for multiple species. Previous studies have looked at the advantages of community‐level approaches for parameter estimation, but not for model selection – the process of choosing which model (and in particular, which subset of environmental variables) to fit to data. We compared the predictive performance of models using the same modelling method (generalised linear models) but choosing the subset of variables to include in the model either simultaneously across all species (community‐level model selection) or separately for each species (species‐specific model selection). Our results across two large presence/absence tree community datasets were inconclusive as to whether there was an overall difference in predictive performance between models fitted via species‐specific vs community‐level model selection. However, we found some evidence that a community approach was best suited to modelling rare species, and its performance decayed with increasing prevalence. That is, when data were sparse there was more opportunity for gains from “borrowing strength” across species via a community‐level approach. Interestingly, we also found that the community‐level approach tended to work better when the model selection problem was more difficult, and more reliably detected “noise” variables that should be excluded from the model.     

A framework integrating physiology,dispersal and land‐use to project species ranges under climate change

To study the potential effects of climate change on species, one of the most popular approaches are species distribution models (SDMs). However, they usually fail to consider important species‐specific biological traits, such as species’ physiological capacities or dispersal ability. Furthermore, there is consensus that climate change does not influence species distributions in isolation, but together with other anthropogenic impacts such as land‐use change, even though studies investigating the relative impacts of different threats on species and their geographic ranges are still rare. Here we propose a novel integrative approach which produces refined future range projections by combining SDMs based on distribution, climate, and physiological tolerance data with empirical data on dispersal ability as well as current and future land‐use. Range projections based on different combinations of these factors show strong variation in projected range size for our study species Emberiza hortulana. Using climate and physiological data alone, strong range gains are projected. However, when we account for land‐use change and dispersal ability, future range‐gain may even turn into a future range loss. Our study highlights the importance of accounting for biological traits and processes in species distribution models and of considering the additive effects of climate and land‐use change to achieve more reliable range projections. Furthermore, with our approach we present a new tool to assess species’ vulnerability to climate change which can be easily applied to multiple species.     

Comparison of approaches to combine species distribution models based on different sets of predictors

Distribution models should take into account the different limiting factors that simultaneously influence species ranges. Species distribution models built with different explanatory variables can be combined into more comprehensive ones, but the resulting models should maximize complementarity and avoid redundancy. Our aim was to compare the different methods available for combining species distribution models. We modelled 19 threatened vertebrate species in mainland Spain, producing models according to three individual explanatory factors: spatial constraints, topography and climate, and human influence. We used five approaches for model combination: Bayesian inference, Akaike weight averaging, stepwise variable selection, updating, and fuzzy logic. We compared the performance of these approaches by assessing different aspects of their classification and discrimination capacity. We demonstrated that different approaches to model combination give rise to disparities in the model outputs. Bayesian integration was systematically affected by an error in the equations that are habitually used in distribution modelling. Akaike weights produced models that were driven by the best single factor and therefore failed at combining the models effectively. The updating and the stepwise approaches shared recalibration as the basic concept for model combination, were very similar in their performance, and showed the highest sensitivity and discrimination capacity. The fuzzy‐logic approach yielded models with the highest classification capacity according to Cohen's kappa. In conclusion: 1) Bayesian integration, employing the currently used equation, and the Akaike weight procedure should be avoided; 2) the updating and stepwise approaches can be considered minor variants of the same recalibrating approach; and 3) there is a trade‐off between this recalibrating approach, which has the highest sensitivity, and fuzzy logic, which has the highest overall classification capacity. Recalibration is better if unfavourable conditions in one environmental factor may be counterbalanced with favourable conditions in a different factor, otherwise fuzzy logic is better.     

A local evaluation of the individual state‐space to scale up Bayesian spatial capture–recapture

Spatial capture–recapture models (SCR) are used to estimate animal density and to investigate a range of problems in spatial ecology that cannot be addressed with traditional nonspatial methods. Bayesian approaches in particular offer tremendous flexibility for SCR modeling. Increasingly, SCR data are being collected over very large spatial extents making analysis computational intensive, sometimes prohibitively so. To mitigate the computational burden of large‐scale SCR models, we developed an improved formulation of the Bayesian SCR model that uses local evaluation of the individual state‐space (LESS). Based on prior knowledge about a species’ home range size, we created square evaluation windows that restrict the spatial domain in which an individual's detection probability (detector window) and activity center location (AC window) are estimated. We used simulations and empirical data analyses to assess the performance and bias of SCR with LESS. LESS produced unbiased estimates of SCR parameters when the AC window width was ≥5σ (σ: the scale parameter of the half‐normal detection function), and when the detector window extended beyond the edge of the AC window by 2σ. Importantly, LESS considerably decreased the computation time needed for fitting SCR models. In our simulations, LESS increased the computation speed of SCR models up to 57‐fold. We demonstrate the power of this new approach by mapping the density of an elusive large carnivore—the wolverine (Gulo gulo)—with an unprecedented resolution and across the species’ entire range in Norway (> 200,000 km²). Our approach helps overcome a major computational obstacle to population and landscape‐level SCR analyses. The LESS implementation in a Bayesian framework makes the customization and fitting of SCR accessible for practitioners working at scales that are relevant for conservation and management.     

Comparison of full-atomic and coarse-grained models to examine the molecular fluctuations of c-AMP dependent protein kinase

Molecular fluctuations of the native conformation of c-AMP dependent protein kinase (cAPK) have been investigated with three different approaches. The first approach is the full atomic normal mode analysis (NMA) with empirical force fields. The second and third approaches are based on a coarse-grained model with a single single-parameter- harmonic potential between close residues in the crystal structure of the molecule without any residue specificity. The second method calculates only the magnitude of fluctuations whereas the third method is developed to find the directionality of the fluctuations which are essential to understand the functional importance of biological molecules. The aim, in this study, is to determine whether using such coarse-grained models are appropriate for elucidating the global dynamic characteristics of large proteins which reduces the size of the system at least by a factor of ten. The mean-square fluctuations of C(alpha) atoms and the residue cross-correlations are obtained by three approaches. These results are then compared to test the results of coarse grained models on the overall collective motions. All three of the approaches show that highly flexible regions correspond to the activation and solvent exposed loops, whereas the conserved residues (especially in substrate binding regions) exhibit almost no flexibility, adding stability to the structure. The anti-correlated motions of the two lobes of the catalytic core provide flexibility to the molecule. High similarities among the results of these methods indicate that the slowest modes governing the most global motions are preserved in the coarse grained models for proteins. This finding may suggest that the general shapes of the structures are representative of their dynamic characteristics and the dominant motions of protein structures are robust at coarse-grained levels.     

Evaluating citizen science data for forecasting species responses to national forest management

The extensive spatial and temporal coverage of many citizen science datasets (CSD) makes them appealing for use in species distribution modeling and forecasting. However, a frequent limitation is the inability to validate results. Here, we aim to assess the reliability of CSD for forecasting species occurrence in response to national forest management projections (representing 160,366 km²) by comparison against forecasts from a model based on systematically collected colonization–extinction data. We fitted species distribution models using citizen science observations of an old‐forest indicator fungus Phellinus ferrugineofuscus. We applied five modeling approaches (generalized linear model, Poisson process model, Bayesian occupancy model, and two MaxEnt models). Models were used to forecast changes in occurrence in response to national forest management for 2020‐2110. Forecasts of species occurrence from models based on CSD were congruent with forecasts made using the colonization–extinction model based on systematically collected data, although different modeling methods indicated different levels of change. All models projected increased occurrence in set‐aside forest from 2020 to 2110: the projected increase varied between 125% and 195% among models based on CSD, in comparison with an increase of 129% according to the colonization–extinction model. All but one model based on CSD projected a decline in production forest, which varied between 11% and 49%, compared to a decline of 41% using the colonization–extinction model. All models thus highlighted the importance of protected old forest for P. ferrugineofuscus persistence. We conclude that models based on CSD can reproduce forecasts from models based on systematically collected colonization–extinction data and so lead to the same forest management conclusions. Our results show that the use of a suite of models allows CSD to be reliably applied to land management and conservation decision making, demonstrating that widely available CSD can be a valuable forecasting resource.     

The challenge of modeling niches and distributions for data‐poor species: a comprehensive approach to model complexity

Models of species ecological niches and geographic distributions now represent a widely used tool in ecology, evolution, and biogeography. However, the very common situation of species with few available occurrence localities presents major challenges for such modeling techniques, in particular regarding model complexity and evaluation. Here, we summarize the state of the field regarding these issues and provide a worked example using the technique Maxent for a small mammal endemic to Madagascar (the nesomyine rodent Eliurus majori). Two relevant model‐selection approaches exist in the literature (information criteria, specifically AICc; and performance predicting withheld data, via a jackknife), but AICc is not strictly applicable to machine‐learning algorithms like Maxent. We compare models chosen under each selection approach with those corresponding to Maxent default settings, both with and without spatial filtering of occurrence records to reduce the effects of sampling bias. Both selection approaches chose simpler models than those made using default settings. Furthermore, the approaches converged on a similar answer when sampling bias was taken into account, but differed markedly with the unfiltered occurrence data. Specifically, for that dataset, the models selected by AICc had substantially fewer parameters than those identified by performance on withheld data. Based on our knowledge of the study species, models chosen under both AICc and withheld‐data‐selection showed higher ecological plausibility when combined with spatial filtering. The results for this species intimate that AICc may consistently select models with fewer parameters and be more robust to sampling bias. To test these hypotheses and reach general conclusions, comprehensive research should be undertaken with a wide variety of real and simulated species. Meanwhile, we recommend that researchers assess the critical yet underappreciated issue of model complexity both via information criteria and performance on withheld data, comparing the results between the two approaches and taking into account ecological plausibility.     

Snake venom potency and yield are associated with prey‐evolution,predator metabolism and habitat structure

Snake venom is well known for its ability to incapacitate and kill prey. Yet, potency and the amount of venom available varies greatly across species, ranging from the seemingly harmless to those capable of killing vast numbers of potential prey. This variation is poorly understood, with comparative approaches confounded by the use of atypical prey species as models to measure venom potency. Here, we account for such confounding issues by incorporating the phylogenetic similarity between a snake's diet and the species used to measure its potency. In a comparative analysis of 102 species we show that snake venom potency is generally prey‐specific. We also show that venom yields are lower in species occupying three dimensional environments and increases with body size corresponding to metabolic rate, but faster than predicted from increases in prey size. These results underline the importance of physiological and environmental factors in the evolution of predator traits.     

On metapopulations and microrefugia: palaeoecological insights

We highlight the importance of microrefugia in the light of population migration and genetic drift by synthesizing lessons learnt from metapopulation and palaeoecological studies. The concept of microrefugia is considered as a long‐term variant of conventional metapopulations, in which microclimatic stability supersedes gene flow in determining species survival. Not all species can maintain populations in microrefugia. Life history traits such as small body size, the capacity for asexual reproduction, and species with light genetic loads favour survival. Microrefugia will facilitate faster rates of species responses to climate change than envisioned in diffusion models, and potentially provide a means to alleviate the negative effects posed by natural or anthropogenic barriers to migration. Predictive models based on relatively coarse‐grained approaches that ignore microrefugia will lead to overestimates of extinction risk. Microrefugia should be identified and conserved, not for the species they contain, as these are likely to turn over with time, but as an important component of landscape diversity that will provide a safe haven for species not yet identified as at risk.     

The use of ruminant models in biomedical perinatal research

Animal models are of critical importance in biomedical research. Although rodents and lagomorphs are the most commonly used species, larger species are required, especially when surgical approaches or new medical devices have to be evaluated. In particular, in the field of perinatal medicine, they are critical for the evaluation of new pharmacologic treatments and the development of new invasive procedures in fetuses. In some areas, such as developmental genetics, reproductive biotechnologies and metabolic programming, the contribution of ruminants is essential. The current report focuses on some of the most outstanding examples of great biomedical advances carried out with ruminant models in the field of perinatal research. Experiments recently carried in our research unit using ruminants are also briefly described.     

Hierarchical spatiotemporal matrix models for characterizing invasions

The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.