Spatial Joint Species Distribution Modeling using Dirichlet Processes

Species distribution models usually attempt to explain presence-absence or abundance of a species at a site in terms of the environmental features (socalled abiotic features) present at the site. Historically, such models have considered species individually. However, it is well-established that species interact to influence presence-absence and abundance (envisioned as biotic factors). As a result, there has been substantial recent interest in joint species distribution models with various types of response, e.g., presence-absence, continuous and ordinal data. Such models incorporate dependence between species response as a surrogate for interaction. The challenge we focus on here is how to address such modeling in the context of a large number of species (e.g., order 102) across sites numbering in the order of 102 or 103 when, in practice, only a few species are found at any observed site. Again, there is some recent literature to address this; we adopt a dimension reduction approach. The novel wrinkle we add here is spatial dependence. That is, we have a collection of sites over a relatively small spatial region so it is anticipated that species distribution at a given site would be similar to that at a nearby site. Specifically, we handle dimension reduction through Dirichlet processes joined with spatial dependence through Gaussian processes. We use both simulated data and a plant communities dataset for the Cape Floristic Region (CFR) of South Africa to demonstrate our approach. The latter consists of presence-absence measurements for 639 tree species on 662 locations. Through both data examples we are able to demonstrate improved predictive performance using the foregoing specification

Multi-species distribution modeling using penalized mixture of regressions

Multi-species distribution modeling, which relates the occurrence of multiple species to environmental variables, is an important tool used by ecologists for both predicting the distribution of species in a community and identifying the important variables driving species co-occurrences. Recently, Dunstan, Foster and Darnell [Ecol. Model. 222 (2011) 955-963] proposed using finite mixture of regression (FMR) models for multi-species distribution modeling, where species are clustered based on their environmental response to form a small number of "archetypal responses." As an illustrative example, they applied their mixture model approach to a presence-absence data set of 200 marine organisms, collected along the Great Barrier Reef in Australia. Little attention, however, was given to the problem of model selection - since the archetypes (mixture components) may depend on different but likely overlapping sets of covariates, a method is needed for performing variable selection on all components simultaneously. In this article, we consider using penalized likelihood functions for variable selection in FMR models. We propose two penalties which exploit the grouped structure of the covariates, that is, each covariate is represented by a group of coefficients, one for each component. This leads to an attractive form of shrinkage that allows a covariate to be removed from all components simultaneously. Both penalties are shown to possess specific forms of variable selection consistency, with simulations indicating they outperform other methods which do not take into account the grouped structure. When applied to the Great Barrier Reef data set, penalized FMR models offer more insight into the important variables driving species co-occurrence in the marine community (compared to previous results where no model selection was conducted), while offering a computationally stable method of modeling complex species-environment relationships (through regularization).Comment: Published at http://dx.doi.org/10.1214/15-AOAS813 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Used-habitat calibration plots: a new procedure for validating species distribution, resource selection, and step-selection models

“Species distribution modeling” was recently ranked as one of the top five “research fronts” in ecology and the environmental sciences by ISI's Essential Science Indicators (Renner and Warton 2013), reflecting the importance of predicting how species distributions will respond to anthropogenic change. Unfortunately, species distribution models (SDMs) often perform poorly when applied to novel environments. Compounding on this problem is the shortage of methods for evaluating SDMs (hence, we may be getting our predictions wrong and not even know it). Traditional methods for validating SDMs quantify a model's ability to classify locations as used or unused. Instead, we propose to focus on how well SDMs can predict the characteristics of used locations. This subtle shift in viewpoint leads to a more natural and informative evaluation and validation of models across the entire spectrum of SDMs. Through a series of examples, we show how simple graphical methods can help with three fundamental challenges of habitat modeling: identifying missing covariates, non-linearity, and multicollinearity. Identifying habitat characteristics that are not well-predicted by the model can provide insights into variables affecting the distribution of species, suggest appropriate model modifications, and ultimately improve the reliability and generality of conservation and management recommendations

Spatial Distribution Modelling of Prothonotary Warbler (Protonotaria citrea) on Breeding Grounds

Ecological niche modeling is used to predict a species’ distribution in a geographic area based on abiotic and biotic variables. Understanding a species’ range is important for conservation and restoration efforts. As anthropogenic forces may alter or deplete habitat, it is important to know the ecological requirements of a species to understand how and what habitat to protect. With the increasing threat of climate change and rising temperature and precipitation, the suitable habitat and the distribution for many species is expected to shift. Migratory species are particularly at risk of these changes as they require suitable habitat not only on their wintering and stopover grounds, but on their breeding grounds. Without suitable breeding grounds, reproductive success is guaranteed to decline for a species. Understanding how these changes affect the range and distribution of a species allows researchers and conservationist to better formulate effective species management plan

Combining local- and large-scale models to predict the distributions of invasive plant species

Habitat-distribution models are increasingly used to predict the potential distributions of invasive species and to inform monitoring. However, these models assume that species are in equilibrium with the environment, which is clearly not true for most invasive species. Although this assumption is frequently acknowledged, solutions have not been adequately addressed. There are several potential methods for improving habitat-distribution models. Models that require only presence data may be more effective for invasive species, but this assumption has rarely been tested. In addition, combining modeling types to form ‘ensemble’ models may improve the accuracy of predictions. However, even with these improvements, models developed for recently invaded areas are greatly influenced by the current distributions of species and thus reflect near- rather than long-term potential for invasion. Larger scale models from species’ native and invaded ranges may better reflect long-term invasion potential, but they lack finer scale resolution. We compared logistic regression (which uses presence/absence data) and two presence-only methods for modeling the potential distributions of three invasive plant species on the Olympic Peninsula in Washington State, USA. We then combined the three methods to create ensemble models. We also developed climate-envelope models for the same species based on larger scale distributions and combined models from multiple scales to create an index of near- and long-term invasion risk to inform monitoring in Olympic National Park (ONP). Neither presence-only nor ensemble models were more accurate than logistic regression for any of the species. Larger scale models predicted much greater areas at risk of invasion. Our index of near- and long-term invasion risk indicates that \u3c4% of ONP is at high near-term risk of invasion while 67-99% of the Park is at moderate or high long-term risk of invasion. We demonstrate how modeling results can be used to guide the design of monitoring protocols and monitoring results can in turn be used to refine models. We propose that by using models from multiple scales to predict invasion risk and by explicitly linking model development to monitoring, it may be possible to overcome some of the limitations of habitat-distribution models

Variation in Spatial Predictions Among Species Distribution Modeling Methods

<p>Prediction maps produced by species distribution models (SDMs) influence decision-making in resource management or designation of land in conservation planning. Many studies have compared the prediction accuracy of different SDM modeling methods, but few have quantified the similarity among prediction maps. There has also been little systematic exploration of how the relative importance of different predictor variables varies among model types. Our objective was to expand the evaluation of SDM performance for 45 plant species in southern California to better understand how map predictions vary among model types, and to explain what factors may affect spatial correspondence, including the selection and relative importance of different environmental variables. Four types of models were tested. Correlation among maps was highest between generalized linear models (GLMs) and generalized additive models (GAMs) and lowest between classification trees and GAMs or GLMs. Correlation between Random Forests (RFs) and GAMs was the same as between RFs and classification trees. Spatial correspondence among maps was influenced the most by model prediction accuracy (AUC) and species prevalence; map correspondence was highest when accuracy was high and prevalence was intermediate. Species functional type and the selection of climate variables also influenced map correspondence. For most (but not all) species, climate variables were more important than terrain or soil in predicting their distributions. Environmental variable selection varied according to modeling method, but the largest differences were between RFs and GLMs or GAMs. Although prediction accuracy was equal for GLMs, GAMs, and RFs, the differences in spatial predictions suggest that it may be important to evaluate the results of more than one model to estimate a range of spatial uncertainty before making planning decisions based on map outputs. This may be particularly important if models have low accuracy or if species prevalence is not intermediate.</p>

Do Community-Level Models Account for the Effects of Biotic Interactions? A Comparison of Community-Level and Species Distribution Modeling of Rocky Mountain Conifers

Community-level models (CLMs) aim to improve species distribution modeling (SDM) methods by attempting to explicitly incorporate the influences of interacting species. However, the ability of CLMs to appropriately account for biotic interactions is unclear. We applied CLM and SDM methods to predict the distributions of three dominant conifer tree species in the U.S. Rocky Mountains and compared CLM and SDM predictive accuracy as well as the ability of each approach to accurately reproduce species co-occurrence patterns. We specifically evaluated the performance of two statistical algorithms, MARS and CForest, within both CLM and SDM frameworks. Across all species, differences in SDM and CLM predictive accuracy were slight and can be attributed to differences in model structure rather than accounting for the effects of biotic interactions. In addition, CLMs generally over-predicted species cooccurrence, while SDMs under-predicted cooccurrence. Our results demonstrate no real improvement in the ability of CLMs to account for biotic interactions relative to SDMs. We conclude that alternative modeling approaches are needed in order to accurately account for the effects of biotic interactions on species distributions

Comparison of habitat-based indices of abundance with fishery-independent biomass estimates from bottom trawl surveys

Rockfish species are notoriously difficult to sample with multispecies bottom trawl survey methods. Typically, biomass estimates have high coefficients of variation and can fluctuate outside the bounds of biological reality from year to year. This variation may be due in part to their patchy distribution related to very specific habitat preferences. We successfully modeled the distribution of five commercially important and abundant rockf ish species. A two-stage modeling method (modeling both presence-absence and abundance) and a collection of important habitat variables were used to predict bottom trawl survey catch per unit of effort. The resulting models explained between 22% and 66% of the variation in rockfish distribution. The models were largely driven by depth, local slope, bottom temperature, abundance of coral and sponge, and measures of water column productivity (i.e., phytoplankton and zooplankton). A year-effect in the models was back-transformed and used as an index of the time series of abundance. The abundance index trajectories of three of five species were similar to the existing estimates of their biomass. In the majority of cases the habitat-based indices exhibited less interannual variability and similar precision when compared with stratified survey-based biomass estimates. These indices may provide for stock assessment models a more stable alternative to current biomass estimates produced by the multispecies bottom trawl survey in the Gulf of Alaska

A multi-scale distribution model for non-equilibrium populations suggests resource limitation in an endangered rodent.

Species distributions are known to be limited by biotic and abiotic factors at multiple temporal and spatial scales. Species distribution models, however, frequently assume a population at equilibrium in both time and space. Studies of habitat selection have repeatedly shown the difficulty of estimating resource selection if the scale or extent of analysis is incorrect. Here, we present a multi-step approach to estimate the realized and potential distribution of the endangered giant kangaroo rat. First, we estimate the potential distribution by modeling suitability at a range-wide scale using static bioclimatic variables. We then examine annual changes in extent at a population-level. We define available habitat based on the total suitable potential distribution at the range-wide scale. Then, within the available habitat, model changes in population extent driven by multiple measures of resource availability. By modeling distributions for a population with robust estimates of population extent through time, and ecologically relevant predictor variables, we improved the predictive ability of SDMs, as well as revealed an unanticipated relationship between population extent and precipitation at multiple scales. At a range-wide scale, the best model indicated the giant kangaroo rat was limited to areas that received little to no precipitation in the summer months. In contrast, the best model for shorter time scales showed a positive relation with resource abundance, driven by precipitation, in the current and previous year. These results suggest that the distribution of the giant kangaroo rat was limited to the wettest parts of the drier areas within the study region. This multi-step approach reinforces the differing relationship species may have with environmental variables at different scales, provides a novel method for defining available habitat in habitat selection studies, and suggests a way to create distribution models at spatial and temporal scales relevant to theoretical and applied ecologists