Issues with modelling the current and future distribution of invasive pathogens
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1. Correlative species distribution models can be used to produce spatially explicit estimates of environmental suitability for organisms. This process can provide meaningful information for a range of purposes (e.g. estimating a species’ current or future distribution, estimating dispersal limits, predicting occupancy for conservation planning) but, like all statistical exercises, is subject to numerous assumptions and can be influenced by several sources of potential bias.
2. In this issue of Journal of Applied Ecology, we (Murray et al. 2011) employ a correlative species distribution model for infection with the pathogen Batrachochytrium dendrobatidis (Bd), cause of amphibian chytridiomycosis, to derive useful information for the immediate management and research of this pathogen in Australia. Also in this issue, Rohr, Halstead & Raffel (2011) comment on some of the potential limitations of our approach and the value of our results in practice.
3. Synthesis and applications. Here we show that while a focus on mechanisms of dispersal and transmission among hosts, as advocated in both studies, is an important objective for modelling Bd distribution under climate change or at invasion fronts, correlative models can be of immediate value for their ability to generate a baseline hypothesis about the current potential distribution of this lethal pathogen and for efficiently identifying gaps in current knowledge. As demonstrated in our paper, this should help improve the immediate allocation of limited research and management resources for future surveillance efforts and proactive species conservation.
In this issue of Journal of Applied Ecology (Murray et al. 2011), we employ a species distribution model (SDM) to spatially estimate environmental suitability for infection with Batrachochytrium dendrobatidis (Bd), cause of the pandemic amphibian disease chytridiomycosis. This new source of information proved to be a significant predictor of amphibian declines in Australia. The implication for researchers and managers is that actions, geographic regions, species and even populations can potentially be targeted for further attention as the most at risk regions and species can be rapidly evaluated.
Rohr, Halstead & Raffel's (2011) commentary is generally encouraging and raises some interesting questions relevant to our study that both scrutinize the details of our models and echo our recommendations for further work. Rohr, Halstead & Raffel's (2011) key contribution is to review some of the questions regarding the validity of SDMs for the prediction of chytridiomycosis distribution and impacts in the future; for example, under climate change or at invasion fronts. Rohr, Halstead & Raffel (2011) conclude, as we do, that a focus on mechanisms, such as dispersal of the pathogen over long distances and transmission among hosts, will be important. However, since these mechanisms are still poorly understood, in many cases correlative SDMs will be of immediate value for their ability to generate a baseline hypothesis about the current potential distribution of this lethal pathogen and for efficiently identifying gaps in current knowledge. As demonstrated in our paper, this should help improve the allocation of limited research and management resources for future surveillance efforts and proactive species conservation.
Key issues for modelling species’ distributions
The issues raised by Rohr, Halstead & Raffel (2011) include some of the general principles of correlation and assumptions for SDMs. Some of the issues, such as dealing with sampling bias and spatial autocorrelation, remain highly active areas of research (e.g. Phillips et al. 2009; Veloz 2009) and under some circumstances may bias the results of correlative SDMs. Over-fitting, model parameterization and model selection are also mentioned by Rohr, Halstead & Raffel (2011) as potential limitations of our models. These are important issues; however, as detailed in our paper, we took great care in building our models to maximize predictive performance and minimize the effects of bias due to these limitations as far as was practically possible. Our hypotheses are strongly underpinned by biological reasoning and our choice of modelling tools and our methods together reflect significant recent advances in correlative species distribution modelling from incomplete information (Elith et al. 2006; VanDerWal et al. 2009). The key strengths and limitations of the Maxent approach have been described extensively elsewhere (Phillips, Anderson & Schapire 2006; Phillips & Dudik 2008; Phillips et al. 2009). Briefly, the Maxent approach avoids or minimizes many of the limitations of earlier bioclimatic ‘envelope’ model methods, such as BIOCLIM and DOMAIN, that are referred to by Rohr, Halstead & Raffel (2011). Our study demonstrates how presence-only datasets of poorly studied wildlife pathogens may be effectively employed in this relatively new framework to identify new avenues for research and management.
With greater traction are Rohr, Halstead & Raffel's (2011) comments relating to the validity and underlying assumptions of using correlative SDMs for modelling the future distribution of chytridiomycosis; for example, under climate change or at invasion fronts. In our study, we did not attempt to incorporate climate change predictions. We did, however, make projections geographically across Australia from our well sampled ‘training’ region (fig. S2; Murray et al. 2011). Two potential issues arise in this case that could lead to spurious projections: (1) invalid statistical extrapolation may occur and (2) models may be biased if occurrence records are not sufficiently representative of the environmental space inhabitable by the organism.
Extrapolation (point 1 above) may occur in geographic or environmental space (these are often linked but are not synonymous) and can be a source of uncertainty in some cases. Species interactions, for example, may impose limits on a species’ observed distribution through competition. Such interactions are unavoidably captured in the occurrence records used in correlative models but, as Rohr, Halstead & Raffel (2011) point out, they are not explicitly modelled. Predictive uncertainty thus arises where the interactions (or other factors) are not transferable to the new geographic area (e.g. the competing species may be absent). In terms of species interactions, however, our model was not unreasonably extrapolative because Bd infects a very broad range of hosts that were available in both training and projection spaces. Extrapolation in environmental space is arguably more important than extrapolation in geographic space. With its ‘clamping’ function, Maxent allows the user to evaluate whether significant extrapolation in environmental space has occurred when making projections (see methods; Murray et al. 2011). Our projections were not extrapolative in this sense either (see results; Murray et al. 2011) and as such this issue is unlikely to be a major source of bias in our study.
Several of Rohr, Halstead & Raffel's (2011) remaining concerns arise from whether our models were built upon occurrence records that fairly represent the environmental space inhabitable by Bd in Australia (point 2 above). This would not be the case for a species that is not at or near equilibrium in the region in which the model is trained (i.e. other factors, such as dispersal routes, may be more important for prediction, as is often the case when modelling invasive species undergoing range expansion). Similarly, this would not be the case if sampling was strongly biased in environmental space. We show that these are also unlikely to be major sources of bias in our study.
On the basis of our results regarding the predictive ability of human population density (HPD) as a variable in the models (fig. S8; Murray et al. 2011), Rohr, Halstead & Raffel (2011) correctly suggest that human associated factors might be affecting the observed distribution of Bd in Australia. We agree and discuss with reference to relevant literature several reasons how this might be the case in relation to our study system and results. In their commentary, Rohr, Halstead & Raffel (2011) speculate further on mechanisms to explain this result and further emphasize the effects that this could have on our results. However, while it is true that, as a single predictor, HPD contained the most unique predictive information that was not together present in the other variables in the model, the loss of this unique information scarcely reduced overall predictive ability (omission equated to c. 1·5% decrease in accuracy). In addition, as a single explanatory factor, HPD was only the sixth best predictor in the model and was considerably worse than the best environmental predictors. The ability of HPD to predict Bd distribution over and above the environmental variables is thus likely to be restricted to a small fraction of the occurrence records. In contrast, the ability of the environmental variables to explain Bd distribution over and above HPD is clearly more significant, particularly as it relates to the aims, hypotheses and methods of our study (Murray et al. 2011). This is not to say that we think that humans have not played a role in the shaping of Bd’s observed distribution in Australia. Our more conservative and biologically plausible interpretations of these results given the uncertainties/lack of supporting evidence are discussed in fig. S8 (Murray et al. 2011) with reference to the relevant literature.
Rohr, Halstead & Raffel (2011) also make two arguments about the effect that humans will have on sampling bias. First they suggest, as we do in fig. S3 (Murray et al. 2011), that sampling is likely to have been biased towards areas of higher environmental suitability for Bd because these are the areas where frog declines and mortalities have occurred due to severe chytridiomycosis. Later, and in contrast to their first suggestion, Rohr, Halstead & Raffel (2011) propose that frequent human introductions and spread should bias the occurrence records towards generally unsuitable environments around ports, cities, highways and the coast (which would act as a giant drift-fence of sorts), where they state that Bd is almost exclusively found.
Bd is not almost exclusively found near ports, cities and the coast in Australia and repeated introductions and human-aided spread within Australia remains a hypothesis in need of substantive evidence. As described in Murray et al. (2010a), Skerratt et al. (in press) and Berger et al. (2004), the majority of frog decline sites in Australia are located in remote, relatively pristine upland wilderness areas away from cities and sampling for Bd in Australia has occurred across a wide range of environments that are likely to be representative of both suitable and unsuitable conditions. Our database consists of opportunistic, systematic and retrospective (museum) sources. Some of these are likely biased towards areas inhabited by humans (e.g. public submission of sick or dead frogs; Berger 2001), while others are biased towards areas in remote wilderness generally far removed from human influences (e.g. McDonald et al. 2005). Quantifying and reducing the overall sampling bias is nevertheless identified as a future priority in our study (Murray et al. 2011).
Hence, while we agree with Rohr, Halstead & Raffel (2011) that methods and routes of dispersal will be important for predicting the future distribution of chytridiomycosis, it is less important for characterizing current distribution in Australia where the majority of potential dispersal appears to have already occurred. This hypothesis is described in detail in the manuscript and largely supported by our results (Murray et al. 2011). Possible exceptions at the northern and southern extremes of Bd’s distribution are discussed in the paper, as are the main sources of bias and the weak signal that HPD retains some explanatory value over and above environmental factors. The value of our results in practice are demonstrated and discussed as are our recommendations for management given the uncertainties (e.g. Phillott et al. 2010). Finally, transparency is one of our study’s key features: all data have been made publicly available for scrutiny and for others to use (Murray et al. 2010a). We hope this fosters researcher coordination and expedites the development of improved models for amphibian conservation.
Key issues for modelling the future distribution of invasive pathogens
Many of Rohr, Halstead & Raffel's (2011) concerns nevertheless remain relevant to predicting the distribution and impacts of chytridiomycosis and other pathogens under climate change and at invasion fronts. In these cases, models need to avoid or be robust to significant extrapolation by being transferable. One way of doing this is to shift the focus from correlative SDMs (which require only occurrence records) to mechanistic or process-based SDMs (which require more complete knowledge of a species’ responses to its biotic and abiotic environment) (see Kearney & Porter 2009 for a review). Combinations of these methods may also offer advantages, as each can inform the other.
Our approach to date for these more extrapolative situations has thus focussed on the mechanisms of Bd’s growth, dispersal and transmission. Simple mechanistic models that link Bd proliferation with environment (using, for example, biophysical performance curves denoting optimal conditions for growth and lethal limits) have already proved useful for describing seasonal and inter-annual infection patterns in wild frogs in subtropical Australia, where environmental suitability for Bd is generally very high but varies temporally (K.A. Murray, unpublished data). These models also show considerable promise for characterising Bd’s fundamental niche and hence potential distribution globally (K.A. Murray, unpublished data). We anticipate that this class of models will be particularly useful for estimating the influence that climate change may have on chytridiomycosis distribution, dynamics and impacts.
In the meantime, correlative SDMs can provide a wealth of useful information that can be immediately adopted. We have demonstrated this in our paper and have subsequently explored how our metric of environmental suitability for infection with Bd may be useful among multiple threats and life-history and ecological traits in more detailed studies of decline risk in amphibians (Murray et al. 2010b). We have also subsequently employed the results to short-list unknown wild hosts for Bd (Murray & Skerratt in press). We therefore encourage the use of correlative SDMs in other regions of the world confronting similar conservation challenges to Australia in the face of this global threat, particularly where data and resources are sparse but biodiversity values are high.