The majority of research into the impacts of global change has focused on abiotic factors such as warming temperatures and increased concentration of carbon dioxide (IPCC-WGII 2007). However, it is becoming clear that the consequences of biodiversity loss on vital ecosystem functions including primary productivity and decomposition are comparable in magnitude to the major abiotic stressors (Hooper et al. 2012, Figure 1). It is thus vital that we understand the drivers of biodiversity loss, which are numerous, interacting, and spatially heterogeneous. Various methods have been employed to understand how environmental change will impact biodiversity, including models of species distributions (e.g. Franklin et al. 2012) and demographic processes (e.g. Jenouvrier et al. 2012).
Figure 1: Changes in primary production as a function of percent local species loss. Effects of species loss on primary production from 62 studies (379 observations). Thick red line, lower productivity as species richness decreases; grey bands and black error bars, 95% confidence intervals. The thin red line shows the inverse of the thick red line to allow comparison of effect magnitudes with environmental changes with positive effects. Dotted grey lines show the mean effect of each environmental change for comparison with the effect of richness. Right axis, effects of other environmental changes. Blue is for increases and red for decreases in productivity. Reprinted by permission from Macmillan Publishers Ltd: Nature (doi:10.1038/nature11118), © 2012
Typically, practitioners 1) fit a model using historical explanatory data, which often includes interpolated climate data and/or remotely sensed products and then 2) use that model to project into the future using climate model output. In other words, models constructed to forecast biodiversity often use ‘output’ from other models as ‘input’ data. However, in most cases the uncertainties presented in the results are derived only from the biological model and ignore uncertainties in the source datasets. Statistically, this is a reasonable approach with the important caveat that the results are conditional on the input datasets. But for policy purposes, it is important that the uncertainties represent the overall confidence in the forecast. The IPCC, for example, has standardized how uncertainties should be handled and described throughout their publications (Mastrandrea et al. 2010) and other disciplines, such as hydrology, have taken this problem seriously (e.g. Liu and Gupta, 2007). Thus ecologists are faced with the important challenge of propagating uncertainties inherent in source datasets through new models to the final results. Unfortunately, this is difficult to achieve with traditional modeling frameworks. Here I will explore some of the implications of failing to propagate uncertainties and offer suggestions of how to improve our ability to improve forecasts.
Uncertainty in source datasets: what difference does it make?
Previous work has revealed that the choice of environmental data can make a significant impact on the results of biodiversity analysis. For example, Soria-Auza, et al. (2010) used the MaxEnt framework (Phillips, Anderson, and Schapire, 2006) to compare estimated the geographic distributions of several bird and fern species using climate data available via WorldClim (Hijmans et al., 2005) and SAGA (Böhner, 2005). Even though the differences these datasets were relatively minor, the authors reported significant differences in the predictions in some regions. In a related study, Peterson and Nakazawa (2008) compared six different sources of environmental datasets (primarily climatic variables) and found significant differences in the predicted potential range of an invasive fire ant (Solenopsis invicta) using the various climatic data sets. In particular, the commonly used WorldClim dataset (Hijmans et al., 2005) failed to accurately predict the full invasive range. In both of these studies, the authors used additional information to assess the relative merit of the predictions derived from various input data sets. However it is common in biodiversity modeling studies that no independent data are available and thus ecologists are faced with either arbitrarily choosing a environmental dataset or making predictions with multiple climate datasets and noting the differences. The situation is similar to the use of GCM output. Typically the output from multiple GCMs are treated independently in ecological analysis (e.g. Beaumont et al., 2008; Lawler et al., 2009) and the differences are explored by comparing the resulting predictions. This is analogous to the independent comparisons of different climate interpolations mentioned above. There has been some effort to develop probabilistic climate projections by treating output from different GCMs as ‘samples’ from a ‘true’ (in the statistical sense) future climate which would allow probabilistic ecological projections (Tebaldi and Knutti, 2007). This approach has not yet been widely adopted, in part because the uncertainties in the output from GCM ensembles are difficult to quantify due to lack of verification and model dependence, bias, and tuning. In interesting explorations of the implications of this type of uncertainty, Conlisk et al. (2012) and Diniz-Filho et al. (2009) used sensitivity analyses to partition the variability of projections made using different niche (or niche-population) models between various sources such as niche model design, general circulation models (GCMs), and emission scenario. They both identified that the choice of niche model was the single largest source of uncertainty. However, the methods were not able to produce a single projection accounting for the various uncertainties.
A solution: Hierarchical models…
Recent developments in Hierarchical Bayesian (HB) statistics have made it possible to incorporate covariate data into the model as a random variable and thus account for the uncertainty of the data in the results (Clark 2005). Propagating uncertainty in this way could be achieved relatively easily by considering the environmental data to have distributions (rather than single values) at each location. For example, Kang, Cressie, and Sain (2012) developed a “consensus climate signal” across six regional climate models using a HB model. The output from that process incorporates the uncertainty across models and could be used for for further ecological analysis. See Chakraborty et al. (2011) for an example of a species distribution model that could incorporate this type of climatic uncertainty into model fitting or projection. A similar approach has been recently explored in epidemiological models that combine algorithmic models with stochastic exposure simulators to estimate human exposure to toxins (Gelfand and Sahu, 2010). This framework could have wide application for developing biodiversity models capable of incorporating data uncertainty into a model and propagating the results through to the model output and results. This would likely lead to projections with wider prediction intervals that we can be more confident in. But regardless of modeling framework, it is important that we improve our quantification of uncertainty because policy and management decisions depend on them.
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