JSTOR

Analyzing Local and Regional Determinants Separately and Simultaneously

Within this single data set, we observe two common patterns of species richness: (1) a positive relationship between local and regional richness (fig. 1A; ) and (2) a strong relationship between a suite of local environmental variables and local richness, in which the primary correlation is with an estimate of productivity (fig. 1C; ). The majority of studies investigating patterns of species richness examine only one of these two types of relationships, and the presence of a strong correlation has been taken (implicitly or explicitly) as evidence for that variable or suite of variables as an important determinant of observed geographic patterns (e.g., Kaspari et al. 2000; Allen et al. 2002; Karlson et al. 2004; Witman et al. 2004). However, when we look at either pattern in more detail we see a significant signal of the other set of variables on species richness. The simple regional richness model significantly underestimates species richness in communities with high NDVI and overestimates richness in communities with low NDVI (fig. 1A, 1B). The equivalent pattern is seen in the local environment model, which underestimates richness when the regional pool is species rich and overestimates it when the regional pool is species poor (fig. 1C, 1D). Because both sets of variables have an important influence on local richness, including both improves the overall fit of the model (fig. 1E, 1F), with the combined model clearly favored in AIC comparisons (ΔAIC_c for the local environment model = 162.0; regional enrichment model = 290.3; combined model = 0; ΔAIC_c values > 10 are considered to represent almost no support for the model). These results are similar to those of Harrison et al. (2006), which indicate that both local environmental factors and regional richness influence the local richness of serpentine floras in California. However, in contrast to Harrison et al.’s results (see also Harrison and Cornell 2008) our analysis suggests that productivity is directly related to richness at the local scale (fig. 1; appendix).

(40 KB)

Figure 1: Comparison of models of local species richness (at the 5‐year timescale) based on regional richness, local environmental factors, and both combined. For illustrative purposes, plots A–E include data for all sites, with predicted values and residuals based on the models generated using the data reserved for model building. In plots B, D, and E, the plus symbols indicate data used to build the model, and the circles indicate data used to test the model. A, Observed local richness as a function of predicted local richness based on the regional enrichment model, color coded by the summer normalized difference vegetation index (NDVI), the single best environmental predictor of local richness. Results are plotted as an interpolated surface of NDVI values (color coded as quantiles) to allow the clear presentation of large numbers of overlapping points. The solid line is the 1:1 line. B, Residuals of the regional enrichment model as a function of summer NDVI. C, Observed local richness as a function of predicted local richness based on the local environment model, with points color coded by regional richness (plotting details as in A). D, Residuals of the local environment model as a function of regional richness. E, Observed versus predicted plot for the combined model including both regional richness and local environmental factors. F, Comparison of the performance of the three models based on proportion of variance explained. The combined model’s variance is partitioned to show the unique contributions of the local environment (blue), regional richness (red), and the variance that is described by some combination of the two sets of factors but is not uniquely ascribable to either (gray). Only data reserved for model testing were used for this final analysis.

Open New Window

If the contributions of local environment and regional richness were independent of one another, then while a combined analysis would produce a model with greater explanatory power, conclusions regarding the importance of either factor on the basis of analyzing it in isolation would be unaffected. However, our results suggest collinearity between regional richness and the local environmental variables (all environmental variables are correlated with regional richness; P values < .005), leading to a substantial fraction of variation that cannot be uniquely ascribed to either local or regional processes (fig. 1F). Had we analyzed either the local environment or regional richness alone, we would have ascribed this nonunique variance to the variables we chose to investigate. In the case of regional richness, its unique importance would have been overestimated by over 100%. In general, studies examining either the local environment or regional richness in isolation risk overemphasizing the importance of the chosen predictors because of the underlying covariance with unconsidered predictor variables. While this is a general problem in regression analyses, it is particularly relevant here because there are many reasons to think that regional richness might frequently covary with local environmental variables (Harrison et al. 2006; Harrison and Cornell 2008). The collinearity between regional richness and local environmental variables also has consequences for the interpretation of individual predictors on local richness (Graham 2003). For example, the coefficient for regional richness decreases by 70% when local environmental variables are added to the model (appendix). Such differences will be crucial when attempting to evaluate theories that make specific predictions about model parameters (e.g., Allen et al. 2002; Algar et al. 2007; Hawkins et al. 2007) because, if the contribution of regional enrichment is not controlled for, then the wrong estimate of the fitted parameter may be compared to the theoretical value.

In addition to yielding improvements in overall model fit and parameter estimation, the combined model substantially decreases the spatial structure of model residuals. The raw richness values exhibit significant spatial autocorrelation at distances up to ∼1,500 km (fig. 2), which could present a problem for modeling the data using nonspatial methods (Lennon 2000). The residuals of the regional enrichment model display similar spatial autocorrelation (fig. 2). Modeling richness with local environmental data reduces autocorrelation in the residuals (see also Hurlbert and White 2005; Hortal et al. 2008), although smaller‐scale positive autocorrelation remains in the shortest distance class. The model combining local environmental factors and regional richness eliminates this remaining residual autocorrelation, resulting in no significant autocorrelation at any scale (fig. 2). This suggests that the residual spatial structure in some local‐scale species richness models may be due to the enrichment of local communities by the regional species pool, potentially reducing the need for spatial regression techniques when richness is modeled using a combined approach (Diniz‐Filho et al. 2003).

(36 KB)

Figure 2: Patterns of spatial autocorrelation (Moran’s I) at the 5‐year timescale for the raw richness data (black) and the residuals of the three models: regional enrichment (red), local environment (blue), and the combined model (green). Confidence intervals (error bars) for Moran’s I are Bonferroni corrected for the number of distance classes (i.e., error bars are equal to ). Zero autocorrelation is shown by the dashed line.

Open New Window

While the inclusion of both regional richness and local environmental variables in a single analysis of species richness is relatively rare (Harrison and Cornell 2008), it is more common to see different scales of environmental variables evaluated in the same analysis (e.g., Rahbek and Graves 2001; Hurlbert and Haskell 2003). More sophisticated analyses using structural equation modeling will be required to tease apart the details of how regional and local environments influence regional and local richness and the effect of regional richness on local richness. That said, our results are qualitatively similar when using different scales of environmental variables, and our simple path analysis supports our general conclusions (appendix).

Spatial Scale, Autocorrelation, and “Pseudoreplication”

Analyses similar to ours have been criticized as being pseudoreplicated because of the spatially autocorrelated nature of the regional species pool (Srivastava 1999). For example, in this study the median percentage of shared species among all pairwise regional pool comparisons was 32%. However, the regional species pool is no different from any other spatially autocorrelated predictor variable. For example, at the scale at which birds perceive elevational differences, most of the Midwest is a single elevational region. This autocorrelation results in an overestimate of the number of degrees of freedom if autocorrelation persists in the model residuals (e.g., Lichstein et al. 2002). To be clear, the pseudoreplication described by Srivastava (1999) in this observational context is simply spatial autocorrelation. Because our central analysis is that of the combined model and the combined model successfully removes spatial autocorrelation from the residuals, our analysis does not overestimate the degrees of freedom and thus yields valid statistical results (Lichstein et al. 2002; Diniz‐Filho et al. 2003; Rangel et al. 2006). Srivastava (1999) recommends that in order to avoid pseudoreplication, local richness values should be averaged to produce only a single value for each broadly defined geographic region. Our analyses support the idea that models based solely on regional richness will exhibit strong autocorrelation (fig. 2) and therefore support Srivastava’s (1999) concern with respect to noncombined analyses as described above. However, her proposed solution of averaging data points within regions eliminates all within‐region variability in local richness and is thus inappropriate for assessing the relative importance of the local environment, which may be important in driving that variability. Studies of local‐regional relationships that remove local‐scale variability by averaging local richness values within a larger region (e.g., Srivastava 1999; Karlson et al. 2004) ignore this meaningful variation and may exaggerate the importance of the regional pool. Our combined model solves this problem by successfully modeling the observed autocorrelation as being driven by meaningful environmental variation and regional enrichment and thus allows individual local‐scale data points to be incorporated without statistical complications. More sophisticated spatially explicit modeling may well provide key additional insights, but the current approach represents a valuable first step toward understanding these patterns.

Temporal Scale and the Relative Importance of Local and Regional Processes

We explored the influence of the temporal resolution used to characterize local species richness and found that increasing the timescale has only a small influence on the overall predictive power of the regression model (fig. 3). However, the proportions of the variance explained by the local environment and regional enrichment changed as the timescale increased (fig. 3). While local environmental variables largely dominate at 1‐year timescales, at decadal timescales, local and regional variables explain similar amounts of variance in local richness. The processes governing species richness are expected to change with the scale of analysis because of changes in the physical and biological processes dominating at different scales (Holling 1992). For example, species interactions occur over days and hectares, whereas speciation dynamics occur over regional to continental extents and geological time periods. As such, it makes sense that regional processes play an increasing role at longer timescales. These results confirm the suggestion that temporal scale should affect the strength, as well as the shape, of the local‐regional richness relationship (Srivastava 1999).

(50 KB)

Figure 3: Effect of timescale on the partitioning of variance of species richness in North American breeding birds into effects of the local environment (blue), regional enrichment (red), and variance explained by some combination of the two sets of factors that cannot be uniquely ascribed to both (gray).

Open New Window

The changes in explained variance result from changes in cumulative local richness with timescale. The accumulation of species occurs because of both increased sampling intensity, whereby rare species that were present at the site are finally sampled, and real turnover, wherein species that were not present in a given year colonize the site (White 2004; White et al. 2006). Species in this latter group include both vagrants and species invading the site in response to changes in environmental conditions. Thus, the species richness of a local site over a broader temporal window increasingly reflects temporal beta diversity relative to single‐year alpha diversity, and it has been shown that beyond timescales of ∼2–3 years, this beta diversity is driven more by ecological processes than sampling intensity (White 2004). As such, our results suggest that local environmental constraints are most important for determining alpha diversity in North American bird communities, while regional enrichment is important for explaining patterns of temporal beta diversity. In the face of environmental variability, richer regional species pools are more likely to contain species that can successfully cope with novel conditions. In addition, even in the absence of environmental change, richer species pools are expected to contribute more species to local communities via mass effects (sensu Schmida and Wilson 1985).

This suggests a possible avenue for integrating local and regional influences on species richness. It has been proposed that local communities are actually composed of two potentially discrete groups of species: (1) core (or source) species, which maintain viable populations at a site because they are well suited to the local ecological conditions, and (2) occasional (or sink or vagrant) species that periodically occur at the site through random colonization events but fail to persist in the system (MacArthur 1960; Magurran and Henderson 2003; Belmaker 2009). Since a site will typically contain some occasional species, this would explain the unique contribution of regional enrichment, even at the shortest timescales. If this hypothesis is valid, then observed regional influences may occur via mass effects, with the number of core species limited by local environmental conditions and the number of occasional species influenced by the richness of the regional pool. The ability of local environmental variables to explain 1‐year richness values may thus reflect the constraints imposed by the local environment that limit the number of core species that can maintain stable populations at that site. Vagrant species would not be expected to be restricted by this limited capacity as only a few dispersing individuals are encountered (MacArthur 1960; Magurran and Henderson 2003; Belmaker 2009). The fact that regional richness becomes increasingly important for understanding local richness over longer temporal windows reflects the fact that the number of species that might ephemerally colonize a site should increase with the time period of sampling (Grinnell 1922) and the size of the species pool. Thus, occasional species richness should be driven by regional enrichment and should be more prevalent at longer timescales. Admittedly, this clear distinction between core and occasional species is overly simplistic. For example, the status of species can change through time, in response to changing environmental conditions or biotic interactions (Brown et al. 2001). In addition, distinguishing between core and occasional species will often be difficult and might require choosing an arbitrary cutoff based on abundance or persistence (e.g., Magurran and Henderson 2003).

Finally, it is also worth noting that as timescale increases, there is an increase in the proportion of variation that cannot be uniquely ascribed to either local or regional influences, and thus, the relative contribution of these processes becomes less distinguishable (fig. 3). As a result, analyses that use local richness measures based on longer timescales, for example, regional floral and faunal lists, risk overestimating the importance of either local or regional processes if both are not examined simultaneously using this type of variance‐partitioning framework.