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Chase & Leibold (2002) demonstrated that the scale transition from a non-positive to a positive productivity-diversity relationship must involve an increase in beta diversity, or among-site dissimilarity in species composition. They found that zooplankton diversity within ponds (i.e. local, or alpha, diversity) followed a unimodal relationship to productivity. However, ponds within high-productivity watersheds were more dissimilar from one another in composition (i.e. had higher beta diversity) than ponds within low-productivity watersheds, thus producing a positive relationship between productivity and watershed-scale diversity (i.e. regional, or gamma, diversity). These authors considered, but found no evidence for, one possible mechanism, namely that environmental heterogeneity increases at higher levels of productivity. They speculated that the mechanism instead involved the existence of alternative stable states at high productivity, an idea that later received a modest amount of support from microcosm experiments (Fukami & Morin 2003). Subsequently, lack of connectivity among ponds was implicated as a necessary condition for the increase in beta diversity with higher productivity (Chase & Ryberg 2004).
Higher beta diversity at higher productivity is likely to be a phenomenon of global generality and importance. In a recent review and meta-analysis, Hillebrand (2004) found that the tropical-temperate diversity gradient is virtually always stronger at the regional scale, e.g. among countries or latitudinal bands, than at the local (field plot) scale, even when total latitudinal extent is held constant. In addition, multiple studies have found that the regional latitudinal diversity gradient is very strongly correlated with measures of energy and water availability that control primary productivity (Francis & Currie 2003; Hawkins et al. 2003; Hillebrand 2004). Taken together, these results mean that global-scale patterns in productivity are positively associated with beta diversity, i.e. with the ratio of regional richness to local richness. Thus, although we are still far from having a satisfactory mechanistic explanation for either the latitudinal richness gradient or the productivity–diversity relationship, further study of beta diversity is clearly needed.
In this study we ask whether beta diversity increases with productivity in a terrestrial herbaceous plant system. We further ask whether such a relationship can be found at the relatively small scale of tens to hundreds of metres, where beta diversity may be caused by heterogeneity in readily observable microhabitat conditions such as slope and aspect, shading, litter, rock cover and animal disturbance. We hypothesize that increasing mean productivity in our system is associated with greater variation in such local microhabitat conditions, in turn leading to higher small-scale spatial differentiation in species composition. If this is true, ours would be the first study to find evidence for one of the major proposed explanations for the positive productivity-beta diversity relationship.
We analysed plant species richness in 105 field sites on serpentine soil in California. Serpentine is a harsh, low-productivity soil that supports a rich flora dominated by native species. In earlier work we found that at a regional scale (e.g. 102−104 km2), species richness in our system was strongly positively correlated with productivity, which in turn was strongly correlated with average annual rainfall (Harrison et al. 2000; Harrison et al. 2004; Harrison et al. 2006). These results were in good agreement with other studies linking regional-scale plant diversity in California to a rainfall-driven gradient in productivity (Richerson & Lum 1980; Hawkins & Porter 2003; Williams et al. 2005).
We considered four components of species richness: ‘alpha’ (1 × 1 m quadrats), ‘within-plot beta’ (dissimilarity among seven quadrats within 50 × 10 m plots), ‘between-slope beta’ (dissimilarity between pairs of 50 × 10 m plots on adjacent north and south-facing slopes), and ‘gamma’ (cumulative richness of each pair of 50 × 10 m plots). Within-plot beta is intended to measure the diversity that is related to general small-scale environmental heterogeneity; between-slope beta is intended to measure the diversity associated with differences in local topography. We only considered herbs, because valid tests of local processes on diversity must sample potentially competing species (Huston 1999), and because we were interested in beta diversity at scales too small for woody species.
We asked three questions. (i) How strongly is variation in the gamma (total) herb richness of our study sites associated with variation in each smaller component of richness (alpha, within-plot beta, between-slope beta)? (ii) How does each component of richness respond to productivity? Specifically, does productivity have a non-positive relationship to alpha, but a positive relationship to beta and gamma diversity? (iii) How does environmental heterogeneity respond to productivity? In particular, is productivity positively associated with either the within-plot variability, or the between-slope variability, in environmental parameters that may affect herb species composition (percentage cover of shade, rocks, bare soil, litter, moss, animal disturbance)?
Using the terminology of Waide et al. (1999), our ‘focus’ was small (1 × 1 m quadrats), but our ‘extent’ was large (our sites spanned roughly 1200 km latitude and 2750 m elevation). This choice of scales should be well suited for the questions we investigated. Most unimodal or negative productivity-diversity relationships are observed in small plots (e.g. Grace 1999; Waide et al. 1999; Gross et al. 2000) and, in general, many authors advocate defining alpha at a small scale where interspecific interactions should be strong and internal spatial heterogeneity relatively low (e.g. Huston 1999; Loreau 2003). However, our large geographical and ecological extent is appropriate because it ensures an ample natural gradient in primary productivity.
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We found a positive association between productivity and beta diversity, similarly to other authors (Chase & Leibold 2002; Chase & Ryberg 2004). Higher values of the productivity measure NDVI, which, in our study system, largely reflects rainfall, are associated with greater dissimilarity in herb species composition between two plots on adjacent north and south slopes. This result was not an artifact of the effect of productivity on the relative amounts of woody and herbaceous cover, as it was also true among the subset of sites with no woody cover, and as it was qualitatively unchanged when herb cover was included in the model. We did not find such an effect for beta diversity at a smaller scale, among 1-m2 quadrats within 50 × 10 m plots.
We found no evidence for the hypothesis that increasing environmental heterogeneity causes the increase in beta diversity at higher levels of productivity. We did find that several measures of within-plot heterogeneity were positively associated with NDVI, namely the coefficients of variation of rock, bare soil and animal disturbance. However, no measure of between-slope environmental heterogeneity showed an increase with NDVI. As only the between-slope beta diversity was positively associated with NDVI, we conclude that the forms of environmental heterogeneity we measured were not capable of explaining the positive relationship of productivity to beta diversity.
Unlike previous authors, we did not find that increasing beta diversity caused a transition from a non-positive productivity-diversity relationship at a smaller scale to a positive one at a larger scale. Instead, we found non-significant relationships of productivity to diversity at both our smaller (alpha, or 1 m2) scale and our larger (gamma, or 1000 m2) scales. Although such results are not uncommon (Waide et al. 1999; Gross et al. 2000), it is possible that using a more localized measure of productivity, such as biomass, would have revealed significant relationships at one or both of these scales. Even if we had, we would still be unlikely to have found a scale transition, because the influence of beta diversity on gamma diversity was weak in our system. Variation in gamma diversity was much more strongly associated with variation in alpha diversity (r2 = 0.60) than with variation in either within-plot (r2 = 0.01) or between-slope (r2 = 0.10) beta diversity. This contrasts with other studies that find a strong positive linkage between environmental heterogeneity, beta diversity and gamma diversity (e.g. Williams et al. 2002). A scale transition would only be possible if beta diversity responded differently to productivity than did alpha diversity and if beta diversity exerted a strong influence on gamma diversity.
As we know that NDVI is a strong positive predictor of regional diversity in our system (Williams et al. 2005; Harrison et al. 2006), the scale transition must happen at a larger scale (i.e. a larger site size) than the one we examined. Larger sites would incorporate a higher level of internal heterogeneity, thus increasing the influence of beta relative to alpha diversity. In addition, previous work (Chase & Ryberg 2004) suggests that if our sites were large enough to include spatially discontinuous localities, such as plots on separate serpentine outcrops, our potential to find a scale transition should be enhanced.
We are left in search of a mechanism to explain the positive association of productivity to beta diversity in our system. The only mechanism besides heterogeneity that has been proposed in the literature is the existence of alternative stable states at high levels of productivity (Chase & Leibold 2002; Fukami & Morin 2003). We do not think this is likely in our system, because serpentine vegetation is characterized by slow growth, infrequent disturbance and generally late-successional conditions (e.g. Whittaker 1960; Safford & Harrison 2004; Harrison et al. 2006). Also, our quadrats and plots were spatially continuous with one another, so it seems unlikely that they could exist in alternative stable states. Instead, we propose an explanation based on regional control of local community patterns (Cornell 1993; Karlson et al. 2004; Ricklefs 2004).
Species-energy theory (Hawkins et al. 2003) predicts that, as productivity increases, regional diversity increases not as a scaled-up consequence of local processes, but because of mechanisms that intrinsically act at a regional scale, for example lower rates of species extinction due to higher regional population sizes. At the same time, resource competition (Tilman 1982; Grime 2001) and assemblage-level thinning (Oksanen 1996; Stevens & Carson 1999) can prevent the additional diversity associated with higher productivity from being absorbed into small localities. Putting these two pieces together, one would predict what we found: an increase in beta diversity with increasing productivity that is not associated with an increase in environmental heterogeneity. Instead, increasing beta diversity could be the by-product of a greater regional number of species ‘spilling over’ among localities as the same number (or fewer) of them are able to coexist within localities. This agrees with the model of Weitz & Rothman (2003), in which the scale transition to a positive productivity-diversity relationship arises from an increase in the size of the regional species pool without any change in local dynamics.
Our proposed explanation is intrinsically difficult to prove because it switches the emphasis from easily observable, local phenomena to regional-scale and long-term processes that are much harder to study (see Ricklefs 2004 for a review of historical explanations for richness gradients). Nonetheless, our results suggest it is valuable to focus on spatial scale as a way of refining the search for explanations of species diversity patterns. We conclude by speculating that beta diversity is higher in the tropics, not necessarily because tropical species have narrower climatic tolerances, as proposed by Janzen (1967), but for reasons similar to those we suggest here. That is, small localities cannot fully absorb the abundance of species that are produced at the regional scale by the high rates of speciation and/or low rates of extinction that are characteristic of highly productive regions.