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1Ecologists seem poised to reap the benefits of recent work examining the effects of energy and resources on plant taxonomic richness in local communities. My goal here is to present a qualitative model to further our understanding about the driving forces of plant taxonomic richness across spatial scales.
2The model attempts to predict local plant species richness based on previous work regarding (i) correlations between temperature, precipitation and richness, (ii) correlations between soil nutrient availability and richness derived from both descriptions and experimental manipulations, and (iii) empirical demonstrations of the importance of the species pool in regulating local species richness.
3The model consists of a phenomenlogical submodel of the multiplicative effects of temperature, water and mineral nutrients on plant species richness, with a spatially implicit submodel of immigration and extinction of species in local communities.
4The model makes the following five testable predictions. (i) Local richness increases linearly with immigration rate of new species and curvilinearly with local extinction rate. (ii) The effects of altered local immigration and extinction rates will be most apparent in local communities embedded in species-rich metacommunities. (iii) Local communities are not saturated, but rather increase in richness directly with increasing metacommunity richness. (iv) Unimodal or hump-shaped productivity-richness relations arise when low water or temperature limit diversity at low productivity and mineral nutrients limit diversity at high productivity. (v) An apparent scale-dependence of the effect productivity on richness should arise when there exists a matching scale-dependence of the underlying environmental drivers. These predictions do not contrast sharply with available data, but remain largely untested.
5I suggest that continued attempts to synthesize the most predictive patterns emerging from the burgeoning global data bases of both taxonomic and genetic diversity will guide us toward mechanistic explanations of the determinants of species richness, suggest why special cases differ from general patterns, and provide additional novel predictions not currently apparent.
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Patterns of biodiversity along latitudinal and productivity gradients are some of our most dramatic patterns in the living world (Wallace 1878; Waide et al. 1999), and there seems to be renewed interest in explaining such large scale patterns (Ricklefs & Schluter 1993; Brown 1995; Currie et al. 2004; Ricklefs 2004). Recent empirical and theoretical studies have examined patterns of plant diversity in relation to specific environmental drivers such as water, temperature and mineral nutrients (Allen et al. 2002; Francis & Currie 2003; Davies et al. 2004; Suding et al. 2005), which all correlate to some degree with latitude and productivity. In addition, it is widely recognized that local plant communities can be strongly influenced by the regional species pool (Partel et al. 2000; Foster 2001; Grace 2001). Here my objectives are to combine existing environment-biodiversity relations into a simple coherent framework, to link local and metacommunity scales and to describe the resulting predictions for local species richness.
Several mechanisms have been proposed to explain these environment–richness relationships. Mechanistic models of physiological tolerance indicate that a wider variety of physiological configurations can survive in benign (warm and wet) conditions than in harsh (cold or dry) conditions (Hall et al. 1992; Kleidon & Mooney 2000; VanderMeulen et al. 2001). Increased speciation rate in warmer environments, due to increases in metabolic rate (including per locus mutation rate) and decreased generation time has also been suggested to enhance diversity (Rohde 1992; Allen et al. 2002). While debate exists concerning these mechanisms (Currie et al. 2004; Huston et al. 2003; Davies et al. 2004), they nonetheless remain plausible explanations of plant diversity gradients.
The above patterns and mechanisms suggest that these relations are scale independent, with very small scale (i.e. neighbourhood) processes driving environment–richness patterns at larger scales (Huston 1999). Predictive relations between temperature, water and richness seem to occur across a wide range of spatial scales. Of the proposed mechanisms for all of these patterns, all operate at the individual (physiological tolerance, mutation rate) or neighbourhood (competition) level. Huston (1999) suggested that the consequences of these small scale processes controlling diversity scale up to larger regions. This is not to say that other, larger scale phenomena do not influence regional patterns of richness (Silvertown 1985; Latham & Ricklefs 1993; Qian & Ricklefs 2000), but rather that small scale processes lead to a coherent set of mechanisms and patterns that are scale-independent and do not depend on historical contingencies.
Toward a heuristic model
Below, I first create a simple model for metacommunities that combines the phenomenological patterns of species richness and temperature, water and nutrients observed at large spatial scales. I begin with patterns at large spatial scales for two reasons. First, the species pool at large spatial scales forms the metacommunity that provides the ecological context for local communities (Ricklefs 2004; Huston 1999; Leibold et al. 2004). Second, related phenomenological models have already been proposed to describe some of the large scale patterns. Following this model for metacommunities, I draw on a metapopulation model to embed the richness of a local community into the metacommunity species pool.
Environmental determinants of metacommunity species richness
The effects of temperature, water and mineral nutrients on plant species richness in large areas seem relatively straightforward. Combining the above patterns in a functional form, we have the basis for a qualitative model for species richness,
(eqn 1 )
where SM, T, W and N are species richness in the metacommunity, temperature, water supply rate and nutrient supply rates, respectively, of a metacommunity, and α and β are positive constants (Fig. 1). The values of the constants are not particularly important for generating the qualitative shapes of the patterns of richness. The forms of the expressions for T, W and N were selected for their simplicity, and because they have strong empirical support. The polynomial term for the temperature effect depends on water availability and derives directly from O’Brien (1998), O’Brien et al. (2000) and Francis & Currie (2003). The Michaelis–Menten form of the water term was selected to describe the form of the precipitation–richness relationship in Francis & Currie (2003). The logistic form of the nutrient term was selected because it does not result in negative values as nutrients increase, and because it results in proportional loss of species with increasing nutrients, consistent with empirical observation (Gough et al. 2000a). Unlike the models of O’Brien (1998) and Francis & Currie (2003), or Huston (1994), this model attempts to combine and reconcile the patterns associated with water and temperature and those associated with soil nutrient availability. Equation 1 reproduces the dominant patterns of plant species richness (Fig. 1), and in doing so, allows direct comparison of the contrasting roles of temperature, water and nutrients. Further, it has implications for effects of productivity on richness.
Embedding a local community into the regional metacommunity
Species richness in a local community changes through immigration or local extinction, and is capable of changing much more rapidly than the richness of a metacommunity. For this reason, I place species richness of a particular local community into a metacommunity framework, presenting one possible derivation below. My representation of the state variable Pj is inspired by and directly analogous to metapopulation models of species distributions among sites (Gotelli 1991; Levins 1969; Hanski 1982). In the model presented here, let the variable of interest, Pj, be the proportion of the species in the metacommunity found in a particular local community j, and let each local community j be embedded in the metacommunity, where metacommunity richnessn SM is scaled to 1. Let propagules (species) derive from the metacommunity in which richness changes relatively slowly and is determined by temperature, water and nutrient availability (metacommunity richness is, therefore in this sense, independent of local species richness), i.e.
(eqn 2 )
This is simply a metapopulation model with propagule rain and rescue effect (Gotelli 1991). Total immigration rate of new species (first term in equation 2) has a maximum at Pj = 0, and decreases linearly with increasing Pj. Gotelli (1991; Gotelli & Kelley 1993) refers to this as propagule rain, where, in this case, per species immigration rate, ij, does not otherwise depend on the richness of other local communities, but merely on the regional pool. Total extinction rate (second term in equation 2) has a maximum at Pj = 0.5. Increasing Pj decreases total extinction rate by increasing the importance of the rescue effect, 1 – Pj (Brown & Kodric-Brown 1977; Hanski 1982). Decreasing Pj merely decreases the likelihood of an extinction, ePj.
The equilibrium solution for this model is
(eqn 3 )
This solution shows an infinite number of stable equilibria of local richness values Pj which depend on specific rates of immigration and extinction in that local community j (equation 3); richness saturates at 1.0 when i > e. This also shows that the effect of i on is linear, whereas the effect of e on is curvilinear, related directly to e−1. This difference between the incremental effects of i and e constitute the first prediction of this model.
We then place this within the metacommunity context, where, combining equation 1 and 3 gives,
(eqn 4 )
Equation 4 represents the effects of the average environmental conditions in a metacommunity and the rates of immigration and extinction in the local community in determining the number of species in that local community. Ecologists recognize that the richness of a local community depends in part on the richness of the surrounding matrix (e.g. Cantero et al. 1999; Partel et al. 2000; Foster & Tilman 2003), and equations 2–4 derive and specify a relation between local community richness and total immigration rate into a local site.
Variation among local communities in any factor or process, such as area or herbivory, that influences local immigration or extinction rates is thus predicted to influence local richness, and this influence should thus be directly proportional to the richness of the metacommunity (Huston 1999). This means that the effects of i/e on richness will be most pronounced and measurable in the most diverse metacommunities (Fig. 2). This constitutes the second prediction of the model.
Another prediction of equation 4 is that local communities are never truly saturated: local richness, Sj, increases linearly with metacommunity richness. This constitutes the third prediction of the model. This is conceptually similar to neutral models which assume that a local community is a random sample of the metacommunity (MacArthur & Wilson 1963; Hubbell 1997, 2001; Bell 2000; Bell 2001). In principle, local communities can saturate if they are sufficiently small. The precise nature of this sampling curve will depend on the size of the local community, and the species abundance distribution of the metacommunity. However, simulations (not shown) indicate that the relation may be indistinguishable from linear for local communities composed of at least several thousand individuals, roughly equivalent to a few millilitres of pond water containing phytoplankton, a hectare of grassland, or 10 hectares of mature forest.
Water, nutrients and temperature control plant productivity, and thus it seems warranted to address what equation 4 might predict about patterns of plant species richness along productivity gradients. Equation 4, however, does not include an explicit representation of productivity. I excluded measures of the environment that include plant performance, such as actual evapotranspiration (cf. Francis & Currie 2003) because of the complex relations between plant biomass, density and richness (Enquist et al. 1998; Stevens & Carson 1999) and on the basis of parsimony (Peters 1991): I would like to see how far we can get in relating the environment to richness, even if there exist intermediate mechanistic linkages (Grime 1979; Huston 1994, 1999).
Data suggest that the effects of productivity on plant species richness are various, and may be positive, negative, unimodal or U-shaped (Waide et al. 1999; Mittelbach et al. 2001, 2003). Equation 1 predicts unimodal patterns of richness along productivity gradients, which are widely cited in the literature (Waide et al. 1999; Mittelbach et al. 2001, 2003; Chalcraft et al. 2004) and arise when nutrients covary positively with either water (Fig. 1c–d) or temperature. In such cases, either low temperature or low water limit both richness and productivity, and high nutrient availability limits richness at high productivity. This constitutes the fourth prediction of the model, and arises in part because of the assumed multiplicative rather than additive effects of nutrients and water or temperature. Other parameter combinations resulting in productivity gradients (e.g. a nutrient gradient with constant water and temperature) predict monotonic productivity–richness relations. The underlying cause of any particular natural productivity gradient is not always clear. For example, either soil moisture or temperature can regulate soil microbial dynamics and create variation in plant available nutrient concentrations (Atlas & Bartha 1998; Chapin III et al. 2002), thereby causing in a natural productivity gradient.
how do the predictions arising fromequation 4fit with existing hypotheses and the available data?
The first prediction, that local richness increases linearly with immigration rate of new species and curvilinearly with local extinction rate, contrasts with predictions of Loreau & Mouquet (1999). They show that richness increases as a sigmoidal function of immigration, although this may appear linear over a wide range of immigration intensities. To my knowledge, these ideas have not been evaluated with any data (cf. Tilman 1993; Stevens et al. 2004).
Second, it predicts that the effects of altered local immigration and extinction rates will be most apparent in local communities embedded in species-rich metacommunities. This was suggested previously by Huston (1999) and Foster (the shifting limitation hypothesis, 2001), with regard to effects of productivity on immigration, extinction and the resulting richness. Specifically, equation 4 predicts that the slope of the richness–biomass relation should be steeper in plots with added seeds (an experimentally enriched species pool). Foster (2001) and Foster et al. (2004) found this to be the case in undisturbed, but not disturbed vegetation. In contrast, Stevens et al. (2004) found no such differences in slopes, and this may have been due to the higher productivity and light interception at their site. Such contrasting findings might be better understood with direct measurement of both immigration and extinction rates.
Third, equation 4 predicts that local communities are not saturated, but rather increase in richness directly with increasing metacommunity richness. This seems consistent with some data sets (Cantero et al. 1999; Partel et al. 2000), but testing this prediction at larger scales is problematic (Huston 1999), and in small enough communities (e.g. a neighbourhood of one individual), it must be false. In practice, we need to look at scales small enough so that competition could limit richness (Huston 1999), but not so small as to be trivial (Munzbergova 2004). Null models may help make quantitative predictions in competition-limited vs. competition-unlimited conditions such as equation 4.
Fourth, equation 4 predicts that unimodal or hump-shaped productivity–richness relations arise when low water or temperature limit diversity at low productivity and mineral nutrients limit diversity at high productivity. This extends Foster's (2001) shifting limitation hypothesis to include very low productivity conditions. This prediction is largely untested, as the large-scale studies that have identified unimodal patterns in plant communities have not generally performed the necessary manipulations across sites.
Fifth, equation 4 predicts that the apparent scale-dependence of the effect of productivity on richness, now widely discussed in the literature, should arise only if there exists a matching scale-dependence of the underlying environmental drivers. This does not seem to have been considered among the hypotheses to explain unimodal patterns in plant communities (Chalcraft et al. 2004). Assessing the spatial scale-dependence of relevant environmental factors seems important to further our understanding of scale-dependent patterns of species richness.