Biodiversity and species interactions: extending Lotka–Volterra community theory

Wilson, William G.; Lundberg, Per; Vázquez, Diego P.; Shurin, Jonathan B.; Smith, Melinda D.; Langford, William T.; Gross, Katherine L.; Mittelbach, Gary G.

doi:10.1046/j.1461-0248.2003.00521.x

Cited by 74 publications

(80 citation statements)

References 38 publications

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“…Such situations can arise through community assembly as strongly interacting species combinations tend to be driven to extinction (Kokkoris et al. 2002; Wilson et al. 2003).…”

Section: Discussionmentioning

confidence: 99%

Diversity–stability relationship varies with latitude in zooplankton

Shurin¹,

Arnott²,

Hillebrand³

et al. 2007

Ecology Letters

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Analyses of temporal patterns of diversity across a wide range of taxa have found that more diverse communities often show smaller compositional changes over time. This generality indicates that high diversity is associated with greater temporal stability in species composition. We examined patterns of diversity and community stability in zooplankton time series data from 36 lakes sampled over a combined 483 years. The species-time relationship was flatter in more species-rich lakes in the temperate zone. However, high-latitude lakes had both low richness and low turnover. These patterns were consistent for turnover both within and among years. Daily, annual and long-term richness were all higher in large lakes while turnover was unaffected by the surface area. Richness on all time scales, as well as turnover within and among years, all declined at high latitude. Species-area relations and latitudinal gradients in richness therefore reflect different temporal components of diversity. Our results suggest that diversity shows strong associations with compositional stability that vary qualitatively across biogeographical provinces. Community stability increases with diversity among lakes in the temperate zone; however, the two are negatively correlated across latitudinal gradients. These patterns indicate that either the direct effects of diversity on stability or their covariance with environmental fluctuations vary with latitude.

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“…Such situations can arise through community assembly as strongly interacting species combinations tend to be driven to extinction (Kokkoris et al. 2002; Wilson et al. 2003).…”

Section: Discussionmentioning

confidence: 99%

Diversity–stability relationship varies with latitude in zooplankton

Shurin¹,

Arnott²,

Hillebrand³

et al. 2007

Ecology Letters

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“…The Lotka-Volterra approach to competition still forms the basis for most theoretical studies investigating community diversity and stability under environmental conditions or species compositions (for recent examples see Kokkoris et al 1999Kokkoris et al , 2002Lehman and Tilman 2000;Loreau 1998Loreau , 2004Rozdilsky and Stone 2001;Wilson et al 2003). In a recent study, for an artificial grassland system that one assumption of the Lotka-Volterra approach was showed, additivity of competitive effects, might not hold (Dormann and Roxburgh 2005).…”

Section: Competition and Community Stabilitymentioning

confidence: 99%

Competition hierarchy, transitivity and additivity: investigating the effect of fertilisation on plant–plant interactions using three common bryophytes

Dormann

2006

Plant Ecol

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The way competition structures plant communities has been investigated intensely over many decades. Dominance structures due to competitive hierarchies, with consequences for species richness, have not received as much experimental attention, since their manipulation is a large logistic undertaking. Here the data from a model system based on bryophytes are presented to investigate competition structure in a three-species system. Grown in monocultures, pairwise and three-species mixtures under no and high nitrogen supply, the three moss species responded strongly to treatment conditions. One of them suffered from nitrogen fertilisation and hence performed better in mixtures, where the dominant species provided physical shelter from apparently toxic nitrogen spray. Accordingly, no linear competitive hierarchy emerged and qualitative transitivity remains restricted to the unfertilised treatments. Faciliation also affected other properties of the competition structure. The reciprocity of competition effects could not be observed. Moreover, the performances in three-species mixtures were not well predictable from the knowledge of monocultures and pairwise mixtures because competitive effects were not additive. This had implications for community stability at equilibrium: all two-species systems were stable, both fertilised and unfertilised, while the three-species system was only stable when fertilised. This stability under fertilisation has probably to do with the facilitative effect of the two dominant species on the third. In this experiment, little support for commonly held ideas was found about the way competition in plant communities is structured. On the other hand, this study shows that moss communities are ideal model systems to test predictions of theoretical models concerning properties and consequences of competition in plant communities.

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“…From experiments we know that diversity is negatively affected by increased nutrient availability, but the exact mechanism is still obscure (Stevens andCarson 1999, Gough et al 2000). One valuable recent study has used the Lotka-Volterra equation system behind the community matrix to this end, but not CMT itself (Wilson et al 2003).…”

Section: Discussionmentioning

confidence: 99%

“…Nevertheless, these 'higher-order effects' (Case and Bender 1981) are emergent properties of the Lotka-Volterra equations, and are also implicitely included in the stability analysis presented here. While we may argue about the appropriateness of the Lotka-Volterra approach (Wilson et al 2003), higher-order interactions are no argument against this approach, and hence against the presented application of community matrix theory in plant ecology.…”

Section: Higher-order Effects Spatial Arrangement Zone Of Influencementioning

confidence: 99%

On community matrix theory in experimental plant ecology

Dormann

2008

Web Ecol.

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Abstract. In multi-species communities the stability of a system is difficult to assess from field observations. This is the case for example for competitive interactions in plant communities. If a mathematical model can be formulated that underlies the processes in the community, a community matrix can be constructed whose elements represent the effects of each species onto every other (and itself) at equilibrium. The most common competition model is the Lotka-Volterra equation set. It contains interspecific competition coefficients to represent the interactions between species. In plant community ecology several attempts have been made to quantify competitive interactions and to assemble a community matrix, so far with limited success. In this paper we discuss a method to use pairwise interaction coefficients from experimental plant communities to analyse feasibility and stability of multi-species sets. The approach is contrasted with that of Wilson and Roxburgh (1992) and is illustrated using data from Roxburgh and Wilson (2000a). Results from Wilson and from this study differ (some times substantially), with our approach being more pessimistic about stability and coexistence in plant communities.

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Biodiversity and species interactions: extending Lotka–Volterra community theory

Cited by 74 publications

References 38 publications

Diversity–stability relationship varies with latitude in zooplankton

Diversity–stability relationship varies with latitude in zooplankton

Competition hierarchy, transitivity and additivity: investigating the effect of fertilisation on plant–plant interactions using three common bryophytes

On community matrix theory in experimental plant ecology

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