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. 2008:2008:654672.
doi: 10.1155/2008/654672. Epub 2008 Dec 11.

Roots of diversity relations

Peter Würtz  1 , Arto Annila
Affiliations

Roots of diversity relations

Peter Würtz et al. J Biophys. 2008.

Abstract

The species-area relationship is one of the central generalizations in ecology; however, its origin has remained a puzzle. Since ecosystems are understood as energy transduction systems, the regularities in species richness are considered to result from ubiquitous imperatives in energy transduction. From a thermodynamic point of view, organisms are transduction mechanisms that distribute an influx of energy down along the steepest gradients to the ecosystem's diverse repositories of chemical energy, that is, populations of species. Transduction machineries, that is, ecosystems assembled from numerous species, may emerge and evolve toward high efficiency on large areas that hold more matter than small ones. This results in the well-known logistic-like relationship between the area and the number of species. The species-area relationship is understood, in terms of thermodynamics, to be the skewed cumulative curve of chemical energy distribution that is commonly known as the species-abundance relationship.

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Figures

Figure 1
Figure 1
Schematic distribution of chemical energy in a simple model ecosystem is described by an energy level diagram. The governing thermodynamic principle is exemplified by considering only one type of base constituents (atoms), but the result has been generalized for diverse base constituents [35]. The number of individuals at trophic level j makes a population N j. The corresponding density-in-energy N jexp (G j/RT) amounts from the number of base constituents n j = jN j that are needed to assemble the population and from the invested energy G j. For a species at a level j in the food web many atoms and much energy are needed to propel its growth and to maintain it in the mature state. Species are equipped with mechanisms to generate these vital flows of energy by numerous reactions (arrows) that absorb high-energy or emit low-energy quanta (wavy arrows). Systems on larger areas, hence having access to more base constituents N = ∑n j, will evolve to larger and more effective energy transduction machineries comprising more species. Coloring emphasizes that species differ from each other by their energy transduction properties, that is, phenotypes.
Figure 2
Figure 2
Species (s) versus area (A) relationship (black) is a cumulative curve of nonequilibrium stationary-state distribution of chemical energy in an ecosystem. The total amount of base constituents N in the system is taken proportional to the area A. The cumulative curve follows mostly the power law (green) but at large areas the logistic form (blue) accounts better for the statistical series. The units on axes depend on the energetics given by γ, units of measurements, and proportionality constants.
Figure 3
Figure 3
Distribution of chemical energy among diverse chemical repositories j, that is, species according to (6). The probability density P(j) of species-area curve is characteristically skewed toward rarity at high-energy trophic levels j. The integral of P(j) sums up all matter that is distributed among populations of all species s in an ecosystem. When the total matter is taken proportional to the area A, the species-area relationship is obtained as the cumulative curve.
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