Malthusian Relativity deals primarily with the evolution of the average life history in populations with asexual, or sexually interbreeding, mobile individuals. In the classical life-history models reviewed by Roff (1992) , Stearns (1992) , Charnov (1993) , Bulmer (1994) and Charlesworth (1994) the optimisation process of natural selection is usually given by density independent r-selection or by density dependent r- and k-selection (reviewed by Mueller, 1997). The basic idea of r- and k-selection was first considered by Fisher (1930) when he proposed the fundamental theorem of natural selection (see Witting, 2000a). But the concept was formally proposed by MacArthur (1962) and MacArthur and Wilson (1967) , and developed theoretically by others (Anderson, 1971; Charlesworth, 1971, 1994; Roughgarden, 1971; Clarke, 1972). The process of r- and k-selection operates through an increase in the intrinsic population dynamic growth rate, which induces an increase in the population dynamic growth rate (r) and/or in the carrying capacity (k).

r- and k-selection is appropriate when the relative fitnesses among the different variants are constant at a given population density. When instead the relative fitnesses are frequency dependent the optimisation process of natural selection is better described by the game theoretical concepts of Evolutionary Stable Strategies (Maynard Smith and Price, 1973; Maynard Smith, 1982) and Continuously Stable Strategies (Eshel and Motro, 1981; Eshel, 1983).

The Evolutionary Stable Strategy (ESS) was defined as the strategy that, once almost fixed in the population, will be advantageous over any other mutant strategy present in a sufficiently low frequency. This concept does not consider the chances by which a population that is not situated at the ESS will evolve toward the ESS. To address the latter question Taylor (1988) and Christiansen (1991) considered the alternative requirement of Convergence Stability. This is the requirement that a small perturbation of the entire population away from the ESS will end up with selective advantage to mutations that carry the population back to the ESS. A strategy that satisfies both the requirements of the Evolutionary Stable Strategy and Convergence Stability was defined as the Continuously Stable Strategy (CSS) by Eshel and Motro (1981) . In the original version proposed by Witting (1997) , the theory of Malthusian Relativity was based on the concept of Convergence Stability. Today, the theory applies the optimisation concept Continuously Stable Strategies to a multi-dimensional life history of continuous traits.

References

• Anderson, W. W. (1971). Genetic equilibrium and population growth under den-ty-regulated selection. The American Naturalist 105, 489--498.
• Bulmer, M. (1994). Theoretical evolutionary ecology. Massachusetts: Sinauer Associates Publishers.
• Charlesworth, B. (1971). Selection in density-regulated populations. Ecology 52, 469--474.
• Charlesworth, B. (1994). Evolution in age-structured populations. 2nd edn. Cambridge: Cambridge University Press.
• Charnov, E. L. (1993). Life history invariants. Some explorations of symmetry in evolutionary ecology. New York: Oxford University Press.
• Christiansen, F. B. (1991). On conditions for evolutionary stability for a continuously varying character. The American Naturalist 138, 37--50.
• Clarke, B. (1972). Density-dependent selection. The American Naturalist 106, 1--13.
• Eshel, I. (1983). Evolutionary and continuous stability. Journal of Theoretical Biology 103, 99--111.
• Eshel, I. & Motro, U. (1981). Kin selection and strong evolutionary stability of mutual help. Theoretical Population Biology 19, 420--433.
• Fisher, R. A. (1930). The genetical theory of natural selection. Oxford: Clarendon.
• MacArthur, R. H. (1962). Some generalized theorems of natural selection. Procedings of the National Academy of Sciences of the USA 46, 1893--1897.
• MacArthur, R. H. & Wilson, E. O. (1967). The theory of island biogeography. Princeton: Princeton University Press.
• Maynard Smith, J. (1982). Evolution and the theory of games. Cambridge: Cambridge University Press.
• Maynard Smith, J. & Price, G. R. (1973). The logic of animal conflict. Nature 246, 15--18.
• Mueller, L. D. (1997). Theoretical and empirical examination of density-dependent selection. Annual Review of Ecology and Systematics 28, 269--288.
• Roff, D. A. (1992). The evolution of life histories. Theory and analysis. New York: University of Chicago Press.
• Roughgarden, J. (1971). Density-dependent natural selection. Ecology 5, 453--468.
• Stearns, S. C. (1992). The evolution of life histories. Oxford: Oxford University Press.
• Taylor, P. D. (1988). Inclusive fitness models with two sexes. Theoretical Population Biology 34, 145--168.
• Witting, L. (1997). A general theory of evolution. By means of selection by density dependent competitive interactions. URL http://www.peregrine.dk, Århus, 330 pp: Peregrine Publisher.
• Witting, L. (2000). Interference competition set limits to the fundamental theorem of natural selection. Acta Biotheoretica 48, 107--120.