Apart from being based on Continuously Stable Strategies, the theory of Malthusian Relativity is based also on a concept of long-term evolution, where evolutionary equilibria are independent of short-term constraints. In A General Theory of Evolution this concept is referred to as all-dimensional optima because it aims at predictions where the life history traits (dimensions) and their covariance follow from the selection process of the model instead of being given as the assumptions of the model. The challenge with this concept is to construct life-history models where the relationships among the different traits reflect only true constraints that cannot be altered by natural selection, i.e., constraints that are evolutionarily fixed because they arise from laws that lie outside the domain of evolutionary biology. In the approach taken it is assumed that the different life-history traits evolve independently of each other unless we have a non-biological law that clearly explains why the different traits should trade-off against one another.

At the level intrinsic to the individual the long-term constraints are defined by physical laws, like those of energetic constraints. The intrinsic components of genetics and phylogeny, on the other hand, tend only to constrain short-term evolution. This is because these components are products of natural selection and, thus, they may be unstable on the longer time-scale. At the level of ecological constraints extrinsic to the individual the long-term constraints tend also to be given by laws of physics. But there are important exceptions that arise from the biological constraints associated with the origin of natural selection.

The origin of natural selection is usually considered to be define by the origin of self-replicators (Michod, 1999; but see Lifson and Lifson, 1999). Self-replicators are also referred to as exponential replicators because the self-replicating process generates an exponential increase in the abundance of self-replicating individuals. And in a limited world it follows that exponential increase induces competition among the individual self-replicators for the limited resources. Thus, through the process of density dependent competition, the origin of self-replication defines the origin of density regulation and density regulated population growth.

Density regulation can arise from exploitative and interactive (interference) competition, also referred to as scramble and contest competition respectively. The density regulation of exploitative competition is the reduction in the per capita share of resource that occurs when the population is increasing, assuming that there are no interactions among individuals. The density regulation of interactive competition arises instead from competitive interactions, where the time and energy that an individual spends interacting with other individuals is an increasing function of the number of individuals in the population. Another essential component of interactive competition is that it causes a bias in resource access in favour the individuals with the highest interactive qualityI have earlier used the term competitive quality but this term is ambiguous because it can also be understood in terms of exploitative competition, i.e., in favour of the individuals that are best at dominating other individuals. Malthusian Relativity deals primarily with the long-term evolutionary transitions to be expected when the component of interactive competition is added to the density dependent environment.

The case with no interactive competition is dealt with by the classical life-history theory (reviewed by Roff, 1992; Stearns, 1992; Charnov, 1993; Bulmer, 1994; Charlesworth, 1994). However, the classical theory is not directly comparable with Malthusian Relativity because the classical models were also developed to deal with short-term evolution. This is generally done by partitioning the life-history traits into two groups that may be referred to as respectively the fundamental and the derived traits. It is then assumed that the derived traits evolve from the short-term constraints of the fundamental traits, with short-term constraints being defined, e.g., by genetic covariance and phylogeny. In this way it is possible to use the optimisation approach of r- and k-selection to predict complex life histories from the assumptions of short-term constraints.

But on the scale of long-term evolution, where the essential constraints are those that cannot be altered by natural selection, the predictions of most classical models collapse to that of simple self-replicating entities (Witting, 1997). The life history collapses because the traits to be explained trade-off against the classical definition of fitness and, thus, these traits cannot be maintained on the longer time-scale where there are no local constraints to prevent evolution toward the long-term optimum. If instead the evolutionary equilibria are given by Continuously Stable Strategies the theory of Malthusian Relativity has shown that the density dependent constraints of interactive competition can select for complex life histories that are stable also on the time-scale of long-term evolution.

References

• Bulmer, M. (1994). Theoretical evolutionary ecology. Massachusetts: Sinauer Associates Publishers.
• 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.
• Lifson, S. & Lifson, H. (1999). A model of prebiotic replication: Survival of the fittest versus extinction of the unfittest. Journal of Theoretical Biology 199, 425--433.
• Michod, R. E. (1999). Darwinian dynamics. Evolutionary transitions in fitness and individuality. Princeton: Princeton University Press.
• Roff, D. A. (1992). The evolution of life histories. Theory and analysis. New York: University of Chicago Press.
• Stearns, S. C. (1992). The evolution of life histories. Oxford: Oxford University Press.
• 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.