m.r.Life ι**=7/3ψ

Reproductive rate

The natural selection of competitive interaction fix-points balance reproductive rates against mortality

The population dynamic feed-back of interactive competition is selecting a reproductive rate that is exactly so high that it produces an equilibrium abundance that generates the level of interference of the competitive interaction fix-point.

To deduce this we have e.g. the competitive interaction fix-point for a body mass in evolutionary equilibrium

ι** = 1 / ψ

This level of interference is also a function of the population density (N), approximated here as ι = γι ln N where γι is the density dependence parameter. The fix-point is thus defining the evolution of an equilibrium abundance

N** = exp(ι**ι)

This equilibrium is defined also by density regulation, described for example by the discrete growth rate (λ) that is regulated from its maximum value of λm = pRm down to one λ = 1 = pRmN* -γ at the population dynamic equilibrium (*) [Rm is maximal lifetime reproduction, p the probability to survive to reproduce, and γ the parameter of density regulation]. For the chosen formulation, density regulation defines N* = (pRm)1/γ, and combined with the abundance of the evolutionary equilibrium we find that the competitive interaction fix-point constrains lifetime reproduction to

Rm** = exp(ι**γ/γι)/p

Lifetime reproduction is thus expected to be inversely related to the probability to survive to reproductive. And as this probability was predicted to be body mass invariant in the sections on inter-specific allometries, we expect a body mass invariant lifetime reproduction.


The probability to survive to reproduce is independent of body mass across 114 bird species (Fig. 1, left), and lifetime reproduction is body mass invariant across 221 species (middle).

And maximal yearly reproduction is inversely related to time-scaled survival (Ry ∝ 1/Tp) across 132 species of birds (Fig. 1, right), indicating a maximal lifetime reproduction that is inversely related to the probability to survive and reproduce [as RyT ∝ Rm ∝ 1/p].

There is also plenty of evidence that shows that populations with increased levels of anthropogenic or natural mortality evolve increased reproductive rates (e.g., Reznick and Bryga, 1987; Reznick et al., 1996; Broman, 2000; Sinclair et al., 2002; Coltman et al., 2003; Olsen et al., 2004; Edeline and Carlson, 2007).

Fig. 1 The body mass (w) dependence for (left) the probability to survive to reproduce (p) and (middle) maximal lifetime reproduction (Rm) across 114 and 221 species of bird. For 132 bird species, the right plot shows maximal yearly reproduction as a function of time-scaled survival (Tp, where T is the age of maturity). p is estimated as yearly survival raised to the power of the age of maturity. From Witting (1997).

Download publications

Biological Reviews 83:259-294 (2008)Download

Inevitable evolution: back to The Origin and beyond the 20th Century paradigm of contingent evolution by historical natural selection

Journal of Theoretical Biology 225:389-406 (2003)Download

Major life-history transitions by deterministic directional natural selection

Peregrine Publisher, Aarhus (1997)Download

A general theory of evolution. By means of selection by density dependent competitive interactions.


  • Browman, H.I. 2000. Theme Section on `Evolution' of fisheries science.. εm Marine Ecology Progress Series 208:299--313.
  • Coltman, D.W., P.O'donoghue, J.T. Jorgenson, J.T. Hogg, C.Strobeck and M.Festa-Bianchet 2003. Undesirable evolutionary consequences of trophy hunting. Nature 426:655--658.
  • Edeline, E., S.M. Carlson, L.C. Stige, I.J. Winfield, J.M. Fletcher, J.B. James, T.O. Haugen, L.A. Vøllestad and N.C. Stenseth 2007. Trait changes in a harvested population are driven by a dynamic tug-of-war between natural and harvest selection. Proceedings of the National Academy of Sciences of the USA 104:15799--15804.
  • Olsen, E.M., M.Heino, G.R. Lilly, M.J. Morgan, J.Brattey, B.Ernande and U.Dieckmann 2004. Maturation trends indicative of rapid evolution preceded the collapse of northern cod. Nature 428:932--935.
  • Reznick, D.N., and H.Bryga 1987. Life-history evolution in guppies. 1. Phenotypic and genotypic changes in an introduction experiment. εm Evolution 41:1370--1385.
  • Reznick, D.N., I.M.J. Butler, F.H. Rodd and P.Ross 1996. Life-history evolution in guppies (Poecilia reticulata) 6. Differential mortality as a mechanism for natural selection. Evolution 50:1651--1660.
  • Sinclair, A.F., D.P. Swain and J.M. Hanson 2002. Disentangling the effects of size-selective mortality, density, and temperature on length-at-age. εm Canadian Journal of Fisheries and Aquatic Sciences 59:372--382.
  • Witting, L. 1997. A general theory of evolution. By means of selection by density dependent competitive interactions. Peregrine Publisher, Århus, 330 pp, URL https://mrLife.org.