Malthusian Relativityι**=7/3ψ
Population dynamics - the evolutionary extension

Sustainable exploitation

Include density dependent selection in models on the sustainable use of natural resources

Fig. 1 Population dynamic functions for baleen whales. Left: Density regulation, with the relative growth rate r/r(max) as a function of the abundance relative to the equilibrium abundance. The space between the two curves contains the best density regulated models, and the different species are shown by different symbols. Right: Selection-delayed dynamics following a population dynamic perturbation; the relative growth rates of increasing whale populations as a function of the minimum abundance imposed by commercial whaling in past centuries. The space between the two curves contains the best selection-delayed models, and the different species are shown by different symbols. Open diamond: bowhead whale; Filled diamond: gray whale; Open circle: southern right whale; Filled circle: North Atlantic right whale; Open square: fin whale; Filled square: blue whale; Star: humpback whale. From Witting (2013).

While density regulation is being identified in an increasing number of species, there are almost no studies that examine whether the growth rates of natural species are determined primarily by density regulation per se or by a selection-delayed acceleration. Such comparisons are essential because direct density regulation occurs also in selection-delayed dynamics, so observations of density regulation do not exclude selection-delayed dynamics.

There is however one comparison that found that the population dynamic growth rates of seven species of baleen whales are outside the expected range for density regulated growth (Fig. 1, left; Witting, 2013). The right plot in Fig. 1 shows instead that the growth rates for the majority of these species behave as predicted by selection-delayed dynamics.

Relating to species with continued harvest or predation, there are plenty of evidence that shows that populations with increased anthropogenic or natural mortality evolve lower body masses and increased reproduction (e.g., Reznick et al., 1996; Haugen and Vøllestad, 2001; Sinclair et al., 2002; Coltman et al., 2003; Carlson et al., 2007; Herczeg et al., 2009; Rossetto et al., 2012). These responses are consistent with selection by density dependent interactive competition in depleted populations, but some of the response may also reflect direct harvest selection from a fishery that takes predominately the larger individuals (e.g., Browman, 2000; Sinclair et al., 2002; Olsen et al., 2004). This difference between direct and indirect harvest selection has been examined in pike (Carlson et al., 2007; Edeline et al., 2007), but it has not yet been quantified on a larger scale.


  • Browman, H.I. 2000. Theme Section on `Evolution' of fisheries science.. Marine Ecology Progress Series 208:299--313.
  • Carlson, S.M., E.Edeline, A.L. Vollestad, T.O. Haugen, I.J. Winfield, J.M. Fletcher, J.BenJames and N.C. Stenseth 2007. Four decades of opposing natural and human-induced artificial selection acting on Windermere pike ( Esox lucius). Ecology Letters 10:512--521.
  • 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.
  • llestad, 2001Haugen:Vollestad:2001Haugen, T.O., and L.A. Vøllestad 2001. A century of life-history evolution in grayling. Genetica 112:475--491.
  • Herczeg, G., A.Gonda and J.Merila 2009. Evolution of gigantism in nine-spined sticklebacks. Evolution 63:3190--3200.
  • 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., 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.
  • Rossetto, M., G.DeLeo, D.Bevacqua and F.Micheli 2012. Allometric scaling of mortality rates with body mass in abalones. Oecologia 168:989--996.
  • 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. Canadian Journal of Fisheries and Aquatic Sciences 59:372--382.
  • Witting, L. 2013. Selection-delayed population dynamics in baleen whales and beyond. Population Ecology 55:377--401.