m.r.Life ι**=7/3ψ

Sustainable exploitation

Population dynamic feed-back selection changes the life history of a species when the population is exploited. This implies that there is no curve of sustainable yield to define an optimum of maximal harvest.

Fig. 1 Left: Density regulation: The relative growth rate r/r(max) declines monotonically with abundance (relative abundance is N/N*). Right: Selection-regulated dynamics: The relative growth rate of an increasing population when it crosses the equilibrium abundance is positively related to the magnitude of the perturbation (the perturbation from equilibrium abundance N* is given as relative abundance N/N*).

Theory on sustainable use arose from ecological concepts that did not consider the importance of evolutionary dynamics; let it be on the shorter timescale of population dynamic perturbations, or on the longer that relates to changes in equilibrium conditions when a rather stable sustainable harvest have persisted for decades or centuries.

Relating to shorter timescales, the density regulated model introduced the concept of recruitment curves (Beverton and Holt, 1957). For constant factors extrinsic to the population, density regulation imposes a monotonic decline in the population dynamic growth rate with density (Fig. 1, left), and this translates into the recruitment curve (Fig. 2, left) that defines a maximum sustainable harvest as a function of abundance.

The growth rate and the potential sustainable harvest is no longer pre-specified by the environment when population dynamics and evolutionary processes operate on similar timescales. For selection-regulated dynamics it is no longer the exponential growth rate, but only the acceleration of the growth rate, that can be determined by the density dependent environment. This implies that a population can have a large, if not infinite, number of growth rates, often with opposite signs, associated with the same environmental conditions. In result, there is no single curve of sustainable yield to define an optimum of maximal harvest (Witting, 2002). The actual growth rate and replacement yield is instead influenced by initial conditions like density independent perturbations, where the larger growth rates follow from the largest perturbations (Fig. 1, right; Witting, 2000, 2013).

Fig. 2 Left: Density regulation: The recruitment curve defines the sustainable harvest for density regulation, with the vertical line indicating the maximum sustainable yield. Right: Selection-regulated dynamics: Increased harvest selects for increase reproduction and an associated increase in the recruitment curve for individuals; illustrated here by three curves that represent three harvest levels that are defined by the slopes of the dotted lines.

On the longer timescale, the traditional view implies that you may aim for an optimal harvest where the population is stabilised close to the abundance of the maximum sustainable yield (Fig. 2, left). With a stabilised population under selection-regulated dynamics, an increased harvest implies selection for increased reproduction, with an associated increase in the potential growth rate and in the recruitment curve of sustainable takes (Fig. 2, right; Witting, 2002). Given sufficient time with constant harvest, selection should stabilise at the equilibrium abundance at the competitive interaction fix-point. This equilibrium abundance of the exploited population should be rather similar to the abundance of the unexploited population; with the major difference being that increased harvest imposes an evolutionary decline in competitive traits like body mass. At the theoretical limit, there seems to be almost no upper limit to the long-term sustainable harvest of individuals, but there is an upper limit to the sustainable harvest of biomass (Witting, 2002).

Download publications

Population Ecology 55:377-401 (2013)Download

Selection-delayed population dynamics in baleen whales and beyond

The Journal of Cetacean Research and Management 5:45-54 (2003)Download

Reconstructing the population dynamics of eastern Pacific gray whales over the past 150 to 400 years

Ecological Modelling 157:51-68 (2002)Download

Evolutionary dynamics of exploited populations selected by density dependent competitive interactions

Peregrine Publisher, Aarhus (1997)Download

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


  • Witting, L. 2000. Population cycles caused by selection by density dependent competitive interactions. Bulletin of Mathematical Biology 62:1109--1136, https://doi.org/10.1006/bulm.2000.0200.
  • Witting, L. 2002. Evolutionary dynamics of exploited populations selected by density dependent competitive interactions. Ecological Modelling 157:51--68, https://doi.org/10.1016/S0304--3800(02)00172--2.
  • Witting, L. 2013. Selection-delayed population dynamics in baleen whales and beyond. Population Ecology 55:377--401, https://dx.doi.org/10.1007/s10144--013--0370--9.