Ecological Archives A025-009-A3
Alexandre Robert, Stéphane Chantepie, Samuel Pavard, François Sarrazin, and Céline Teplitsky. 2015. Actuarial senescence can increase the risk of extinction of mammal populations. Ecological Applications 25:116–124. http://dx.doi.org/10.1890/14-0221.1
Appendix C. Relationship between the equilibrium number of adult individuals (K) and the maximal number of mating events (MEmax).
Carrying capacities (K) were expressed in terms of maximal number of mature individuals throughout the article. However, in stochastic models, regulation was mechanistically implemented using a maximal number of mating events (MEmax). Such limitation may result from either a limited number of reproduction sites or a critical density of individuals. We determined the relationship between MEmax and K through linear regressions. Preliminary analysis indicated that (1) the relationship between MEmax and K varies with the life cycle considered (the relationship was thus different between the 58 species considered and between the Senecence Model and Null Models for each species, we thus performed distinct regressions for each of these scenarios); (2) in all populations with λ>1, when including a maximal number of mating events (MEmax≤500), pseudo-equilibria were reached rapidly (less than 100 time steps in all cases). We thus considered a similar time horizon of 100 time steps to determine the relationship between MEmax and K for all populations.
In each case, 500 population trajectories were run for 20 values of MEmax randomly drawn from the interval [10, 500]. The average number of mature individuals (=K) obtained after 100 time steps was recorded. MEmax was linearly regressed over K for these 20 values and the slope and intercept of regression were used to quantify the relationship between MEmax and K. The operation was repeated for the 232 scenarios (58 species, with one Senescence and three alternative Null models for each species). The linearity of regressions was checked by adding a quadratic component and comparing it to the linear model. In all cases, the quadratic component did not significantly improve model fit and R² was >0.99 in the simple linear regression.
For life cycles (either Senescence or Null Models) for which λ<1, the relationship between MEmax and K was impossible to assess due to the absence of non-zero pseudo equilibrium. In these cases, we assumed a number of nests equal to x*K (where x was the median ratio MEmax/K obtained with life cycles for which λ>1).