Eco-evolutionary dynamics of living systems: Theory

As a contribution to the theory of structured population models, a rigorous proof was constructed of the convergence of individual-based stochastic population models with deterministically changing individual states to the integral-equation models that provide the main toolbox for their practical analysis (Metz and Tran, 2013). Continuing EEP’s earlier foundational efforts in adaptive dynamics theory, several contributions were made to the underpinning and extension of the adaptive-dynamics toolbox.

1. The biological justifications of the assumptions underlying this toolbox were systematically reviewed (Metz, 2012).
2. It was investigated how generalized concepts of the individual can provide quick routes for deriving insights from seemingly complicated models (Metz, 2013).
3. A flexible approximation was derived for the invasion probability of incremental mutants in fluctuating environments, one of the essential ingredients in the canonical equation (CE) of adaptive dynamics theory (Ripa and Dieckmann, 2013).
4. The first rigorous proof was given of the convergence to the CE for Mendelian diploids (Collet et al., 2012).
5. The extension of the CE to function-valued traits and the corresponding calculation of evolutionary endpoints using Pontryagin’s maximum principle from control theory were explored (Parvinen et al., 2013).
6. A method was derived to calculate the CE’s selection gradient from fitness-return arguments commonly used by biologists, which also established a new theoretical link between these arguments and the so-called co-states involved in Pontryagin’s maximum principle (Metz and Johansson, submitted).
7. Within the realm of monomorphic adaptive dynamics, it was analyzed to what extent and how the adaptive dynamics of complicated life histories depends on properties of their life-cycle graphs (Rueffler et al., 2013).
8. Necessary and sufficient conditions were derived for when lifetime offspring numbers, and hence fitness, can be calculated as simple sums over the contributions of a life-cycle graph’s fertility loops (Rueffler and Metz, 2013).

To establish an objective basis for the integrative comparison of selection pressures and of the benefits of potential management interventions across traits, populations, and species, the utilities of alternative methods for standardizing empirically determined selection gradients were compared, with the mean standardized gradient, also called fitness elasticity, coming out as the clear winner (Matsumura et al., 2012; Figure 6 ).

Last edited: 31 October 2013