Eco-evolutionary dynamics of living systems: Theory

Many real-world biological mechanisms can be properly represented mathematically only in terms of measure-valued processes. Drawing on recent mathematical developments, Evolution and Ecology Program (EEP) researchers have underpinned and extended classical methods to deal with such more realistic ecological situations.

In particular, scientists respectively underpinned models of the deterministic theory of physiologically structured populations and the adaptive dynamics describing clonal and one-locus Mendelian evolution [1] [2] [3].

Finally, after 25 years of successful use, it was proven that the so-called escalator boxcar train method for numerically solving physiologically structured population models has indeed the required convergence property [4] .

A number of efforts have extended the reach of the canonical equation of adaptive dynamics theory to function-valued traits [5], to complex interaction structures [6], to physiologically structured populations with multi-locus Mendelian genetics [7], and to research on  stochastically fluctuating environments [8]. 

Gratifyingly, in all these cases the extensions have kept the basic form of the equation intact, with only some terms having to be modified with scalar factors to account for the additional complexity.

In view of the current unprecedented expansion of model-based analyses, it is now imperative to derive high-level rules that capture the essentials of large classes of models in one go.

In this spirit, it was shown how a concept of individual focusing on relations used in modeling instead of on ontological perceptions, can aid in spotting simple mathematical relationships in complicated ecological and evolutionary models [9].

Scientists derived the necessary and sufficient conditions under which life-cycle graphs allow simple interpretable expressions for the average number of offspring an individual produces over its lifetime [10]. Such expressions were used to elucidate what the structure of an organism’s life-cycle graph can already tell its life-history evolution [11].

To better understand limitations on the adaptability of ecological traits, researchers examined how mechanical constraints affect spine evolution [12]. Finally, it was shown how size-dependent energy acquisition, biomass production, and mortality rates, lie at the heart of various population dynamical and community dynamical phenomena [13].

One of the key features of adaptive dynamics theory is that it is the only theoretical framework that on its own, i.e., without invoking additional ad hoc hypotheses, predicts the generation of biological diversity.

Simple rules for predicting such generation in evolutionary models allowing for finite mutational steps were developed [14]. It was also elucidated how patterns of diversity arising under competitive interactions depend on the shape of the underlying competition functions [15] (Figure 1).

Figure 1. Example of an innovative mathematical analysis elucidating biodiversity patterns. In ecology, competition functions (orange) describe how the intensity of competition among individuals changes with their spatial or phenotypic distance (along the horizontal axis). Understanding how the Fourier transform (red) of such a function affects the resultant fitness landscape (green) enables predicting that clustered populations and/or multiple species (blue) arise if the Fourier transform has a negative minimum, with the wavelength at this minimum determining the inter-cluster gap.

A study eased the access to adaptive dynamics theory for a larger public by summarizing its essential features and reviewing its relationship with related frameworks, illustrated through didactically chosen examples [16].

Last edited: 22 May 2014