Analysis of Evolutionary Processes: The Adaptive Dynamics Approach and Its Applications.2008
The aim of this book is to present Adaptive Dynamics (AD), a quantitative approach
for the study of evolutionary processes that has recently received a great deal of
attention.
Traditionally, the effects of demographic and evolutionary changes have been
considered separately. This is due to the fact that mutations are typically rare
events,..... However, the real
dynamics of populations integrate both demographic and evolutionary changes.
Thus, demographic and evolutionary dy-
namics are entangled in a feedback loop,
AD explicitly takes into account the coupling between demography and evo-
lution, describes the process of selection by means of deterministic demographic
models, and stochastically characterizes the occurrence of mutations. By separat-
ing the demographic and evolutionary timescales, i.e., by looking at the limit case
of extremely rare and small mutations, AD derives a deterministic approximation
of the evolutionary dynamics of adaptive traits, in terms of an ordinary differen-
tial equation defined on the evolutionary timescale: the AD canonical equation
(Dieckmann and Law, 1996). Such an equation is typically nonlinear, so that, in
accordance with the theory of nonlinear dynamical systems, one can in principle
expect evolutionary dynamics to be characterized by several long-term evolutionary
regimes, reached, in the long run, from different ancestral conditions. Moreover,
long-term evolutionary regimes can be stationary (evolutionary equilibria), as well
as nonstationary (periodic or even more complex chaotic evolutionary regimes),
and this formally supports the so-called Red Queen hypothesis proposed by Van
Valen (1973), which suggests that evolutionary processes have the potential to sus-
tain never-ending evolutionary change.
The timescale separation argument also allows AD to describe the evolution of
diversity in the community. Diversity, abstractly measured by the number of co-
evolving groups of identical individuals, can change due to mechanisms that are
exogenous to the community, like immigrations of new forms of individuals or the
accidental extinction of resident groups. However, evolutionary change is endoge-
nously responsible of the evolution of diversity.
Until now AD has been applied in population biology. However, there are many
other areas, in particular in social sciences, economics, and engineering, to which
AD could virtually be applied. In fact, natural or artificial systems can often be
modeled as composed of agents or units that compete on a short-term (demo-
graphic) timescale, in accordance with their characteristic features, and transmit
such features to agents or units of the next generation. If agent or units with in-
novative features occasionally appear in the system, the long-term (evolutionary)
dynamics of the characteristic features are driven by an innovation-competition
process that can be studied through the AD canonical equation.
In the first chapter we give an overview of evolutionary processes with emphasis
on evolutionary biology.
In the second chapter we survey the main quantitative approaches to evolutionary dynamics. We identify seven approaches (population genetics,
individual-based evolutionary models,
quantitative genetics,
evolutionary game theory,
replicator dynamics,
fitness landscapes, and AD)
and point out some of their advantages and limitations. Thus, Chapter 2 should be viewed as a rudimentary introduction to the model-based approaches to evolutionary dynamics.
By contrast, Chapter 3 is the key chapter of the book. There we sketch all the
steps that lead to the formal derivation of the AD canonical equation and discuss
the mechanisms of evolutionary branching and extinction
All remaining chapters are twofold. Each of them introduces a new feature of
evolutionary dynamics viewed through the lenses of AD, but at the same time deals
with a particular application that is of interest per se.
Chapter 4. Evolutionary Branching and the Origin of Diversity
A Market Model and Its AD Canonical Equation
Chapter 5. Multiple Attractors and Cyclic Evolutionary Regimes
A Model of Resource-Consumer Coevolution
Chapter 6. Catastrophes of Evolutionary Regimes
A Model for the Evolution of Cooperation
Catastrophic Disappearance of Evolutionary Attractors
Evolutionary Branching and the Origin of Cheaters\
Chapter 7. Branching-Extinction Evolutionary Cycles 172
A Model of Cannibalistic Demographic Interactions
Coevolution of Dwarfs and Giants
The Branching-Extinction Evolutionary Cycle
Chapter 8. Demographic Bistability and Evolutionary Reversals
Asymmetric Competition and the Occurrence of Evolutionary Reversals
Slow-Fast Approximation of the AD Canonical Equation
Chapter 9. Slow-Fast Populations Dynamics and Evolutionary Ridges
The AD Canonical Equation for General Demographic Attractors
Evolutionary Sliding and Pseudo-equilibria
Chapter 10. The First Example of Evolutionary Chaos
A Tritrophic Food Chain Model and Its AD Canonical Equation
The Chaotic Evolutionary Attractor
Feigenbaum Cascade of Period-doubling Bifurcations
