Adaptive dynamics is a mathematical theory that links

population dynamics to long-term evolution driven by

mutation and natural selection. It provides methods of

model formulation, methods of model analysis as well

as mathematical theorems that relate phenomena on

an evolutionary time scale to processes and structures

defined in ecological and population dynamical terms.

ECOLOGICAL TIME SCALE

The ecological time scale concerns the question which mutant phenotypes that are not yet present in a population of given resident phenotypes could invade if they were produced by a mutation, and what would be the outcome of such an invasion in terms of which phenotypes will remain in the population and which will be eliminated. These questions concern dynamics in a space of population densities of different phenotypes. In the course we focus on the population dynamics given by (systems of) ordinary differential equations.

EVOLUTIONARY TIME SCALE

The evolutionary time scale is about the long-term consequences of many successive ecological invasion-elimination events in terms of changes in the phenotypic composition of the population. The evolutionary time scale thus concerns dynamics in the space of all possible phenotypes. This dynamics is essentially non-deterministic (e.g., due to the random nature of the effect of a mutation on the phenotype) and is studied using difference inclusions, and in limiting case of infinitesimally small mutation steps, the Focker-Planck equation or the transport equation.

EXAMPLES

Examples are largely taken from recent publications in the scientific literature.

PERSPECTIVE

Adaptive dynamics is a new but rapidly developing theory that poses various interesting and mathematically challenging problems. From an applications point of view, a great strength of adaptive dynamics is its capability to model evolution in systems with complicated ecological interactions. Adaptive dynamics is being applied by a growing number of researchers both within mathematics and biology to a wide variety of concrete ecological-evolutionary problems.

REFERENCES

Adaptive dynamics is new, and there does not exist a comprehensive textbook on adaptive dynamics. For an extensive list of references to both theory and applications of adaptive dynamics in the scientific literature, see the website http://www.mv.helsinki.fi/home/kisdi/ad.htm

LECTURE NOTES

Lecture will be produced on the go as the course advances. Older lecture notes are available here https://wiki.helsinki.fi/display/mathstatKurssit/Adaptive+dynamics,+fall...

For older exercises and solutions see past AD courses on my home page https://wiki.helsinki.fi/display/mathstatHenkilokunta/Geritz,+Stefan

EXAMINATION

There will be no exam -- instead there will be project assignments. In the second half of the course, the project assignments take the place of the homework exercises. The lecturer or the assistant will be available for advise during the normal time and place of the exercise classes. A written report and a 15 minute in-class presentation of the report take the place of the exam, i.e., the grade is based on the report and the presentation. The presentations take place during the last week of the course.

PREREQUISITES

Basic knowledge of differential equations, probability theory and some skills in programming (preferably Mathematica or Maple).