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Types of selection. Cyclical environment. Environmental state 1 (summer). Environmental state 2 (winter). Directional. Stabilizing. Disruptive. Interaction between species. Host-parasite case. Mutualistic case. constant fertility selection. Simulation. Frequency depended selection.
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Types of selection Cyclical environment Environmental state 1 (summer) Environmental state 2 (winter) Directional Stabilizing Disruptive Interaction between species Host-parasite case Mutualistic case
Frequency depended selection Simple lest case of frequency dependence: haploid selection
Mean fitness is not maximize at this is stable le point Simulation
Diploid frequency-dependent selection Simulation
In 1976 Sir Robert May, then a professor of biology at Princeton, pointed out that the logistic map led to chaotic dynamics. The logistic mapping g is defined by xn+1 = g(xn) = rxn(1 - xn).
What is deterministic chaos? Lyapunov's exponents: Chaotic divergence of the trajectories, started in closed points Non-chaotic
Lorenz Attractor Tamari Attractor
Chaos in Weather Chaos in Weather
Fractals reproducing realistic shapes, such as mountains, clouds, or plants, can be generated by the iteration of one or more affine transformations. An affine transformation is a recursive transformation of the type • Each affine transformation will generally yield a new attractor in the final image. The form of the attractor is given through the choice of the coefficients a, b, c, d, e, and f, which uniquely determine the affine transformation. To get a desire shape, the collage of several attractors may be used (i.e. several affine transformations). This method is referred to as an Iterated Function System (IFS). • An example of an iterated function system is the black spleenwort fern. It is constructed through the use of four affine transformations (with weighted probabilities):
Inbreeding • Non-random mating (between related individuals) • Leads to correlation between genotypes of mates • Frequencies are no longer products of allele frequencies • Leads to reduction in heterozygosity (measured by F) • Can rederive evolutionary equations using these new genotype frequencies AA Aa aa p2 + pqF 2pq - 2pqF q2 + pqF