**Lecture notes**
**Adaptation: Optimal models for predicting adaptive strategies**
**I. Aims and assumptions of optimal models**
A. Aim: to find which of two or more phenotypes (or some tradeoff between the two) would be optimal in terms of individual fitness B. Major assumptions of all optimal models: 1. There is heritable variation for a trait, but the details of inheritance (i.e., the genetics) are ignored 2. Populations are treated as asexually reproducing 3. The models are based on game theory, developed to arrive at best solutions; however, natural selection arrives at the most easily attainable solution, which may not be the best according to a priori design considerations (see previous examples) **II. Frequency-independent models**
A. Major assumption (in addition to those listed above): The optimal strategy is not dependent on the frequency of the trait in the population (e.g., an optimal feeding strategy is not dependent on how other members of the population feed, as in the case where a particular food supply is infinitely ample) B. Construction of the model: The optimal strategy is the one that maximizes the benefit (via fitness) of a strategy in relation to the cost of carrying out the strategy (e.g., a diet that maximizes caloric intake relative to the caloric cost of collecting and handling the food) C. Sample prediction of the model: If an optimum type of food is sufficiently abundant, the optimum strategy is to specialize on the type of food that yields the most calories per cost (energy spent collecting and handling the food); specialization in this case only arises from the quality and abundance of a food source, not from competition (one result of which might be (divergent) specialization on different resources) **II. ** **Frequency-dependent models**
A. Major assumption (in addition to those listed in I.A.2.): Fitness (*w*_{i}) contributed by a trait (such as a strategy), *i*, is determined by pairwise interactions among individuals that have trait *i* or an alternative trait (or strategy) *j*: *w*_{i} = *w*_{0} + [*p E*_{ii}] + [*q E*_{ij}] ,
where *p* and *q* are the frequencies of individuals in a population with traits *i* and *j* (note that *q* = 1 - *p* if *i* and *j* are the only alternatives),
*w*_{0} is the fitness of an individual in the absence of any interaction,
*E*_{ii} is the change in fitness to an individual expressing trait *i* when he/she interacts with another individual also carrying trait *i*, and
*E*_{ij} is the change in fitness to an *i* individual due to an interaction with a *j* individual. B. Construction of the model for particular situations is performed by making a "payoff matrix" that presents relative benefits to particular phenotypes due to particular interactions: |