Individual Versus Social Learning: Evolutionary Analysis in a Fluctuating Environment

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Abstract
A model for haploid asexual inheritance of social and individual learning is proposed. Animals of one genotype, individual learners (IL), behave optimally for the current environment and, except for a fixed cost due to learning errors, have the optimal fitness in that environment. Animals of the other genotype are social learners (SL) each ofwhom copies a random individual from the previous generation. However, the phenotype of a social learner depends on whom it copies. If it copies an IL or a correctly behaving SL, it has the ``correct'' phenogenotype, SLC. Otherwise, its behavior is maladaptive and we call its phenogenotype SLW. Different models for the environmental fluctuation produce different dynamics for the frequency of SL animals. An infinite state environment is such that when it changes, it never reverts to an earlier state. If it changes every generation, social learning can never succeed. If, however, a generation in which the environment changes is followed by l -1 generations of environmental stasis and $l greater than or equal to 3, some fitness sets do allow the maintenance of social learning. Analogous results are shown for a randomly fluctuating environment, and for cyclic two-state environments. In a second type of model, each animal can learn individually with probability L. We examine the evolutionary stability properties of this probability inthe infinite state environment. When a generation of change is followed by l-1 generations of stasis, fitness parameters can be found that produce an evolutionarily stable nonzero probability of social learning. In all of the models treated, the greater the probability of environmental change, the more difficult it is for social learning to evolve.
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