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Many evolutionary biologists collect genetic data from natural populations and then need to investigate the relationship among these populations to compare different biogeographic hypotheses. MIGRATE, a useful tool for exploring relationships between populations and comparing hypotheses, has existed since 1998. Throughout the years, it has steadily improved in both the quality of algorithms used and in the efficiency of carrying out those calculations, thus allowing for a larger number of loci to be evaluated. This efficiency has been enhanced, as MIGRATE has been developed to perform many of its calculations concurrently when running on a computer cluster. The program is based on the coalescence theory and uses Bayesian inference to estimate posterior probability densities of all the parameters of a user‐specified population model. Complex models, which include migration and colonization parameters, can be specified. These models can be evaluated using marginal likelihoods, thus allowing a user to compare the merits of different hypotheses. The three presented protocols will help novice users to develop sophisticated analysis techniques useful for their research projects. © 2019 The Authors. Basic Protocol 1: First steps with MIGRATE Basic Protocol 2: Population model specification Basic Protocol 3: Prior distribution specification Basic Protocol 4: Model selection Support Protocol 1: Installing the program MIGRATE Support Protocol 2: Installation of parallel MIGRATE

In this paper, a new numerical method for solving fractional optimal control problems by using hybrid functions is presented. The Riemann–Liouville fractional integral operator for hybrid functions is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well-developed algorithms may be applied. The method is computationally very attractive and gives very accurate results.

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