A full-scale experiment in evolutionary biology is hardly possible as either extremely expensive and lengthy, or unethical (or, more often, both). Under these circumstances, mathematical modelling offers an excellent alternative to a natural experiment.

In this presentation, I introduce a unifying paradigm of mathematical modelling in evolutionary biology, that utilise the concept of variant space (rather than genotype or phenotype space). This conceptual approach allows to construct a mechanistic model of (micro-)evolution on the bases of any of the many existing models of population dynamics (such as models of viral dynamics, cancer dynamics, etc.). Depending on a specific type of the model that serves as a basis, the resulting model of evolution can be formulated as deterministic, stochastic or probabalistic model. An important property of a resulting model is that the model is essentially mechanistic (that is, based upon the first principles): in contrast to earlier suggested phenomenological (data-based) models, for a mechanistic model all model parameters, as well as obtained results, can be straightforwardly interpreted. 

As case study, I consider RNA virus within host evolution. Using a well-know deterministic HIV dynamics model as a basis, I show how a variant-space model of within-host viral evolution can be formulated. Simulations exhibit dynamics that closely resembles the real-life clinical observations.

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