Simulating Genomes and Populations in the Mutation Space: An example with the evolution of HIV drug resistance

When representing individuals as mutations with respect to a wild genotype we obtain an improvement of several orders of magnitude in both computation space and time. This is due to the great amount of redundant information present in the genomes within populations. We depict the basic algorithms, mutation, recombination and fitness, needed to implement this kind of model. This sort of representation is appropriate to investigate properties of the viral quasispecieces theory. We demonstrate the model efficiency with an example of the evolution of drug resistance in HIV-1. The result obtained seems to corroborate that the evolution of resistance is extremely dependent on the population size and the progeny number of the virus. In addition this seems also to agree with the recently proposed idea that there is no universally applicable unique value of effective population size for HIV-1 but this will depend on the specific process of interest under study. In the case of the evolution of resistance in a short time period, it seems that no low or medium effective population sizes as 10 3 -10 5 should be assumed though in other situations it could.

We propose a forward simulation framework to represent individuals just as the mutations they carry with respect to the wild genotype. The new framework seems to be an efficient way for forward modeling genomes and/or populations in the computer. Taking advantage of the new modeling, we also show the importance of population sizes being large enough for HIV-1 to get resistance phenotypes faster in time.

There are many different situations in current population biology research where simulating populations at a genetic and/or ecological level is very useful. Some examples include exploring complex situations such as molecular clock-like evolution [1], the evolution of drug-resistance in HIV-1 [2], human impacts onto genetic diversity under different demographic scenarios [3], human populations undergoing complex diseases [4,5], speciation processes [6], etc.

Simulation of populations also allows modeling spatially explicit situations as epidemiological ones [7] and different ecological and evolutionary scenarios with interest in conservation and management of populations [8,9]. In addition, population simulation of genetic datasets allows getting expectations of parameters which are otherwise difficult to obtain such as genome-wide mutation rates [10] or the effect of deleterious mutational load on populations [11].

When simulating biological populations under different evolutionary genetic models, backward or forward strategies can be followed. Backward simulations, also called coalescent-based simulations, are computationally very efficient because they are backward based on the history of lineages with survived offspring in the current population ignoring, however, all those lineages whose offspring did not arrive to the present [12]. Hence, coalescence is a sample-based theory relevant to the study of population samples and DNA sequence data. Due to its efficiency, it has also been used to derive several algorithms to estimate parameter values that maximize the probability of the given data [13]. From its beginnings, the basic coalescence has been extended in several useful ways to include structured population models [14,15] [ [16][17][18], changes in population size [19][20][21], recombination [22,23] and selection [24][25][26][27][28][29].

By contrast, forward simulations are less efficient because the whole history of the sample is followed from past to present. However, the coalescent framework imposes some limitations not present in the forward simulation. The first of all is the same that causes its efficiency, namely, the coalescence does not keep track of the complete ancestral information. Thus, if the interest is focused on the evolutionary process itself, rather than on its outcome, forward simulations should be preferred [30]. Second, coalescent simulations are complicated by simple genetic forces such as selection, and alt

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