To examine the role of natural selection on fecundity in a variety ofCaenorhabditis elegans genetic backgrounds, we used an experimental evolution protocol to evolve 14 distinct genetic strains over 15-20 generations. Beginning with three founder worms for each strain, we were able to generate 790 distinct genealogies, which provided information on both the effects of natural selection and the evolvability of each strain. Among these genotypes are a wildtype (N2) and a collection of mutants with targeted mutations in the daf-c, daf-d, and AMPK pathways. The overarching goal of our analysis is two-fold: to observe differences in reproductive fitness and observe related changes in reproductive timing. This yields two outcomes. The first is that the majority of selective effects on fecundity occur during the first few generations of evolution, while the negative selection for reproductive timing occurs on longer timescales. The second finding reveals that positive selection on fecundity results in positive and negative selection on reproductive timing, both of which are strain-dependent. Using a derivative of population size per generation called the reproductive carry-over (RCO) measure, it is found that the fluctuation and shape of the probability distribution may be informative in terms of developmental selection. While these consist of general patterns that transcend mutations in a specific gene, changes in the RCO measure may nevertheless be products of selection. In conclusion, we discuss the broader implications of these findings, particularly in the context of genotype-fitness maps and the role of uncharacterized mutations in individual variation and evolvability.
Non-Identifiable Pedigrees and a Bayesian Solution
Some methods aim to correct or test for relationships or to reconstruct the pedigree, or family tree. We show that these methods cannot resolve ties for correct relationships due to identifiability of the pedigree likelihood which is the probability of inheriting the data under the pedigree model. This means that no likelihood-based method can produce a correct pedigree inference with high probability. This lack of reliability is critical both for health and forensics applications.
In this paper we present the first discussion of multiple typed individuals in non-isomorphic pedigrees, P and Q, where the likelihoods are non-identifiable, Pr[G | P,θ]=Pr[G | Q,θ], for all input data G and all recombination rate parameters θ. While there were previously known non-identifiable pairs, we give an example having data for multiple individuals.
Additionally, deeper understanding of the general discrete structures driving these non-identifiability examples has been provided, as well as results to guide algorithms that wish to examine only identifiable pedigrees. This paper introduces a general criteria for establishing whether a pair of pedigrees is non-identifiable and two easy-to-compute criteria guaranteeing identifiability. Finally, we suggest a method for dealing with non-identifiable likelihoods: use Bayes rule to obtain the posterior from the likelihood and prior. We propose a prior guaranteeing that the posterior distinguishes all pairs of pedigrees.
Shortened version published as: B. Kirkpatrick. Non-identifiable pedigrees and a Bayesian solution. Int. Symp. on Bioinformatics Res. and Appl. (ISBRA), 7292:139-152 2012.