Distance from Sub-Saharan Africa Predicts Mutational Load in Diverse Human Genomes

The Out-of-Africa (OOA) dispersal ∼50,000 y ago is characterized by a series of founder events as modern humans expanded into multiple continents. Population genetics theory predicts an increase of mutational load in populations undergoing serial founder effects during range expansions. To test this hypothesis, we have sequenced full genomes and high-coverage exomes from seven geographically divergent human populations from Namibia, Congo, Algeria, Pakistan, Cambodia, Siberia, and Mexico. We find that individual genomes vary modestly in the overall number of predicted deleterious alleles. We show via spatially explicit simulations that the observed distribution of deleterious allele frequencies is consistent with the OOA dispersal, particularly under a model where deleterious mutations are recessive. We conclude that there is a strong signal of purifying selection at conserved genomic positions within Africa, but that many predicted deleterious mutations have evolved as if they were neutral during the expansion out of Africa. Under a model where selection is inversely related to dominance, we show that OOA populations are likely to have a higher mutation load due to increased allele frequencies of nearly neutral variants that are recessive or partially recessive.

Neutral biodiversity theory can explain the imbalance of phylogenetic trees but not the tempo of their diversification

Numerous evolutionary studies have sought to explain the distribution of diversity across the limbs of the tree of life. At the same time, ecological studies have sought to explain differences in diversity and relative abundance within and among ecological communities. Traditionally, these patterns have been considered separately, but models that consider processes operating at the level of individuals, such as neutral biodiversity theory (NBT), can provide a link between them. Here, we compare evolutionary dynamics across a suite of NBT models. We show that NBT can yield phylogenetic tree topologies with imbalance closely resembling empirical observations. In general, metacommunities that exhibit greater disparity in abundance are characterized by more imbalanced phylogenetic trees. However, NBT fails to capture the tempo of diversification as represented by the distribution of branching events through time. We suggest that population-level processes might therefore help explain the asymmetry of phylogenetic trees, but that tree shape might mislead estimates of evolutionary rates unless the diversification process is modeled explicitly.

A feasible theory of truth over combinatory algebra

We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system TPT has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic. The proof that the theory TPT is feasible is not easy. It is not possible to apply a standard realisation approach. For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.