Purely competitive evolutionary dynamics for games

We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial, are governed. In each period, the population is randomly sorted into pairs, which engage in a once-off play of the game; the probability that a member propagates its type to its offspring is proportional only to its payoff within the pair. We show that if a type is dominant (obtains higher payoffs in games with both other types), its 'pure' population state, comprising only members of that type, is globally attracting. If there is no dominant type, there is an unstable 'mixed' fixed point; the population state eventually oscillates between the three near-pure states. We then allow for mutations, where offspring have a non-zero probability of randomly changing their type. In this case, the existence of a dominant type renders a point near its pure state globally attracting. If no dominant type exists, a supercritical Hopf bifurcation occurs at the unique mixed fixed point, and above a critical (typically low) mutation rate, this fixed point becomes globally attracting: the implication is that even very low mutation rates can stabilize a system that would, in the absence of mutations, be unstable.Comment: 13 pages, 6 figure

What is the SARB's inflation targeting policy, and is it appropriate?

Since its adoption of inflation targeting in 2000, the South African Reserve Bank has been accused of placing too great an emphasis on meeting its inflation target, and too small an emphasis on the high rate of unemployment in the country. On the other hand, the SARB has regularly missed its inflation target. We attempt to characterise the SARB's inflation targeting policy by analysing the Bank's interest rate setting behaviour before and after the adoption of inflation targeting, making use of Taylor-like rules to determine whether the SARB has emphasised inflation, the output gap, the real exchange rate, and asset price deviations in its monetary policy. We find that the SARB has significantly changed its behaviour with the adoption of inflation targeting, and show that the SARB runs a very flexible inflation targeting regime, with strong emphasis on the output gap. Indeed, we find evidence that the emphasis on inflation is too low, and potentially conducive to instability in the inflation process

What is the SARB's inflation targeting policy, and is it appropriate?

Since its adoption of inflation targeting in 2000, the South African Reserve Bank has been accused of placing too great an emphasis on meeting its inflation target, and too small an emphasis on the high rate of unemployment in the country. On the other hand, the SARB has regularly missed its inflation target. We attempt to characterise the SARB's inflation targeting policy by analysing the Bank's interest rate setting behaviour before and after the adoption of inflation targeting, making use of Taylor-like rules to determine whether the SARB has emphasised inflation, the output gap, the real exchange rate, and asset price deviations in its monetary policy. We find that the SARB has significantly changed its behaviour with the adoption of inflation targeting, and show that the SARB runs a very flexible inflation targeting regime, with strong emphasis on the output gap. Indeed, we find evidence that the emphasis on inflation is too low, and potentially conducive to instability in the inflation process

The evolution of queen control over worker reproduction in the social Hymenoptera

Abstract A trademark of eusocial insect species is reproductive division of labor, in which workers forego their own reproduction while the queen produces almost all offspring. The presence of the queen is key for maintaining social harmony, but the specific role of the queen in the evolution of eusociality remains unclear. A long‐discussed scenario is that a queen either behaviorally or chemically sterilizes her workers. However, the demographic and ecological conditions that enable such manipulation are still debated. We study a simple model of evolutionary dynamics based on haplodiploid genetics. Our model is set in the commonly observed case where workers have lost the ability to lay female (diploid) eggs by mating, but retain the ability to lay male (haploid) eggs. We consider a mutation that acts in a queen, causing her to control the reproductive behavior of her workers. Our mathematical analysis yields precise conditions for the evolutionary emergence and stability of queen‐induced worker sterility. These conditions do not depend on the queen's mating frequency. We find that queen control is always established if it increases colony reproductive efficiency, but can evolve even if it decreases colony efficiency. We further derive the conditions under which queen control is evolutionarily stable against invasion by mutant workers who have recovered the ability to lay male eggs

Interpreting population- and family-based genome-wide association studies in the presence of confounding

A central aim of genome-wide association studies (GWASs) is to estimate direct genetic effects: the causal effects on an individual’s phenotype of the alleles that they carry. However, estimates of direct effects can be subject to genetic and environmental confounding and can also absorb the “indirect” genetic effects of relatives’ genotypes. Recently, an important development in controlling for these confounds has been the use of within-family GWASs, which, because of the randomness of mendelian segregation within pedigrees, are often interpreted as producing unbiased estimates of direct effects. Here, we present a general theoretical analysis of the influence of confounding in standard population-based and within-family GWASs. We show that, contrary to common interpretation, family-based estimates of direct effects can be biased by genetic confounding. In humans, such biases will often be small per-locus, but can be compounded when effect-size estimates are used in polygenic scores (PGSs). We illustrate the influence of genetic confounding on population- and family-based estimates of direct effects using models of assortative mating, population stratification, and stabilizing selection on GWAS traits. We further show how family-based estimates of indirect genetic effects, based on comparisons of parentally transmitted and untransmitted alleles, can suffer substantial genetic confounding. We conclude that, while family-based studies have placed GWAS estimation on a more rigorous footing, they carry subtle issues of interpretation that arise from confounding

Interpreting population- and family-based genome-wide association studies in the presence of confounding

A central aim of genome-wide association studies (GWASs) is to estimate direct genetic effects: the causal effects on an individual's phenotype of the alleles that they carry. However, estimates of direct effects can be subject to genetic and environmental confounding and can also absorb the "indirect" genetic effects of relatives' genotypes. Recently, an important development in controlling for these confounds has been the use of within-family GWASs, which, because of the randomness of mendelian segregation within pedigrees, are often interpreted as producing unbiased estimates of direct effects. Here, we present a general theoretical analysis of the influence of confounding in standard population-based and within-family GWASs. We show that, contrary to common interpretation, family-based estimates of direct effects can be biased by genetic confounding. In humans, such biases will often be small per-locus, but can be compounded when effect-size estimates are used in polygenic scores (PGSs). We illustrate the influence of genetic confounding on population- and family-based estimates of direct effects using models of assortative mating, population stratification, and stabilizing selection on GWAS traits. We further show how family-based estimates of indirect genetic effects, based on comparisons of parentally transmitted and untransmitted alleles, can suffer substantial genetic confounding. We conclude that, while family-based studies have placed GWAS estimation on a more rigorous footing, they carry subtle issues of interpretation that arise from confounding

Assortative mating enhances postzygotic barriers to gene flow via ancestry bundling

Hybridization and subsequent genetic introgression are now known to be common features of the histories of many species, including our own. Following hybridization, selection often purges introgressed DNA genome-wide. While assortative mating can limit hybridization in the first place, it is also known to play an important role in postzygotic selection against hybrids and, thus, the purging of introgressed DNA. However, this role is usually thought of as a direct one: a tendency for mates to be conspecific reduces the sexual fitness of hybrids, reducing the transmission of introgressed ancestry. Here, we explore a second, indirect role of assortative mating as a postzygotic barrier to gene flow. Under assortative mating, parents covary in their ancestry, causing ancestry to be "bundled" in their offspring and later generations. This bundling effect increases ancestry variance in the population, enhancing the efficiency with which postzygotic selection purges introgressed DNA. Using whole-genome simulations, we show that the bundling effect can comprise a substantial portion of mate choice's overall effect as a postzygotic barrier to gene flow. We then derive a simple method for estimating the impact of the bundling effect from standard metrics of assortative mating. Applying this method to data from a diverse set of hybrid zones, we find that the bundling effect increases the purging of introgressed DNA by between 1.2-fold (in a baboon system with weak assortative mating) and 14-fold (in a swordtail system with strong assortative mating). Thus, assortative mating's bundling effect contributes substantially to the genetic isolation of species