Matthew J Maxwell

Suppose 50-year-old Sue now has lung cancer, due to the fact that C = c & A = g (meaning that Sue smoked c cigarettes and inhaled g grams of asbestos over the previous 30 years), and that neither cause caused the other. Given this, a retrospective question arises – did one of those actual causes have a stronger influence than the other on her getting lung cancer? We propose a “zeroing-out” criterion for making sense of this question; it says that C = c was a stronger causal influence than A = g precisely when Pr(lung cancer | C = c & A = g) – Pr(lung cancer | C = 0 & A = g) > Pr(lung cancer | C = c & A = g) – Pr(lung cancer | C = c & A = 0). Zeroing-out uses Pr(lung cancer | C = c & A = g) as a baseline and relates that baseline to two counterfactual probabilities. We discuss how zeroing-out applies to three evolutionary examples − the influences of selection and drift on the fixation of an allele, the influences of group and individual selection on the evolution of altruism, and the influences of stabilizing selection and ancestral influence (aka “phylogenetic inertia”) on the evolution of tetrapody in land vertebrates. Zeroing-out differs from an “adding-in” criterion, which uses Sue’s probability of having lung cancer at age 50, given her actual state at age 20 (at which time she was cancer free and C = 0 & A = 0) as a baseline and asks whether her risk of having lung cancer at age 50 would be greater if C = c were true of the 30 years in between than it would be if A = g were true of those years. Zeroing-out and adding-in generate identical criteria for comparing causal influences in this example because the probabilities are related “monotonically” (a concept we define). We then describe examples in which monotonicity fails and the two criteria differ. We prove theorems that describe when the two criteria disagree and when they do not. We then consider how zeroing-out and adding-in are related to six quantitative measures of causal strength that have been proposed. Inter alia, we discuss how our framework is related to interventionism.

Population genetics relies heavily on homozygosity statistics. Over the past two decades, however, as the number and applications of homozygosity-based statistics has increased, there has been a crisis of confidence. Homozygosity statistics are mathematically constrained by other population genetics statistics, such as maximum allele frequency, creating problems for interpretation and portability. Mathematical investigations into these constraints have been criticized for being irrelevant to biology. Noah Rosenberg’s new book Mathematical Properties of Population-Genetic Statistics is his response to these concerns. While accepting many of the criticisms, Rosenberg shows that careful attention to purely mathematical constraints on homozygosity can be leveraged to design new statistics to achieve new goals.

Evolutionary gradualism, the randomness of mutations, and the hypothesis that natural selection exerts a pervasive and substantial influence on evolutionary outcomes are pair-wise logically independent. Can the claims about selection and mutation be used to formulate an argument for gradualism? In his Genetical Theory of Natural Selection, R.A. Fisher made an important start at this project in his famous “geometric argument” by showing that a random mutation that has a smaller effect on two or more phenotypes will have a higher average fitness than a random mutation that has a larger phenotypic effect. Motoo Kimura’s demonstration that a gene’s probability of fixation depends on both the selection coefficient and the effective population size shows that Fisher’s argument for gradualism was mistaken. Here we analyze Fisher’s argument and explain how Kimura’s theory leads to a conclusion that Fisher did not anticipate. We identify a fallacy that reasoning about fitness differences and their evolutionary consequences should avoid. We then distinguish forward-directed from backward-directed versions of gradualism. The backward-directed thesis about a single mutation may be correct, but the forward-directed thesis is not. After that we consider a sequence of random mutations that all affect the same cluster of phenotypes and Allen Orr’s idea that there is an optimal sequence of mutation sizes, moving from larger to smaller as the population approaches a fixed optimum. This provides a likelihood justification for a forward-directed version of gradualism when there is a fixed optimum, but it also provides an argument against forward-directed gradualism if the optimum shifts substantially as the population evolves. Finally, we consider whether genome-wide association studies (GWASs) can furnish empirical evidence that bears on the truth of gradualism. The version of gradualism that GWASs directly bear on concerns the phenotypic effect size of a gene after it arises by mutation and has reached an appreciable frequency, not the phenotypic size of the mutation event itself.

Eugenic arguments are not a thing of the past. In 2016, geneticist Michael Lynch published an article in Genetics arguing that human mental and physical performance are declining at a rate of 1% per generation. This estimate is not based on measurements of performance but on an argument from mutational load: Medical interventions are relaxing selection on the human population, which will lead to a buildup of deleterious mutations. This simple argument from mutational load is invalid. When the argument is made valid, it is not obvious that there are any significant consequences for human population health.