Nonlinear social evolution and the emergence of collective action.

Organisms from microbes to humans engage in a variety of social behaviors, which affect fitness in complex, often nonlinear ways. The question of how these behaviors evolve has consequences ranging from antibiotic resistance to human origins. However, evolution with nonlinear social interactions is challenging to model mathematically, especially in combination with spatial, group, and/or kin assortment. We derive a mathematical condition for natural selection with synergistic interactions among any number of individuals. This result applies to populations with arbitrary (but fixed) spatial or network structure, group subdivision, and/or mating patterns. In this condition, nonlinear fitness effects are ascribed to collectives, and weighted by a new measure of collective relatedness. For weak selection, this condition can be systematically evaluated by computing branch lengths of ancestral trees. We apply this condition to pairwise games between diploid relatives, and to dilemmas of collective help or harm among siblings and on spatial networks. Our work provides a rigorous basis for extending the notion of "actor", in the study of social evolution, from individuals to collectives.

Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs.

The spatial structure of an evolving population affects the balance of natural selection versus genetic drift. Some structures amplify selection, increasing the role that fitness differences play in determining which mutations become fixed. Other structures suppress selection, reducing the effect of fitness differences and increasing the role of random chance. This phenomenon can be modeled by representing spatial structure as a graph, with individuals occupying vertices. Births and deaths occur stochastically, according to a specified update rule. We study death-Birth updating: An individual is chosen to die and then its neighbors compete to reproduce into the vacant spot. Previous numerical experiments suggested that amplifiers of selection for this process are either rare or nonexistent. We introduce a perturbative method for this problem for weak selection regime, meaning that mutations have small fitness effects. We show that fixation probability under weak selection can be calculated in terms of the coalescence times of random walks. This result leads naturally to a new definition of effective population size. Using this and other methods, we uncover the first known examples of transient amplifiers of selection (graphs that amplify selection for a particular range of fitness values) for the death-Birth process. We also exhibit new families of "reducers of fixation", which decrease the fixation probability of all mutations, whether beneficial or deleterious.

Accelerated head growth in early development of individuals with autism.

Macrocephaly is one of the most consistent physical findings reported in autistic individuals. Previous studies attempted to determine if macrocephaly is associated with risk for autism. This study hypothesizes that an abnormal acceleration in head growth during early development, rather than macrocephaly, is associated with autism risk. To investigate this hypothesis, head circumference data were examined in 251 individuals from 82 multiplex (at least two individuals with autism) and 113 sporadic (no family history) families with autism. This examination included longitudinal measurements for 79 individuals. Nineteen percent of the original 251 individuals were found to have macrocephaly (head circumference >97%). Abnormal acceleration in head growth was defined as an increase of 25 or more percentile points in head circumference between two consecutive measurements. Thirty-five percent of individuals with multiple head circumference records had an abnormal increase in head circumference. Furthermore, autistic individuals with accelerated head growth in early childhood displayed higher levels of adaptive functioning and less social impairment. This study confirms the presence of abnormal acceleration in head growth during the first and second months of life in a subgroup of autistic individuals.

Analysis of European mitochondrial haplogroups with Alzheimer disease risk.

We examined the association of mtDNA variation with Alzheimer disease (AD) risk in Caucasians (989 cases and 328 controls) testing the effect of individual haplogroups and single nucleotide polymorphisms (SNPs). Logistic regression analyses were used to assess risk of haplogroups and SNPs with AD in both main effects and interaction models. Males classified as haplogroup U showed an increase in risk (OR = 2.30; 95% CI, 1.03-5.11; P = 0.04) of AD relative to the most common haplogroup H, while females demonstrated a significant decrease in risk with haplogroup U (OR = 0.44 ; 95% CI, 0.24-0.80; P = 0.007). Our results were independent of APOE genotype, demonstrating that the effect of mt variation is not confounded by APOE4 carrier status. We suggest that variations within haplogroup U may be involved in AD expression in combination with environmental exposures or nuclear proteins other than APOE.