The evolution of extraordinary self-sacrifice.

From a theoretical perspective, individuals are expected to sacrifice their welfare only when the benefits outweigh the costs. In nature, however, the costs of altruism and spite can be extreme, as in cases of irreversible sterility and self-destructive weaponry. Here we show that "extraordinary" self-sacrifice-in which actors pay costs that exceed the benefits they give or the costs they impose on recipients-can evolve in structured populations, where social actions bring secondary benefits to neighboring kin.

Teaching math in real time.

Narrative, first-person accounts of a collective, traumatic event preserve the authenticity of the experience and defend against inaccurate retrospective idealizations. Such artifacts allow us time to process the event, extract the lessons it has for us, and to bring these lessons to bear on our practices. I offer my own narrative here, as a practitioner and researcher, of daily experiences of teaching mathematics in the USA during the SARS-CoV-2 pandemic.

Orb-web spiders as Bayesian learners.

Orb-web spiders typically construct their webs with a vertical asymmetry: the hub, or meeting point of the radial threads, is often above the geometric center of the web. Previous explanations for this asymmetry involve differences in up/down running speed and mass, but fail to account adequately for ontogenetic changes in vertical asymmetry. The current article argues that the hub location is determined so as to maximize the expected number of prey and is updated, partially, in response to predation experience.

Environmental evolutionary graph theory.

Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have received relatively less attention. Here we present a structured population model where different individuals are best suited to different regions of their environment.

Evolutionary game dynamics in populations with heterogenous structures.

Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place.

Hamilton's inclusive fitness in finite-structured populations.

Hamilton's formulation of inclusive fitness has been with us for 50 years. During the first 20 of those years attention was largely focused on the evolutionary trajectories of different behaviours, but over the past 20 years interest has been growing in the effect of population structure on the evolution of behaviour and that is our focus here. We discuss the evolutionary journey of the inclusive-fitness effect over this epoch, nurtured as it was in an essentially homogeneous environment (that of 'transitive' structures) having to adapt in different ways to meet the expectations of heterogeneous structures.

Reproductive value in graph-structured populations.

Evolutionary graph theory has grown to be an area of intense study. Despite the amount of interest in the field, it seems to have grown separate from other subfields of population genetics and evolution. In the current work I introduce the concept of Fisher's (1930) reproductive value into the study of evolution on graphs.

An inclusive fitness analysis of synergistic interactions in structured populations.

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or 'synergistic' fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other.

Resistance and relatedness on an evolutionary graph.

When investigating evolution in structured populations, it is often convenient to consider the population as an evolutionary graph-individuals as nodes, and whom they may act with as edges. There has, in recent years, been a surge of interest in evolutionary graphs, especially in the study of the evolution of social behaviours. An inclusive fitness framework is best suited for this type of study.

An analysis of the orientation of an orb-web spider.

In nature, orb-web spinning spiders are often observed residing on the hub of their web, facing down. An explanation of this phenomenon has only recently appeared in the literature [Zschokke, S., Nakata, K.