Universality of evolutionary trajectories under arbitrary forms of self-limitation and competition.

The assumption of constant population size is central in population genetics. It led to a large body of results that is robust to modeling choices and that has proven successful to understand evolutionary dynamics. In reality, allele frequencies and population size are both determined by the interaction between a population and the environment. Relaxing the constant-population assumption has two big drawbacks. It increases the technical difficulty of the analysis, and it requires specifying a mechanism for the saturation of the population size, possibly making the results contingent on model details. Here we develop a framework that encompasses a great variety of systems with an arbitrary mechanism for population growth limitation. By using techniques based on scale separation for stochastic processes, we are able to calculate analytically properties of evolutionary trajectories, such as the fixation probability. Remarkably, these properties assume a universal form with respect to our framework, which depends on only three parameters related to the intergeneration timescale, the invasion fitness, and the carrying capacity of the strains. In other words, different systems, such as Lotka-Volterra or a chemostat model (contained in our framework), share the same evolutionary outcomes after a proper remapping of their parameters. An important and surprising consequence of our results is that the direction of selection can be inverted, with a population evolving to reach lower values of invasion fitness.

Evolutionary stability of antigenically escaping viruses.

Antigenic variation is the main immune escape mechanism for RNA viruses like influenza or SARS-CoV-2. While high mutation rates promote antigenic escape, they also induce large mutational loads and reduced fitness. It remains unclear how this cost-benefit trade-off selects the mutation rate of viruses. Using a traveling wave model for the coevolution of viruses and host immune systems in a finite population, we investigate how immunity affects the evolution of the mutation rate and other nonantigenic traits, such as virulence. We first show that the nature of the wave depends on how cross-reactive immune systems are, reconciling previous approaches. The immune-virus system behaves like a Fisher wave at low cross-reactivities, and like a fitness wave at high cross-reactivities. These regimes predict different outcomes for the evolution of nonantigenic traits. At low cross-reactivities, the evolutionarily stable strategy is to maximize the speed of the wave, implying a higher mutation rate and increased virulence. At large cross-reactivities, where our estimates place H3N2 influenza, the stable strategy is to increase the basic reproductive number, keeping the mutation rate to a minimum and virulence low.

Emergent statistical laws in single-cell transcriptomic data.

Large-scale data on single-cell gene expression have the potential to unravel the specific transcriptional programs of different cell types. The structure of these expression datasets suggests a similarity with several other complex systems that can be analogously described through the statistics of their basic building blocks. Transcriptomes of single cells are collections of messenger RNA abundances transcribed from a common set of genes just as books are different collections of words from a shared vocabulary, genomes of different species are specific compositions of genes belonging to evolutionary families, and ecological niches can be described by their species abundances. Following this analogy, we identify several emergent statistical laws in single-cell transcriptomic data closely similar to regularities found in linguistics, ecology, or genomics. A simple mathematical framework can be used to analyze the relations between different laws and the possible mechanisms behind their ubiquity. Importantly, treatable statistical models can be useful tools in transcriptomics to disentangle the actual biological variability from general statistical effects present in most component systems and from the consequences of the sampling process inherent to the experimental technique.

Inspecting the interaction between human immunodeficiency virus and the immune system through genetic turnover.

Chronic infections of the human immunodeficiency virus (HIV) create a very complex coevolutionary process, where the virus tries to escape the continuously adapting host immune system. Quantitative details of this process are largely unknown and could help in disease treatment and vaccine development. Here we study a longitudinal dataset of ten HIV-infected people, where both the B-cell receptors and the virus are deeply sequenced. We focus on simple measures of turnover, which quantify how much the composition of the viral strains and the immune repertoire change between time points. At the single-patient level, the viral-host turnover rates do not show any statistically significant correlation, however, they correlate if one increases the amount of statistics by aggregating the information across patients. We identify an anti-correlation: large changes in the viral pool composition come with small changes in the B-cell receptor repertoire. This result seems to contradict the naïve expectation that when the virus mutates quickly, the immune repertoire needs to change to keep up. However, a simple model of antagonistically evolving populations can explain this signal. If it is sampled at intervals comparable with the sweep time, one population has had time to sweep while the second cannot start a counter-sweep, leading to the observed anti-correlation. This article is part of the theme issue 'Interdisciplinary approaches to predicting evolutionary biology'.

NoisET: Noise Learning and Expansion Detection of T-Cell Receptors.

High-throughput sequencing of T- and B-cell receptors makes it possible to track immune repertoires across time, in different tissues, in acute and chronic diseases and in healthy individuals. However, quantitative comparison between repertoires is confounded by variability in the read count of each receptor clonotype due to sampling, library preparation, and expression noise. We review methods for accounting for both biological and experimental noise and present an easy-to-use python package NoisET that implements and generalizes a previously developed Bayesian method. It can be used to learn experimental noise models for repertoire sequencing from replicates, and to detect responding clones following a stimulus. We test the package on different repertoire sequencing technologies and data sets. We review how such approaches have been used to identify responding clonotypes in vaccination and disease data. Availability: NoisET is freely available to use with source code at github.com/statbiophys/NoisET.

Generosity, selfishness and exploitation as optimal greedy strategies for resource sharing.

Resource sharing outside the kinship bonds is rare. Besides humans, it occurs in chimpanzee, wild dogs and hyenas, as well as in vampire bats. Resource sharing is an instance of animal cooperation, where an animal gives away part of the resources that it owns for the benefit of a recipient. Taking inspiration from blood-sharing in vampire bats, here we show the emergence of generosity in a Markov game, which couples the resource sharing between two players with the gathering task of that resource. At variance with the classical evolutionary models for cooperation, the optimal strategies of this game can be potentially learned by animals during their life-time. The players act greedily, that is, they try to individually maximize only their personal income. Nonetheless, the analytical solution of the model shows that three non trivial optimal behaviours emerge depending on conditions. Besides the obvious case when players are selfish in their choice of resource division, there are conditions under which both players are generous. Moreover, we also found a range of situations in which one selfish player exploits another generous individual, for the satisfaction of both players. Our results show that resource sharing is favoured by three factors: a long time horizon over which the players try to optimize their own game, the similarity among players in their ability of performing the resource-gathering task, as well as by the availability of resources in the environment. These concurrent requirements lead to identify necessary conditions for the emergence of generosity.

Zipf and Heaps laws from dependency structures in component systems.

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sublinear, and saturating) that we characterize quantitatively.