Why is cyclic dominance so rare?

Natural populations can contain multiple types of coexisting individuals. How does natural selection maintain such diversity within and across populations? A popular theoretical basis for the maintenance of diversity is cyclic dominance, illustrated by the rock-paper-scissor game. However, it appears difficult to find cyclic dominance in nature. Why is this the case? Focusing on continuously produced novel mutations, we theoretically addressed the rareness of cyclic dominance. We developed a model of an evolving population and studied the formation of cyclic dominance. Our results showed that the chance for cyclic dominance to emerge is lower when the newly introduced type is similar to existing types compared to the introduction of an unrelated type. This suggests that cyclic dominance is more likely to evolve through the assembly of unrelated types whereas it rarely evolves within a community of similar types

Killer on the road?-cells from pancreatic preneoplastic lesions disseminate through pancreatic ducts on their way to cancer

Pancreatic ductal adenocarcinoma (PDAC) is ranked the fourth most common cause of cancer related deaths in western countries with a 5-year survival rate of less than 8 (1). It is estimated to be even the second most common cause by 2030 as there are no successful treatment options (2). Due to the lack of early and specific symptoms as well as non-invasive biomarkers, the majority of patients is diagnosed at an advanced and already metastasized disease stage, where palliative treatment remains the only option (3). Thus, in order to improve the dismal prognosis of PDAC patients, a much better understanding of PDAC evolution is urgently needed allowing earlier detection of the disease and providing novel therapeutic modalities

Vaccination strategies when vaccines are scarce: on conflicts between reducing the burden and avoiding the evolution of escape mutants

When vaccine supply is limited but population immunization urgent, theallocation of the available doses needs to be carefully considered. Oneaspect of dose allocation is the time interval between the first and thesecond injections in two-dose vaccines. By stretching this interval, more indi-viduals can be vaccinated with the first dose more quickly, which can bebeneficial in reducing case numbers, provided a single dose is sufficientlyeffective. On the other hand, there has been concern that intermediatelevels of immunity in partially vaccinated individuals may favour theevolution of vaccine escape mutants. In that case, a large fraction of half-vaccinated individuals would pose a risk—but only if they encounter thevirus. This raises the question whether there is a conflict between reducingthe burden and the risk of vaccine escape evolution or not. We develop anSIR-type model to assess the population-level effects of the timing of thesecond dose. Trade-offs can occur both if vaccine escape evolution is morelikely or if it is less likely in half-vaccinated than in unvaccinated individ-uals. Their presence or absence depends on the efficacies for susceptibilityand transmissibility elicited by a single dose

The Covid-19 pandemic: basic insights from basic mathematical models

Mathematical models for the spread of infectious diseases have a long history. From the start of the Covid-19 pandemic, there was a huge public interest in applying such models, since they help to understand general features of epidemic spread and support the assessment of possible mitigation measures – and their later relaxation. We describe and discuss some well-established mathematical models for epidemic spread, starting from the susceptible-infected-recovered (SIR) model and branching processes and discussing insights from network-based models. During the Covid-19 pandemic, such classical models have also been extended to include many additional aspects that affect epidemic spread, such as mobility patterns or testing possibilities. However, such complex models are increasingly difficult to assess from the outside. In a situation where their predictions can directly affect the lives of millions of people, this can become a severe problem. We argue that simple mathematical models have huge merits and can explain many of the key features of more complex models, such as the importance of heterogeneity in disease transmission. For example, basic models allow inferring whether super-spreading, where very few infected individuals cause the vast majority of secondary cases, should be the rule or the exception – with wide-ranging consequences for the possible success of mitigation measures. In addition, these basic models are simple enough to be understood and implemented without expert knowledge in theoretical epidemiology or computer science. Thus, they offer a level of transparency that can be important for a society to accept mitigation measures

Lotka–Volterra dynamics kills the Red Queen: population size fluctuations and associated stochasticity dramatically change host-parasite coevolution

Background: Host-parasite coevolution is generally believed to follow Red Queen dynamics consisting of ongoing oscillations in the frequencies of interacting host and parasite alleles. This belief is founded on previous theoretical work, which assumes infinite or constant population size. To what extent are such sustained oscillations realistic? Results: Here, we use a related mathematical modeling approach to demonstrate that ongoing Red Queen dynamics is unlikely. In fact, they collapse rapidly when two critical pieces of realism are acknowledged: (i) population size fluctuations, caused by the antagonism of the interaction in concordance with the Lotka-Volterra relationship; and (ii) stochasticity, acting in any finite population. Together, these two factors cause fast allele fixation. Fixation is not restricted to common alleles, as expected from drift, but also seen for originally rare alleles under a wide parameter space, potentially facilitating spread of novel variants. Conclusion: Our results call for a paradigm shift in our understanding of host-parasite coevolution, strongly suggesting that these are driven by recurrent selective sweeps rather than continuous allele oscillations

On the evolutionary origins of host–microbe associations

Animals can provide benefits to their associated microbes—}and these can, in turn, positively affect their hosts. But how do such mutually beneficial associations arise in the first place? In particular, when animal and microbe initially have independent lifestyles, this is not clear. By developing a model of animal and microbial life cycles on patchy habitats, we show how their overlapping ecologies of development and dispersal can lead to the enrichment of certain microbes in the dispersing animals, even in the absence of specific mutualistic benefits. This enrichment can then set the stage for the evolution of more specific host{–}microbe associations, which also implies that host enrichment per se is not an indicator of a beneficial host{–}microbe symbiosis.Many microorganisms with high prevalence in host populations are beneficial to the host and maintained by specialized transmission mechanisms. Although microbial promotion of host fitness and specificity of the associations undoubtedly enhance microbial prevalence, it is an open question whether these symbiotic traits are also a prerequisite for the evolutionary origin of prevalent microbial taxa. To address this issue, we investigate how processes without positive microbial effects on host fitness or host choice can influence the prevalence of certain microbes in a host population. Specifically, we develop a theoretical model to assess the conditions under which particular microbes can become enriched in animal hosts even when they are not providing a specific benefit to a particular host. We find increased prevalence of specific microbes in a host when both show some overlap in their lifecycles, and especially when both share dispersal routes across a patchy habitat distribution. Our results emphasize that host enrichment per se is not a reliable indicator of beneficial host{–microbe interactions. The resulting increase in time spent associated with a host may nevertheless give rise to new selection conditions, which can favor microbial adaptations toward a host-associated lifestyle, and, thus, it could be the foundation for subsequent evolution of mutually beneficial coevolved symbioses.A Python implementation of the model underlying the results in this paper has been deposited in GitHub (https://github.com/misieber/patchbiota)

Modeling host-associating microbes under selection

The concept of fitness is often reduced to a single component, such as the replication rate in a given habitat. For species with multi-step life cycles, this can be an unjustified oversimplification, as every step of the life cycle can contribute to the overall reproductive success in a specific way. In particular, this applies to microbes that spend part of their life cycles associated to a host. In this case, there is a selection pressure not only on the replication rates, but also on the phenotypic traits associated to migrating from the external environment to the host and vice-versa (i.e., the migration rates). Here, we investigate a simple model of a microbial lineage living, replicating, migrating and competing in and between two compartments: a host and an environment. We perform a sensitivity analysis on the overall growth rate to determine the selection gradient experienced by the microbial lineage. We focus on the direction of selection at each point of the phenotypic space, defining an optimal way for the microbial lineage to increase its fitness. We show that microbes can adapt to the two-compartment life cycle through either changes in replication or migration rates, depending on the initial values of the traits, the initial distribution across the two compartments, the intensity of competition, and the time scales involved in the life cycle versus the time scale of adaptation (which determines the adequate probing time to measure fitness). Overall, our model provides a conceptual framework to study the selection on microbes experiencing a host-associated life cycle

Evolution of irreversible somatic differentiation

A key innovation emerging in complex animals is irreversible somatic differentiation: daughters of a vegetative cell perform a vegetative function as well, thus, forming a somatic lineage that can no longer be directly involved in reproduction. Primitive species use a different strategy: vegetative and reproductive tasks are separated in time rather than in space. Starting from such a strategy, how is it possible to evolve life forms which use some of their cells exclusively for vegetative functions? Here, we developed an evolutionary model of development of a simple multicellular organism and found that three components are necessary for the evolution of irreversible somatic differentiation: (i) costly cell differentiation, (ii) vegetative cells that significantly improve the organism’s performance even if present in small numbers, and (iii) large enough organism size. Our findings demonstrate how an egalitarian development typical for loose cell colonies can evolve into germ-soma differentiation dominating metazoans.Competing Interest StatementThe authors have declared no competing interest

The Emergence of Altruistic Punishment: Via Freedom to Enforcement

In human societies, cooperative behaviour in public goods interactions is usually enforced through institutions that impose sanctions on free-riders. Many experiments on public goods games have shown that in the absence of such institutions, individuals are often willing to punish defectors, even at a cost to themselves, effectively taking the law into their own hands. Theoretical models confirm that social norms prescribing the punishment of deviant behaviour are stable: once established, they prevent invasion by dissident minorities. But how can such costly punishing behaviour gain a foothold in the population? A surprisingly simple model shows that if individuals have the option to stand aside and abstain from the public goods interaction, this paves the way for the emergence and establishment of cooperative behaviour based on the punishment of defectors. Thus the freedom to withdraw from the public enterprise leads to a self-enforcing prosocial norm. Paradoxically, the option of individual autarky may be an important step for the emergence of institutions punishing the non-cooperation of their members. Conversely, public goods interactions which are obligatory rather than voluntary are unlikely to gain a foothold in the population

Host-parasite coevolution in populations of constant and variable size

The matching-allele and gene-for-gene models are widely used in math- ematical approaches that study the dynamics of host-parasite interactions. Agrawal and Lively (Evolutionary Ecology Research 4:79-90, 2002) captured these two models in a single framework and numerically explored the associated time discrete dynamics of allele frequencies. Here, we present a detailed analytical investigation of this unifying framework in continuous time and provide a generalization. We extend the model to take into account changing population sizes, which result from the antagonistic nature of the interaction and follow the Lotka-Volterra equations. Under this extension, the population dynamics become most complex as the model moves away from pure matching-allele and becomes more gene-for-gene-like. While the population densities oscillate with a single oscillation frequency in the pure matching-allele model, a second oscillation frequency arises under gene-for-gene-like conditions. These observations hold for general interaction parameters and allow to infer generic patterns of the dynamics. Our results suggest that experimentally inferred dynamical patterns of host-parasite coevolution should typically be much more complex than the popular illustrations of Red Queen dynamics. A single parasite that infects more than one host can substantially alter the cyclic dynamics