Chaotic turnover of rare and abundant species in a strongly interacting model community.

The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species toward rarity or abundance is crucial to assessing ecosystem resilience and adaptation to changing environmental conditions. In plankton communities in particular, large temporal fluctuations in species abundances have been associated with chaotic dynamics. On the other hand, microbial diversity is overwhelmingly sustained by a "rare biosphere" of species with very low abundances. We consider here the possibility that interactions within a species-rich community can relate both phenomena. We use a Lotka-Volterra model with weak immigration and strong, disordered, and mostly competitive interactions between hundreds of species to bridge single-species temporal fluctuations and abundance distribution patterns. We highlight a generic chaotic regime where a few species at a time achieve dominance but are continuously overturned by the invasion of formerly rare species. We derive a focal-species model that captures the intermittent boom-and-bust dynamics that every species undergoes. Although species cannot be treated as effectively uncorrelated in their abundances, the community's effect on a focal species can nonetheless be described by a time-correlated noise characterized by a few effective parameters that can be estimated from time series. The model predicts a nonunitary exponent of the power-law abundance decay, which varies weakly with ecological parameters, consistent with observation in marine protist communities. The chaotic turnover regime is thus poised to capture relevant ecological features of species-rich microbial communities.

Dynamics in a behavioral-epidemiological model for individual adherence to a nonpharmaceutical intervention.

The SARS-CoV-2 pandemic has highlighted the importance of behavioral drivers in epidemic dynamics. With the relaxation of mandated nonpharmaceutical interventions (NPIs) formerly in place to decrease transmission, such as mask-wearing or social distancing, adherence to an NPI is now the result of individual decision-making. To study these coupled dynamics, we embed a game-theoretic model for individual NPI adherence within an epidemiological model. When the disease is endemic, we find that our model has multiple (but none concurrently stable) equilibria: one each with zero, complete, or partial NPI adherence. Surprisingly, for the equilibrium with partial NPI adherence, the number of infections is independent of the transmission rate. Therefore, in that regime, a change in the rate of pathogen transmission, e.g., due to another (mandated) NPI or a new variant, has no effect on endemic infection levels. On the other hand, we show that vaccination successfully decreases endemic infection levels, and, unexpectedly, also reduces the number of susceptibles at equilibrium when there is partial adherence. From a game-theoretic perspective, we find that highly effective NPIs lead at most to partial adherence. As this effectiveness decreases, partially effective NPIs initially lead to increases in population-level adherence, especially if the risk is high enough. However, a completely ineffective NPI results in no adherence. Furthermore, we identify parameter regions where the individual incentives may not align with those of society as a whole. Overall, our findings illustrate complexities that can arise due to behavioral-epidemiological feedback and suggest appropriate measures to avoid more pessimistic population-level outcomes.

Individual costs and societal benefits of interventions during the COVID-19 pandemic.

Individual and societal reactions to an ongoing pandemic can lead to social dilemmas: In some cases, each individual is tempted to not follow an intervention, but for the whole society, it would be best if they did. Now that in most countries, the extent of regulations to reduce SARS-CoV-2 transmission is very small, interventions are driven by individual decision-making. Assuming that individuals act in their best own interest, we propose a framework in which this situation can be quantified, depending on the protection the intervention provides to a user and to others, the risk of getting infected, and the costs of the intervention. We discuss when a tension between individual and societal benefits arises and which parameter comparisons are important to distinguish between different regimes of intervention use.

Suppressors of fixation can increase average fitness beyond amplifiers of selection.

Evolutionary dynamics on graphs has remarkable features: For example, it has been shown that amplifiers of selection exist that-compared to an unstructured population-increase the fixation probability of advantageous mutations, while they decrease the fixation probability of disadvantageous mutations. So far, the theoretical literature has focused on the case of a single mutant entering a graph-structured population, asking how the graph affects the probability that a mutant takes over a population and the time until this typically happens. For continuously evolving systems, the more relevant case is that mutants constantly arise in an evolving population. Typically, such mutations occur with a small probability during reproduction events. We thus focus on the low mutation rate limit. The probability distribution for the fitness in this process converges to a steady state at long times. Intuitively, amplifiers of selection are expected to increase the population's mean fitness in the steady state. Similarly, suppressors of selection are expected to decrease the population's mean fitness in the steady state. However, we show that another set of graphs, called suppressors of fixation, can attain the highest population mean fitness. The key reason behind this is their ability to efficiently reject deleterious mutants. This illustrates the importance of the deleterious mutant regime for the long-term evolutionary dynamics, something that seems to have been overlooked in the literature so far.

The possible modes of microbial reproduction are fundamentally restricted by distribution of mass between parent and offspring.

Multiple modes of asexual reproduction are observed among microbial organisms in natural populations. These modes are not only subject to evolution, but may drive evolutionary competition directly through their impact on population growth rates. The most prominent transition between two such modes is the one from unicellularity to multicellularity. We present a model of the evolution of reproduction modes, where a parent organism fragments into smaller parts. While the size of an organism at fragmentation, the number of offspring, and their sizes may vary a lot, the combined mass of fragments is limited by the mass of the parent organism. We found that mass conservation can fundamentally limit the number of possible reproduction modes. This has important direct implications for microbial life: For unicellular species, the interplay between cell shape and kinetics of the cell growth implies that the largest and the smallest possible cells should be rod shaped rather than spherical. For primitive multicellular species, these considerations can explain why rosette cell colonies evolved a mechanistically complex binary split reproduction. Finally, we show that the loss of organism mass during sporulation can explain the macroscopic sizes of the formally unicellular microorganism Myxomycetes plasmodium. Our findings demonstrate that a number of seemingly unconnected phenomena observed in unrelated species may be different manifestations of the same underlying process.

Sharp thresholds limit the benefit of defector avoidance in cooperation on networks.

Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors, or they may lead to self-organized patterns, where some patches become safe havens that maintain an elevated cooperator density. Here we analyze the transition between these states mathematically. We show that safe havens form once a certain threshold in connectivity is crossed. This threshold can be analytically linked to the structure of the patch network and specifically to certain network motifs. Surprisingly, a forgiving defector avoidance strategy may be most favorable for cooperators. Our results demonstrate that the analysis of cooperation games in ecological metacommunity models is mathematically tractable and has the potential to link topics such as macroecological patterns, behavioral evolution, and network topology.

Self-loops in evolutionary graph theory: Friends or foes?

Evolutionary dynamics in spatially structured populations has been studied for a long time. More recently, the focus has been to construct structures that amplify selection by fixing beneficial mutations with higher probability than the well-mixed population and lower probability of fixation for deleterious mutations. It has been shown that for a structure to substantially amplify selection, self-loops are necessary when mutants appear predominately in nodes that change often. As a result, for low mutation rates, self-looped amplifiers attain higher steady-state average fitness in the mutation-selection balance than well-mixed populations. But what happens when the mutation rate increases such that fixation probabilities alone no longer describe the dynamics? We show that self-loops effects are detrimental outside the low mutation rate regime. In the intermediate and high mutation rate regime, amplifiers of selection attain lower steady-state average fitness than the complete graph and suppressors of selection. We also provide an estimate of the mutation rate beyond which the mutation-selection dynamics on a graph deviates from the weak mutation rate approximation. It involves computing average fixation time scaling with respect to the population sizes for several graphs.

On the evolutionary origins of host-microbe associations.

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.

Generation Time in Stage-Structured Populations under Fluctuating Environments.

AbstractA common measure of generation time is the average distance between two recruitment events along a genetic lineage. In populations with stage structure that live in a constant environment, this generation time can be computed from the elasticities of stable population growth to fecundities, and it is equivalent to another common measure of generation time: the average parental age of reproductive-value-weighted offspring. Here, we show three things. First, when the environment fluctuates, the average distance between two recruitment events along a genetic lineage is computed from the elasticities of the stochastic growth rate to fecundities. Second, under environmental stochasticity, this measure of generation time remains equivalent to the average parental age of reproductive-value-weighted offspring. Third, the generation time of a population in a fluctuating environment may deviate from the generation time the population would have in the average environment.

Neutrality in the Metaorganism.

Almost all animals and plants are inhabited by diverse communities of microorganisms, the microbiota, thereby forming an integrated entity, the metaorganism. Natural selection should favor hosts that shape the community composition of these microbes to promote a beneficial host-microbe symbiosis. Indeed, animal hosts often pose selective environments, which only a subset of the environmentally available microbes are able to colonize. How these microbes assemble after colonization to form the complex microbiota is less clear. Neutral models are based on the assumption that the alternatives in microbiota community composition are selectively equivalent and thus entirely shaped by random population dynamics and dispersal. Here, we use the neutral model as a null hypothesis to assess microbiata composition in host organisms, which does not rely on invoking any adaptive processes underlying microbial community assembly. We show that the overall microbiota community structure from a wide range of host organisms, in particular including previously understudied invertebrates, is in many cases consistent with neutral expectations. Our approach allows to identify individual microbes that are deviating from the neutral expectation and are therefore interesting candidates for further study. Moreover, using simulated communities, we demonstrate that transient community states may play a role in the deviations from the neutral expectation. Our findings highlight that the consideration of neutral processes and temporal changes in community composition are critical for an in-depth understanding of microbiota-host interactions.

The impact of phenotypic heterogeneity of tumour cells on treatment and relapse dynamics.

Intratumour heterogeneity is increasingly recognized as a frequent problem for cancer treatment as it allows for the evolution of resistance against treatment. While cancer genotyping becomes more and more established and allows to determine the genetic heterogeneity, less is known about the phenotypic heterogeneity among cancer cells. We investigate how phenotypic differences can impact the efficiency of therapy options that select on this diversity, compared to therapy options that are independent of the phenotype. We employ the ecological concept of trait distributions and characterize the cancer cell population as a collection of subpopulations that differ in their growth rate. We show in a deterministic model that growth rate-dependent treatment types alter the trait distribution of the cell population, resulting in a delayed relapse compared to a growth rate-independent treatment. Whether the cancer cell population goes extinct or relapse occurs is determined by stochastic dynamics, which we investigate using a stochastic model. Again, we find that relapse is delayed for the growth rate-dependent treatment type, albeit an increased relapse probability, suggesting that slowly growing subpopulations are shielded from extinction. Sequential application of growth rate-dependent and growth rate-independent treatment types can largely increase treatment efficiency and delay relapse. Interestingly, even longer intervals between decisions to change the treatment type may achieve close-to-optimal efficiencies and relapse times. Monitoring patients at regular check-ups may thus provide the temporally resolved guidance to tailor treatments to the changing cancer cell trait distribution and allow clinicians to cope with this dynamic heterogeneity.

Evolution of multicellular life cycles under costly fragmentation.

A fascinating wealth of life cycles is observed in biology, from unicellularity to the concerted fragmentation of multicellular units. However, the understanding of factors driving their evolution is still limited. We show that costs of fragmentation have a major impact on the evolution of life cycles due to their influence on the growth rates of the associated populations. We model a group structured population of undifferentiated cells, where cell clusters reproduce by fragmentation. Fragmentation events are associated with a cost expressed by either a fragmentation delay, an additional risk, or a cell loss. The introduction of such fragmentation costs vastly increases the set of possible life cycles. Based on these findings, we suggest that the evolution of life cycles involving splitting into multiple offspring can be directly associated with the fragmentation cost. Moreover, the impact of this cost alone is strong enough to drive the emergence of multicellular units that eventually split into many single cells, even under scenarios that strongly disfavour collectives compared to solitary individuals.

Stochastic colonization of hosts with a finite lifespan can drive individual host microbes out of equilibrium.

Macroorganisms are inhabited by microbial communities that often change through the lifespan of an individual. One of the factors contributing to this change is colonization from the environment. The colonization of initially microbe-free hosts is particularly interesting, as their microbiome depends entirely on microbes of external origin. We present a mathematical model of this process with a particular emphasis on the effect of ecological drift and a finite host lifespan. Our results indicate the host lifespan becomes especially relevant for short-living organisms (e.g. Caenorhabditis elegans, Drosophila melanogaster, and Danio rerio). In this case, alternative microbiome states (often called enterotypes), the coexistence of microbe-free and colonized hosts, and a reduced probability of colonization can be observed in our model. These results unify multiple reported observations around colonization and suggest that no selective or deterministic drivers are necessary to explain them.

Cellular hysteresis as a principle to maximize the efficacy of antibiotic therapy.

Antibiotic resistance has become one of the most dramatic threats to global health. While novel treatment options are urgently required, most attempts focus on finding new antibiotic substances. However, their development is costly, and their efficacy is often compromised within short time periods due to the enormous potential of microorganisms for rapid adaptation. Here, we developed a strategy that uses the currently available antibiotics. Our strategy exploits cellular hysteresis, which is the long-lasting, transgenerational change in cellular physiology that is induced by one antibiotic and sensitizes bacteria to another subsequently administered antibiotic. Using evolution experiments, mathematical modeling, genomics, and functional genetic analysis, we demonstrate that sequential treatment protocols with high levels of cellular hysteresis constrain the evolving bacteria by (i) increasing extinction frequencies, (ii) reducing adaptation rates, and (iii) limiting emergence of multidrug resistance. Cellular hysteresis is most effective in fast sequential protocols, in which antibiotics are changed within 12 h or 24 h, in contrast to the less frequent changes in cycling protocols commonly implemented in hospitals. We found that cellular hysteresis imposes specific selective pressure on the bacteria that disfavors resistance mutations. Instead, if bacterial populations survive, hysteresis is countered in two distinct ways, either through a process related to antibiotic tolerance or a mechanism controlled by the previously uncharacterized two-component regulator CpxS. We conclude that cellular hysteresis can be harnessed to optimize antibiotic therapy, to achieve both enhanced bacterial elimination and reduced resistance evolution.

How long do Red Queen dynamics survive under genetic drift? A comparative analysis of evolutionary and eco-evolutionary models.

BACKGROUND: Red Queen dynamics are defined as long term co-evolutionary dynamics, often with oscillations of genotype abundances driven by fluctuating selection in host-parasite systems. Much of our current understanding of these dynamics is based on theoretical concepts explored in mathematical models that are mostly (i) deterministic, inferring an infinite population size and (ii) evolutionary, thus ecological interactions that change population sizes are excluded. Here, we recall the different mathematical approaches used in the current literature on Red Queen dynamics. We then compare models from game theory (evo) and classical theoretical ecology models (eco-evo), that are all derived from individual interactions and are thus intrinsically stochastic. We assess the influence of this stochasticity through the time to the first loss of a genotype within a host or parasite population. RESULTS: The time until the first genotype is lost ("extinction time"), is shorter when ecological dynamics, in the form of a changing population size, is considered. Furthermore, when individuals compete only locally with other individuals extinction is even faster. On the other hand, evolutionary models with a fixed population size and competition on the scale of the whole population prolong extinction and therefore stabilise the oscillations. The stabilising properties of intra-specific competitions become stronger when population size is increased and the deterministic part of the dynamics gain influence. In general, the loss of genotype diversity can be counteracted with mutations (or recombination), which then allow the populations to recurrently undergo negative frequency-dependent selection dynamics and selective sweeps. CONCLUSION: Although the models we investigated are equal in their biological motivation and interpretation, they have diverging mathematical properties both in the derived deterministic dynamics and the derived stochastic dynamics. We find that models that do not consider intraspecific competition and that include ecological dynamics by letting the population size vary, lose genotypes - and thus Red Queen oscillations - faster than models with competition and a fixed population size.

Interacting cells driving the evolution of multicellular life cycles.

Evolution of complex multicellular life began from the emergence of a life cycle involving the formation of cell clusters. The opportunity for cells to interact within clusters provided them with an advantage over unicellular life forms. However, what kind of interactions may lead to the evolution of multicellular life cycles? Here, we combine evolutionary game theory with a model for the emergence of multicellular groups to investigate how cell interactions can influence reproduction modes during the early stages of the evolution of multicellularity. In our model, the presence of both cell types is maintained by stochastic phenotype switching during cell division. We identify evolutionary optimal life cycles as those which maximize the population growth rate. Among all interactions captured by two-player games, the vast majority promotes two classes of life cycles: (i) splitting into unicellular propagules or (ii) fragmentation into two offspring clusters of equal (or almost equal) size. Our findings indicate that the three most important characteristics, determining whether multicellular life cycles will evolve, are the average performance of homogeneous groups, heterogeneous groups, and solitary cells.

The invasion of de-differentiating cancer cells into hierarchical tissues.

Many fast renewing tissues are characterized by a hierarchical cellular architecture, with tissue specific stem cells at the root of the cellular hierarchy, differentiating into a whole range of specialized cells. There is increasing evidence that tumors are structured in a very similar way, mirroring the hierarchical structure of the host tissue. In some tissues, differentiated cells can also revert to the stem cell phenotype, which increases the risk that mutant cells lead to long lasting clones in the tissue. However, it is unclear under which circumstances de-differentiating cells will invade a tissue. To address this, we developed mathematical models to investigate how de-differentiation is selected as an adaptive mechanism in the context of cellular hierarchies. We derive thresholds for which de-differentiation is expected to emerge, and it is shown that the selection of de-differentiation is a result of the combination of the properties of cellular hierarchy and de-differentiation patterns. Our results suggest that de-differentiation is most likely to be favored provided stem cells having the largest effective self-renewal rate. Moreover, jumpwise de-differentiation provides a wider range of favorable conditions than stepwise de-differentiation. Finally, the effect of de-differentiation on the redistribution of self-renewal and differentiation probabilities also greatly influences the selection for de-differentiation.

Generation Time Measures the Trade-Off between Survival and Reproduction in a Life Cycle.

Survival and fertility are the two most basic components of fitness, and they drive the evolution of a life cycle. A trade-off between them is usually present: when survival increases, fertility decreases-and vice versa. Here we show that at an evolutionary optimum, the generation time is a measure of the strength of the trade-off between overall survival and overall fertility in a life cycle. Our result both helps to explain the known fact that the generation time describes the speed of living in the slow-fast continuum of life cycles and may have implications for the extrapolation from model organisms of longevity to humans.

How many samples are needed to infer truly clonal mutations from heterogenous tumours?

BACKGROUND: Modern cancer treatment strategies aim to target tumour specific genetic (or epigenetic) alterations. Treatment response improves if these alterations are clonal, i.e. present in all cancer cells within tumours. However, the identification of truly clonal alterations is impaired by the tremendous intra-tumour genetic heterogeneity and unavoidable sampling biases. METHODS: Here, we investigate the underlying causes of these spatial sampling biases and how the distribution and sizes of biopsies in sampling protocols can be optimised to minimize such biases. RESULTS: We find that in the ideal case, less than a handful of samples can be enough to infer truly clonal mutations. The frequency of the largest sub-clone at diagnosis is the main factor determining the accuracy of truncal mutation estimation in structured tumours. If the first sub-clone is dominating the tumour, higher spatial dispersion of samples and larger sample size can increase the accuracy of the estimation. In such an improved sampling scheme, fewer samples will enable the detection of truly clonal alterations with the same probability. CONCLUSIONS: Taking spatial tumour structure into account will decrease the probability to misclassify a sub-clonal mutation as clonal and promises better informed treatment decisions.

Invasion and effective size of graph-structured populations.

Population structure can strongly affect evolutionary dynamics. The most general way to describe population structures are graphs. An important observable on evolutionary graphs is the probability that a novel mutation spreads through the entire population. But what drives this spread of a mutation towards fixation? Here, we propose a novel way to understand the forces driving fixation by borrowing techniques from evolutionary demography to quantify the invasion fitness and the effective population size for different graphs. Our method is very general and even applies to weighted graphs with node dependent fitness. However, we focus on analytical results for undirected graphs with node independent fitness. The method will allow to conceptually integrate evolutionary graph theory with theoretical genetics of structured populations.