Not just a theory--the utility of mathematical models in evolutionary biology

How does plant chemodiversity evolve? Testing five hypotheses in one population genetic model

Plant chemodiversity, the diversity of plant-specialized metabolites, is an important dimension of biodiversity. However, there are so far few mathematical models to test verbal hypotheses on how chemodiversity evolved. Here, we develop such a model to test predictions of five hypotheses: the 'fluctuating selection hypothesis', the 'dominance reversal hypothesis', the interaction diversity hypothesis, the synergy hypothesis, and the screening hypothesis. We build a population genetic model of a plant population attacked by herbivore species whose occurrence fluctuates over time. We study the model using mathematical analysis and individual-based simulations. As predicted by the 'dominance reversal hypothesis', chemodiversity can be maintained if alleles conferring a defense metabolite are dominant with respect to the benefits, but recessive with respect to costs. However, even smaller changes in dominance can maintain polymorphism. Moreover, our results underpin and elaborate predictions of the synergy and interaction diversity hypotheses, and, to the extent that our model can address it, the screening hypotheses. By contrast, we found only partial support for the 'fluctuating selection hypothesis'. In summary, we have developed a flexible model and tested various verbal models for the evolution of chemodiversity. Next, more mechanistic models are needed that explicitly consider the organization of metabolic pathways.

Six personas to adopt when framing theoretical research questions in biology

Theory is a critical component of the biological research process, and complements observational and experimental approaches. However, most biologists receive little training on how to frame a theoretical question and, thus, how to evaluate when theory has successfully answered the research question. Here, we develop a guide with six verbal framings for theoretical models in biology. These correspond to different personas one might adopt as a theorist: 'Advocate', 'Explainer', 'Instigator', 'Mediator', 'Semantician' and 'Tinkerer'. These personas are drawn from combinations of two starting points (pattern or mechanism) and three foci (novelty, robustness or conflict). We illustrate each of these framings with examples of specific theoretical questions, by drawing on recent theoretical papers in the fields of ecology and evolutionary biology. We show how the same research topic can be approached from slightly different perspectives, using different framings. We show how clarifying a model's framing can debunk common misconceptions of theory: that simplifying assumptions are bad, more detail is always better, models show anything you want and modelling requires substantial maths knowledge. Finally, we provide a roadmap that researchers new to theoretical research can use to identify a framing to serve as a blueprint for their own theoretical research projects.

phyddle: software for phylogenetic model exploration with deep learning

Many realistic phylogenetic models lack tractable likelihood functions, prohibiting their use with standard inference methods. We present phyddle, a pipeline-based toolkit for performing phylogenetic modeling tasks using likelihood-free deep learning approaches. phyddle coordinates modeling tasks through five analysis steps (Simulate, Format, Train, Estimate, and Plot) that transform raw phylogenetic datasets as input into numerical and visualized model-based output. Benchmarks show that phyddle accurately performs a range of inference tasks, such as estimating macroevolutionary parameters, selecting among continuous trait evolution models, and passing coverage tests for epidemiological models, even for models that lack tractable likelihoods. phyddle has a flexible command-line interface, making it easy to integrate deep learning approaches for phylogenetics into research workflows. Learn more about phyddle at https://phyddle.org.

Polymorphism and the Red Queen: the selective maintenance of allelic variation in a deteriorating environment

Although allelic variation is ubiquitous in natural populations, our theoretical models are poor at predicting the existence and properties of these observed polymorphisms. In this study, inspired by Van Valen's Red Queen hypothesis, we modeled the effect of viability selection in a deteriorating environment on the properties of allelic variation in populations subject to recurrent mutation. In Monte Carlo simulations, we found that levels of polymorphism consistently built up over time. We censused the simulated populations after 10,000 generations of mutation and selection, revealing that, compared with models assuming a constant environment, the mean number of alleles was greater, as was the range of allele numbers. These results were qualitatively robust to the addition of genetic drift and to the relaxation of the assumption that the viabilities of phenogenotypes containing a new mutation are independent of each other (i.e. incorporating a model of generalized dominance). The broad range of allele numbers realized in the simulated populations-from monomorphisms to highly polymorphic populations-more closely corresponds to the observed range from numerous surveys of natural populations than previously found in theoretical studies. This match suggests that, contrary to the views of some writers, selection may actively maintain genetic variation in natural populations, particularly if the selective environment is gradually becoming harsher. Our simulations also generated many populations with heterozygote advantage, a mismatch with real data that implies that this selective property must arise extremely rarely in natural populations.

Developing a predictive science of the biosphere requires the integration of scientific cultures

Increasing the speed of scientific progress is urgently needed to address the many challenges associated with the biosphere in the Anthropocene. Consequently, the critical question becomes: How can science most rapidly progress to address large, complex global problems? We suggest that the lag in the development of a more predictive science of the biosphere is not only because the biosphere is so much more complex, or because we do not have enough data, or are not doing enough experiments, but, in large part, because of unresolved tension between the three dominant scientific cultures that pervade the research community. We introduce and explain the concept of the three scientific cultures and present a novel analysis of their characteristics, supported by examples and a formal mathematical definition/representation of what this means and implies. The three cultures operate, to varying degrees, across all of science. However, within the biosciences, and in contrast to some of the other sciences, they remain relatively more separated, and their lack of integration has hindered their potential power and insight. Our solution to accelerating a broader, predictive science of the biosphere is to enhance integration of scientific cultures. The process of integration-Scientific Transculturalism-recognizes that the push for interdisciplinary research, in general, is just not enough. Unless these cultures of science are formally appreciated and their thinking iteratively integrated into scientific discovery and advancement, there will continue to be numerous significant challenges that will increasingly limit forecasting and prediction efforts.

The floating duck syndrome: biased social learning leads to effort-reward imbalances

An increasingly common phenomenon in modern work and school settings is individuals taking on too many tasks and spending effort without commensurate rewards. Such an imbalance of efforts and rewards leads to myriad negative consequences, such as burnout, anxiety and disease. Here, we develop a model to explain how such effort-reward imbalances can come about as a result of biased social learning dynamics. Our model is based on a phenomenon that on some US college campuses is called 'the floating duck syndrome'. This phrase refers to the social pressure on individuals to advertise their successes but hide the struggles and the effort put in to achieve them. We show that a bias against revealing the true effort results in social learning dynamics that lead others to underestimate the difficulty of the world. This in turn leads individuals to both invest too much total effort and spread this effort over too many activities, reducing the success rate from each activity and creating effort-reward imbalances. We also consider potential ways to counteract the floating duck effect: we find that solutions other than addressing the root cause, biased observation of effort, are unlikely to work.

Pathogen evolution following spillover from a resident to a migrant host population depends on interactions between host pace of life and tolerance to infection

Changes to migration routes and phenology create novel contact patterns among hosts and pathogens. These novel contact patterns can lead to pathogens spilling over between resident and migrant populations. Predicting the consequences of such pathogen spillover events requires understanding how pathogen evolution depends on host movement behaviour. Following spillover, pathogens may evolve changes in their transmission rate and virulence phenotypes because different strategies are favoured by resident and migrant host populations. There is conflict in current theoretical predictions about what those differences might be. Some theory predicts lower pathogen virulence and transmission rates in migrant populations because migrants have lower tolerance to infection. Other theoretical work predicts higher pathogen virulence and transmission rates in migrants because migrants have more contacts with susceptible hosts. We aim to understand how differences in tolerance to infection and host pace of life act together to determine the direction of pathogen evolution following pathogen spillover from a resident to a migrant population. We constructed a spatially implicit model in which we investigate how pathogen strategy changes following the addition of a migrant population. We investigate how differences in tolerance to infection and pace of life between residents and migrants determine the effect of spillover on pathogen evolution and host population size. When the paces of life of the migrant and resident hosts are equal, larger costs of infection in the migrants lead to lower pathogen transmission rate and virulence following spillover. When the tolerance to infection in migrant and resident populations is equal, faster migrant paces of life lead to increased transmission rate and virulence following spillover. However, the opposite can also occur: when the migrant population has lower tolerance to infection, faster migrant paces of life can lead to decreases in transmission rate and virulence. Predicting the outcomes of pathogen spillover requires accounting for both differences in tolerance to infection and pace of life between populations. It is also important to consider how movement patterns of populations affect host contact opportunities for pathogens. These results have implications for wildlife conservation, agriculture and human health.

Modeling endosymbioses: Insights and hypotheses from theoretical approaches

Endosymbiotic relationships are pervasive across diverse taxa of life, offering key avenues for eco-evolutionary dynamics. Although a variety of experimental and empirical frameworks have shed light on critical aspects of endosymbiosis, theoretical frameworks (mathematical models) are especially well-suited for certain tasks. Mathematical models can integrate multiple factors to determine the net outcome of endosymbiotic relationships, identify broad patterns that connect endosymbioses with other systems, simplify biological complexity, generate hypotheses for underlying mechanisms, evaluate different hypotheses, identify constraints that limit certain biological interactions, and open new lines of inquiry. This Essay highlights the utility of mathematical models in endosymbiosis research, particularly in generating relevant hypotheses. Despite their limitations, mathematical models can be used to address known unknowns and discover unknown unknowns.

The evolution of chemodiversity in plants-From verbal to quantitative models

Plants harbour a great chemodiversity, that is diversity of specialised metabolites (SMs), at different scales. For instance, individuals can produce a large number of SMs, and populations can differ in their metabolite composition. Given the ecological and economic importance of plant chemodiversity, it is important to understand how it arises and is maintained over evolutionary time. For other dimensions of biodiversity, that is species diversity and genetic diversity, quantitative models play an important role in addressing such questions. Here, we provide a synthesis of existing hypotheses and quantitative models, that is mathematical models and computer simulations, for the evolution of plant chemodiversity. We describe each model's ingredients, that is the biological processes that shape chemodiversity, the scales it considers and whether it has been formalized as a quantitative model. Although we identify several quantitative models, not all are dynamic and many influential models have remained verbal. To fill these gaps, we outline our vision for the future of chemodiversity modelling. We identify quantitative models used for genetic variation that may be adapted for chemodiversity, and we present a flexible framework for the creation of individual-based models that address different scales of chemodiversity and combine different ingredients that bring this chemodiversity about.

Multi-scale effects of habitat loss and the role of trait evolution

Habitat loss (HL) is a major cause of species extinctions. Although the effects of HL beyond the directly impacted area have been previously observed, they have not been modelled explicitly, especially in an eco-evolutionary context. To start filling this gap, we study a two-patch deterministic consumer-resource model, with one of the patches experiencing loss of resources as a special case of HL. Our model allows foraging and mating within a patch as well as between patches. We then introduce heritable variation in consumer traits related to resource utilization and patch use to investigate eco-evolutionary dynamics and compare results with constant and no trait variation scenarios. Our results show that HL in one patch can indeed reduce consumer densities in the neighbouring patch but can also increase consumer densities in the neighbouring patch when the resources are overexploited. Yet at the landscape scale, the effect of HL on consumer densities is consistently negative. Patch isolation increases consumer density in the patch experiencing HL but has generally negative effects on the neighbouring patch, with context-dependent results at the landscape scale. With high cross-patch dependence and coupled foraging and mating preferences, local HL can sometimes even lead to landscape-level consumer extinction. Eco-evolutionary dynamics can rescue consumers from such extinction in some cases if their death rates are sufficiently small. More generally, trait evolution had positive or negative effects on equilibrium consumer densities after HL, depending on the evolving trait and the spatial scale considered. In summary, our findings show that HL at a local scale can affect the neighbouring patch and the landscape as a whole, where heritable trait variation can, in some cases, alleviate the impact of HL. We thus suggest joint consideration of multiple spatial scales and trait variation when assessing and predicting the impacts of HL.

Open plains are not a level playing field for hominid consonant-like versus vowel-like calls

Africa's paleo-climate change represents an "ecological black-box" along the evolutionary timeline of spoken language; a vocal hominid went in and, millions of years later, out came a verbal human. It is unknown whether or how a shift from forested, dense habitats towards drier, open ones affected hominid vocal communication, potentially setting stage for speech evolution. To recreate how arboreal proto-vowels and proto-consonants would have interacted with a new ecology at ground level, we assessed how a series of orangutan voiceless consonant-like and voiced vowel-like calls travelled across the savannah. Vowel-like calls performed poorly in comparison to their counterparts. Only consonant-like calls afforded effective perceptibility beyond 100 m distance without requiring repetition, as is characteristic of loud calling behaviour in nonhuman primates, typically composed by vowel-like calls. Results show that proto-consonants in human ancestors may have enhanced reliability of distance vocal communication across a canopy-to-ground ecotone. The ecological settings and soundscapes experienced by human ancestors may have had a more profound impact on the emergence and shape of spoken language than previously recognized.

A mathematical representation of the reactive scope model

Researchers have long sought to understand and predict an animal's response to stressful stimuli. Since the introduction of the concept of homeostasis, a variety of model frameworks have been proposed to describe what is necessary for an animal to remain within this stable physiological state and the ramifications of leaving it. Romero et al. (Horm Behav 55(3):375-389, 2009) introduced the reactive scope model to provide a novel conceptual framework for the stress response that assumes an animal's ability to tolerate a stressful stimulus may degrade over time in response to the stimulus. We provide a mathematical formulation for the reactive scope model using a system of ordinary differential equations and show that this model is capable of recreating existing experimental data. We also provide an experimental method that may be used to verify the model as well as several potential additions to the model. If future experimentation provides the necessary data to estimate the model's parameters, the model presented here may be used to make quantitative predictions about physiological mediator levels during a stress response and predict the onset of homeostatic overload.

Feeding the fever: Complex host-pathogen dynamics along continuous resource gradients

Food has long been known to perform dual functions of nutrition and medicine, but mounting evidence suggests that complex host-pathogen dynamics can emerge along continuous resource gradients. Empirical examples of nonmonotonic responses of infection with increasing host resources (e.g., low prevalence at low and high resource supply but high prevalence at intermediate resources) have been documented across the tree of life, but these dynamics, when observed, often are interpreted as nonintuitive, idiosyncratic features of pathogen and host biology. Here, by developing generalized versions of existing models of resource dependence for within- and among-host infection dynamics, we provide a synthetic view of nonmonotonic infection dynamics. We demonstrate that where resources jointly impact two (or more) processes (e.g., growth, defense, transmission, mortality, predation), nonmonotonic infection dynamics, including alternative states, can emerge across a continuous resource supply gradient. We review the few empirical examples that concurrently measured resource effects on multiple rates and pair this with a wide range of examples in which resource dependence of multiple rates could generate nonmonotonic infection outcomes under realistic conditions. This review and generalized framework highlight the likely generality of such resource effects in natural systems and point to opportunities ripe for future empirical and theoretical work.

Gaps in modelling animal migration with evolutionary game theory: infection can favour the loss of migration

Ongoing environmental changes alter how natural selection shapes animal migration. Understanding how these changes play out theoretically can be done using evolutionary game theoretic (EGT) approaches, such as looking for evolutionarily stable strategies. Here, we first describe historical patterns of how EGT models have explored different drivers of migration. We find that there are substantial gaps in both the taxa (mammals, amphibians, reptiles, insects) and mechanisms (mutualism, interspecific competition) included in past EGT models of migration. Although enemy interactions, including parasites, are increasingly considered in models of animal migration, they remain the least studied of factors for migration considered to date. Furthermore, few papers look at changes in migration in response to perturbations (e.g. climate change, new species interactions). To address this gap, we present a new EGT model to understand how infection with a novel parasite changes host migration. We find three possible outcomes when migrants encounter novel parasites: maintenance of migration (despite the added infection cost), loss of migration (evolutionary shift to residency) or population collapse, depending on the risk and cost of getting infected, and the cost currency. Our work demonstrates how emerging infection can alter animal behaviour such as migration. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Defining the Benefits of Antibiotic Resistance in Commensals and the Scope for Resistance Optimization

Antibiotic resistance is a major medical and public health challenge, characterized by global increases in the prevalence of resistant strains. The conventional view is that all antibiotic resistance is problematic, even when not in pathogens. Resistance in commensal bacteria poses risks, as resistant organisms can provide a reservoir of resistance genes that can be horizontally transferred to pathogens or may themselves cause opportunistic infections in the future. While these risks are real, we propose that commensal resistance can also generate benefits during antibiotic treatment of human infection, by promoting continued ecological suppression of pathogens. To define and illustrate this alternative conceptual perspective, we use a two-species mathematical model to identify the necessary and sufficient ecological conditions for beneficial resistance. We show that the benefits are limited to species (or strain) interactions where commensals suppress pathogen growth and are maximized when commensals compete with, rather than prey on or otherwise exploit pathogens. By identifying benefits of commensal resistance, we propose that rather than strictly minimizing all resistance, resistance management may be better viewed as an optimization problem. We discuss implications in two applied contexts: bystander (nontarget) selection within commensal microbiomes and pathogen treatment given polymicrobial infections. IMPORTANCE Antibiotic resistance is commonly viewed as universally costly, regardless of which bacterial cells express resistance. Here, we derive an opposing logic, where resistance in commensal bacteria can lead to reductions in pathogen density and improved outcomes on both the patient and public health scales. We use a mathematical model of commensal-pathogen interactions to define the necessary and sufficient conditions for beneficial resistance, highlighting the importance of reciprocal ecological inhibition to maximize the benefits of resistance. More broadly, we argue that determining the benefits as well as the costs of resistances in human microbiomes can transform resistance management from a minimization to an optimization problem. We discuss applied contexts and close with a review of key resistance optimization dimensions, including the magnitude, spectrum, and mechanism of resistance.

Inter-annual facilitation via pollinator support arises with species-specific germination rates in a model of plant-pollinator communities

Facilitation is likely important for understanding community diversity dynamics, but its myriad potential mechanisms are under-investigated. Studies of pollinator-mediated facilitation in plants, for example, are typically focused on how co-flowering species facilitate each other's pollination within a season. However, pollinator-mediated facilitation could also arise in the form of inter-annual pollination support, where co-occurring plant populations mutually facilitate each other by providing dynamic stability to support a pollinator population through time. In this work, I test this hypothesis with simulation models of annual flowering plant and bee pollinator populations to determine if and how inter-annual pollination support affects the persistence and/or stability of simulated communities. Two-species plant communities persisted at higher rates than single-species communities, and facilitation was strongest in communities with low mean germination rates and highly species-specific responses to environmental variation. Single-species communities were often more stable than their counterparts, likely because of survivorship-persistent single-species communities were necessarily more stable through time to support pollinators. This work shows that competition and facilitation can simultaneously affect plant population dynamics. It also importantly identifies key features of annual plant communities that might exhibit inter-annual pollination support- those with low germination rates and species-specific responses to variation.

Genetic conflicts and the case for licensed anthropomorphizing

The use of intentional language in biology is controversial. It has been commonly applied by researchers in behavioral ecology, who have not shied away from employing agential thinking or even anthropomorphisms, but has been rarer among researchers from more mechanistic corners of the discipline, such as population genetics. One research area where these traditions come into contact—and occasionally clash—is the study of genetic conflicts, and its history offers a good window to the debate over the use of intentional language in biology. We review this debate, paying particular attention to how this interaction has played out in work on genomic imprinting and sex chromosomes. In light of this, we advocate for a synthesis of the two approaches, a form of licensed anthropomorphizing. Here, agential thinking’s creative potential and its ability to identify the fulcrum of evolutionary pressure are combined with the rigidity of formal mathematical modeling.

EcoEvoApps: Interactive apps for theoretical models in ecology and evolutionary biology

The integration of theory and data drives progress in science, but a persistent barrier to such integration in ecology and evolutionary biology is that theory is often developed and expressed in the form of mathematical models that can feel daunting and inaccessible for students and empiricists with variable quantitative training and attitudes towards math. A promising way to make mathematical models more approachable is to embed them into interactive tools with which one can visually evaluate model structures and directly explore model outcomes through simulation. To promote such interactive learning of quantitative models, we developed EcoEvoApps, a collection of free, open-source, and multilingual R/Shiny apps that include model overviews, interactive model simulations, and code to implement these models directly in R. The package currently focuses on canonical models of population dynamics, species interactions, and landscape ecology. These apps help illustrate fundamental results from theoretical ecology and can serve as valuable teaching tools in classroom settings. We present data from student surveys which show that students rate these apps as useful learning tools, and that using interactive apps leads to substantial gains in students' interest and confidence in working with mathematical models. This points to the potential for interactive activities to make theoretical models more accessible to a wider audience, and thus facilitate the feedback between theory and data across ecology and evolutionary biology.

What Makes Inventions Become Traditions?

Although anthropology was the first academic discipline to investigate cultural change, many other disciplines have made noteworthy contributions to understanding what influences the adoption of new behaviors. Drawing on a broad, interdisciplinary literature covering both humans and nonhumans, we examine ( a) which features of behavioral traits make them more transmissible, ( b) which individual characteristics of inventors promote copying of their inventions, ( c) which characteristics of individuals make them more prone to adopting new behaviors, ( d) which characteristics of dyadic relationships promote cultural transmission, ( e) which properties of groups (e.g., network structures) promote transmission of traits, and ( f) which characteristics of groups promote retention, rather than extinction, of cultural traits. One of anthropology's strengths is its readiness to adopt and improve theories and methods from other disciplines, integrating them into a more holistic approach; hence, we identify approaches that might be particularly useful to biological and cultural anthropologists, and knowledge gaps that should be filled.

Religious celibacy brings inclusive fitness benefits

The influence of inclusive fitness interests on the evolution of human institutions remains unclear. Religious celibacy constitutes an especially puzzling institution, often deemed maladaptive. Here, we present sociodemographic data from an agropastoralist Buddhist population in western China, where parents sometimes sent a son to the monastery. We find that men with a monk brother father more children, and grandparents with a monk son have more grandchildren, suggesting that the practice is adaptive. We develop a model of celibacy to elucidate the inclusive fitness costs and benefits associated with this behaviour. We show that a minority of sons being celibate can be favoured if this increases their brothers' reproductive success, but only if the decision is under parental, rather than individual, control. These conditions apply to monks in our study site. Inclusive fitness considerations appear to play a key role in shaping parental preferences to adopt this cultural practice.

Epigenetic induction may speed up or slow down speciation with gene flow

Speciation is less likely to occur when there is gene flow between nascent species. Natural selection can oppose gene flow and promote speciation if there is variation in ecological conditions among the nascent species' locations. Previous theory on ecological speciation with gene flow has focused primarily on the role of genetic variation in ecological traits, largely neglecting the role of nongenetic inheritance or transgenerational plasticity. Here, we build and analyze models incorporating both genetic and epigenetic inheritance, the latter representing a form of nongenetic inheritance. We investigate the rate of speciation for a population that inhabits two patches connected by migration, and find that adaptively biased epigenetic induction can speed up or slow down speciation, depending on the form of the map from genotype and epigenotype to phenotype. While adaptively relevant epigenetic variation can speed up speciation by reducing the fitness of migrants and hybrids, it can also slow down speciation. This latter effect occurs when the epialleles are able to achieve adaptation faster than the genetic alleles, thereby weakening selection on the latter.

BioSANS: A software package for symbolic and numeric biological simulation

Modeling biochemical systems can provide insights into behaviors that are difficult to observe or understand. It requires software, programming, and understanding of the system to build a model and study it. Softwares exist for systems biology modeling, but most support only certain types of modeling tasks. Desirable features including ease in preparing input, symbolic or analytical computation, parameter estimation, graphical user interface, and systems biology markup language (SBML) support are not seen concurrently in one software package. In this study, we developed a python-based software that supports these features, with both deterministic and stochastic propagations. The software can be used by graphical user interface, command line, or as a python import. We also developed a semi-programmable and intuitively easy topology input method for the biochemical reactions. We tested the software with semantic and stochastic SBML test cases. Tests on symbolic solution and parameter estimation were also included. The software we developed is reliable, well performing, convenient to use, and compliant with most of the SBML tests. So far it is the only systems biology software that supports symbolic, deterministic, and stochastic modeling in one package that also features parameter estimation and SBML support. This work offers a comprehensive set of tools and allows for better availability and accessibility for studying kinetics and dynamics in biochemical systems.

Phylogenetic inference of where species spread or split across barriers

SignificanceGeography molds how species evolve in space. Strong geographical barriers to movement, for instance, both inhibit dispersal between regions and allow isolated populations to diverge as new species. Weak barriers, by contrast, permit species range expansion and persistence. These factors present a conundrum: How strong must a barrier be before between-region speciation outpaces dispersal? We designed a phylogenetic model of dispersal, extinction, and speciation that allows regional features to influence rates of biogeographic change and applied it to the neotropical radiation of Anolis lizards. Separation by water induces a threefold steeper barrier to movement than equivalent distances over land. Our model will help biologists detect relationships between evolutionary processes and the spatial contexts in which they operate.

Sexual dimorphism in phenotypic plasticity and persistence under environmental change: An extension of theory and meta-analysis of current data

Populations must adapt to environmental changes to remain viable. Both evolution and phenotypic plasticity contribute to adaptation, with plasticity possibly being more important for coping with rapid change. Adaptation is complex in species with separate sexes, as the sexes can differ in the strength or direction of natural selection, the genetic basis of trait variation, and phenotypic plasticity. Many species show sex differences in plasticity, yet how these differences influence extinction susceptibility remains unclear. We first extend theoretical models of population persistence in changing environments and show that persistence is affected by sexual dimorphism for phenotypic plasticity, trait genetic architecture, and sex-specific selection. Our models predict that female-biased adaptive plasticity-particularly in traits with modest-to-low cross-sex genetic correlations-typically promotes persistence, though we also identify conditions where sexually monomorphic or male-biased plasticity promotes persistence. We then perform a meta-analysis of sex-specific plasticity under manipulated thermal conditions. Although examples of sexually dimorphic plasticity are widely observed, systematic sex differences are rare. An exception-cold resistance-is systematically female-biased and represents a trait wherein sexually dimorphic plasticity might elevate population viability in changing environments. We discuss our results in light of debates about the roles of evolution and plasticity in extinction susceptibility.

A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis

The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo. This process is characterised by the formation of EPC clusters during its early stages and, while much progress has been made in identifying various mechanisms underlying cluster formation, we are still far from a comprehensive description of such spatio-temporal dynamics. In order to achieve this, we propose a novel mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of nonlocal partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion. We conduct a linear stability analysis on the system and solve the equations numerically. We then conduct a parametric analysis of the numerical solutions of the one-dimensional problem to investigate the role of underlying dynamics on the speed of cluster formation and the size of clusters, measured via appropriate metrics for the cluster width and compactness. We verify the key results of the parametric analysis with simulations of the two-dimensional problem. Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation of clusters, suggesting chemotaxis is responsible for the cluster topology while matrix degradation is responsible for the speed of cluster formation. Our results also indicate that the nonlocal cell-to-cell adhesion term in our model, even though it initially causes cells to aggregate, is not sufficient to ensure clusters are stable over long time periods. Consequently, new modelling strategies for cell-to-cell adhesion are required to stabilise in silico clusters. We end the paper with a thorough discussion of promising, fruitful future modelling and experimental research perspectives.

System drift and speciation

Even if a species' phenotype does not change over evolutionary time, the underlying mechanism may change, as distinct molecular pathways can realize identical phenotypes. Here we use linear system theory to explore the consequences of this idea, describing how a gene network underlying a conserved phenotype evolves, as the genetic drift of small changes to these molecular pathways causes a population to explore the set of mechanisms with identical phenotypes. To do this, we model an organism's internal state as a linear system of differential equations for which the environment provides input and the phenotype is the output, in which context there exists an exact characterization of the set of all mechanisms that give the same input-output relationship. This characterization implies that selectively neutral directions in genotype space should be common and that the evolutionary exploration of these distinct but equivalent mechanisms can lead to the reproductive incompatibility of independently evolving populations. This evolutionary exploration, or system drift, is expected to proceed at a rate proportional to the amount of intrapopulation genetic variation divided by the effective population size ( Ne$N_e$ ). At biologically reasonable parameter values this could lead to substantial interpopulation incompatibility, and thus speciation, on a time scale of Ne$N_e$ generations. This model also naturally predicts Haldane's rule, thus providing a concrete explanation of why heterogametic hybrids tend to be disrupted more often than homogametes during the early stages of speciation.

Writing Accessible Theory in Ecology and Evolution: Insights from Cognitive Load Theory

Theories underpin science. In biology, theories are often formalized in the form of mathematical models, which may render them inaccessible to those lacking mathematical training. In the present article, we consider how theories could be presented to better aid understanding. We provide concrete recommendations inspired by cognitive load theory, a branch of psychology that addresses impediments to knowledge acquisition. We classify these recommendations into two classes: those that increase the links between new and existing information and those that reduce unnecessary or irrelevant complexities. For each, we provide concrete examples to illustrate the scenarios in which they apply. By enhancing a reader's familiarity with the material, these recommendations lower the mental capacity required to learn new information. Our hope is that these recommendations can provide a pathway for theoreticians to increase the accessibility of their work and for empiricists to engage with theory, strengthening the feedback between theory and experimentation.

Trajectories of Idea Emergence in Dialogic Collaborative Problem Solving: Toward a Complex Dynamic Systems Perspective

According to the complex dynamic systems (CDS) perspective, learning emerges at various system levels. This study built a coherent theoretical framework based on CDS and Bakhtinian dialogic theory and further employed the concept of attractor (i.e., certain stable states that recur over time) in CDS theory to investigate the trajectories of idea emergence and how they diversified group outcomes in dialogic collaborative problem solving (D-CPS). Two contrasting groups were compared using visual and qualitative analysis approaches. The analysis based on idea tree diagrams showed that new ideas emergent in group discussion tended to attract local utterances and performed features of attractors in CDS in both high-performing and low-performing groups. The analysis based on idea hierarchy diagrams revealed how ideas emerged at various system levels. It was also found that status problems were likely to affect the functioning of regulative feedback loops, which might give rise to different structures of idea evolution. This study proposed CDS theory as an alternative perspective, augmented by the ethical considerations of Bakhtinian dialogism, for examining the dynamics of D-CPS.

Insect-host control of obligate, intracellular symbiont density

Many insects rely on intracellular bacterial symbionts to supplement their specialized diets with micronutrients. Using data from diverse and well-studied insect systems, we propose three lines of evidence suggesting that hosts have tight control over the density of their obligate, intracellular bacterial partners. First, empirical studies have demonstrated that the within-host symbiont density varies depending on the nutritional and developmental requirements of the host. Second, symbiont genomes are highly reduced and have limited capacity for self-replication or transcriptional regulation. Third, several mechanisms exist for hosts to tolerate, regulate and remove symbionts including physical compartmentalization and autophagy. We then consider whether such regulation is adaptive, by discussing the relationship between symbiont density and host fitness. We discuss current limitations of empirical studies for exploring fitness effects in host-symbiont relationships, and emphasize the potential for using mathematical models to formalize evolutionary hypotheses and to generate testable predictions for future work.

Estimation of the strength of mate preference from mated pairs observed in the wild

A number of key processes in evolution are driven by individuals preferring mates with particular phenotypes. However, despite long‐standing interest, it is difficult to quantify the strength of mate preference from phenotypic observations in nature in a way that connects directly to key parameters in theoretical models. To bridge the gap between mathematical models and empirical data, we develop a novel maximum likelihood‐based method to estimate the strength and form of mate preference, where preference depends on traits expressed in both males and females. Using simulated data, we demonstrate that our method accurately infers model parameters, including the strength of mate preference and the optimal offset match between trait values in mated pairs when model assumptions are satisfied. Applying our method to two previous studies of assortative mating in marine gastropods and the European common frog, we support previous findings, but also give additional insight into the role of mate preference in each system. Our method can be generalized to a variety of plant and animal taxa that exhibit mating preferences to facilitate the testing of evolutionary hypotheses and link empirical data to theoretical models of assortative mating, sexual selection, and speciation.

Culture without copying or selection

Typical examples of cultural phenomena all exhibit a degree of similarity across time and space at the level of the population. As such, a fundamental question for any science of culture is, what ensures this stability in the first place? Here we focus on the evolutionary and stabilising role of 'convergent transformation', in which one item causes the production of another item whose form tends to deviate from the original in a directed, non-random way. We present a series of stochastic models of cultural evolution investigating its effects. The results show that cultural stability can emerge and be maintained by virtue of convergent transformation alone, in the absence of any form of copying or selection process. We show how high-fidelity copying and convergent transformation need not be opposing forces, and can jointly contribute to cultural stability. We finally analyse how non-random transformation and high-fidelity copying can have different evolutionary signatures at population level, and hence how their distinct effects can be distinguished in empirical records. Collectively, these results supplement existing approaches to cultural evolution based on the Darwinian analogy, while also providing formal support for other frameworks - such as Cultural Attraction Theory - that entail its further loosening.

Social media summary

Culture can be produced and maintained by convergent transformation, without copying or selection involved.

How can we fully realize the potential of mathematical and biological models to reintegrate biology?

Both mathematical models and biological model systems stand as tractable representations of complex biological systems or behaviors. They facilitate research and provide insights, and they can describe general rules. Models that represent biological processes or formalize general hypotheses are essential to any broad understanding. Mathematical or biological models necessarily omit details of the natural systems and thus may ultimately be "incorrect" representations. A key challenge is that tractability requires relatively simple models but simplification can result in models that are incorrect in their qualitative, broad implications if the abstracted details matter. Our paper discusses this tension, and how we can improve our inferences from models. We advocate for further efforts dedicated to model development, improvement, and acceptance by the scientific community, all of which may necessitate a more explicit discussion of the purpose and power of models. We argue that models should play a central role in reintegrating biology as a way to test our integrated understanding of how molecules, cells, organs, organisms, populations, and ecosystems function.

Evaluating kin and group selection as tools for quantitative analysis of microbial data

Kin selection and multilevel selection theory are often used to interpret experiments about the evolution of cooperation and social behaviour among microbes. But while these experiments provide rich, detailed fitness data, theory is mostly used as a conceptual heuristic. Here, we evaluate how kin and multilevel selection theory perform as quantitative analysis tools. We reanalyse published microbial datasets and show that the canonical fitness models of both theories are almost always poor fits because they use statistical regressions misspecified for the strong selection and non-additive effects we show are widespread in microbial systems. We identify analytical practices in empirical research that suggest how theory might be improved, and show that analysing both individual and group fitness outcomes helps clarify the biology of selection. A data-driven approach to theory thus shows how kin and multilevel selection both have untapped potential as tools for quantitative understanding of social evolution in all branches of life.

The evolution of habitat construction with and without phenotypic plasticity

Habitat construction and phenotypic plasticity are alternative responses to variable environments. We explored evolution along an environmental gradient of habitat construction alone and in combination with phenotypic plasticity using individual-based simulations that manipulated the fitness benefit of construction and whether construction maintained or eliminated that gradient. Construction was favored when its benefits were more likely to flow to the immediate offspring of the constructing individuals. Habitat construction and phenotypic plasticity traded off against each other or plasticity was selected against, depending on how the optimum environment varied and with the fitness value of construction. When selection favored differences in the amount of construction along the environmental gradient, genetic differentiation for habitat construction increased as the fitness value of construction increased. The degree to which each adaptive response was likely to evolve also depended on the precise ordering of life history events. Adaptive habitat construction does not always occur and may be selected against.

Skin deep: The decoupling of genetic admixture levels from phenotypes that differed between source populations

OBJECTIVES

In genetic admixture processes, source groups for an admixed population possess distinct patterns of genotype and phenotype at the onset of admixture. Particularly in the context of recent and ongoing admixture, such differences are sometimes taken to serve as markers of ancestry for individuals-that is, phenotypes initially associated with the ancestral background in one source population are assumed to continue to reflect ancestry in that population. Such phenotypes might possess ongoing significance in social categorizations of individuals, owing in part to perceived continuing correlations with ancestry. However, genotypes or phenotypes initially associated with ancestry in one specific source population have been seen to decouple from overall admixture levels, so that they no longer serve as proxies for genetic ancestry. Here, we aim to develop an understanding of the joint dynamics of admixture levels and phenotype distributions in an admixed population.

METHODS

We devise a mechanistic model, consisting of an admixture model, a quantitative trait model, and a mating model. We analyze the behavior of the mechanistic model in relation to the model parameters.

RESULTS

We find that it is possible for the decoupling of genetic ancestry and phenotype to proceed quickly, and that it occurs faster if the phenotype is driven by fewer loci. Positive assortative mating attenuates the process of dissociation relative to a scenario in which mating is random with respect to genetic admixture and with respect to phenotype.

CONCLUSIONS

The mechanistic framework suggests that in an admixed population, a trait that initially differed between source populations might serve as a reliable proxy for ancestry for only a short time, especially if the trait is determined by few loci. It follows that a social categorization based on such a trait is increasingly uninformative about genetic ancestry and about other traits that differed between source populations at the onset of admixture.

Ecosystem engineering in the Quaternary of the West Coast of South Africa

Despite advances in our understanding of the geographic and temporal scope of the Paleolithic record, we know remarkably little about the evolutionary and ecological consequences of changes in human behavior. Recent inquiries suggest that human evolution reflects a long history of interconnections between the behavior of humans and their surrounding ecosystems (e.g., niche construction). Developing expectations to identify such phenomena is remarkably difficult because it requires understanding the multi-generational impacts of changes in behavior. These long-term dynamics require insights into the emergent phenomena that alter selective pressures over longer time periods which are not possible to observe, and are also not intuitive based on observations derived from ethnographic time scales. Generative models show promise for probing these potentially unexpected consequences of human-environment interaction. Changes in the uses of landscapes may have long term implications for the environments that hominins occupied. We explore other potential proxies of behavior and examine how modeling may provide expectations for a variety of phenomena.

Lessons from movement ecology for the return to work: Modeling contacts and the spread of COVID-19

Human behavior (movement, social contacts) plays a central role in the spread of pathogens like SARS-CoV-2. The rapid spread of SARS-CoV-2 was driven by global human movement, and initial lockdown measures aimed to localize movement and contact in order to slow spread. Thus, movement and contact patterns need to be explicitly considered when making reopening decisions, especially regarding return to work. Here, as a case study, we consider the initial stages of resuming research at a large research university, using approaches from movement ecology and contact network epidemiology. First, we develop a dynamical pathogen model describing movement between home and work; we show that limiting social contact, via reduced people or reduced time in the workplace are fairly equivalent strategies to slow pathogen spread. Second, we develop a model based on spatial contact patterns within a specific office and lab building on campus; we show that restricting on-campus activities to labs (rather than labs and offices) could dramatically alter (modularize) contact network structure and thus, potentially reduce pathogen spread by providing a workplace mechanism to reduce contact. Here we argue that explicitly accounting for human movement and contact behavior in the workplace can provide additional strategies to slow pathogen spread that can be used in conjunction with ongoing public health efforts.

Towards an Evolutionary Theory of Stress Responses

All organisms have a stress response system to cope with environmental threats, yet its precise form varies hugely within and across individuals, populations, and species. While the physiological mechanisms are increasingly understood, how stress responses have evolved remains elusive. Here, we show that important insights can be gained from models that incorporate physiological mechanisms within an evolutionary optimality analysis (the 'evo-mecho' approach). Our approach reveals environmental predictability and physiological constraints as key factors shaping stress response evolution, generating testable predictions about variation across species and contexts. We call for an integrated research programme combining theory, experimental evolution, and comparative analysis to advance scientific understanding of how this core physiological system has evolved.

Disease modeling for public health: added value, challenges, and institutional constraints

Public health policymakers face increasingly complex questions and decisions and need to deal with an increasing quantity of data and information. For policy advisors to make use of scientific evidence and to assess available intervention options effectively and therefore indirectly for those deciding on and implementing public health policies, mathematical modeling has proven to be a useful tool. In some areas, the use of mathematical modeling for public health policy support has become standard practice at various levels of decision-making. To make use of this tool effectively within public health organizations, it is necessary to provide good infrastructure and ensure close collaboration between modelers and policymakers. Based on experience from a national public health institute, we discuss the strategic requirements for good modeling practice for public health. For modeling to be of maximal value for a public health institute, the organization and budgeting of mathematical modeling should be transparent, and a long-term strategy for how to position and develop mathematical modeling should be in place.

How to Translate a Verbal Theory Into a Formal Model

Abstract. Turning verbal theories into formal models is an essential business of a mature science. Here I elaborate on taxonomies of models, provide ten lessons for translating a verbal theory into a formal model, and discuss the specific challenges involved in collaborations between modelers and non-modelers. It’s a start.

A modern method of multiple working hypotheses to improve inference in ecology

Science provides a method to learn about the relationships between observed patterns and the processes that generate them. However, inference can be confounded when an observed pattern cannot be clearly and wholly attributed to a hypothesized process. Over-reliance on traditional single-hypothesis methods (i.e. null hypothesis significance testing) has resulted in replication crises in several disciplines, and ecology exhibits features common to these fields (e.g. low-power study designs, questionable research practices, etc.). Considering multiple working hypotheses in combination with pre-data collection modelling can be an effective means to mitigate many of these problems. We present a framework for explicitly modelling systems in which relevant processes are commonly omitted, overlooked or not considered and provide a formal workflow for a pre-data collection analysis of multiple candidate hypotheses. We advocate for and suggest ways that pre-data collection modelling can be combined with consideration of multiple working hypotheses to improve the efficiency and accuracy of research in ecology.

Experimental evolutionary simulations of learning, memory and life history

Humans possess an unusual combination of traits, including our cognition, life history, demographics and geographical distribution. Many theories propose that these traits have coevolved. Such hypotheses have been explored both theoretically and empirically, with experiments examining whether human behaviour meets theoretical expectations. However, theory must make assumptions about the human mind, creating a potentially problematic gap between models and reality. Here, we employ a series of 'experimental evolutionary simulations' to reduce this gap and to explore the coevolution of learning, memory and childhood. The approach combines aspects of theory and experiment by inserting human participants as agents within an evolutionary simulation. Across experiments, we find that human behaviour supports the coevolution of learning, memory and childhood, but that this is dampened by rapid environmental change. We conclude by discussing both the implications of these findings for theories of human evolution and the utility of experimental evolutionary simulations more generally. This article is part of the theme issue 'Life history and learning: how childhood, caregiving and old age shape cognition and culture in humans and other animals'.

Fifty years of Theoretical Population Biology

The year 2020 marks the 50th anniversary of Theoretical Population Biology. This special issue examines the past and continuing contributions of the journal. We identify some of the most important developments that have taken place in the pages of TPB, connecting them to current research and to the numerous forms of significance achieved by theory in population biology.