Population genetics in microchannels.

SignificanceMany microbial populations proliferate in small channels. In such environments, reproducing cells organize in parallel lanes. Reproducing cells shift these lanes, potentially expelling other cells from the channel. In this paper, we combine theory and experiments to understand how these dynamics affects the diversity of a microbial population. We theoretically predict that genetic diversity is quickly lost along lanes of cells. Our experiments confirm that a population of proliferating Escherichia coli in a microchannel organizes into lanes of genetically identical cells within a few generations. Our findings elucidate the effect of lane formation on populations evolution, with potential applications ranging from microbial ecology in soil to dynamics of epithelial tissues in higher organisms.

Density-dependent species interactions modulate alpine treeline shifts.

Species interactions such as facilitation and competition play a crucial role in driving species range shifts. However, density dependence as a key feature of these processes has received little attention in both empirical and modelling studies. Herein, we used a novel, individual-based treeline model informed by rich in situ observations to quantify the contribution of density-dependent species interactions to alpine treeline dynamics, an iconic biome boundary recognized as an indicator of global warming. We found that competition and facilitation dominate in dense versus sparse vegetation scenarios respectively. The optimal balance between these two effects was identified at an intermediate vegetation thickness where the treeline elevation was the highest. Furthermore, treeline shift rates decreased sharply with vegetation thickness and the associated transition from positive to negative species interactions. We thus postulate that vegetation density must be considered when modelling species range dynamics to avoid inadequate predictions of its responses to climate warming.

An individual-based model to explore the impact of psychological stress on immune infiltration into tumour spheroids.

In recentin vitroexperiments on co-culture between breast tumour spheroids and activated immune cells, it was observed that the introduction of the stress hormone cortisol resulted in a decreased immune cell infiltration into the spheroids. Moreover, the presence of cortisol deregulated the normal levels of the pro- and anti-inflammatory cytokines IFN-γand IL-10. We present an individual-based model to explore the interaction dynamics between tumour and immune cells under psychological stress conditions. With our model, we explore the processes underlying the emergence of different levels of immune infiltration, with particular focus on the biological mechanisms regulated by IFN-γand IL-10. The set-up of numerical simulations is defined to mimic the scenarios considered in the experimental study. Similarly to the experimental quantitative analysis, we compute a score that quantifies the level of immune cell infiltration into the tumour. The results of numerical simulations indicate that the motility of immune cells, their capability to infiltrate through tumour cells, their growth rate and the interplay between these cell parameters can affect the level of immune cell infiltration in different ways. Ultimately, numerical simulations of this model support a deeper understanding of the impact of biological stress-induced mechanisms on immune infiltration.

Neutral processes underlying the macro eco-evolutionary dynamics of mixed-ploidy systems.

Polyploidy, i.e. the occurrence of multiple sets of chromosomes, is regarded as an important phenomenon in plant ecology and evolution, with all flowering plants likely having a polyploid ancestry. Owing to genome shock, minority cytotype exclusion and reduced fertility, polyploids emerging in diploid populations are expected to face significant challenges to successful establishment. Their establishment and persistence are often explained by possible fitness or niche differences that would relieve the competitive pressure with diploid progenitors. Experimental evidence for such advantages is, however, not unambiguous, and considerable niche overlap exists among most polyploid species and their diploid counterparts. Here, we develop a neutral spatially explicit eco-evolutionary model to understand whether neutral processes can explain the eco-evolutionary patterns of polyploids. We present a general mechanism for polyploid establishment by showing that sexually reproducing organisms assemble in space in an iterative manner, reducing frequency-dependent mating disadvantages and overcoming potential reduced fertility issues. Moreover, we construct a mechanistic theoretical framework that allows us to understand the long-term evolution of mixed-ploidy populations and show that our model is remarkably consistent with recent phylogenomic estimates of species extinctions in the Brassicaceae family.

The effect of population model choice and network topologies on extinction time patterns in dendritic ecological networks.

Models of populations in habitat networks are vital for understanding and linking processes and patterns across individuals, environments, ecological interactions, and population structures. River ecosystem models combine the physical structure of the networks with the biological processes of the organisms using structural and functional models, respectively. Previous studies on dendritic river networks have employed different functional (population) models and either directly claimed or implied that the results illustrate general properties of actual river systems. However, these studies have used different approaches and assumptions when modeling population characteristics and behavior, and it is possible that inferences regarding a system may vary based on the combination of functional model and the spatial structure of a network. This study aims to understand if different functional models in river systems produce substantially different model results and, therefore, whether conclusions are model-dependent. We compare variation in extinction time and occupancy proportion of river networks with linear, trellis, dendritic and ring-lattice topologies, using three population models (uniform, age-class and individual based) and one metapopulation-based (patch-occupancy) model. Dendritic, linear, and trellis structures did not show notable differences among extinction times for any of the four models. The difference between topologies was higher for the patch-occupancy model compared to the three population models. There were significant differences in the variations of patch-occupancy between the metapopulation and the population models, but the three population models of differing complexity produced broadly similar results. Therefore, if the occupancy data is obtained based on local subpopulations, spatial arrangement and connectivity does not appear to be the sole predictor of single-species metapopulation responses. We conclude that the outputs from functional models are robust to assumptions and varying levels of detail as long as they contain at least some detail at the level of individuals within habitat nodes. Also, if we are modeling network-scale populations, models that include at least some detailed information on individuals are a far better choice than considering populations implicitly.

How to scale up from animal movement decisions to spatiotemporal patterns: An approach via step selection.

Uncovering the mechanisms behind animal space use patterns is of vital importance for predictive ecology, thus conservation and management of ecosystems. Movement is a core driver of those patterns so understanding how movement mechanisms give rise to space use patterns has become an increasingly active area of research. This study focuses on a particular strand of research in this area, based around step selection analysis (SSA). SSA is a popular way of inferring drivers of movement decisions, but, perhaps less well appreciated, it also parametrises a model of animal movement. Of key interest is that this model can be propagated forwards in time to predict the space use patterns over broader spatial and temporal scales than those that pertain to the proximate movement decisions of animals. Here, we provide a guide for understanding and using the various existing techniques for scaling up step selection models to predict broad-scale space use patterns. We give practical guidance on when to use which technique, as well as specific examples together with code in R and Python. By pulling together various disparate techniques into one place, and providing code and instructions in simple examples, we hope to highlight the importance of these techniques and make them accessible to a wider range of ecologists, ultimately helping expand the usefulness of SSA.

Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems.

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Agent-Based and Continuum Models for Spatial Dynamics of Infection by Oncolytic Viruses.

The use of oncolytic viruses as cancer treatment has received considerable attention in recent years, however the spatial dynamics of this viral infection is still poorly understood. We present here a stochastic agent-based model describing infected and uninfected cells for solid tumours, which interact with viruses in the absence of an immune response. Two kinds of movement, namely undirected random and pressure-driven movements, are considered: the continuum limit of the models is derived and a systematic comparison between the systems of partial differential equations and the individual-based model, in one and two dimensions, is carried out. In the case of undirected movement, a good agreement between agent-based simulations and the numerical and well-known analytical results for the continuum model is possible. For pressure-driven motion, instead, we observe a wide parameter range in which the infection of the agents remains confined to the center of the tumour, even though the continuum model shows traveling waves of infection; outcomes appear to be more sensitive to stochasticity and uninfected regions appear harder to invade, giving rise to irregular, unpredictable growth patterns. Our results show that the presence of spatial constraints in tumours' microenvironments limiting free expansion has a very significant impact on virotherapy. Outcomes for these tumours suggest a notable increase in variability. All these aspects can have important effects when designing individually tailored therapies where virotherapy is included.

Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems.

Theoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al. Nat Commun 10:4716, 2019). To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when MFPMs fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs' applicability in cancer research.

Teaching the Modeling of Human-Environment Systems: Acknowledging Complexity with an Agent-Based Model.

Agent-based modeling is a promising tool for familiarizing students with complex systems as well as programming skills. Human-environment systems, for instance, entail complex interdependencies that need to be considered when modeling these systems. This complexity is often neglected in teaching modeling approaches. For a heterogeneous group of master's students at a German university, we pre-built an agent-based model. In class, this was used to teach modeling impacts of land use policies and markets on ecosystem services. As part of the course, the students had to perform small research projects with the model in groups of two. This study aims to evaluate how well students could deal with the complexity involved in the model based on their group work outcomes. Chosen indicators were, e.g., the appropriateness of their research goals, the suitability of the methods applied, and how well they acknowledged the limitations. Our study results revealed that teaching complex systems does not need to be done with too simplistic models. Most students, even with little background in modeling and programming, were able to deal with the complex model setup, conduct small research projects, and have a thoughtful discussion on the limitations involved. With adequate theoretical input during lectures, we recommend using models that do not hide the complexity of the systems but foster a realistic simplification of the interactions. Supplementary Information: The online version contains supplementary material available at 10.1007/s10956-022-10022-z.

Demographic consequences of heterogeneity in conspecific density dependence among mast-fruiting tropical trees.

The role of conspecific density dependence (CDD) in the maintenance of species richness is a central focus of tropical forest ecology. However, tests of CDD often ignore the integrated effects of CDD over multiple life stages and their long-term impacts on population demography. We combined a 10-year time series of seed production, seedling recruitment and sapling and tree demography of three dominant Southeast Asian tree species that adopt a mast-fruiting phenology. We used these data to construct individual-based models that examine the effects of CDD on population growth rates (λ) across life-history stages. Recruitment was driven by positive CDD for all species, supporting the predator satiation hypothesis, while negative CDD affected seedling and sapling growth of two species, significantly reducing λ. This negative CDD on juvenile growth overshadowed the positive CDD of recruitment, suggesting the cumulative effects of CDD during seedling and sapling development has greater importance than the positive CDD during infrequent masting events. Overall, CDD varied among positive, neutral and negative effects across life-history stages for all species, suggesting that assessments of CDD on transitions between just two stages (e.g. seeds seedlings or juveniles mature trees) probably misrepresent the importance of CDD on population growth and stability.

A mathematical model to study the impact of intra-tumour heterogeneity on anti-tumour CD8+ T cell immune response.

Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune response against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the percentage of immunogenic cells (i.e. tumour cells that are effectively targeted by immune cells) in a tumour are both expressions of ITH. Here, we present a spatially explicit stochastic individual-based model of the interaction dynamics between tumour cells and CD8+ T cells, which makes it possible to dissect out the specific impact of these two expressions of ITH on anti-tumour immune response. The set-up of numerical simulations of the model is defined so as to mimic scenarios considered in previous experimental studies. Moreover, the ability of the model to qualitatively reproduce experimental observations of successful and unsuccessful immune surveillance is demonstrated. First, the results of numerical simulations of this model indicate that the presence of a larger number of sub-populations of tumour cells that express different antigens is associated with a reduced ability of CD8+ T cells to mount an effective anti-tumour immune response. Secondly, the presence of a larger percentage of tumour cells that are not effectively targeted by CD8+ T cells may reduce the effectiveness of anti-tumour immunity. Ultimately, the mathematical model presented in this paper may provide a framework to help biologists and clinicians to better understand the mechanisms that are responsible for the emergence of different outcomes of immunotherapy.

Competition delays multi-drug resistance evolution during combination therapy.

Combination therapies have shown remarkable success in preventing the evolution of resistance to multiple drugs, including HIV, tuberculosis, and cancer. Nevertheless, the rise in drug resistance still remains an important challenge. The capability to accurately predict the emergence of resistance, either to one or multiple drugs, may help to improve treatment options. Existing theoretical approaches often focus on exponential growth laws, which may not be realistic when scarce resources and competition limit growth. In this work, we study the emergence of single and double drug resistance in a model of combination therapy of two drugs. The model describes a sensitive strain, two types of single-resistant strains, and a double-resistant strain. We compare the probability that resistance emerges for three growth laws: exponential growth, logistic growth without competition between strains, and logistic growth with competition between strains. Using mathematical estimates and numerical simulations, we show that between-strain competition only affects the emergence of single resistance when resources are scarce. In contrast, the probability of double resistance is affected by between-strain competition over a wider space of resource availability. This indicates that competition between different resistant strains may be pertinent to identifying strategies for suppressing drug resistance, and that exponential models may overestimate the emergence of resistance to multiple drugs. A by-product of our work is an efficient strategy to evaluate probabilities of single and double resistance in models with multiple sequential mutations. This may be useful for a range of other problems in which the probability of resistance is of interest.

Habitat fragmentation and species diversity in competitive communities.

Habitat loss is one of the key drivers of the ongoing decline of biodiversity. However, ecologists still argue about how fragmentation of habitat (independent of habitat loss) affects species richness. The recently proposed habitat amount hypothesis posits that species richness only depends on the total amount of habitat in a local landscape. In contrast, empirical studies report contrasting patterns: some find positive and others negative effects of fragmentation per se on species richness. To explain this apparent disparity, we devise a stochastic, spatially explicit model of competitive species communities in heterogeneous habitats. The model shows that habitat loss and fragmentation have complex effects on species diversity in competitive communities. When the total amount of habitat is large, fragmentation per se tends to increase species diversity, but if the total amount of habitat is small, the situation is reversed: fragmentation per se decreases species diversity.

Bridging the gap between individual-based and continuum models of growing cell populations.

Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations that describe the evolution of cellular densities in response to pressure gradients generated by population growth. Little prior work has explored the relation between such continuum models and related single-cell-based models. We present here a simple stochastic individual-based model for the spatial dynamics of multicellular systems whereby cells undergo pressure-driven movement and pressure-dependent proliferation. We show that nonlinear partial differential equations commonly used to model the spatial dynamics of growing cell populations can be formally derived from the branching random walk that underlies our discrete model. Moreover, we carry out a systematic comparison between the individual-based model and its continuum counterparts, both in the case of one single cell population and in the case of multiple cell populations with different biophysical properties. The outcomes of our comparative study demonstrate that the results of computational simulations of the individual-based model faithfully mirror the qualitative and quantitative properties of the solutions to the corresponding nonlinear partial differential equations. Ultimately, these results illustrate how the simple rules governing the dynamics of single cells in our individual-based model can lead to the emergence of complex spatial patterns of population growth observed in continuum models.

Modelling collective cell migration: neural crest as a model paradigm.

A huge variety of mathematical models have been used to investigate collective cell migration. The aim of this brief review is twofold: to present a number of modelling approaches that incorporate the key factors affecting cell migration, including cell-cell and cell-tissue interactions, as well as domain growth, and to showcase their application to model the migration of neural crest cells. We discuss the complementary strengths of microscale and macroscale models, and identify why it can be important to understand how these modelling approaches are related. We consider neural crest cell migration as a model paradigm to illustrate how the application of different mathematical modelling techniques, combined with experimental results, can provide new biological insights. We conclude by highlighting a number of future challenges for the mathematical modelling of neural crest cell migration.

Evidence of local adaptation in a waterfall-climbing Hawaiian goby fish derived from coupled biophysical modeling of larval dispersal and post-settlement selection.

BACKGROUND: Local adaptation of marine and diadromous species is thought to be a product of larval dispersal, settlement mortality, and differential reproductive success, particularly in heterogeneous post-settlement habitats. We evaluated this premise with an oceanographic passive larval dispersal model coupled with individual-based models of post-settlement selection and reproduction to infer conditions that underlie local adaptation in Sicyopterus stimpsoni, an amphidromous Hawaiian goby known for its ability to climb waterfalls. RESULTS: Our model results demonstrated that larval dispersal is spatio-temporally asymmetric, with more larvae dispersed from the southeast (the Big Island) to northwest (Kaua'i) along the archipelago, reflecting prevailing conditions such as El Niño/La Niña oscillations. Yet connectivity is nonetheless sufficient to result in homogenous populations across the archipelago. We also found, however, that ontogenetic shifts in habitat can give rise to adaptive morphological divergence when the strength of predation-driven post-settlement selection crosses a critical threshold. Notably, our simulations showed that larval dispersal is not the only factor determining the likelihood of morphological divergence. We found adaptive potential and evolutionary trajectories of S. stimpsoni were greater on islands with stronger environmental gradients and greater variance in larval cohort morphology due to fluctuating immigration. CONCLUSIONS: Contrary to expectation, these findings indicate that immigration can act in concert with selection to favor local adaptation and divergence in species with marine larval dispersal. Further development of model simulations, parameterized to reflect additional empirical estimates of abiotic and biotic factors, will help advance our understanding of the proximate and ultimate mechanisms driving adaptive evolution, population resilience, and speciation in marine-associated species.

Elevated mutation rates are unlikely to evolve in sexual species, not even under rapid environmental change.

BACKGROUND: Organisms are expected to respond to changing environmental conditions through local adaptation, range shift or local extinction. The process of local adaptation can occur by genetic changes or phenotypic plasticity, and becomes especially relevant when dispersal abilities or possibilities are somehow constrained. For genetic changes to occur, mutations are the ultimate source of variation and the mutation rate in terms of a mutator locus can be subject to evolutionary change. Recent findings suggest that the evolution of the mutation rate in a sexual species can advance invasion speed and promote adaptation to novel environmental conditions. Following this idea, this work uses an individual-based model approach to investigate if the mutation rate can also evolve in a sexual species experiencing different conditions of directional climate change, under different scenarios of colored stochastic environmental noise, probability of recombination and of beneficial mutations. The color of the noise mimicked investigating the evolutionary dynamics of the mutation rate in different habitats. RESULTS: The results suggest that the mutation rate in a sexual species experiencing directional climate change scenarios can evolve and reach relatively high values mainly under conditions of complete linkage of the mutator locus and the adaptation locus. In contrast, when they are unlinked, the mutation rate can slightly increase only under scenarios where at least 50% of arising mutations are beneficial and the rate of environmental change is relatively fast. This result is robust under different scenarios of stochastic environmental noise, which supports the observation of no systematic variation in the mutation rate among organisms experiencing different habitats. CONCLUSIONS: Given that 50% beneficial mutations may be an unrealistic assumption, and that recombination is ubiquitous in sexual species, the evolution of an elevated mutation rate in a sexual species experiencing directional climate change might be rather unlikely. Furthermore, when the percentage of beneficial mutations and the population size are small, sexual species (especially multicellular ones) producing few offspring may be expected to react to changing environments not by adaptive genetic change, but mainly through plasticity. Without the ability for a plastic response, such species may become - at least locally - extinct.

A Residence Time Theory for Biodiversity.

From microorganisms to the largest macroorganisms, much of Earth's biodiversity is subject to forces of physical turnover. Residence time is the ratio of an ecosystem's size to its rate of flow and provides a means for understanding the influence of physical turnover on biological systems. Despite its use across scientific disciplines, residence time has not been integrated into the broader understanding of biodiversity, life history, and the assembly of ecological communities. Here we propose a residence time theory for the growth, activity, abundance, and diversity of traits and taxa in complex ecological systems. Using thousands of stochastic individual-based models to simulate energetically constrained life-history processes, we show that our predictions are conceptually sound and mutually compatible and that they support ecological relationships that underpin much of biodiversity theory. We discuss the importance of residence time across the ecological hierarchy and propose how residence time can be integrated into theories ranging from population genetics to macroecology.

A stochastic individual-based model to explore the role of spatial interactions and antigen recognition in the immune response against solid tumours.

Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally focus only on one of these key aspects. We present here a spatial stochastic individual-based model that explicitly captures antigen expression and recognition. In our model, each cancer cell is characterised by an antigen profile which can change over time due to either epimutations or mutations. The immune response against the cancer cells is initiated by the dendritic cells that recognise the tumour antigens and present them to the cytotoxic T cells. Consequently, T cells become activated against the tumour cells expressing such antigens. Moreover, the differences in movement between inactive and active immune cells are explicitly taken into account by the model. Computational simulations of our model clarify the conditions for the emergence of tumour clearance, dormancy or escape, and allow us to assess the impact of antigenic heterogeneity of cancer cells on the efficacy of immune action. Ultimately, our results highlight the complex interplay between spatial interactions and adaptive mechanisms that underpins the immune response against solid tumours, and suggest how this may be exploited to further develop cancer immunotherapies.