The statistical building blocks of animal movement simulations.

Animal movement plays a key role in many ecological processes and has a direct influence on an individual's fitness at several scales of analysis (i.e., next-step, subdiel, day-by-day, seasonal). This highlights the need to dissect movement behavior at different spatio-temporal scales and develop hierarchical movement tools for generating realistic tracks to supplement existing single-temporal-scale simulators. In reality, animal movement paths are a concatenation of fundamental movement elements (FuMEs: e.g., a step or wing flap), but these are not generally extractable from a relocation time-series track (e.g., sequential GPS fixes) from which step-length (SL, aka velocity) and turning-angle (TA) time series can be extracted. For short, fixed-length segments of track, we generate their SL and TA statistics (e.g., means, standard deviations, correlations) to obtain segment-specific vectors that can be cluster into different types. We use the centroids of these clusters to obtain a set of statistical movement elements (StaMEs; e.g.,directed fast movement versus random slow movement elements) that we use as a basis for analyzing and simulating movement tracks. Our novel concept is that sequences of StaMEs provide a basis for constructing and fitting step-selection kernels at the scale of fixed-length canonical activity modes: short fixed-length sequences of interpretable activity such as dithering, ambling, directed walking, or running. Beyond this, variable length pure or characteristic mixtures of CAMs can be interpreted as behavioral activity modes (BAMs), such as gathering resources (a sequence of dithering and walking StaMEs) or beelining (a sequence of fast directed-walk StaMEs interspersed with vigilance and navigation stops). Here we formulate a multi-modal, step-selection kernel simulation framework, and construct a 2-mode movement simulator (Numerus ANIMOVER_1), using Numerus RAMP technology. These RAMPs run as stand alone applications: they require no coding but only the input of selected parameter values. They can also be used in R programming environments as virtual R packages. We illustrate our methods for extracting StaMEs from both ANIMOVER_1 simulated data and empirical data from two barn owls (Tyto alba) in the Harod Valley, Israel. Overall, our new bottom-up approach to path segmentation allows us to both dissect real movement tracks and generate realistic synthetic ones, thereby providing a general tool for testing hypothesis in movement ecology and simulating animal movement in diverse contexts such as evaluating an individual's response to landscape changes, release of an individual into a novel environment, or identifying when individuals are sick or unusually stressed.

A general multi-scale description of metastable adaptive motion across fitness valleys.

We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph G = ( V , E ) . The evolution is driven by a linear birth rate, a density dependent logistic death rate and the possibility of mutations along the directed edges in E. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between Bovier et al. (Ann Appl Probab 29(6):3541-358, 2019) and Coquille et al. (Electron J Probab 26:1-37, 2021) we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales, corresponding to the widths of these fitness valleys. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between them. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scales, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.

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.

Extrapolation of Metal Toxicity Data for the Rotifer Brachionus calyciflorus Using an Individual-Based Population Model.

Ecological risk assessment (ERA) of metals typically starts from standardized toxicity tests, the data from which are then extrapolated to derive safe concentrations for the envisioned protection goals. Because such extrapolation in conventional ERA lacks ecological realism, ecological modeling is considered as a promising new approach for extrapolation. Many published population models are complex, that is, they include many processes and parameters, and thus require an extensive dataset to calibrate. In the present study, we investigated how individual-based models based on a reduced version of the Dynamic Energy Budget theory (DEBkiss IBM) could be applied for metal effects on the rotifer Brachionus calyciflorus. Data on survival over time and reproduction at different temperatures and food conditions were used to calibrate and evaluate the model for copper effects. While population growth and decline were well predicted, the underprediction of population density and the mismatch in the onset of copper effects were attributed to the simplicity of the approach. The DEBkiss IBM was applied to toxicity datasets for copper, nickel, and zinc. Predicted effect concentrations for these metals based on the maximum population growth rate were between 0.7 and 3 times higher in all but one case (10 times higher) than effect concentrations based on the toxicity data. The size of the difference depended on certain characteristics of the toxicity data: both the steepness of the concentration-effect curve and the relative sensitivity of lethal and sublethal effects played a role. Overall, the present study is an example of how a population model with reduced complexity can be useful for metal ERA. Environ Toxicol Chem 2024;43:324-337. © 2023 SETAC.

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.

Extensions of mean-field approximations for environmentally-transmitted pathogen networks.

Many pathogens spread via environmental transmission, without requiring host-to-host direct contact. While models for environmental transmission exist, many are simply constructed intuitively with structures analogous to standard models for direct transmission. As model insights are generally sensitive to the underlying model assumptions, it is important that we are able understand the details and consequences of these assumptions. We construct a simple network model for an environmentally-transmitted pathogen and rigorously derive systems of ordinary differential equations (ODEs) based on different assumptions. We explore two key assumptions, namely homogeneity and independence, and demonstrate that relaxing these assumptions can lead to more accurate ODE approximations. We compare these ODE models to a stochastic implementation of the network model over a variety of parameters and network structures, demonstrating that with fewer restrictive assumptions we are able to achieve higher accuracy in our approximations and highlighting more precisely the errors produced by each assumption. We show that less restrictive assumptions lead to more complicated systems of ODEs and the potential for unstable solutions. Due to the rigour of our derivation, we are able to identify the reason behind these errors and propose potential resolutions.

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.

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.

Discrete and continuum models for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes and tumour cells.

We present an individual-based model for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes (CTLs) and tumour cells. In this model, every cell is viewed as an individual agent whose phenotypic state is modelled by a discrete variable. For tumour cells, this variable represents a parameterization of the antigen expression profiles, while for CTLs it represents a parameterization of the target antigens of T-cell receptors (TCRs). We formally derive the deterministic continuum limit of this individual-based model, which comprises a non-local partial differential equation for the phenotype distribution of tumour cells coupled with an integro-differential equation for the phenotype distribution of CTLs. The biologically relevant homogeneous steady-state solutions of the continuum model equations are found. The linear-stability analysis of these steady-state solutions is then carried out in order to identify possible conditions on the model parameters that may lead to different outcomes of immune competition and to the emergence of patterns of phenotypic coevolution between tumour cells and CTLs. We report on computational results of the individual-based model, and show that there is a good agreement between them and analytical and numerical results of the continuum model. These results shed light on the way in which different parameters affect the coevolutionary dynamics between tumour cells and CTLs. Moreover, they support the idea that TCR-tumour antigen binding affinity may be a good intervention target for immunotherapy and offer a theoretical basis for the development of anti-cancer therapy aiming at engineering TCRs so as to shape their affinity for cancer targets.

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.

Epidemiological modelling of the health and economic effects of COVID-19 control in Australia's second wave.

Background: We investigated the public health and economy outcomes of different levels of social distancing to control a 'second wave' outbreak in Australia and identify implications for public health management of COVID-19. Methods: Individual-based and compartment models were used to simulate the effects of different social distancing and detection strategies on Australian COVID-19 infections and the economy from March to July 2020. These models were used to evaluate the effects of different social distancing levels and the early relaxation of suppression measures, in terms of public health and economy outcomes. Results: The models, fitted to observations up to July 2020, yielded projections consistent with subsequent cases and showed that better public health outcomes and lower economy costs occur when social distancing measures are more stringent, implemented earlier and implemented for a sufficiently long duration. Early relaxation of suppression results in worse public health outcomes and higher economy costs. Conclusions: Better public health outcomes (reduced COVID-19 fatalities) are positively associated with lower economy costs and higher levels of social distancing; achieving zero community transmission lowers both public health and economy costs compared to allowing community transmission to continue; and early relaxation of social distancing increases both public health and economy costs.

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.

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.

Suboptimal foraging theory: How inaccurate predictions and approximations can make better models of adaptive behavior.

Optimal foraging theory (OFT) is based on the ecological concept that organisms select behaviors that convey future fitness, and on the mathematical concept of optimization: finding the alternative that provides the best value of a fitness measure. As implemented in, for example, state-based dynamic modeling, OFT is powerful for one key problem of modern ecology: modeling behavior as a tradeoff among competing fitness elements such as growth, risk avoidance, and reproductive output. However, OFT is not useful for other modern problems such as representing feedbacks within systems of interacting, unique individuals: When we need to model foraging by each of many individuals that interact competitively or synergistically, optimization is impractical or impossible-there are no optimal behaviors. For such problems we can, however, still use the concept of future fitness to model behavior by replacing optimization with less precise (but perhaps more realistic) techniques for ranking alternatives. Instead of simplifying the systems we model until we can find optimal behavior, we can use theory based on inaccurate predictions, coarse approximations, and updating to produce good behavior in more complex and realistic contexts. This so-called state- and prediction-based theory (SPT) can, for example, produce realistic foraging decisions by each of many unique, interacting individuals when growth rates and predation risks vary over space and time. Because SPT lets us address more natural complexity and more realistic problems, it is more easily tested against more kinds of observation and more useful in management ecology. A simple foraging model illustrates how SPT readily accommodates complexities that make optimization intractable. Other models use SPT to represent contingent decisions (whether to feed or hide, in what patch) that are tradeoffs between growth and predation risk, when both growth and risk vary among hundreds of patches, vary unpredictably over time, depend on characteristics of the individuals, are subject to feedbacks from competition, and change over the daily light cycle. Modern ecology demands theory for tradeoff behaviors in complex contexts that produce feedbacks; when optimization is infeasible, we should not be afraid to use approximate fitness-seeking methods instead.

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.

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.