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Direct encounters, in which two or more individuals are physically close to one another, are a topic of increasing interest as more and better movement data become available. Recent progress, including the development of statistical tools for estimating robust measures of changes in animals’ space use over time, facilitates opportunities to link direct encounters between individuals with the long-term consequences of those encounters. Working with movement data for coyotes (Canis latrans) and grizzly bears (Ursus arctos horribilis), we investigate whether close intraspecific encounters were associated with spatial shifts in the animals’ range distributions, as might be expected if one or both of the individuals involved in an encounter were seeking to reduce or avoid conflict over space. We analyze the movement data of a pair of coyotes in detail, identifying how a change in home range overlap resulting from altered movement behavior was apparently a consequence of a close intraspecific encounter. With grizzly bear movement data, we approach the problem as population-level hypothesis tests of the spatial consequences of encounters. We find support for the hypotheses that (1) close intraspecific encounters between bears are, under certain circumstances, associated with subsequent changes in overlap between range distributions and (2) encounters defined at finer spatial scales are followed by greater changes in space use. Our results suggest that animals can undertake long-term, large-scale spatial changes in response to close intraspecific encounters that have the potential for conflict. Overall, we find that analyses of movement data in a pairwise context can (1) identify distances at which individuals’ proximity to one another may alter behavior and (2) facilitate testing of population-level hypotheses concerning the potential for direct encounters to alter individuals’ space use.

Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behaviour, neglecting how landscape heterogeneity influences individual movement. We relax this assumption and introduce a reaction–advection–diffusion equation that describes population dynamics when individuals exhibit space-dependent movement bias toward preferred regions. Our model incorporates two types of these preferred regions: a high-quality habitat patch, termed ‘habitat’, which is included to model avoidance of degraded habitats like deforested regions; and a preferred location, such as a chemoattractant source or a watering hole, that we allow to be asymmetrically located with respect to habitat edges. In this scenario, the critical habitat size depends on both the relative position of the preferred location and the movement bias intensities. When preferred locations are near habitat edges, the critical habitat size can decrease when diffusion increases, a phenomenon called the drift paradox. Also, ecological traps arise when the habitat overcrowds due to excessive attractiveness or the preferred location is near a low-quality region. Our results highlight the importance of species-specific movement behaviour and habitat preference as drivers of population dynamics in fragmented landscapes and, therefore, in the design of protected areas.

Theoretical models in ecology often assume well-mixed populations and thus that individuals interact with one another with the same probability regardless of their spatial location. This strong assumption results in mathematically very tractable models, often based on ordinary differential equations for the population size, that have taught us a lot about how populations change over time. However, these models do not account for the fact that populations are spatially structured, which favors interactions between nearby individuals. In this presentation, I will present some of our recent work investigating the effect of space in shaping population dynamics. First, I will very briefly discuss how stochastic spatial models, from lattice models to systems of interacting particles, can provide more accurate descriptions of ecological populations and how to analyze them computationally and analytically. Then, I will use a specific example based on an asymmetric voter model to show how modeling spatial processes can reverse the outcome of species competition predicted by a well-mixed model.

Collective behaviors, in which many individuals exhibit some degree of behavioral coordination, are frequent in nature and observed across a continuum of scales, from microbial aggregates to ungulate migrations. Intriguingly, however, such coordination is sometimes imperfect, and “out-of-sync” individuals exist in many of these systems. The roots of such imperfect coordination, and hence the mechanisms underlying the emergence of out-of-sync individuals, will undoubtedly differ across systems. Nevertheless, the occurrence of imperfect coordination across such different systems and scales raises fundamental questions about its causes and consequences. Are “out-of-sync” individuals merely inevitable byproducts of large-scale coordination attempts, or can they, at least in some systems, be a variable trait that selection can shape with potential ecological consequences? I will address this question by combining empirical data on slime-mold imperfect aggregation and observed patterns of partial migration observed within three ungulate specie. In each of these systems, we find that the number of individuals that do not engage in the collective behavior is unrelated to the total population size, suggesting that a complex individual decision-making process underlies the onset of the collective behavior. Using a minimalistic modeling framework, we propose that imperfectly synchronized collective behaviors are, in fact, a dynamic population partition process that originates from each individual making a stochastic signal-based decision. The parallelisms between these two seemingly different systems suggest that imperfectly synchronized collective behaviors could be critical to understanding social behaviors and ecological dynamics across scales.

Collective behaviors, in which many individuals exhibit some degree of behavioral coordination, are frequent in nature and observed across a continuum of scales, from microbial aggregates to ungulate migrations. Intriguingly, however, such coordination is sometimes imperfect, and “out-of-sync” individuals exist in many of these systems. The roots of such imperfect coordination, and hence the mechanisms underlying the emergence of out-of-sync individuals, will undoubtedly differ across systems. Nevertheless, the occurrence of imperfect coordination across such different systems and scales raises fundamental questions about its causes and consequences. Are “out-of-sync” individuals merely inevitable byproducts of large-scale coordination attempts, or can they, at least in some systems, be a variable trait that selection can shape with potential ecological consequences? I will address this question by combining empirical data on slime-mold imperfect aggregation and observed patterns of partial migration observed within three ungulate specie. In each of these systems, we find that the number of individuals that do not engage in the collective behavior is unrelated to the total population size, suggesting that a complex individual decision-making process underlies the onset of the collective behavior. Using a minimalistic modeling framework, we propose that imperfectly synchronized collective behaviors are, in fact, a dynamic population partition process that originates from each individual making a stochastic signal-based decision. The parallelisms between these two seemingly different systems suggest that imperfectly synchronized collective behaviors could be critical to understanding social behaviors and ecological dynamics across scales.

In this lecture, I will present an overview of existing mathematical models to describe patterns of animal movement.

Populations very often self-organize into regular spatial patterns with important ecological and evolutionary consequences. Yet, most existing models neglect the effect that external biophysical drivers might have both on pattern formation and the spatiotemporal population dynamics once patterns form. Here, we investigate the effect of environmental flows on pattern formation and population dynamics using a spatially nonlocal logistic model (or Fisher-Kolmogorov equation) coupled to a simple shear and a Rankine vortex flow. We find that, whereas population abundance generally decreases with increasing flow intensity, the effect of the flow on the pattern instability depends on the spatial structure of the flow velocity field. This result shows that the velocity field interacts with the spatial feedbacks responsible for pattern formation in non-trivial ways, leading to a variety of spatiotemporal population dynamics regimes in which the total population abundance can exhibit either regular oscillations with a characteristic frequency or more erratic dynamics without a well-defined period. More generally, the diversity of spatiotemporal population dynamics caused by the interplay between self-organizing feedbacks and environmental flows highlights the importance of incorporating environmental and biophysical processes when studying both ecological pattern formation and its consequences.

Below-ground plant interactions are a key driver of vegetation pattern formation. However, many existing models rely on functional forms for these interactions that frequently lack empirical support. This gap between models and data stems primarily from our limited understanding of below-ground plant growth processes. Unlike aboveground shoot competition, the study of below-ground plant growth is hampered by our inability to observe roots. We have few observations of intact root systems in soil and lack a comprehensive theory for root system responses to their environment. In this presentation, I will first review previous theoretical efforts to explain plant below-ground competition and discuss how they lead to seemingly contradictory predictions. Then, I will introduce our recent theoretical and experimental work and show how it resolves existing controversy and provides a unifying framework to study below-ground plant interactions, both competitive and facilitative. I will conclude by discussing future research lines that depart from our results, including extensions to larger spatial scales and applying this new modeling approach to vegetation patterns.

Intraspecific interactions are key drivers of population dynamics because they establish relations between individual fitness and population density. The component Allee effect is defined as a positive correlation between any fitness component of a focal organism and population density, and it can lead to positive density dependence in the population per capita growth rate. The spatial population structure is key to determining whether and to which extent a component Allee effect will manifest at the demographic level because it determines how individuals interact with one another. However, existing spatial models to study the Allee effect impose a fixed spatial structure, which limits our understanding of how a component Allee effect and the spatial dynamics jointly determine the existence of demographic Allee effects. To fill this gap, we introduce a spatially-explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. Depending on the intensity of the individual-level processes, the population exhibits a variety of spatial patterns, including evenly spaced aggregates of organisms, that determine the demographic-level by-products of an existing individual-level component Allee effect. We find that aggregation increases population abundance and allows populations to survive in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component Allee effect from manifesting at the population level or restrict it to the level of each independent group. These results provide a mechanistic understanding of how component Allee effects might operate for different spatial population structures and show at the population level. Because populations subjected to demographic Allee effects exhibit highly nonlinear dynamics, especially at low abundances, our results contribute to a better

Theory questions the persistence of non-reciprocal interactions in which one plant has a positive net effect on a neighbor that, in return, has a negative net impact on its benefactor—a phenomenon known as antagonistic facilitation. We develop a spatially explicit consumer-resource model for below-ground plant competition between ecosystem engineers, plants able to mine resources and make them available for any other plant in the community, and exploiters. We use the model to determine in what environmental conditions antagonistic facilitation via soil resource engineering emerges as an optimal strategy. Antagonistic facilitation emerges in stressful environments where ecosystem engineers’ self-benefits from mining resources outweigh the competition with opportunistic neighbors. Among all potential causes of stress considered in the model, the key environmental parameter driving changes in the interaction between plants is the proportion of the resource that becomes readily available for plant consumption in the absence of any mining activity. Our results align with theories of primary succession and the stress gradient hypothesis. However, we find that the total root biomass and its spatial allocation through the root system, often used to measure the sign of the interaction between plants, do not predict facilitation reliably.

The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how self-organization is triggered, namely, reaction-diffusion and spatially nonlocal models. Nevertheless, these models implicitly assume smooth propagation scenarios, neglecting that individuals many times interact by exchanging short and abrupt pulses of the mediating substance. A recently proposed framework advances in the direction of properly accounting for these short-scale fluctuations by applying a coarse-graining procedure on the pulse dynamics. In this paper, we generalize the coarse-graining procedure and apply the extended formalism to new scenarios in which mediators influence individuals' reproductive success or their motility. We show that, in the slow- and fast-mediator limits, pulsed interactions recover, respectively, the reaction-diffusion and nonlocal models, providing a mechanistic connection between them. Furthermore, at each limit, the spatial stability condition is qualitatively different, leading to a timescale-induced transition where spatial patterns emerge as mediator dynamics becomes sufficiently fast.

The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how self-organization is triggered, namely, reaction-diffusion and spatially nonlocal models. Nevertheless, these models implicitly assume smooth propagation scenarios, neglecting that individuals many times interact by exchanging short and abrupt pulses of the mediating substance. A recently proposed framework advances in the direction of properly accounting for these short-scale fluctuations by applying a coarse-graining procedure on the pulse dynamics. In this paper, we generalize the coarse-graining procedure and apply the extended formalism to new scenarios in which mediators influence individuals' reproductive success or their motility. We show that, in the slow- and fast-mediator limits, pulsed interactions recover, respectively, the reaction-diffusion and nonlocal models, providing a mechanistic connection between them. Furthermore, at each limit, the spatial stability condition is qualitatively different, leading to a timescale-induced transition where spatial patterns emerge as mediator dynamics becomes sufficiently fast.

Direct encounters, in which two or more individuals are physically close to one another, are a topic of increasing interest as more and better movement data become available. Recent progress, including the development of statistical tools for estimating robust measures of changes in animals’ space use over time, facilitates opportunities to link direct encounters between individuals with the long-term consequences of those encounters. Working with movement data for coyotes (Canis latrans) and grizzly bears (Ursus arctos horribilis), we investigate whether close intraspecific encounters were associated with spatial shifts in the animals’ range distributions, as might be expected if one or both of the individuals involved in an encounter were seeking to reduce or avoid conflict over space. We analyze the movement data of a pair of coyotes in detail, identifying how a shift in home range location resulting from altered movement behavior was apparently a consequence of a close intraspecific encounter. With grizzly bear 50 movement data, we approach the problem from the perspective of a set of encounter pairs within a population. We find support for the hypotheses that 1) close intraspecific encounters between bears are, on average, associated with subsequent shifts in range distributions and 2) encounters defined at finer spatial scales are followed by greater changes in space use. Our results suggest that animals can undertake long-term, large-scale spatial shifts in response to close intraspecific encounters that have the potential for conflict. These results lend support for existing theory on the evolution of territories and space use (e.g., Maynard-Smith’s bourgeois strategy regarding low-conflict coexistence). Overall, we find that analyses of movement data in a pairwise context can 1) identify distances at which individuals’ proximity to one another may alter behavior and 2) facilitate testing of population-level hypotheses concerning the potential for direct enc

Intraspecific interactions are key drivers of population dynamics because they establish relations between individual fitness and population density. The component Allee effect is defined as a positive correlation between any fitness component of a focal organism and population density, and it can lead to positive density dependence in the population per capita growth rate. The spatial population structure is key to determining whether and to which extent a component Allee effect will manifest at the demographic level because it determines how individuals interact with one another. However, existing spatial models to study the Allee effect impose a fixed spatial structure, which limits our understanding of how a component Allee effect and the spatial dynamics jointly determine the existence of demographic Allee effects. To fill this gap, we introduce a spatially-explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. Depending on the intensity of the individual-level processes, the population exhibits a variety of spatial patterns, including evenly spaced aggregates of organisms, that determine the demographic-level by-products of an existing individual-level component Allee effect. We find that aggregation increases population abundance and allows populations to survive in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component Allee effect from manifesting at the population level or restrict it to the level of each independent group. These results provide a mechanistic understanding of how component Allee effects might operate for different spatial population structures and show at the population level. Because populations subjected to demographic Allee effects exhibit highly nonlinear dynamics, especially at low abundances, our results contribute to a better

Plant interactions, understood as the net effect of an individual on the fitness of a neighbor, vary in strength and can shift from negative interference to positive facilitation as the environmental conditions change in time and space. However, the biophysical mechanisms underlying these changes are not well understood. Additionally, evolutionary theory questions the stability of antagonistic facilitation. Using a mechanistic model for belowground resource competition between individual plants, we find that, under stress conditions, antagonistic facilitation is evolutionarily stable even when both interacting plants compete for resources. This supports the theory of ecosystem engineers in primary succession and nurse plants in the stress gradient hypothesis. Furthermore, we find that the proportion of the limiting resource that spontaneously becomes available to any plant is the key environmental parameter determining the evolutionary stability of facilitation. This represents a challenge and a potential confusion factor for empirical studies.

Animals moving through landscapes need to strike a balance between finding sufficient resources to grow and reproduce while minimizing encounters with predators 1,2. Because encounter rates are determined by the average distance over which directed motion persists 1,3–5, this trade-off should be apparent in individuals’ movement. Using GPS data from 1,396 individuals across 62 species of terrestrial mammals, we show how predators maintained directed motion ~7 times longer than for similarly-sized prey, revealing how prey species must trade off search efficiency against predator encounter rates. Individual search strategies were also modulated by resource abundance, with prey species forced to risk higher predator encounter rates when resources were scarce. These findings highlight the interplay between encounter rates and resource availability in shaping broad patterns mammalian movement strategies.

Ecologists have long investigated how the demographic and movement parameters of a population determine its spatial spread and the critical habitat size that can sustain it. Yet, most existing models make oversimplifying assumptions about individual movement behavior, neglecting how landscape heterogeneity influences dispersal. We relax this assumption and introduce a reaction-advection-diffusion model that describes the spatial density distribution of a population with space-dependent movement bias toward preferred regions, including avoidance of degraded habitats. In this scenario, the critical habitat size depends on the spatial location of the habitat edges with respect to the preferred regions and on the intensity of the movement bias components. In particular, we identify parameter regions where the critical habitat size decreases when diffusion increases, a phenomenon known as the “drift paradox”. We also find that biased movement toward low-quality or highly populated regions can reduce the population size, therefore creating ecological traps. Our results emphasize the importance of species-specific movement behavior and habitat selection as drivers of population dynamics in fragmented landscapes and, therefore, the need to account for them in the design of protected areas.

Marine plankton play a crucial role in carbon storage, oxygen production, global climate, and ecosystem function. Planktonic ecosystems are embedded in a Lagrangian patches of water that are continuously moving, stretching, and diluting. These processes drive inhomegeneities on a range of scales, with implications for the integrated ecosystem properties, but are hard to characterize. We present a theoretical framework which accounts for all these aspects; tracking the water patch hosting a drifting ecosystem along with its physical, environmental, and biochemical features. The model resolves patch dilution and internal physical mixing as a function of oceanic strain and diffusion. Ecological dynamics are parameterized by an idealized nutrient and phytoplankton population and we specifically capture the propagation of the biochemical spatial variances to represent within-patch heterogeneity. We find that, depending only on the physical processes to which the water patch is subjected, the plankton biomass response to a resource perturbation can vary several fold. This work indicates that we must account for these processes when interpreting and modeling marine ecosystems and provides a framework with which to do so.

Marine plankton play a crucial role in carbon storage, oxygen production, global climate, and ecosystem function. Planktonic ecosystems are embedded in a Lagrangian patches of water that are continuously moving, stretching, and diluting. These processes drive inhomegeneities on a range of scales, with implications for the integrated ecosystem properties, but are hard to characterize. We present a theoretical framework which accounts for all these aspects; tracking the water patch hosting a drifting ecosystem along with its physical, environmental, and biochemical features. The model resolves patch dilution and internal physical mixing as a function of oceanic strain and diffusion. Ecological dynamics are parameterized by an idealized nutrient and phytoplankton population and we specifically capture the propagation of the biochemical spatial variances to represent within-patch heterogeneity. We find that, depending only on the physical processes to which the water patch is subjected, the plankton biomass response to a resource perturbation can vary several fold. This work indicates that we must account for these processes when interpreting and modeling marine ecosystems and provides a framework with which to do so.

Ecologists have long investigated how the demographic and movement parameters of a population determine its spatial spread and the critical habitat size that can sustain it. Yet, most existing models make oversimplifying assumptions about individual movement behavior, neglecting how landscape heterogeneity influences dispersal. We relax this assumption and introduce a reaction-advection-diffusion model that describes the spatial density distribution of a population with space-dependent movement bias toward preferred regions, including avoidance of degraded habitats. In this scenario, the critical habitat size depends on the spatial location of the habitat edges with respect to the preferred regions and on the intensity of the movement bias components. In particular, we identify parameter regions where the critical habitat size decreases when diffusion increases, a phenomenon known as the “drift paradox”. We also find that biased movement toward low-quality or highly populated regions can reduce the population size, therefore creating ecological traps. Our results emphasize the importance of species-specific movement behavior and habitat selection as drivers of population dynamics in fragmented landscapes and, therefore, the need to account for them in the design of protected areas.

Plant interactions, understood as the net effect of an individual on the fitness of a neighbor, vary in strength and can shift from negative interference to positive facilitation as the environmental conditions change in time and space. However, the biophysical mechanisms underlying these changes are not well understood. Additionally, evolutionary theory questions the stability of antagonistic facilitation. Using a mechanistic model for belowground resource competition between individual plants, we find that, under stress conditions, antagonistic facilitation is evolutionarily stable even when both interacting plants compete for resources. This supports the theory of ecosystem engineers in primary succession and nurse plants in the stress gradient hypothesis. Furthermore, we find that the proportion of the limiting resource that spontaneously becomes available to any plant is the key environmental parameter determining the evolutionary stability of facilitation. This represents a challenge and a potential confusion factor for empirical studies.

Animals moving through landscapes need to strike a balance between finding sufficient resources to grow and reproduce while minimizing encounters with predators 1,2. Because encounter rates are determined by the average distance over which directed motion persists 1,3–5, this trade-off should be apparent in individuals’ movement. Using GPS data from 1,396 individuals across 62 species of terrestrial mammals, we show how predators maintained directed motion ~7 times longer than for similarly-sized prey, revealing how prey species must trade off search efficiency against predator encounter rates. Individual search strategies were also modulated by resource abundance, with prey species forced to risk higher predator encounter rates when resources were scarce. These findings highlight the interplay between encounter rates and resource availability in shaping broad patterns mammalian movement strategies.

Direct encounters, in which two or more individuals are physically close to one another, are a topic of increasing interest as more and better movement data become available. Recent progress, including the development of statistical tools for estimating robust measures of changes in animals’ space use over time, facilitates opportunities to link direct encounters between individuals with the long-term consequences of those encounters. Working with movement data for coyotes (Canis latrans) and grizzly bears (Ursus arctos horribilis), we investigate whether close intraspecific encounters were associated with spatial shifts in the animals’ range distributions, as might be expected if one or both of the individuals involved in an encounter were seeking to reduce or avoid conflict over space. We analyze the movement data of a pair of coyotes in detail, identifying how a shift in home range location resulting from altered movement behavior was apparently a consequence of a close intraspecific encounter. With grizzly bear 50 movement data, we approach the problem from the perspective of a set of encounter pairs within a population. We find support for the hypotheses that 1) close intraspecific encounters between bears are, on average, associated with subsequent shifts in range distributions and 2) encounters defined at finer spatial scales are followed by greater changes in space use. Our results suggest that animals can undertake long-term, large-scale spatial shifts in response to close intraspecific encounters that have the potential for conflict. These results lend support for existing theory on the evolution of territories and space use (e.g., Maynard-Smith’s bourgeois strategy regarding low-conflict coexistence). Overall, we find that analyses of movement data in a pairwise context can 1) identify distances at which individuals’ proximity to one another may alter behavior and 2) facilitate testing of population-level hypotheses concerning the potential for direct enc

Intraspecific interactions are key drivers of population dynamics because they establish relations between individual fitness and population density. The component Allee effect is defined as a positive correlation between any fitness component of a focal organism and population density, and it can lead to positive density dependence in the population per capita growth rate. The spatial population structure is key to determining whether and to which extent a component Allee effect will manifest at the demographic level because it determines how individuals interact with one another. However, existing spatial models to study the Allee effect impose a fixed spatial structure, which limits our understanding of how a component Allee effect and the spatial dynamics jointly determine the existence of demographic Allee effects. To fill this gap, we introduce a spatially-explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. Depending on the intensity of the individual-level processes, the population exhibits a variety of spatial patterns, including evenly spaced aggregates of organisms, that determine the demographic-level by-products of an existing individual-level component Allee effect. We find that aggregation increases population abundance and allows populations to survive in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component Allee effect from manifesting at the population level or restrict it to the level of each independent group. These results provide a mechanistic understanding of how component Allee effects might operate for different spatial population structures and show at the population level. Because populations subjected to demographic Allee effects exhibit highly nonlinear dynamics, especially at low abundances, our results contribute to a better

The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how self-organization is triggered, namely, reaction-diffusion and spatially nonlocal models. Nevertheless, these models implicitly assume smooth propagation scenarios, neglecting that individuals many times interact by exchanging short and abrupt pulses of the mediating substance. A recently proposed framework advances in the direction of properly accounting for these short-scale fluctuations by applying a coarse-graining procedure on the pulse dynamics. In this paper, we generalize the coarse-graining procedure and apply the extended formalism to new scenarios in which mediators influence individuals' reproductive success or their motility. We show that, in the slow- and fast-mediator limits, pulsed interactions recover, respectively, the reaction-diffusion and nonlocal models, providing a mechanistic connection between them. Furthermore, at each limit, the spatial stability condition is qualitatively different, leading to a timescale-induced transition where spatial patterns emerge as mediator dynamics becomes sufficiently fast.

Animal encounters are key components of population dynamics, community dynamics, and evolutionary processes. Consequently, measuring encounter rates (i.e. encounters per time) can be insightful. Encounter rates can be measured from animal tracking data, using metrics that can be split into two groups. The first group consists of trajectory-based metrics, i.e. measures based on serial records of animal locations. This first group includes PROX, the number of observed per number of samples. The second group, in contrast, consists of metrics based on home range overlap, including the Bhattacharyya coefficient (BC). In this study, we argue both types of metrics are limited. Trajectory-based metrics are direct measures of encounter rates but have statistical estimation issues due to their dependency on the frequency of location sampling. Meanwhile, home-rangebased metrics are statistically sound but are not proportional to encounter rates. To overcome both challenges, we proposed a new metric, Relative Encounter Rate (RER). RER increases linearly with the number of encounters and does not depend on the frequency of sampling (i.e. it is scale-invariant). In an individual-based simulation, we measured how RER, BC, and PROX relative error under different sample sizes and sampling frequencies. Further, we compared these metrics in three empirical case studies. We tested Jaguars for polygyny, deforestation effects on tapir connectivity, and an extension of the dearest enemy hypothesis with brown bears. We also compared partner hierarchy according to BC and RER in Jaguar mating clusters. In the simulation study, we found PROX overestimates the encounter rate when data has a low sampling frequency. The simulation also indicates BC overestimated encounters. Furthermore, PROX led to false positives in the Tapir and Bear case studies. In addition, PROX was incapable of detecting many individual relationships in the jaguar polygyny study. RER does not depend on sampling frequency (

Plant interactions, understood as the net effect of an individual on the fitness of a neighbor, vary in strength and can shift from negative interference to positive facilitation as the environmental conditions change in time and space. However, the biophysical mechanisms underlying these changes are not well understood. Additionally, evolutionary theory questions the stability of antagonistic facilitation. Using a mechanistic model for belowground resource competition between individual plants, we find that, under stress conditions, antagonistic facilitation is evolutionarily stable even when both interacting plants compete for resources. This supports the theory of ecosystem engineers in primary succession and nurse plants in the stress gradient hypothesis. Furthermore, we find that the proportion of the limiting resource that spontaneously becomes available to any plant is the key environmental parameter determining the evolutionary stability of facilitation. This represents a challenge and a potential confusion factor for empirical studies.

Marine plankton play a crucial role in carbon storage, oxygen production, global climate, and ecosystem function. Planktonic ecosystems are embedded in a Lagrangian patches of water that are continuously moving, stretching, and diluting. These processes drive inhomegeneities on a range of scales, with implications for the integrated ecosystem properties, but are hard to characterize. We present a theoretical framework which accounts for all these aspects; tracking the water patch hosting a drifting ecosystem along with its physical, environmental, and biochemical features. The model resolves patch dilution and internal physical mixing as a function of oceanic strain and diffusion. Ecological dynamics are parameterized by an idealized nutrient and phytoplankton population and we specifically capture the propagation of the biochemical spatial variances to represent within-patch heterogeneity. We find that, depending only on the physical processes to which the water patch is subjected, the plankton biomass response to a resource perturbation can vary several fold. This work indicates that we must account for these processes when interpreting and modeling marine ecosystems and provides a framework with which to do so.

The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how self-organization is triggered, namely, reaction-diffusion and spatially nonlocal models. Nevertheless, these models implicitly assume smooth propagation scenarios, neglecting that individuals many times interact by exchanging short and abrupt pulses of the mediating substance. A recently proposed framework advances in the direction of properly accounting for these short-scale fluctuations by applying a coarse-graining procedure on the pulse dynamics. In this paper, we generalize the coarse-graining procedure and apply the extended formalism to new scenarios in which mediators influence individuals' reproductive success or their motility. We show that, in the slow- and fast-mediator limits, pulsed interactions recover, respectively, the reaction-diffusion and nonlocal models, providing a mechanistic connection between them. Furthermore, at each limit, the spatial stability condition is qualitatively different, leading to a timescale-induced transition where spatial patterns emerge as mediator dynamics becomes sufficiently fast.

Intraspecific interactions are key drivers of population dynamics because they establish relations between individual fitness and population density. The component Allee effect is defined as a positive correlation between any fitness component of a focal organism and population density, and it can lead to positive density dependence in the population per capita growth rate. The spatial population structure is key to determining whether and to which extent a component Allee effect will manifest at the demographic level because it determines how individuals interact with one another. However, existing spatial models to study the Allee effect impose a fixed spatial structure, which limits our understanding of how a component Allee effect and the spatial dynamics jointly determine the existence of demographic Allee effects. To fill this gap, we introduce a spatially-explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. Depending on the intensity of the individual-level processes, the population exhibits a variety of spatial patterns, including evenly spaced aggregates of organisms, that determine the demographic-level by-products of an existing individual-level component Allee effect. We find that aggregation increases population abundance and allows populations to survive in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component Allee effect from manifesting at the population level or restrict it to the level of each independent group. These results provide a mechanistic understanding of how component Allee effects might operate for different spatial population structures and show at the population level. Because populations subjected to demographic Allee effects exhibit highly nonlinear dynamics, especially at low abundances, our results contribute to a better

Collective behaviors, in which many individuals exhibit some degree of behavioral coordination, are frequent across the tree of life and observed across a continuum of scales, from microbial aggregates to ungulate migrations. Intriguingly, however, such coordination is sometimes imperfect, and “out-of-sync” individuals have been reported in several of these systems. For example, in the model social amoeba Dictyostelium discoideum, free-living cells aggregate in a multicellular fruiting body upon starvation, while others remain in the unicellular phase. In several ungulate species, hundreds of thousands of individuals coordinate with each other to migrate across seasonal ranges, but resident populations that fail to migrate also exist. The roots of such imperfect coordination, and hence the mechanisms underlying the emergence of out-of-sync individuals, will undoubtedly differ across systems. Nevertheless, the occurrence of imperfect coordination across such different systems and scales raises fundamental questions about its causes and consequences. Are “out-of-sync” individuals merely inevitable byproducts of large-scale coordination attempts, or can they, at least in some systems, be a variable trait that selection can shape with potential ecological consequences?

Introduction to the group research.

Despite the importance of ungulate migrations, we lack a complete understanding of why some ungulates species migrate and some do not. Moreover, at the population level, some migrate and others remain behind as residents, a phenomenon known as partial migration. Even though progress has been made towards understanding long-term fitness benefits of partial migration, the underlying decision-making process that makes some individuals migrate and others remain within one single range remain unknown. In this presentation I will combine empirical data from three different migrant ungulate species and mathematical modeling to address this question. I will first show that, across these three ungulate species, the number of residents is unrelated to total population size, a pattern predicted by no previous modeling framework. Next, I will introduce a new model of ungulate partial migration wherein individuals probabilistically decide to start migrating based on the intensity of environmental and social cues. Within this modeling framework, residents arise for most parameter combinations and the number of residents is largely invariant with total population size. Therefore, this new model explains the ubiquity of residents in migratory ungulate populations and presents novel patterns to be tested with further data collection.

A large body of existing ecological theory relies on very strong and unrealistic assumptions about the way individuals move and get to interact with each other and with the environment. Specifically, several models assume that individuals behave like the molecules of an ideal gas: following completely random trajectories through the entire area occupied by the population and only interacting with each other when their trajectories intersect. In this presentation, I will first discuss how traditional population dynamics models emerge from ideal gas assumptions. Then, I will present our ongoing research to refine those models using more elaborated tools from random walk theory, spatially-extended nonlinear dynamical systems, and stochastic calculus. I will discuss examples covering both the development of new theory and its application ecological data.

Plant roots determine carbon uptake, survivorship, and agricultural yield and represent a large proportion of the world’s vegetation carbon pool. The study of below-ground plant growth, unlike aboveground shoot competition, is hampered by our inability to observe roots. We have few observations of intact root systems in soil and lack a comprehensive theory for root system responses to their environment. In this presentation, I will first review previous theoretical efforts to explain plant below-ground competition and discuss how they lead to seemingly contradictory predictions. Then, I will introduce our recent theoretical and experimental work and show how it resolves existing controversy and provides a unifying framework to study below-ground plant interactions, both competitive and facilitative. I will conclude by discussing future research lines that depart from our results and how they can be addressed with extensions of our framework

A lot of ecological theory relies on ordinary-differential-equation models that assume well-mixed systems and do not incorporate any information about the spatial distribution of organisms. However, ecosystems present spatial heterogeneities at different scales that can impact individual fitness and, ultimately, population dynamics. I will present an alternative approach to describe the spatiotemporal dynamics of a population of interacting agents. To this end, I will consider a system with nonlinear birth-death rates and positive and negative inter-individual interactions acting at different spatial ranges. I will first describe the stochastic, individual-level rules that govern the reproduction and death of each individual. Then, using field-theory techniques, I will derive a non-local partial differential equation for the population density and compare its predictions with those obtained assuming well-mixed populations. Finally, I will discuss the ecological relevance of our results and how this approach can be extended to more complex scenarios.

From microbial colonies to entire landscapes, biological systems often self-organize into regular spatial patterns, which might have significant ecological consequences. Several models have been proposed to explain the emergence of these patterns. Most of them rely on a Turing-like activation-inhibition scale-dependent feedback whereby interactions favoring growth dominate at short distances and inhibitory, competitive interactions dominate in the long-range. However, the importance of short-range positive interactions for pattern formation remains disputable. Alternative theories predict their emergence from long-range inhibition alone. In this presentation, I will explain how self-organized patterns might emerge in purely competitive models. I will first present in which conditions long-range competition alone can generate regular patterns of population density in systems with one and two species. Then, I will discuss the ecological implications of those patterns both for population persistence and species coexistence.

Water-limited ecosystems are incredibly complex systems covering 40% of Earth's land surface, mostly in developing countries, and are home to 35% of the world population. A paradigmatic property of these ecosystems is the spatial self-organization of vegetation, which leads to strikingly regular spatial distributions of plants. These self-organized spatial patterns have been suggested as important ecosystem health indicators. Specifically, pattern shapes may indicate the proximity of the ecosystem to undergo a desertification transition. Despite this potential ecological importance, the plant interactions that underlie pattern formation remain unclear. Without strong empirical evidence of how these patterns emerge, mathematical modeling has been crucial in formulating different hypotheses. However, models assuming different mechanistic origins reproduce the same series of patterns but predict contradicting ecological consequences for them. In this context, a new approach to understanding vegetation dynamics in water-limited ecosystems that focus on unveiling how plants interact with each other and how those interactions scale to large population sizes to create emergent patterns is needed. In this presentation, I will first give an overview of existing models for vegetation pattern formation and their connection to well-known physical systems. Then, I will present our efforts to study vegetation dynamics in water-limited ecosystems, using a combination of models and greenhouse experiments.

Despite the importance of ungulate migrations, we lack a complete understanding of why some ungulates species migrate and some do not. Moreover, at the population level, some migrate and others remain behind as residents, a phenomenon known as partial migration. Even though progress has been made towards understanding long-term fitness benefits of partial migration, the underlying decision-making process that makes some individuals migrate and others remain within one single range remain unknown. In this presentation I will combine empirical data from three different migrant ungulate species and mathematical modeling to address this question. I will first show that, across these three ungulate species, the number of residents is unrelated to total population size, a pattern predicted by no previous modeling framework. Next, I will introduce a new model of ungulate partial migration wherein individuals probabilistically decide to start migrating based on the intensity of environmental and social cues. Within this modeling framework, residents arise for most parameter combinations and the number of residents is largely invariant with total population size. Therefore, this new model explains the ubiquity of residents in migratory ungulate populations and presents novel patterns to be tested with further data collection.

Theoretical models in ecology often assume well-mixed populations and thus that individuals interact with one another with the same probability regardless of their spatial location. This strong assumption results in mathematically very tractable models, often based on ordinary differential equations for the population size, that have taught us a lot about how populations change over time. However, these models do not account for the fact that populations are spatially structured, which favors interactions between nearby individuals. In this presentation, I will present some of our recent work investigating the effect of space in shaping population dynamics. First, I will discuss how stochastic spatial models, from lattice models to systems of interacting particles, can provide more accurate descriptions of ecological populations and how to analyze them computationally and analytically. Then, I will use a specific example based on an asymmetric voter model to show how modeling spatial processes can reverse the outcome of species competition predicted by a well-mixed model.

A lot of ecological theory relies on ordinary-differential-equation models that assume well-mixed systems and do not incorporate any information about the spatial distribution of organisms. However, ecosystems present spatial heterogeneities at different scales that can impact individual fitness and, ultimately, population dynamics. I will present an alternative approach to describe the spatiotemporal dynamics of a population of interacting agents. To this end, I will consider a system with nonlinear birth-death rates and positive and negative inter-individual interactions acting at different spatial ranges. I will first describe the stochastic, individual-level rules that govern the reproduction and death of each individual. Then, using field-theory techniques, I will derive a non-local partial differential equation for the population density and compare its predictions with those obtained assuming well-mixed populations. Finally, I will discuss the ecological relevance of our results and how this approach can be extended to more complex scenarios.

Set of Python scripts used to produce paper results

Marine plankton play a crucial role in carbon storage, oxygen production, global climate, and ecosystem function. Planktonic ecosystems are embedded in a Lagrangian patches of water that are continuously moving, stretching, and diluting. These processes drive inhomegeneities on a range of scales, with implications for the integrated ecosystem properties, but are hard to characterize. We present a theoretical framework which accounts for all these aspects; tracking the water patch hosting a drifting ecosystem along with its physical, environmental, and biochemical features. The model resolves patch dilution and internal physical mixing as a function of oceanic strain and diffusion. Ecological dynamics are parameterized by an idealized nutrient and phytoplankton population and we specifically capture the propagation of the biochemical spatial variances to represent within-patch heterogeneity. We find that, depending only on the physical processes to which the water patch is subjected, the plankton biomass response to a resource perturbation can vary several fold. This work indicates that we must account for these processes when interpreting and modeling marine ecosystems and provides a framework with which to do so.

Animal encounters are key components of population dynamics, community dynamics, and evolutionary processes. Consequently, measuring encounter rates (i.e. encounters per time) can be insightful. Encounter rates can be measured from animal tracking data, using metrics that can be split into two groups. The first group consists of trajectory-based metrics, i.e. measures based on serial records of animal locations. This first group includes PROX, the number of observed per number of samples. The second group, in contrast, consists of metrics based on home range overlap, including the Bhattacharyya coefficient (BC). In this study, we argue both types of metrics are limited. Trajectory-based metrics are direct measures of encounter rates but have statistical estimation issues due to their dependency on the frequency of location sampling. Meanwhile, home-rangebased metrics are statistically sound but are not proportional to encounter rates. To overcome both challenges, we proposed a new metric, Relative Encounter Rate (RER). RER increases linearly with the number of encounters and does not depend on the frequency of sampling (i.e. it is scale-invariant). In an individual-based simulation, we measured how RER, BC, and PROX relative error under different sample sizes and sampling frequencies. Further, we compared these metrics in three empirical case studies. We tested Jaguars for polygyny, deforestation effects on tapir connectivity, and an extension of the dearest enemy hypothesis with brown bears. We also compared partner hierarchy according to BC and RER in Jaguar mating clusters. In the simulation study, we found PROX overestimates the encounter rate when data has a low sampling frequency. The simulation also indicates BC overestimated encounters. Furthermore, PROX led to false positives in the Tapir and Bear case studies. In addition, PROX was incapable of detecting many individual relationships in the jaguar polygyny study. RER does not depend on sampling frequency (

The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how self-organization is triggered, namely, reaction-diffusion and spatially nonlocal models. Nevertheless, these models implicitly assume smooth propagation scenarios, neglecting that individuals many times interact by exchanging short and abrupt pulses of the mediating substance. A recently proposed framework advances in the direction of properly accounting for these short-scale fluctuations by applying a coarse-graining procedure on the pulse dynamics. In this paper, we generalize the coarse-graining procedure and apply the extended formalism to new scenarios in which mediators influence individuals' reproductive success or their motility. We show that, in the slow- and fast-mediator limits, pulsed interactions recover, respectively, the reaction-diffusion and nonlocal models, providing a mechanistic connection between them. Furthermore, at each limit, the spatial stability condition is qualitatively different, leading to a timescale-induced transition where spatial patterns emerge as mediator dynamics becomes sufficiently fast.

Intraspecific interactions are key drivers of population dynamics because they establish relations between individual fitness and population density. The component Allee effect is defined as a positive correlation between any fitness component of a focal organism and population density, and it can lead to positive density dependence in the population per capita growth rate. The spatial population structure is key to determining whether and to which extent a component Allee effect will manifest at the demographic level because it determines how individuals interact with one another. However, existing spatial models to study the Allee effect impose a fixed spatial structure, which limits our understanding of how a component Allee effect and the spatial dynamics jointly determine the existence of demographic Allee effects. To fill this gap, we introduce a spatially-explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. Depending on the intensity of the individual-level processes, the population exhibits a variety of spatial patterns, including evenly spaced aggregates of organisms, that determine the demographic-level by-products of an existing individual-level component Allee effect. We find that aggregation increases population abundance and allows populations to survive in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component Allee effect from manifesting at the population level or restrict it to the level of each independent group. These results provide a mechanistic understanding of how component Allee effects might operate for different spatial population structures and show at the population level. Because populations subjected to demographic Allee effects exhibit highly nonlinear dynamics, especially at low abundances, our results contribute to a better

Marine plankton play a crucial role in carbon storage, oxygen production, global climate, and ecosystem function. Planktonic ecosystems are embedded in a Lagrangian patches of water that are continuously moving, stretching, and diluting. These processes drive inhomegeneities on a range of scales, with implications for the integrated ecosystem properties, but are hard to characterize. We present a theoretical framework which accounts for all these aspects; tracking the water patch hosting a drifting ecosystem along with its physical, environmental, and biochemical features. The model resolves patch dilution and internal physical mixing as a function of oceanic strain and diffusion. Ecological dynamics are parameterized by an idealized nutrient and phytoplankton population and we specifically capture the propagation of the biochemical spatial variances to represent within-patch heterogeneity. We find that, depending only on the physical processes to which the water patch is subjected, the plankton biomass response to a resource perturbation can vary several fold. This work indicates that we must account for these processes when interpreting and modeling marine ecosystems and provides a framework with which to do so.

Direct encounters, in which two or more individuals are physically close to one another, are a topic of increasing interest as more and better movement data become available. Recent progress, including the development of statistical tools for estimating robust measures of changes in animals’ space use over time, facilitates opportunities to link direct encounters between individuals with the long-term consequences of those encounters. Working with movement data for coyotes (Canis latrans) and grizzly bears (Ursus arctos horribilis), we investigate whether close intraspecific encounters were associated with spatial shifts in the animals’ range distributions, as might be expected if one or both of the individuals involved in an encounter were seeking to reduce or avoid conflict over space. We analyze the movement data of a pair of coyotes in detail, identifying how a shift in home range location resulting from altered movement behavior was apparently a consequence of a close intraspecific encounter. With grizzly bear 50 movement data, we approach the problem from the perspective of a set of encounter pairs within a population. We find support for the hypotheses that 1) close intraspecific encounters between bears are, on average, associated with subsequent shifts in range distributions and 2) encounters defined at finer spatial scales are followed by greater changes in space use. Our results suggest that animals can undertake long-term, large-scale spatial shifts in response to close intraspecific encounters that have the potential for conflict. These results lend support for existing theory on the evolution of territories and space use (e.g., Maynard-Smith’s bourgeois strategy regarding low-conflict coexistence). Overall, we find that analyses of movement data in a pairwise context can 1) identify distances at which individuals’ proximity to one another may alter behavior and 2) facilitate testing of population-level hypotheses concerning the potential for direct enc

Ecologists have long investigated how the demographic and movement parameters of a population determine its spatial spread and the critical habitat size that can sustain it. Yet, most existing models make oversimplifying assumptions about individual movement behavior, neglecting how landscape heterogeneity influences dispersal. We relax this assumption and introduce a reaction-advection-diffusion model that describes the spatial density distribution of a population with space-dependent movement bias toward preferred regions, including avoidance of degraded habitats. In this scenario, the critical habitat size depends on the spatial location of the habitat edges with respect to the preferred regions and on the intensity of the movement bias components. In particular, we identify parameter regions where the critical habitat size decreases when diffusion increases, a phenomenon known as the “drift paradox”. We also find that biased movement toward low-quality or highly populated regions can reduce the population size, therefore creating ecological traps. Our results emphasize the importance of species-specific movement behavior and habitat selection as drivers of population dynamics in fragmented landscapes and, therefore, the need to account for them in the design of protected areas.

Animals moving through landscapes need to strike a balance between finding sufficient resources to grow and reproduce while minimizing encounters with predators 1,2. Because encounter rates are determined by the average distance over which directed motion persists 1,3–5, this trade-off should be apparent in individuals’ movement. Using GPS data from 1,396 individuals across 62 species of terrestrial mammals, we show how predators maintained directed motion ~7 times longer than for similarly-sized prey, revealing how prey species must trade off search efficiency against predator encounter rates. Individual search strategies were also modulated by resource abundance, with prey species forced to risk higher predator encounter rates when resources were scarce. These findings highlight the interplay between encounter rates and resource availability in shaping broad patterns mammalian movement strategies.