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Spot patterns, in which vegetation patches form a hexagonal lattice, are frequent in nature and could serve as an early-warning indicator of abrupt vegetation collapses. Consequently, they have been intensively studied using both individual-based models and density-based field equations. Yet, the relationship between these two approaches remains unclear, particularly in scenarios where vegetation dynamics exhibit strong long-range spatial correlations and traditional mean-field approximations fail. To solve this issue, we develop a new method that refines mean-field approximations by describing both the dynamics of the biomass density field and its spatial correlations. This new approach harnesses the strengths of both individual and density-based mdoels, treating spatial correlations explicitly and allowing for the identification of spatial instabilities resulting in periodic patterns. Our results indicate that this new approximation predicts the parameter regimes where regular periodic patterns emerge more accurately than mean-field models, suggesting that it could provide a more robust framework to perform further nonlinear analysis.

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., Comment: 27 pages, 10 figures

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.

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 behavior, 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 behavior and habitat preference as drivers of population dynamics in fragmented landscapes and, therefore, in the design of protected areas., Comment: 21 pages, 8 figures

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 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 rates. Depending on the intensity of the individual processes the population exhibits a variety of spatial patterns 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 operate for different spatial population structures and show at the population level. Our results contribute to better understanding population dynamics in the presence of Allee effects and can potentially inform population management strategies.

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 modelling marine ecosystems and provides a framework with which to do so.

Self-organized spatial patterns of vegetation are frequent in drylands and, because pattern shape correlates with water availability, they have been suggested as important indicators of ecosystem health. However, the mechanisms underlying pattern emergence remain unclear. Some theories hypothesize that patterns could result from a water-mediated scale-dependent feedback (SDF) whereby interactions favoring plant growth dominate at short distances and growth-inhibitory interactions dominate in the long range. However, we know little about how the presence of a focal plant affects the fitness of its neighbors as a function of the inter-individual distance, which is expected to be highly ecosystem-dependent. This lack of empirical knowledge and system dependency challenge the relevance of SDF as a unifying theory for vegetation pattern formation. Assuming that plant interactions are always inhibitory and only their intensity is scale-dependent, alternative theories also recover the typical vegetation patterns observed in nature. Importantly, although these alternative hypotheses lead to visually indistinguishable patterns, they predict contrasting desertification dynamics, which questions the potential use of vegetation patterns as ecosystem-state indicators. To help resolve this issue, we first review existing theories for vegetation self-organization and their conflicting predictions about desertification dynamics. Second, we discuss potential empirical tests via manipulative experiments to identify pattern-forming mechanisms and link them to specific desertification dynamics. A comprehensive view of models, the mechanisms they intend to capture, and experiments to test them in the field will help to better understand both how patterns emerge and improve predictions on the fate of the ecosystems where they form., Comment: 20 pages, 6 figures

We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the nonlocal interactions. In both cases, nonlocal interactions can create spatial patterns of population densities in which highly populated clumps alternate with unpopulated regions. This non-populated regions provide spatial niches for a weaker competitor to establish in the community and persist in conditions in which local models predict competitive exclusion. Moreover, depending on the balance between local and nonlocal competition intensity, the clumps of the weaker competitor vary from M-like structures with higher densities of individuals accumulating at the edges of each clump to triangular structures with most individuals occupying their centers. These results suggest that long-range competition, through the creation of spatial patterns in population densities, might be an important driving force behind the rich diversity of species observed in real ecological communities.

We introduce an asymmetric noisy voter model to study the joint effect of immigration and a competition-dispersal tradeoff in the dynamics of two species competing for space in regular lattices. Individuals of one species can invade a nearest-neighbor site in the lattice, while individuals of the other species are able to invade sites at any distance but are less competitive locally, i.e., they establish with a probability $g \le 1$. The model also accounts for immigration, modeled as an external noise that may spontaneously replace an individual at a lattice site by another individual of the other species. This combination of mechanisms gives rise to a rich variety of outcomes for species competition, including exclusion of either species, mono-stable coexistence of both species at different population proportions, and bi-stable coexistence with proportions of populations that depend on the initial condition. Remarkably, in the bi-stable phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to a half loop dynamics associated to a cusp catastrophe, which causes the irreversible loss of the species with the shortest dispersal range., Comment: 13 pages, 9 figures, 3 appendices

Encounter rates link movement strategies to intra- and inter-specific interactions, and therefore translate individual movement behavior into higher-level ecological processes. Indeed, a large body of interacting population theory rests on the law of mass action, which can be derived from assumptions of Brownian motion in an enclosed container with exclusively local perception. These assumptions imply completely uniform space use, individual home ranges equivalent to the population range, and encounter dependent on movement paths actually crossing. Mounting empirical evidence, however, suggests that animals use space non-uniformly, occupy home ranges substantially smaller than the population range, and are often capable of nonlocal perception. Here, we explore how these empirically supported behaviors change pairwise encounter rates. Specifically, we derive novel analytical expressions for encounter rates under Ornstein-Uhlenbeck motion, which features non-uniform space use and allows individual home ranges to differ from the population range. We compare OU-based encounter predictions to those of Reflected Brownian Motion, from which the law of mass action can be derived. For both models, we further explore how the interplay between the scale of perception and home range size affects encounter rates. We find that neglecting realistic movement and perceptual behaviors can systematically bias encounter rate predictions., Comment: 21 pages, 7 figures, 10 appendices

Eco-evolutionary frameworks can explain certain features of communities in which ecological and evolutionary processes occur over comparable timescales. Here, we investigate whether an evolutionary dynamics may interact with the spatial structure of a prey-predator community in which both species show limited mobility and predator perceptual ranges are subject to natural selection. In these conditions, our results unveil an eco-evolutionary feedback between species spatial mixing and predators perceptual range: different levels of mixing select for different perceptual ranges, which in turn reshape the spatial distribution of prey and its interaction with predators. This emergent pattern of interspecific interactions feeds back to the efficiency of the various perceptual ranges, thus selecting for new ones. Finally, since prey-predator mixing is the key factor that regulates the intensity of predation, we explore the community-level implications of such feedback and show that it controls both coexistence times and species extinction probabilities.

Biofilms are microbial collectives that occupy a diverse array of surfaces. The function and evolution of biofilms are strongly influenced by the spatial arrangement of different strains and species within them, but how spatiotemporal distributions of different genotypes in biofilm populations originate is still underexplored. Here, we study the origins of biofilm genetic structure by combining model development, numerical simulations, and microfluidic experiments using the human pathogen Vibrio cholerae. Using spatial correlation functions to quantify the differences between emergent cell lineage segregation patterns, we find that strong adhesion often, but not always, maximizes the size of clonal cell clusters on flat surfaces. Counterintuitively, our model predicts that, under some conditions, investing in adhesion can reduce rather than increase clonal group size. Our results emphasize that a complex interaction of fluid flow and cell adhesiveness can underlie emergent patterns of biofilm genetic structure. This structure, in turn, has an outsize influence on how biofilm-dwelling populations function and evolve., Comment: 32 pages (4 figures; 8 SI Fig; SI Text)

Vegetation patterns are abundant in arid and semiarid ecosystems, but how they form remains unclear. One of the most extended theories lies in the existence of scale-dependent feedbacks (SDF) in plant-to-plant and plant-water interactions. Short distances are dominated by facilitative interactions, whereas competitive interactions dominate at larger scales. These feedbacks shape spatially inhomogeneous distributions of water that ultimately drive the emergence of patterns of vegetation. Even though the presence of facilitative and competitive interactions is clear, they are often hard to disentangle in the field, and therefore their relevance in vegetation pattern formation is still disputable. Here, we review the biological processes that have been proposed to explain pattern formation in arid ecosystems and how they have been implemented in mathematical models. We conclude by discussing the existence of similar structures in different biological and physical systems., Comment: 17 pages, 4 figures

This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts and mathematical tools that are going to be used in subsequent chapters are presented. Firstly, the different levels of description usually employed in the models are explained. Secondly, the mathematical relationships among them are presented. Finally, the notation and terminology that will be used later on are explained. The second part is devoted to studying vegetation pattern formation in regions where precipitations are not frequent and resources for plant growth are scarce. This part comprises two chapters. The third part of the thesis develops a series of mathematical models describing the collective movement and behavior of some animal species. Its primary objective is to investigate the effect that communication among foragers has on searching times and the formation of groups. It consists of two chapters. The fourth part covers the effect of stochastic temporal disorder, mimicking climate and environmental variability, on systems formed by many interacting particles. These models may serve as an example of ecosystems. The thesis ends with a summary and devising future research lines., Comment: PhD Thesis

Many natural processes rely on optimizing the success ratio of a search process. We use an experimental setup consisting of a simple online game in which players have to find a target hidden on a board, to investigate the how the rounds are influenced by the detection of cues. We focus on the search duration and the statistics of the trajectories traced on the board. The experimental data are explained by a family of random-walk-based models and probabilistic analytical approximations. If no initial information is given to the players, the search is optimized for cues that cover an intermediate spatial scale. In addition, initial information about the extension of the cues results, in general, in faster searches. Finally, strategies used by informed players turn into non-stationary processes in which the length of each displacement evolves to show a well-defined characteristic scale that is not found in non-informed searches., Comment: 17 pages, 10 figures

Studies of cooperation in microbes often focus on one fitness component, with little information about or attention to the ecological context, and this can lead to paradoxical results. The life cycle of the social amoeba Dictyostelium discoideum includes a multicellular stage in which not necessarily clonal amoebae aggregate upon starvation to form a possibly chimeric (genetically heterogeneous) fruiting body made of dead stalk and spores. The lab-measured reproductive skew in the spores of chimeras indicates strong social antagonism; this should result in low genotypic diversity, which is inconsistent with observations from nature. Two studies have suggested that this inconsistency stems from the one-dimensional assessment of fitness (spore production) and that the solution lies in tradeoffs between multiple traits, e.g.: spore size versus viability; and staying vegetative versus becoming dormant. We theoretically explore different tradeoff-implementing mechanisms and provide a unifying ecological framework in which the two tradeoffs above, as well as novel ones, arise collectively in response to characteristics of the environment. We find that spore production comes at the expense of vegetative cell production, time to development, and, depending on the experimental setup, spore size and viability. Furthermore, we find that all existing experimental results regarding chimeric mixes can be qualitatively recapitulated without needing to invoke social interactions, which allows for simple resolutions to previously paradoxical results. We conclude that the complexities of life histories, including social behavior and multicellularity, can only be understood in the appropriate multidimensional ecological context., Comment: 40 pages, 6 figures + 9 Supplementary figures

D. discoideum has been recently suggested as an example of bet-hedging. Upon starvation a population of unicellular amoebae splits between aggregators, which form a fruiting body made of a stalk and resistant spores, and non-aggregators. Spores are favored by long starvation periods, but vegetative cells can exploit resources in fast-recovering environments. This partition can be understood as a bet-hedging strategy that evolves in response to stochastic starvation times. A genotype is defined by a different balance between each type of cells. In this framework, if the ecological conditions are defined in terms of the mean starvation time (i.e. time between onset of starvation and the arrival of a new food pulse), a single genotype dominates each environment, which is inconsistent with the huge genetic diversity observed in nature. We investigate whether seasonality, represented by a periodic alternation in the mean starvation times, allows the coexistence of several strategies. We use a non-spatial (well-mixed) setting where different strains compete for a pulse of resources. We find that seasonality, which we model via two seasons, induces a temporal storage effect that can promote the stable coexistence of multiple genotypes. Two conditions need to be met. First, the distributions of starvation times in each season cannot overlap in order to create two well differentiated habitats within the year. Second, numerous growth-starvation cycles have to occur during each season to allow well-adapted strains to grow and survive the subsequent unfavorable period. Additional tradeoffs among life-history traits can expand the range of coexistence and increase the number of coexisting strategies, contributing towards explaining the genetic diversity observed in D. discoideum, Comment: 33 pages, 7 figures

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological organisms (like mussels) that tend to cluster at short ranges as a defensive strategy, and strongly disperse if there is a high population pressure at large ranges for optimizing foraging. We perform stochastic simulations of a particle-level model of the system, and derive and analyze a continuous density description (a nonlinear diffusion equation). In both cases we show that this interplay of scale-dependent-behaviors gives rise to a rich formation of spatial patterns ranging from labyrinths to periodic cluster arrangements. In most cases these clusters have the very peculiar appearance of ring-like structures, i.e., organisms arranging in the perimeter of the clusters, that we discuss in detail., Comment: 13 pages, 9 figures

The minimal ecological requirements for formation of regular vegetation patterns in semiarid systems have been recently questioned. Against the general belief that a combination of facilitative and competitive interactions is necessary, recent theoretical studies suggest that, under broad conditions, nonlocal competition among plants alone may induce patterns. In this paper, we review results along this line, presenting a series of models that yield spatial patterns when finite-range competition is the only driving force. A preliminary derivation of this type of model from a more detailed one that considers water-biomass dynamics is also presented. Keywords: Vegetation patterns, nonlocal interactions, Comment: 8 pages, 4 figures

We investigated the relationships between search efficiency, movement strategy, and non-local communication in the biological context of animal foraging. We considered situations where the members of a population of foragers perform either Gaussian jumps or Levy flights, and show that the search time is minimized when communication among individuals occurs at intermediate ranges, independently of the type of movement. Additionally, while Brownian strategies are more strongly influenced by the communication mechanism, Levy flights still result in shorter overall search durations., Comment: 9 pages, 6 figures

Regular vegetation patterns in semiarid ecosystems are believed to arise from the interplay between long-range competition and facilitation processes acting at smaller distances. We show that, under rather general conditions, long-range competition alone may be enough to shape these patterns. To this end we propose a simple, general model for the dynamics of vegetation, which includes only long-range competition between plants. Competition is introduced through a nonlocal term, where the kernel function quantifies the intensity of the interaction. We recover the full spectrum of spatial structures typical of vegetation models that also account for facilitation in addition to competition., Comment: 21 pages, 3 figures

We investigate the relationship between communication and search efficiency in a biological context by proposing a model of Brownian searchers with long-range pairwise interaction. After a general study of the properties of the model, we show an application to the particular case of acoustic communication among Mongolian gazelle, for which data are available, searching for good habitat areas. Using Monte Carlo simulations and density equations, our results point out that the search is optimal (i.e. the mean first hitting time among searchers is minimum) at intermediate scales of communication, showing that both an excess and a lack of information may worsen it., Comment: 5 pages, 3 figures