arXiv subjects

Ricardo Martinez-Garcia

Publications and source records attributed to Ricardo Martinez-Garcia.

At least 19 recordsLinked to original sources

arXiv2026

The role of root allometry and root overlap in vegetation pattern formation

We investigate how root allometry and below-ground root competition due to root overlap affect the conditions for pattern formation in non-local scalar vegetation models. We start from a spatially explicit two-component vegetation-water system in which plants acquire soil water through their laterally extended root systems, with root allometry represented by an interaction kernel whose spatial extent increases with the above-ground biomass density. In the limit of fast water dynamics, we eliminate the water variable, resulting in a non-local scalar model for the vegetation dynamics. This reduction reveals that accounting for root overlap naturally leads to a double integral structure in the scalar model, in contrast to the single convolution term commonly used to model non-local competition for resources. For the resulting scalar model, we identify two distinct mechanisms that can drive Turing instabilities. The first instability mechanism requires root growth to outpace mortality, while the second mechanism relies on the development of competitive pressure zones, in which vegetation growth is impeded by the cumulative competitive pressure exerted by neighbouring areas with higher biomass density. Root allometry promotes the occurrence of both instability mechanisms, while root overlap inhibits the emergence of competitive pressure zones. Hence, our results show that both root allometry and root overlap are important features to consider when studying vegetation pattern formation.

nlin.PS↗

arXiv2026

Higher-Order Competition as a Minimal Mechanism for Spatial Pattern Diversity in Population Dynamics

We show that negative feedback alone generates the diversity of self-organized shapes usually attributed to scale-dependent activation-inhibition. For a broad class of kernels, pairwise competition models only generate hexagonal spot arrays. Higher-order terms eliminate this restriction and promote stripes and gaps. Combining individual-based simulations and nonlinear analysis, we derive the pattern-selection thresholds and construct the full state diagram, including an unusual spots-stripes-spots sequence. Spot patterns are thus not a reliable indicator of proximity to a tipping point.

nlin.AO↗

arXiv2026

Fixation probabilities for multi-allele Moran dynamics with weak selection

Fixation probabilities are essential for characterizing stochastic evolutionary dynamics, but analytical results remain limited mainly to systems with two competing types. We develop a perturbative framework to compute fixation probabilities in multi-allele Moran processes under weak selection. Exploiting the general structure of the backward Fokker-Planck operator in this regime, we show that fixation probabilities admit a systematic expansion around their neutral solution. We first introduce the framework for $M$ competing alleles with multivariate polynomial fitness functions. We then apply it to three biologically motivated examples: a constant-fitness model, which we solve for an arbitrary number of alleles; a three-allele coordination game in which allele fitness increases with its frequency in the population; and a three-allele model of clonal interference between mutualistic alleles. These results extend the analytical understanding of fixation probabilities beyond pairwise interactions, establishing a framework for investigating multi-strategy stochastic evolutionary dynamics.

q-bio.PE↗

arXiv2026

Range residency determines how movement persistence shapes encounter rates

Encounters between individuals link movement behavior to population-level processes such as predation and disease transmission. For many animal species, movement can be modeled as a multiscale stochastic process, dominated by directional persistence at short time scales and range residency at long time scales. Their separate effects on encounters are well understood: range residency can raise or lower encounter rates depending on home-range overlap, whereas moving with higher directional persistence systematically increases them. However, how directional persistence and range residency jointly determine encounters remains unknown. We present an analytical encounter theory for movement models that combine both features. In this framework, we derive a threshold in home-range overlap above which directional persistence diminishes, rather than enhances, encounters. At shorter time scales, attraction toward the home-range center displaces individual locations, altering encounter rates even when range residency is not measurable in movement tracks. Movement models fitted to short tracks can therefore describe trajectories accurately yet under- or overestimate the encounters derived from those trajectories, depending on home range spatial configuration. Encounter rates are a more demanding target for inference than movement parameters themselves.

q-bio.PE↗

arXiv2026

Self-organized vegetation patterns promote persistence of plant-pollinator mutualisms under environmental stress

Mutualisms are key for structuring ecological communities, but they are sensitive to environmental change and fluctuations in population size. Consequently, how mutualisms achieve stability remains an open question in ecological theory. Motivated by previous results in competitive and predator-prey interactions, we hypothesize that self-organized pattern formation can act as a key stabilizing mechanism of mutualistic interactions. We test this hypothesis using a two-species reaction-diffusion model of a plant-pollinator system that incorporates non-local plant competition and local mutualistic interactions. We first perform a linear stability analysis to determine the conditions under which non-local competition can trigger vegetation pattern formation. We then compute the bifurcation diagrams for both spatial and homogeneous solutions and find that pattern formation enables coexistence at mutualistic strengths below the threshold required in well-mixed populations. This stability gain increases as environmental conditions worsen, because local maxima in vegetation density create the conditions for community persistence despite globally harsh conditions. Moreover, in the strong mutualism limit, the spatial system exhibits multistability between patterned and homogeneous solutions, creating alternative stable configurations that can buffer against fluctuations in population abundance. Spatial self-organization thus stabilizes mutualistic communities through spatial patterns, potentially driving plant-pollinator persistence in stressed environments, including arid ecosystems.

q-bio.PE↗

arXiv2026

Vegetation pattern formation induced by local growth outpacing susceptibility to non-local competition

In this work, we present and analyze a general framework for vegetation dynamics in arid and semi-arid ecosystems in which non-local interactions are purely competitive. The generality of the formulation enables a systematic search for ecological mechanisms that may lead to self-organized patterns. We identify two distinct mechanisms generating Turing instabilities across a broad class of models. The first mechanism arises from intensified competition in the areas between vegetated patches due to the cumulative pressure from their surroundings, and is well-documented in the literature. The second mechanism is novel and occurs when local growth outpaces competitive susceptibility near the uniform equilibrium. The analytical findings are complemented by numerical simulations of two benchmark models, both exhibiting a supercritical Turing bifurcation that leads to the formation of stable and robust vegetation patterns.

nlin.PS↗

arXiv2026

How animal movement influences wildlife-vehicle collision risk: a mathematical framework for range-resident species

Wildlife-vehicle collisions (WVC) threaten both biodiversity and human safety worldwide. Despite empirical efforts to characterize the major determinants of WVC risk and optimize mitigation strategies, we still lack a theoretical framework linking traffic, landscape, and individual movement features to collision risk. Here, we introduce such a framework by leveraging recent advances in movement ecology and reaction-diffusion stochastic processes with partially absorbing boundaries. Focusing on range-resident terrestrial mammals -- responsible for most fatal WVCs -- we model interactions with a single linear road and derive exact expressions for key survival statistics, including mean collision time and road-induced lifespan reduction. These quantities are expressed in terms of measurable parameters, such as traffic intensity or road width, and movement parameters that can be robustly estimated from relocation data, such as home-range crossing times, home-range sizes, or distance between home-range center and road. Therefore, our work provides an effective theoretical framework integrating movement and road ecology, laying the foundation for data-driven, evidence-based strategies to mitigate WVCs and promote safer, more sustainable transportation networks.

q-bio.PE↗

arXiv2026

Extinction and persistence criteria in non-local Klausmeier model of vegetation dynamics on flat landscapes

This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system and provide a rigorous analysis of the conditions required for vegetation survival. Our results identify a critical patch size governed by the trade-off between local growth and boundary losses; habitats smaller than this threshold lead to inevitable extinction. Furthermore, we derive a critical maximal biomass density below which the population collapses to a desert state, regardless of the domain size. We determine stability criteria for stationary solutions and describe the emergence of stable, non-trivial biomass distributions. Numerical experiments comparing sub-Gaussian and super-Gaussian kernels confirm that non-local dispersal mechanisms, particularly those with fat tails, enhance ecosystem resilience by allowing vegetation to persist in smaller, fragmented habitats than predicted by classical local diffusion models.

math.AP↗

arXiv2025

How spatial patterns can lead to less resilient ecosystems

Several theoretical models predict that spatial patterning increases ecosystem resilience. However, these predictions rely on simplifying assumptions, such as assuming isotropic and infinitely large ecosystems, and empirical evidence directly linking spatial patterning to enhanced resilience remains scarce. We introduce a unifying framework, encompassing existing models for vegetation pattern formation in water-stressed ecosystems, that relaxes these assumptions. This framework incorporates finite vegetated areas surrounded by desert and anisotropic environmental conditions that lead to non-reciprocal plant interactions. Under these more realistic conditions, we identify a novel desertification mechanism, known as nonlinear convective instability in physics but largely overlooked in ecology. These instabilities form when non-reciprocal interactions destabilize the vegetation-desert interface and can trigger desertification fronts even under stress levels where isotropic models predict stability. Importantly, ecosystems exhibiting periodic vegetation patterns are more susceptible to nonlinear convective instabilities than those with homogeneous vegetation, suggesting that spatial patterning may reduce, rather than enhance, resilience. These findings challenge the prevailing view that self-organized patterning enhances ecosystem resilience and provide a new framework for investigating how spatial dynamics shape the stability and resilience of ecological systems under changing environmental conditions.

q-bio.PE↗

arXiv2025

Flow spatial structure determines pattern instabilities in nonlocal models of population dynamics

We investigate how environmental flows influence spatial pattern formation and population dynamics using two nonlocal models of population dynamics, which we couple to two different stationary flows. Combining numerical simulations and analytical approximations, we show that the spatial structure of the flow's velocity field determines the pattern formation instability. For a simple shear flow, where one of the primary axes of the population pattern can become aligned with the flow, the onset of pattern formation remains unaffected. In contrast, a vortex flow delays the pattern instability relative to the no-flow case. The velocity field, therefore, interacts with the spatial feedbacks responsible for pattern formation in complex ways, which also leads to different oscillatory time series of population abundance. In some cases, the population undergoes regular oscillations with a characteristic frequency, while in others, the dynamics exhibits long erratic transients with no well-defined period before settling into a more regular behavior.

q-bio.PE↗

arXiv2025

Spatial moment dynamics and biomass density equations provide complementary, yet limited, descriptions of pattern formation in individual-based simulations

Spatial patterning is common in ecological systems and has been extensively studied via different modeling approaches. Individual-based models (IBMs) accurately describe nonlinear interactions at the organism level and the stochastic spatial dynamics that drives pattern formation, but their computational cost scales quickly with system complexity, limiting their practical use. Population-level approximations such as spatial moment dynamics (SMD) -- which describe the moments of organism distributions -- and coarse-grained biomass density models have been developed to address this limitation. However, the extent to which these approximated descriptions accurately capture the spatial patterns and population sizes emerging from individual-level simulations remains an open question. We investigate this issue considering a prototypical population dynamics IBM with long-range dispersal and intraspecific competition, for which we derive both its SMD and coarse-grained density approximations. We systematically compare the performance of these two approximations at predicting IBM population abundances and spatial patterns. Our results highlight that SMD and density-based approximations complement each other by correctly capturing these two population features within different parameter regimes. Importantly, we identify regions of the parameter space in which neither approximation performed well, which should encourage the development of more refined IBM approximation approaches.

q-bio.PE↗

arXiv2025

Ergodicity shapes inference in biological reactions driven by a latent trajectory

Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random intervals, when an underlying, often unobserved and therefore latent, dynamical system occupies a set of reactive states within its phase space. We show how the ergodicity of this latent dynamical system, i.e. existence of a well-behaved limiting stationary distribution, constrains the statistics of the reaction counts. This formulation makes explicit the conditions under which the counting process approaches a limiting Poisson process, a subject of debate in the application of counting processes to different fields. We show that the overdispersal relative to this limit encodes properties of the latent trajectory through its hitting times. These results set bounds on how information about a latent process can be inferred from a local detector, which we explore for two biophysical scenarios. First, in estimating an animal's activity level by how often it crosses a detector, we show how the mean count can fail to give any information on movement parameters, which are encoded in higher order moments. Second, we show how the variance of the inter-reaction time sets a fundamental limit on how precisely the size of a population of trajectories can be inferred by a detector, vastly generalizing the Berg-Purcell limit for chemosensation. Overall, we develop a flexible theoretical framework to quantify inter-event time distributions in reaction-diffusion systems that clarifies existing debates in the literature and explicitly shows which properties of latent processes can be inferred from observed reactions.

cond-mat.stat-mech↗

arXiv2025

Demographic effects of aggregation in the presence of a component Allee effect

The component Allee effect (AE) is the positive correlation between an organism's fitness component and population density. Depending on the population spatial structure, which determines the interactions between organisms, a component AE might lead to positive density-dependence in the population per capita growth rate and establish a demographic AE. However, existing spatial models impose a fixed population spatial structure, which limits the understanding of how a component AE and spatial dynamics jointly determine the existence of demographic AEs. We introduce a spatially explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. This framework predicts various spatial patterns depending on its specific parameterization, including evenly spaced aggregates of organisms, that determine the demographic-level by-products of the component AE. We find that aggregation increases population abundance and allows population survival in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component AE from manifesting at the population level or restrict it to the level of each independent aggregate. These results provide a mechanistic understanding of how component AEs might operate for different spatial structures and manifest at larger scales.

q-bio.PE↗

arXiv2025

Spatial competition and repulsion: pattern formation and the role of movement

This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and repulsion are both anti-crowding interactions, collective effects may lead to clusters of individuals, which can arrange periodically. Through the analysis of two models, it provides insights into the similarities and differences in the patterns formed and underlines the role of movement in shaping the spatial distribution of biological populations.

q-bio.PE↗

arXiv2024

Pulsed interactions unify reaction-diffusion and spatial nonlocal models for biological pattern formation

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.

q-bio.PE↗

arXiv2024

Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size

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.

q-bio.PE↗

arXiv2023

A Lagrangian model for drifting ecosystems reveals heterogeneity-driven enhancement of marine plankton blooms

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.

q-bio.PE↗

arXiv2022

Integrating theory and experiments to link local mechanisms and ecosystem-level consequences of vegetation patterns in drylands

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.

q-bio.PE↗