Patchy Environment Research Articles

Untangling the mobility dynamics in a patchy environment: An SEIR epidemic model with vertical transmission

Congenital Rubella, AIDS, and other human diseases may pass from mother to fetus through the placenta. On the other side, insects and plants often transmit vertically by their eggs/seeds. Here, we study an SEIR epidemic model with vertical transmission in a multi‐patch context to explore the spread of disease in a population divided into distinct regions. The local and global stability of disease‐free equilibrium for the n‐patch model system has been determined in terms of the basic reproduction number . Moreover, we discuss the existence and stability of endemic equilibrium for different cases in two symmetric regions. Our findings indicate that when is less than one, the disease‐free equilibrium is globally asymptotically stable, whereas when is greater than one, it is unstable. As a result, for , the model system has an unique endemic equilibrium that is always locally asymptotically stable. The dynamics of the proposed model system depending on the distribution of infected individuals across various regions have been studied. The findings suggest that the movements from high disease risk regions to low disease risks may increase the number of the infected population in the community. The value of could be enhanced by increasing the values of any vertical transmission parameter. However, the changes in the values of are relatively minor. Our findings also imply that while migrations of all individuals across symmetric regions do not leave any impact on the equilibrium state of the infected population, they do affect the trajectory of the solution to reach a steady‐state. The flow of people between the two symmetrical regions could not alter the endemicity.

Dispersal of optimal foragers in a patchy environment: Simulations with a mathematical model and tests of predictions in field experiments

To predict the effect of density on the dispersal of foraging parasitoids, we developed a spatially explicit individual-based model in which parasitoids move among host patches at random but use an optimal decision-rule about when to leave these patches. We used a simple decision rule where an individual forager exploits a patch as long as the instantaneous attack rate is higher than the average attack rate it has experienced in the environment. Such a rule implies that foragers compute and remember attack rates as they forage. Simulations with different combinations of patch distribution, host density, mutual interference, and parasitoid density predicted that dispersal distance should increase with parasitoid density. To test this prediction, we used data from two field experiments in which we released either few or many adults of the aphid parasitoid Aphelinus asychis in replicated sites, and subsequently assessed dispersal from the spatial distribution of parasitoid offspring. In the first experiment, we did not to detect a relation between the number released and dispersal distance, but in the second experiment, dispersal distance increased with initial density, as predicted by our model. We propose two hypotheses to explain the discrepancy between the experiments. Different levels of environmental variability among experiments, resulting from differences in experimental designs, could cause differences in statistical conclusions. However, there could be a threshold density below which dispersal is not density-dependent, and this threshold may have been exceeded in the second experiment where large releases involved many more individuals than in the first experiment. In any case, our approach linked individual behavior and spatial distribution, and our results show that the insect distributions in the field can be predicted, qualitatively, from theory about individual behavior.

Effects of diffusion and advection on predator-prey dynamics in an advective patchy environment

In this paper, we investigate a specialist predator-prey model within a closed patchy network of streams. Specifically, we focus on the dynamics and asymptotic profiles of positive steady states. Our findings reveal that specialist predators can successfully invade when the mortality rate remains sufficiently low. Additionally, we explore the effects of diffusion and advection on these steady states and the overall species concentration.

Patchy energy landscapes promote stability of small groups of active particles

Group formation and coordination are fundamental characteristics of living matter, essential for performing tasks and ensuring survival. Interactions between individuals play a key role in group formation, and the impact of resource distributions is a vibrant area of research. As of now, an understanding of how patchy resource distributions determine group dynamics is not yet fully understood. Studying active particles in controlled optical landscapes as energy sources, we demonstrate a non-monotonic dependency of group size on landscape patchiness, with the smallest groups forming when the patches match the active particles’ size. A similar relationship is observed in terms of group stability, evidenced by a reduced rate of individual exchange in patchy environments compared to homogeneous conditions. Reduced group sizes can be beneficial to optimise resources in heterogeneous environments and to control information flow within populations. Our results provide insights into the role of patchy landscapes and uneven energy distributions in active matter and hold implications for refining swarm intelligence algorithms, enhancing crowd management techniques, and tailoring colloidal self-assembly.

Dynamics of the generalized Rosenzweig–MacArthur model in a changing and patchy environment

In this paper, we propose a generalized Rosenzweig–MacArthur predator–prey model with two patches and Allee effects in predators. In a constant environment, for the single-patch model we show the existence of degenerate Bogdanov–Takens bifurcation with codimension up to 4 and degenerate Hopf bifurcation with codimension up to 3, which indicate that the nilpotent cusp of codimension 4 is the organizing center of the bifurcation set. Our results show that Allee effects in predators can not only induce much more complex bifurcations and dynamics (such as three limit cycles, multitype tristability), but also serve as a destabilizing factor to make predators extinction (deterministically) when the environment is sufficiently enriched, which provides strong support for the so-called “paradox of enrichment”. For the two-patch model, we numerically reveal the existence of eight positive steady states including two new coexisting attractors, which means that population dispersal can help species coexist or increase the population abundance. In a changing environment, for the single-patch model we find that the population can track unstable states, fast positive or slow negative environmental change can be beneficial to predators by delaying or even avoiding extinction; while for the two-patch model we observe some interesting phenomena: fast negative (or slow positive) environmental change can make predators in different patches trend to extinction synchronously, and rate-induced different regime shifts.

The relative importance of metabolic rate and body size to space use behavior in aquatic invertebrates.

Elucidating the underlying mechanisms behind variations of animal space and resource use is crucial to pinpoint relevant ecological phenomena. Organism's traits related to its energy requirements might be central in explaining behavioral variation, as the ultimate goal of a forager is to fulfill its energy requirements. However, it has remained poorly understood how energy requirements and behavioral patterns are functionally connected. Here we aimed to assess how body mass and standard metabolic rate (SMR) influence behavioral patterns in terms of cumulative space use and time spent in an experimental patchy environment, both within species and among individuals irrespective of species identity. We measured the behavioral patterns and SMR of two invertebrate species, that is, amphipod Gammarus insensibilis, and isopod Lekanesphaera monodi, individually across a range of body masses. We found that species of G. insensibilis have higher SMR level, in addition to cumulatively exploring a larger space than L. monodi. Cumulative space use scaled allometrically with body mass, and it scaled isometrically with SMR in both species. While time spent similarly in both species was characterized by negative body mass and SMR dependence, it was observed that L. monodi individuals tended to stay longer in resource patches compared to G. insensibilis individuals. Our results further showed that within species, body mass and metabolic rate explained a similar amount of variation in behavior modes. However, among individuals, regardless of species identity, SMR had stronger predictive power for behavioral modes compared to body mass. This suggests that SMR might offer a more generalized and holistic description of behavioral patterns that extend beyond species identity. Our study on the metabolic and body mass scaling of space and resource use behavior sheds light on higher-order ecological processes such as species' competitive coexistence along the spatial and trophic dimensions.

May Not Tell Us Everything: Transient Disease Dynamics of Some SIR Models Over Patchy Environments.

This paper examines the short-term or transient dynamics of SIR infectious disease models in patch environments. We employ reactivity of an equilibrium and amplification rates, concepts from ecology, to analyze how dispersals/travels between patches, spatial heterogeneity, and other disease-related parameters impact short-term dynamics. Our findings reveal that in certain scenarios, due to the impact of spatial heterogeneity and the dispersals, the short-term disease dynamics over a patch environment may disagree with the long-term disease dynamics that is typically reflected by the basic reproduction number. Such an inconsistence can mislead the public, public healthy agencies and governments when making public health policy and decisions, and hence, these findings are of practical importance.

SIS Epidemic Spreading Under Multilayer Population Dispersal in Patchy Environments

We study SIS epidemic spreading models under population dispersal on multi-layer networks. We consider a patchy environment in which each patch comprises individuals belonging to different classes. Individuals disperse to other patches on a multi-layer network in which each layer corresponds to a class. The dispersal on each layer is modeled by a Continuous Time Markov Chain (CTMC). At each time, individuals disperse according to their CTMC and subsequently interact with the local individuals in the patch according to an SIS model. We establish the existence of various equilibria under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. We also derive simple conditions that highlight the influence of the multi-layer network on the stability of these equilibria. For this model, we study optimal intervention strategies using a convex optimization framework. Finally, we numerically illustrate the influence of the multi-layer network structure and the effectiveness of the optimal intervention strategies.

Annual species' experimental germination responses to light and temperature do not correspond with their microhabitat associations in the field

AbstractQuestionsAnnual species have evolved sets of germination cues that are thought to be predictive of the post‐germination environment. In naturally patchy environments, germination microsites often vary considerably in the amount of light they receive and in the diurnal temperature fluctuations they experience. However, whether species' differential germination responses to light and temperature are associated with their spatial patterns of occurrence remains largely untested.LocationMediterranean‐climate woodlands in Southwest Western Australia.MethodsWe surveyed species' occurrences in annual plant communities in 150 quadrats across gradients of canopy cover and litter cover. Nineteen species recorded in this survey were then included in a germination experiment that manipulated (1) Light vs Dark (12 h light or continuous dark) approximating seeds near the soil surface vs those covered by litter and (2) Cold vs Warm temperature regimes (7/18°C and 7/24°C) approximating diurnal fluctuations experienced in shaded vs sun‐exposed microsites, respectively.ResultsIn the germination experiment, six species had highest germination probabilities in the Light treatment (regardless of temperature), five in Cold + Light, one in Warm + Light, two were indifferent to the treatments, and four did not germinate at all. Binomial linear mixed‐effects models showed that species' maximum responses to light and temperature did not explain their spatial distributions along canopy cover and litter cover gradients, contrary to theoretical expectations of germination being a strong driver of species' occurrences.ConclusionsDespite variation in species' responses to experimental treatments, no association was found with their field microsite associations. Germination strategies in our system were wider than expected for Mediterranean systems. Our results support that germination cues are not strong drivers of microhabitat associations in this system.

Competition-exclusion and coexistence in a two-strain SIS epidemic model in patchy environments

Competition-exclusion and coexistence in a two-strain SIS epidemic model in patchy environments

Global dynamics of a Lotka-Volterra competition system in an advective patchy environment

Global dynamics of a Lotka-Volterra competition system in an advective patchy environment

The Ideal Free Distribution with travel costs

This article studies the effect of travel costs on population distribution in a patchy environment. The Ideal Free Distribution with travel costs is defined in the article as the distribution under which it is not profitable for individuals to move, i.e., the movement between patches ceases. It is shown that depending on the travel costs between patches, the Ideal Free Distribution may be unique, there may be infinitely many possible IFDs, or no Ideal Free Distribution exists. In the latter case, animal distribution can converge to an equilibrium of distributional dynamics at which individuals do disperse, but the net movement between patches ceases. Such distributional equilibrium corresponds to balanced dispersal.

A micro RNA mediates shoot control of root branching

Plants extract mineral nutrients from the soil, or from interactions with mutualistic soil microbes via their root systems. Adapting root architecture to nutrient availability enables efficient resource utilization, particularly in patchy and dynamic environments. Root growth responses to soil nitrogen levels are shoot-mediated, but the identity of shoot-derived mobile signals regulating root growth responses has remained enigmatic. Here we show that a shoot-derived micro RNA, miR2111, systemically steers lateral root initiation and nitrogen responsiveness through its root target TML (TOO MUCH LOVE) in the legume Lotus japonicus, where miR2111 and TML were previously shown to regulate symbiotic infections with nitrogen fixing bacteria. Intriguingly, systemic control of lateral root initiation by miR2111 and TML/HOLT (HOMOLOGUE OF LEGUME TML) was conserved in the nonsymbiotic ruderal Arabidopsis thaliana, which follows a distinct ecological strategy. Thus, the miR2111-TML/HOLT regulon emerges as an essential, conserved factor in adaptive shoot control of root architecture in dicots.

An almost periodic Ross–Macdonald model with time delay in a patchy environment

An almost periodic multi-patch Ross–Macdonald model with the incubation of virus in hosts and in vectors is investigated in this paper. The existence of the almost periodic disease-free solution and the definition of basic reproduction ratio R0 are given. It is shown that the disease will die out when there exists a small invasion and the same dispersal rate in patches if R0<1, while the disease is uniformly persistent if R0>1. At last, numerical simulations illustrate the above results. In addition, a comparison between the almost periodic and periodic models shows that the periodic model may underestimate or overestimate the basic reproduction ratio.

Neural evidence of switch processes during semantic and phonetic foraging in human memory

Humans may retrieve words from memory by exploring and exploiting in "semantic space" similar to how nonhuman animals forage for resources in physical space. This has been studied using the verbal fluency test (VFT), in which participants generate words belonging to a semantic or phonetic category in a limited time. People produce bursts of related items during VFT, referred to as "clustering" and "switching." The strategic foraging model posits that cognitive search behavior is guided by a monitoring process which detects relevant declines in performance and then triggers the searcher to seek a new patch or cluster in memory after the current patch has been depleted. An alternative body of research proposes that this behavior can be explained by an undirected rather than strategic search process, such as random walks with or without random jumps to new parts of semantic space. This study contributes to this theoretical debate by testing for neural evidence of strategically timed switches during memory search. Thirty participants performed category and letter VFT during functional MRI. Responses were classified as cluster or switch events based on computational metrics of similarity and participant evaluations. Results showed greater hippocampal and posterior cerebellar activation during switching than clustering, even while controlling for interresponse times and linguistic distance. Furthermore, these regions exhibited ramping activity which increased during within-patch search leading up to switches. Findings support the strategic foraging model, clarifying how neural switch processes may guide memory search in a manner akin to foraging in patchy spatial environments.

Colour-specific diet specialization is associated with differences in owlet weight in a polymorphic owl: influence of the trophic quality variation.

The niche divergence hypothesis proposes that the evolution and maintenance of colour polymorphism is based on a mechanism of disruptive selection. In a trophic context, the hypothesis predicts that individuals differing in colour vary in their trophic niche, either because they differ in foraging efficiency or feed in different habitats. A major evolutionary conundrum is how these expectations are affected by variation in trophic quality. Using an owl species with colour plumage polymorphism, the Eurasian scops owl Otus scops, we examined diet and habitat segregation during reproduction in relation to plumage colouration and trophic quality. Intensive sampling revealed that trophic quality for scops owls (i.e. abundance of grasshoppers and locusts) varied more among territories than between years, but scops owls did not segregate among territories of different quality by their colouration. However, we found that sex, plumage colouration and territory differences in trophic quality explained differences in the degree of dietary specialization. Brownish males delivered a higher diversity of prey to the nest than greyish ones in high trophic quality territories. We also found that the more diverse the diet provided by males, the heavier the owlets at fledging. Our study provides evidence for a different sensitivity to trophic quality of the colour morphs with potential fitness consequences in scops owls. We highlight the importance of studying the mechanisms leading to the persistence of colour polymorphism in patchy environments, since segregation may pass otherwise unnoticed if only habitats or years with similar conditions are considered.

Mathematical analysis of the dynamics of a fractional‐order tuberculosis epidemic in a patchy environment under the influence of re‐infection

In human societies, memory has a significant impact on the procedure of progression and control of epidemics. Therefore, fractional differential equations govern an epidemic model, including the memory effect. Since infectious diseases can spread from one place to another, human movement impacts the prevalence of such diseases. In this study, we present a two‐patch model for tuberculosis with fractional order and exogenous re‐infection, in which susceptible individuals can move without any obstacle between the patches. The present work establishes the effect of population movement and the backward bifurcation phenomenon on the prevalence of the tuberculosis epidemic with fractional‐order derivatives. Furthermore, to show that the proposed model has backward bifurcation, we provide some conditions between the model's parameters, so in this case, the model of tuberculosis has numerous boundary points. We show the tuberculosis model can exhibit backward bifurcation neither in case of exogenous re‐infection, with some conditions, nor in the situation that the model is vacant from any re‐infection. In contrast, the disease‐free equilibrium of the model is globally asymptotically stable when . Furthermore, we investigate the fractional‐order derivative on the spread of infection. The results show that can perform the function of adventure or expertise of people about the disease background.

Stability analysis of an HIV/AIDS epidemic model with sexual transmission in a patchy environment

ABSTRACT A multi-patch HIV/AIDS model with heterosexual transmission is formulated to investigate the impact of population migration on the spread of HIV/AIDS. We derive the basic reproduction number R 0 and prove that if R 0 < 1 , the disease-free equilibrium is globally asymptotically stable. If R 0 > 1 and certain conditions are satisfied, the endemic equilibrium is globally asymptotically stable. We apply the model to two patches and conduct numerical simulations. If HIV/AIDS becomes extinct in each patch when two patches are isolated, the disease remains extinct in two patches when the population migration occurs; if HIV/AIDS spreads in each patch when two patches are isolated, the disease remains persistent in two patches when the population migration occurs; if the disease disappears in one patch and spreads in the other patch when they are isolated, the disease can spread or disappear in two patches if migration rates of individuals are suitably chosen.

Spatial Propagation for an Epidemic Model in a Patchy Environment

Spatial Propagation for an Epidemic Model in a Patchy Environment

The Plant Invader Alternanthera philoxeroides Benefits from Clonal Integration More than Its Native Co-Genus in Response to Patch Contrast.

Different connected parts of clonal plants often grow in different patches and the resource contrast between patches has an important effect on the material transfer between the connected ramets. However, it is unclear whether the effect of clonal integration differs between the invasive clonal plant and the related native species in response to patch contrast. To explore this, we grew the clonal fragment pairs of plant invader Alternanthera philoxeroides and its co-genus native species A. sessilis under high contrast, low contrast, and no contrast (control) nutrient patch environments, respectively, and with stolon connections either severed or kept intact. The results showed that, at the ramet level, clonal integration (stolon connection) significantly improved the growth of apical ramets of both species, and such positive effects were significantly greater in A. philoxeroides than in A. sessilis. Moreover, clonal integration greatly increased the chlorophyll content index of apical ramets and the growth of basal ramets in A. philoxeroides but not in A. sessilis under low and high contrast. At the whole fragment level, the benefits of clonal integration increased with increasing patch contrast, and such a positive effect was more pronounced in A. philoxeroides than in A. sessilis. This study demonstrated that A. philoxeroides possesses a stronger ability of clonal integration than A. sessilis, especially in patchy environments with a higher degree of heterogeneity, suggesting that clonal integration may give some invasive clonal plants a competitive advantage over native species, thus facilitating their invasion in patchy habitats.