Patchy Environment Research Articles

Traveling waves for an epidemic system with bilinear incidence in a periodic patchy environment

Traveling waves for an epidemic system with bilinear incidence in a periodic patchy environment

Dispersal engendered synchronization and stability of mediated infectious diseases in the patchy environment using mean-field diffusive coupling

Mobility of humans and mediating agents significantly affects the scope of mediated infectious diseases. The spatial transmission of mediated infectious diseases ultimately depends on the movement of hosts and mediators. To comprehend the causes, predict, evaluate, and restrict epidemic transmission, it is crucial to investigate the dynamics of mediated infectious diseases in the presence of mobility. The network of mediators and the host metapopulation are related to the spatial coupling for disease dissemination. Thus, in this article, the metapopulation dynamics of the mediated infectious disease model is studied in a patchy environment where the hosts and mediators population is divided into sub-population. Two networks are used to represent the patchy environment: the hosts or humans network and the mediators network. Mean field diffusive coupling is used to connect the network patches. Both homogeneous and heterogeneous networks are investigated in terms of dynamics. Dispersal engenders the patches of corresponding networks to synchronize and reach bistable states of non-trivial amplitude death. Numerical simulations are performed to demonstrate the change from one state to another state, caused by transcritical bifurcation. The stability of disease free equilibrium and endemic equilibrium is also determined by the reproduction number R0.

Alternating selection for dispersal and multicellularity favors regulated life cycles

The evolution of complex multicellularity opened paths to increased morphological diversity and organizational novelty. This transition involved three processes: cells remained attached to one another to form groups, cells within these groups differentiated to perform different tasks, and the groups evolved new reproductive strategies.1,2,3,4,5 Recent experiments identified selective pressures and mutations that can drive the emergence of simple multicellularity and cell differentiation,6,7,8,9,10,11 but the evolution of life cycles, particularly how simple multicellular forms reproduce, has been understudied. The selective pressure and mechanisms that produced a regular alternation between single cells and multicellular collectives are still unclear.12 To probe the factors regulating simple multicellular life cycles, we examined a collection of wild isolates of the budding yeast S.cerevisiae.12,13 We found that all these strains can exist as multicellular clusters, a phenotype that is controlled by the mating-type locus and strongly influenced by the nutritional environment. Inspired by this variation, we engineered inducible dispersal in a multicellular laboratory strain and demonstrated that a regulated life cycle has an advantage over constitutively single-celled or constitutively multicellular life cycles when the environment alternates between favoring intercellular cooperation (a low sucrose concentration) and dispersal (a patchy environment generated by emulsion). Our results suggest that the separation of mother and daughter cells is under selection in wild isolates and is regulated by their genetic composition and the environments they encounter and that alternating patterns of resource availability may have played a role in the evolution of life cycles.

Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment

We studied a host-parasite model qualitatively. The host-parasitoid model is obtained by modifying the Nicholson-Bailey model so that the number of hosts that parasitoids can't attack is fixed. Topological classification of equilibria is achieved with the implementation of linearization. Furthermore, Neimark-Sacker bifurcation is explored using the bifurcation theory of normal forms at interior steady-state. The bifurcation in the model is controlled by implementing two control strategies. The theoretical studies are backed up by numerical simulations, which show the conclusions and their importance.

Resilience of Pyrenean Forests after Recurrent Historical Deforestations

The long-term resilience of Pyrenean forests in the face of historical anthropogenic clearing remains largely unknown. In this paper, a high-resolution (decadal to subdecadal) paleoecological study of mid-elevation Pyrenean forests is presented that encompasses the last two millennia. This long-term record was obtained after sediment coring, dating (varve counting) and pollen analysis of annually laminated (varved) sediments from Lake Montcortès, situated at 1027 m elevation, in the transition between the Mediterranean and montane forest belts. This allowed the definition of three major deforestation/recovery cycles during the Roman, Medieval and Modern times. Each DR cycle is characterized considering three different levels: overall forest trends, forest type and individual taxa. Overall, the studied forests exhibited high resilience, as they recovered almost completely after each deforestation event (bulk resilience). The critical point of no return (tipping point) beyond which forests would have irreversibly disappeared from the region was never reached, even after deforestation magnitudes above 60%. The different forest types identified (conifer, sclerophyll and deciduous) persisted over time, showing similar heterogeneous patterns with minor spatial reorganizations (mosaic resilience). Individually, the main forest taxa underwent minor variations in their relative abundances, always within the same attraction domains (community resilience). The high levels of resilience documented in these Pyrenean forests are attributed to the action of metapopulation and metacommunity processes and mechanisms in a highly dynamic patchy environment. Conservation actions should be focused on the maintenance of these spatial patterns and the associated ecological dynamics.

Evolution of Dispersal in Advective Patchy Environments

We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end (e.g., due to the flow into a lake or ocean). The two competing species are assumed to have the same growth rates but different advection and random dispersal rates. We focus our studies on the properties of an associated eigenvalue problem which characterizes the extinction/persistence dynamics of the underlying patch population model. We also derive conditions on the advection and random dispersal rates under which a mutant species can or cannot invade the resident species.

Traveling Wave of Biological Invasion: Effects of Swapping Migration

The problem of biological invasion is an issue of increasing significance in conservation ecology. Fisher equation is one of the traditional methods to describe biological invasion. In ecosystems, however, species usually live in patchy environments. In this study, a modified Fisher equation is derived, where the recently developed “swapping migration” is applied and the relation between invasion velocity and patch capacity is discussed.

Multiscale relationships between humpback whales and forage species hotspots within a large marine ecosystem.

Fluctuations in prey abundance, composition, and distribution can impact predators, and when predators and fisheries target the same species, predators become essential to ecosystem-based management. Because of the difficulty in collecting concomitant predator-prey data at appropriate scales in patchy environments, few studies have identified strong linkages between cetaceans and prey, especially across large geographic areas. During summer 2018, a line-transect survey for cetaceans and coastal pelagic species was conducted over the continental shelf and slope of British Columbia, Canada, and the US West Coast, allowing for a large-scale investigation of predator-prey spatial relationships. We report on a case study of humpback whales (Megaptera novaeangliae) and their primary prey-Pacific herring (Clupea pallasii), northern anchovy (Engraulis mordax), and krill-using generalized additive models to explore the relationships between whale abundance on 10-km transect segments and prey metrics. Prey metrics included direct measures of biomass densities on segments and an original hotspot metric. For each prey species, segments in the upper fifth percentile for biomass density (across all segments) were designated hotspots, and whale counts on a segment were evaluated for their relationship to number of hotspot segments (species-specific and multispecies) within 25, 50, or 100 km. Whale abundance was not strongly related to direct measures of biomass densities, whereas models using hotspot metrics were more effective at describing variation in whale abundance, underscoring that evaluating prey at relevant and measurable scales is critical in patchy, dynamic marine environments. Our analysis highlighted differences in the distribution and prey availability for three humpback whale distinct population segments (DPSs) as defined under the US Endangered Species Act, including threatened and endangered DPSs that forage within the California Current Large Marine Ecosystem. These linkages provide insights into which prey species whales may be targeting in different regions and across multiple scales and, consequently, how climatic variability and anthropogenic risks may differentially impact these distinct predator-prey assemblages. By identifying scale-appropriate prey hotspots that co-occur with humpback whale aggregations, and with targeted, consistent prey sampling and estimations of potential consumption rates by whales, these findings can help inform the conservation and management of humpback whales within an ecosystem-based management framework.

Transmission dynamics and high infectiousness of Coronavirus Disease 2019

<p style='text-indent:20px;'>Coronavirus disease 2019 (COVID-19) has rapidly spread around the world since the early 2020. Recently, a second wave of COVID-19 has resurged in many countries. The transmission dynamics and infectiousness of the COVID-19 pandemic remain unclear, and developing strategies to mitigate the severity of the pandemic is a top priority for global public health. According to the infection mechanism of COVID-19, a novel susceptible-asymptomatic-symptomatic-recovered (SASR) model with control variables in a patchy environment was proposed not only to consider the key characteristics of asymptomatic infection and the effects of seasonal variation but also to incorporate different control measures for multiple transmission routes. The basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ R_{0} $\end{document}</tex-math></inline-formula> was established to describe the spreading behavior in the natural state over a long time horizon, and the natural reproduction number <inline-formula><tex-math id="M2">\begin{document}$ R_{n} $\end{document}</tex-math></inline-formula>, which describes the development trend of the disease during a short time in the future, was defined according to the actual propagation characteristics. In addition, the effective reproduction number <inline-formula><tex-math id="M3">\begin{document}$ R_{e} $\end{document}</tex-math></inline-formula> considering the control strategies was proposed to evaluate the impact of non-pharmaceutical interventions. The results of numerical simulations for COVID-19 cases in Wuhan, China, based on the SASR model indicate that <inline-formula><tex-math id="M4">\begin{document}$ R_{0} $\end{document}</tex-math></inline-formula> was 3.58, <inline-formula><tex-math id="M5">\begin{document}$ R_{n} $\end{document}</tex-math></inline-formula> ranged from 2.37 to 4.91, and <inline-formula><tex-math id="M6">\begin{document}$ R_{e} $\end{document}</tex-math></inline-formula> decreased gradually from 4.83 on December 8, 2019 to 0.31 on March 8, 2020, reaching 1.40 on January 23, 2020, when the lockdown was lifted in Wuhan. We further concluded that the total number of infections, including asymptomatic infections, was approximately 301, 804 as of March 8, 2020, in Wuhan, China. In particular, this article proposes a dynamic method to distinguish the impact of natural factors and human interventions on the development of the pandemic, and provides a theoretical basis for fighting the global COVID-19 pandemic.</p>

Dynamics analysis of an SVEIR epidemic model in a patchy environment.

In this paper, we propose a multi-patch SVEIR epidemic model that incorporates vaccination of both newborns and susceptible populations. We determine the basic reproduction number $ R_{0} $ and prove that the disease-free equilibrium $ P_{0} $ is locally and globally asymptotically stable if $ R_{0} < 1, $ and it is unstable if $ R_{0} > 1. $ Moreover, we show that the disease is uniformly persistent in the population when $ R_{0} > 1. $ Numerical simulations indicate that vaccination strategies can effectively control disease spread in all patches while population migration can either intensify or prevent disease transmission within a patch.

An SIS epidemic model with mass action infection mechanism in a patchy environment

AbstractIn this paper, we study an SIS (susceptible–infected–susceptible) epidemic model with mass action infection mechanism in a patchy environment. We first analyze the long‐time dynamics of the model in terms of the basic reproduction number , and prove under certain conditions that the disease‐free equilibrium (DFE) is globally attractive if whereas the endemic equilibrium (EE) is globally attractive if . Then we establish the existence and uniqueness of EE provided , which is achieved, among other ingredients, by reducing the equilibrium problem into the one involving only the component of infected population. We further investigate the asymptotic profile of EE as the motility rate of the susceptible and/or infected population becomes small. We also perform the theoretical analysis on the corresponding model with linear birth/death effect. By comparing the findings of the models considered here with those of other closely related ones, our results suggest that the variation of total population, individual motility, infection mechanism, and spatial heterogeneity all can play significant roles in the dynamics of disease transmission, which may shed light on the practical implications for predicting the patterns of disease outbreak and designing optimal control strategies.

An SIS epidemic model in a patchy environment with pulse vaccination and quarantine

An SIS epidemic model in an m-patch environment with pulse vaccination and quarantine at two different fixed moments is formulated by impulsive differential equations in this paper. The sufficient conditions for the extinction and persistence of the disease are derived and the threshold value R0 is obtained by using the persistence theory of impulsive systems, the impulsive-type Floquet theory and the perturbation techniques. That is, the infection-free periodic solution is globally asymptotically stable if R0<1, and the impulsive system becomes uniformly persistent if R0>1. When m=2, two special cases are considered to illustrate joint impact of the pulse vaccination and quarantine and population mobility on the disease dynamics. Numerical simulations are given to show the effectiveness of the theoretical results.

Intra- and Inter-Specific Competitions of Two Stage-Structured Species in a Patchy Environment

Intra- and Inter-Specific Competitions of Two Stage-Structured Species in a Patchy Environment

Adaptation to a heterogeneous patchy environment with non-local dispersion

In this work, we provide an asymptotic analysis of the solutions to an elliptic integrodifferential equation. This equation describes the evolutionary equilibria of a phenotypically structured population, subject to selection, mutation, and both local and non-local dispersion in a spatially heterogeneous, possibly patchy, environment. Considering small effects of mutations, we provide an asymptotic description of the equilibria of the phenotypic density. This asymptotic description involves a Hamilton–Jacobi equation with constraint coupled with an eigenvalue problem. Based on such analysis, we characterize some qualitative properties of the phenotypic density at equilibrium depending on the heterogeneity of the environment. In particular, we show that when the heterogeneity of the environment is low, the population concentrates around a single phenotypic trait leading to a unimodal phenotypic distribution. On the contrary, a strong fragmentation of the environment leads to multi-modal phenotypic distributions.

Intraspecific plant variation and nonhost herbivores affect parasitoid host location behaviour

Parasitoids need to find their hosts in patchy environments that differ in profitability. To maximize foraging efficiency, parasitoids use volatile information of plants on which their hosts feed. The blend of plant volatiles emitted is affected by genetic variation in plants and by the herbivore species feeding on the plant. How parasitoids deal with variation in plant volatiles induced by host or nonhost herbivores on various plant genotypes in a plant stand is unclear. In a wind tunnel, we examined foraging behaviour of the parasitoid Cotesia glomerata in mixes of white cabbage cultivars with host ( Pieris brassicae ) and nonhost herbivores ( Mamestra brassicae or Delia radicum ). We specifically studied the efficiency of parasitoids in locating a host-infested plant when having to pass three other plants that varied in volatile emission by cultivar and herbivore identity. We show that foraging decisions of C. glomerata are affected by the apparency of volatile cues from upwind host-infested plants. We found that parasitoids flew over the first three plants more often when the last plant was a host-infested attractive cultivar and the first three plants were a less attractive cultivar, regardless of the presence of host or nonhost herbivores. Furthermore, parasitoids spent more time on the first three plants if these were infested with host or nonhost larvae, and this effect was stronger when the first three plants were of the attractive cultivar. Our results suggest that parasitoids may more easily locate host herbivores on plant genotypes with more apparent volatile information. However, host location efficiency is affected by the contrast with other plumes of plant volatiles derived from genotypic variation in plants and induction of volatiles by nonhost herbivores. Apparency of information on upwind patches influences patch residence time and patch choice and is an important component of optimal foraging in parasitoids. • Foraging decisions by Cotesia glomerata are affected by the apparency of information. • Profitability of upwind patches affects foraging decisions on the current patch. • Nonhost herbivores with traits similar to the host reduced host location efficiency. • Established parasitoid cultivar preferences are nuanced in complex plant mixtures.

Corrigendum

Corrigendum

Genomic analysis of a reef-building coral, Acropora digitifera, reveals complex population structure and a migration network in the Nansei Islands, Japan.

Understanding the structure and connectivity of coral populations is fundamental for developing marine conservation policies, especially in patchy environments such as archipelagos. The Nansei Islands, extending more than 1000 km in southwestern Japan, are characterized by high levels of biodiversity and endemism, supported by coral reefs, which make this region ideal for assessing genetic attributes of coral populations. In this study, we conducted population genomic analyses based on genome-wide, single-nucleotide polymorphisms (SNPs) of Acropora digitifera, a common species in the Nansei Islands. By merging newly obtained genome resequencing data with previously published data, we identified more than 4 million genome-wide SNPs in 303 colonies collected at 22 locations, with sequencing coverage ranging from 3.91× to 27.41×. While population structure analyses revealed genetic similarities between the southernmost and northernmost locations, separated by >1000 km, several subpopulations in intermediate locations suggested limited genetic admixture, indicating conflicting migration tendencies in the Nansei Islands. Although migration networks revealed a general tendency of northward migration along the Kuroshio Current, a substantial amount of southward migration was also detected, indicating important contributions of minor ocean currents to coral larval dispersal. Moreover, heterogeneity in the transition of effective population sizes among locations suggests different histories for individual subpopulations. The unexpected complexity of both past and present population dynamics in the Nansei Islands implies that heterogeneity of ocean currents and local environments, past and present, have influenced the population structure of this species, and similar unexpected population complexities may be expected for other marine species with similar reproductive modes.

Asymptotic stability problem of predator–prey system with linear diffusion

Abstract As the primary killer of health, the class of infectious diseases is the greatest threat to humanity. At present, international methods of studying the large-scale spatial transmission of sudden infectious diseases from the perspective of dynamics can be divided into two categories. On the one hand, top international biomedical and medical teams discuss the restraining effects of some prevention and control strategies on infectious diseases, such as smallpox, malaria, hand, foot and mouth disease and pandemic influenza, from the perspective of pragmatism. On the other hand, researchers in theoretical physics and network science tend to use compound population network models to explore the internal dynamic mechanism of spatial transmission of infectious diseases. This paper establishes a Lotka–Volterra dispersal predator–prey system in a patchy environment. It shows the existence of model boundary equilibria and asymptotic stability under an appropriate condition. This paper adopts the method of global Lyapunov function and the results of graph theory. We also consider a predator–prey dynamical model in a patchy environment, where the prey and predator individuals in each compartment can travel among n patches.

Mathematical analysis of autonomous and non‐autonomous age‐structured reaction‐diffusion‐advection population model

In this paper, we study an age‐structured reaction‐diffusion‐advection population model. First, we use a non‐densely defined operator to the linear age‐structured reaction‐diffusion‐advection population model in a patchy environment. By spectral analysis, we obtain the asynchronous exponential growth of the population model. Then we consider nonlinear death rate and birth rate, which all depend on the function related to the generalized total population, and we prove the existence of a steady state of the system. Finally, we study the age‐structured reaction‐diffusion‐advection population model in non‐autonomous situations. We give the comparison principle and prove the eventual compactness of semiflow by using integrated semigroup. We also prove the existence of compact attractors under the periodic situation.

Understanding the structure of cognitive noise.

Human cognition is fundamentally noisy. While routinely regarded as a nuisance in experimental investigation, the few studies investigating properties of cognitive noise have found surprising structure. A first line of research has shown that inter-response-time distributions are heavy-tailed. That is, response times between subsequent trials usually change only a small amount, but with occasional large changes. A second, separate, line of research has found that participants' estimates and response times both exhibit long-range autocorrelations (i.e., 1/f noise). Thus, each judgment and response time not only depends on its immediate predecessor but also on many previous responses. These two lines of research use different tasks and have distinct theoretical explanations: models that account for heavy-tailed response times do not predict 1/f autocorrelations and vice versa. Here, we find that 1/f noise and heavy-tailed response distributions co-occur in both types of tasks. We also show that a statistical sampling algorithm, developed to deal with patchy environments, generates both heavy-tailed distributions and 1/f noise, suggesting that cognitive noise may be a functional adaptation to dealing with a complex world.