Dynamics of Competitive Systems with Diffusion Between Source-Sink Patches.

This paper considers two-species competitive systems with one-species' diffusion between patches. Each species can persist alone in the corresponding patch (a source), while the mobile species cannot survive in the other (a sink). Using the method of monotone dynamical systems, we give a rigorous analysis on persistence of the system, prove local/global stability of the equilibria and show new types of bi-stability. These results demonstrate that diffusion could lead to results reversing those without diffusion, which extend the principle of competitive exclusion: Diffusion could lead to persistence of the mobile competitor in the sink, make it reach total abundance larger than if non-diffusing and even exclude the opponent. The total abundance is shown to be a distorted function (surface) of diffusion rates, which extends both previous theory and experimental observations. A novel strategy of diffusion is deduced in which the mobile competitor could drive the opponent into extinction, and then approach the maximal abundance. Initial population density and diffusive asymmetry play a role in the competition. Our work has potential applications in biodiversity conservation and economic competition.

Effects of Prey's Diffusion on Predator-Prey Systems with Two Patches.

This paper considers predator-prey systems in which the prey can move between source and sink patches. First, we give a complete analysis on global dynamics of the model. Then, we show that when diffusion from the source to sink is not large, the species would coexist at a steady state; when the diffusion is large, the predator goes to extinction, while the prey persists in both patches at a steady state; when the diffusion is extremely large, both species go to extinction. It is derived that diffusion in the system could lead to results reversing those without diffusion. That is, diffusion could change species' coexistence if non-diffusing, to extinction of the predator, and even to extinction of both species. Furthermore, we show that intermediate diffusion to the sink could make the prey reach total abundance higher than if non-diffusing, larger or smaller diffusion rates are not favorable. The total abundance, as a function of diffusion rates, can be both hump-shaped and bowl-shaped, which extends previous theory. A novel finding of this work is that there exist diffusion scenarios which could drive the predator into extinction and make the prey reach the maximal abundance. Diffusion from the sink to source and asymmetry in diffusion could also lead to results reversing those without diffusion. Meanwhile, diffusion always leads to reduction of the predator's density. The results are biologically important in protection of endangered species.

Effect of Stressors on the Carrying Capacity of Spatially Distributed Metapopulations.

Stressors such as antibiotics, herbicides, and pollutants are becoming increasingly common in the environment. The effects of stressors on populations are typically studied in homogeneous, nonspatial settings. However, most populations in nature are spatially distributed over environmentally heterogeneous landscapes with spatially restricted dispersal. Little is known about the effects of stressors in these more realistic settings. Here, we combine laboratory experiments with novel mathematical theory to rigorously investigate how a stressor's physiological effect and spatial distribution interact with dispersal to influence population dynamics. We prove mathematically that if a stressor increases the death rate and/or simultaneously decreases the population growth rate and yield, a homogeneous distribution of the stressor leads to a lower total population size than if the same amount of the stressor was heterogeneously distributed. We experimentally test this prediction on spatially distributed populations of budding yeast (Saccharomyces cerevisiae). We find that the antibiotic cycloheximide increases the yeast death rate but reduces the growth rate and yield. Consistent with our mathematical predictions, we observe that a homogeneous spatial distribution of cycloheximide minimizes the total equilibrium size of experimental metapopulations, with the magnitude of the effect depending predictably on the dispersal rate and the geographic pattern of antibiotic heterogeneity. Our study has implications for assessing the population risk posed by pollutants, antibiotics, and global change and for the rational design of strategies for employing toxins to control pathogens and pests.

Population abundance in predator-prey systems with predator's dispersal between two patches.

This paper considers predator-prey systems in which the predator moves between two patches. One patch is a source, where the predator and prey can persist, while the other is a sink where the predator cannot survive. Our aim is to show whether or not the dispersal is beneficial to the predator's total abundance at equilibrium. Using dynamical systems theory, we demonstrate conditions under which a dispersing predator can persist. Our analysis shows that the predator equilibrium abundance at intermediate dispersal rates can be higher than that without dispersal, while extremely large or small dispersal rates could result in predator's extinction. Moreover, we find an explicit expression for the total abundance, which clearly shows the role of dispersal rates and asymmetry on the predator's abundance. Numerical simulations confirm and extend our results.

Dispersal asymmetry in a two-patch system with source-sink populations.

This paper analyzes source-sink systems with asymmetric dispersal between two patches. Complete analysis on the models demonstrates a mechanism by which the dispersal asymmetry can lead to either an increased total size of the species population in two patches, a decreased total size with persistence in the patches, or even extinction in both patches. For a large growth rate of the species in the source and a fixed dispersal intensity, (i) if the asymmetry is small, the population would persist in both patches and reach a density higher than that without dispersal, in which the population approaches its maximal density at an appropriate asymmetry; (ii) if the asymmetry is intermediate, the population persists in both patches but reaches a density less than that without dispersal; (iii) if the asymmetry is large, the population goes to extinction in both patches; (iv) asymmetric dispersal is more favorable than symmetric dispersal under certain conditions. For a fixed asymmetry, similar phenomena occur when the dispersal intensity varies, while a thorough analysis is given for the low growth rate of the species in the source. Implications for populations in heterogeneous landscapes are discussed, and numerical simulations confirm and extend our results.

Persistence and Oscillations of Plant-Pollinator-Herbivore Systems.

This paper considers plant-pollinator-herbivore systems where the plant produces food for the pollinator, the pollinator provides pollination service for the plant in return, while the herbivore consumes both the food and the plant itself without providing pollination service. Based on these resource-consumer interactions, we form a plant-pollinator-herbivore model which includes the intermediary food. Using qualitative method and Kuznetsov theorem, we show global dynamics of the subsystems, uniform persistence of the whole system and periodic oscillation by Hopf bifurcation. Rigorous analysis on the system demonstrates mechanisms by which varying parameters could make the system transition between extinction of herbivore, coexistence of the three species at steady states, coexistence in periodic oscillations and extinction of pollinator. It is shown that (i) in plant-pollinator interactions, the plant would produce food; (ii) in plant-herbivore interactions, the plant would produce toxin; (iii) in the presence of both pollinator and herbivore, the plant would produce both food and toxin, and intermediate productions are analytically given by which the plant can reach its maximal density; and (iv) an appropriate toxin production could drive the herbivore into extinction, an unappropriate one would drive the pollinator into extinction, while too much toxin production will drive the plant itself into extinction. The analysis leads to explanations for experimental observations and provides new insights.

Population abundance of two-patch competitive systems with asymmetric dispersal.

This paper considers two-species competitive systems with two patches, in which one of the species can move between the patches. One patch is a source where each species can persist alone, but the other is a sink where the mobile species cannot survive. Based on rigorous analysis on the model, we show global stability of equilibria and bi-stability in the first octant Int[Formula: see text]. Then total population abundance of each species is explicitly expressed as a function of dispersal rates, and the function of the mobile species displays a distorted surface, which extends previous theory. A novel prediction of this work is that appropriate dispersal could make each competitor approach total population abundance larger than if non-dispersing, while the dispersal could reverse the competitive results in the absence of dispersal and promote coexistence of competitors. It is also shown that intermediate dispersal is favorable, large or small one is not good, while extremely large or small dispersal will result in extinction of species. These results are important in ecological conservation and management.

Energetic constraints and the paradox of a diffusing population in a heterogeneous environment.

Previous mathematical analyses have shown that, for certain parameter ranges, a population, described by logistic equations on a set of connected patches, and diffusing among them, can reach a higher equilibrium total population when the local carrying capacities are heterogeneously distributed across patches, than when carrying capacities having the same total sum are homogeneously distributed across the patches. It is shown here that this apparently paradoxical result is explained when the resultant differences in energy inputs to the whole multi-patch system are taken into account. We examine both Pearl-Verhulst and Original Verhulst logistic models and show that, when total input of energy or limiting resource, is constrained to be the same in the homogeneous and heterogeneous cases, the total population in the heterogeneous patches can never reach an asymptotic equilibrium that is greater than the sum of the carrying capacities over the homogeneous patches. We further show that, when the dynamics of the limiting resources are explicitly modeled, as in a chemostat model, the paradoxical result of the logistic models does not occur. These results have implications concerning the use of some ubiquitous equations of population ecology in modeling populations in space.

Pollination-mutualisms in a two-patch system with dispersal.

In this paper, we consider a two-patch pollination-mutualism model with dispersal, which is derived from resource-service exchange between the plant and pollinator. The pollinator is assumed to persist in one patch in the presence of pollination-mutualisms, while it can (or cannot) survive alone in the other. Rigorous study on the model exhibits that solutions of the equations are nonnegative and bounded, and there exist stable positive equilibria under conditions. Theoretical analysis on the equilibria demonstrates that if the pollinator can survive alone in the other patch, a small dispersal can make the pollinator approach higher total population abundance than if non-dispersing. If the pollinator cannot survive alone in the other patch, a small or large dispersal can make the pollinator approach higher size than if non-dispersing, which is not intuitive. A novel prediction of this work is that the pollinator with dispersal can reach high population abundance even though the mutualistic plant approaches a low density, while constructing a high-quality patch for pollinator can lead to extra individuals for both plant and pollinator via dispersal. Numerical simulations confirm and extend our results.

Global dynamics of parasitism-competition systems with one host and multiple parasites.

This paper studies a new parasitism-competition model with one host and multiple parasites, where a plant is the host and nectar robbers are the parasites that compete for nectar of the plant but do not kill and eat the host itself. Based on the plant-nectar-robber interaction, a parasitism model is derived, which is different from previous parasitism models. Then the two-species model is extended to an n-dimensional system characterizing one plant and multiple robbers. Using dynamical system theory, qualitative behavior of the two-species model is exhibited by excluding existence of periodic solution, and global dynamics of the n-species system in the positive octant are completely shown. The dynamics demonstrate necessary and sufficient conditions for the principle of competitive exclusion to hold. It is shown that when the principle of competitive exclusion holds, at least one of the robbers is driven into extinction by other parasites while the others coexist with the plant at a steady state; When the principle of competitive exclusion does not hold, nectar robbers either coexist at a steady state or both go to extinction. The result also demonstrates a mechanism by which abiotic factors lead to persistence of nectar robbing.

Population abundance of a two-patch chemostat system with asymmetric diffusion.

This paper considers a two-patch chemostat system with asymmetric diffusion, which characterizes laboratory experiments and includes exploitable nutrients. Using dynamical system theory, we demonstrate global stability of the one-patch model, and show uniform persistence of the two-patch system, which leads to existence of a stable positive equilibrium. Analysis on the equilibrium demonstrates mechanisms by which varying the asymmetric diffusion can make the total population abundance in heterogeneous environments larger than that without diffusion, even larger than that in the corresponding homogeneous environments with or without diffusion. The mechanisms are shown to be effective even in source-sink populations. A novel finding of this work is that the asymmetry combined with high diffusion intensity can reverse the predictions of symmetric diffusion in previous studies, while intermediate asymmetry is shown to be favorable but extremely large or extremely small asymmetry is unfavorable. Our results are consistent with experimental observations and provide new insights. Numerical simulations confirm and extend the results.

Asymptotic State of a Two-Patch System with Infinite Diffusion.

Mathematical theory has predicted that populations diffusing in heterogeneous environments can reach larger total size than when not diffusing. This prediction was tested in a recent experiment, which leads to extension of the previous theory to consumer-resource systems with external resource input. This paper studies a two-patch model with diffusion that characterizes the experiment. Solutions of the model are shown to be nonnegative and bounded, and global dynamics of the subsystems are completely exhibited. It is shown that there exist stable positive equilibria as the diffusion rate is large, and the equilibria converge to a unique positive point as the diffusion tends to infinity. Rigorous analysis on the model demonstrates that homogeneously distributed resources support larger carrying capacity than heterogeneously distributed resources with or without diffusion, which coincides with experimental observations but refutes previous theory. It is shown that spatial diffusion increases total equilibrium population abundance in heterogeneous environments, which coincides with real data and previous theory while a new insight is exhibited. A novel prediction of this work is that these results hold even with source-sink populations and increasing diffusion rate of consumer could change its persistence to extinction in the same-resource environments.

Global dynamics of a mutualism-competition model with one resource and multiple consumers.

Recent simulation modeling has shown that species can coevolve toward clusters of coexisting consumers exploiting the same limiting resource or resources, with nearly identical ratios of coefficients related to growth and mortality. This paper provides a mathematical basis for such as situation; a full analysis of the global dynamics of a new model for such a class of n-dimensional consumer-resource system, in which a set of consumers with identical growth to mortality ratios compete for the same resource and in which each consumer is mutualistic with the resource. First, we study the system of one resource and two consumers. By theoretical analysis, we demonstrate the expected result that competitive exclusion of one of the consumers can occur when the growth to mortality ratios differ. However, when these ratios are identical, the outcomes are complex. Either equilibrium coexistence or mutual extinction can occur, depending on initial conditions. When there is coexistence, interaction outcomes between the consumers can transition between effective mutualism, parasitism, competition, amensalism and neutralism. We generalize to the global dynamics of a system of one resource and multiple consumers. Changes in one factor, either a parameter or initial density, can determine whether all of the consumers either coexist or go to extinction together. New results are presented showing that multiple competing consumers can coexist on a single resource when they have coevolved toward identical growth to mortality ratios. This coexistence can occur because of feedbacks created by all of the consumers providing a mutualistic service to the resource. This is biologically relevant to the persistence of pollination-mutualisms.

Dynamics of Intraguild Predation Systems with Intraspecific Competition.

This paper considers intraguild predation (IGP) systems where species in the same community kill and eat each other and there is intraspecific competition in each species. The IGP systems are characterized by a lattice gas model, in which reaction between sites on the lattice occurs in a random and independent way. Global dynamics of the model with two species demonstrate mechanisms by which IGP leads to survival/extinction of species. It is shown that an intermediary level of predation promotes survival of species, while over-predation or under-predation could result in species extinction. An interesting result is that increasing intraspecific competition of one species can lead to extinction of one or both species, while increasing intraspecific competitions of both species would result in coexistence of species in facultative predation. Initial population densities of the species are also shown to play a role in persistence of the system. Then the analysis is extended to IGP systems with one species. Numerical simulations confirm and extend our results.

Persistence of pollination mutualisms in the presence of ants.

This paper considers plant-pollinator-ant systems in which the plant-pollinator interaction is mutualistic but ants have both positive and negative effects on plants. The ants also interfere with pollinators by preventing them from accessing plants. While a Beddington-DeAngelis (BD) formula can describe the plant-pollinator interaction, the formula is extended in this paper to characterize the pollination mutualism under the ant interference. Then, a plant-pollinator-ant system with the extended BD functional response is discussed, and global dynamics of the model demonstrate the mechanisms by which pollination mutualism can persist in the presence of ants. When the ant interference is strong, it can result in extinction of pollinators. Moreover, if the ants depend on pollination mutualism for survival, the strong interference could drive pollinators into extinction, which consequently lead to extinction of the ants themselves. When the ant interference is weak, a cooperation between plant-ant and plant-pollinator mutualisms could occur, which promotes survival of both ants and pollinators, especially in the case that ants (respectively, pollinators) cannot survive in the absence of pollinators (respectively, ants). Even when the level of ant interference remains invariant, varying ants' negative effect on plants can result in survival/extinction of both ants and pollinators. Therefore, our results provide an explanation for the persistence of pollination mutualism when there exist ants.

A cooperative system of two species with bidirectional interactions.

Cooperation between species is often regarded to mean that the increase of each species promotes the growth of the other. The well-known cooperative model is the Lotka-Volterra equations (LVEs). In the LVEs, population densities of species increase infinitely as the cooperation is strong, which is called the divergence problem. Moreover, LVEs never exhibit an Allee effect in the case of obligate cooperation. In order to avoid these problems, several models have been established although most of them are rather complex. In this paper, we consider a cooperative system of two species with bidirectional interactions, in which each species also has negative feedback on the other. Population densities of the species will not increase infinitely because of the limited resource and negative feedback. Then, we focus on an extended lattice model of cooperation, which is deduced from reactions on lattice and has the same form as that of LVEs. In the case of obligate cooperation, the model predicts an Allee effect. Global dynamics of the system exhibit essential features of cooperation and basic mechanisms by which the cooperation can lead to coexistence/extinction of species. Intermediate cooperation is shown to be beneficial in cooperation under certain conditions, while extremely strong cooperation is demonstrated to lead to extinction of one/both species. Numerical simulations confirm and extend our results.

Invasibility of nectarless flowers in plant-pollinator systems.

This paper considers plant-pollinator systems in which plants are divided into two categories: The plants that secret a substantial volume of nectar in their flowers are called secretors, while those without secreting nectar are called nonsecretors (cheaters). The interaction between pollinators and secretors is mutualistic, while the interaction between pollinators and nonsecretors is parasitic. Both interactions can be described by Beddington-DeAngelis functional responses. Using dynamical systems theory, we show global dynamics of a pollinator-secretor-cheater model and demonstrate mechanisms by which nectarless flowers/nonsecretors can invade the pollinator-secretor system and by which the three species could coexist. We define a threshold in the nonsecretors' efficiency in translating pollinator-cheater interaction into fitness, which is determined by parameters (factors) in the systems. When their efficiency is above the threshold, non-secretors can invade the pollinator-secretor system. While the nonsecretors' invasion often leads to their persistence in pollinator-secretor systems, the model demonstrates situations in which the non-secretors' invasion can drive secretors into extinction, which consequently leads to extinction of the nonsecretors themselves.

Dynamics of plant-pollinator-robber systems.

Plant-pollinator-robber systems are considered, where the plants and pollinators are mutualists, the plants and nectar robbers are in a parasitic relation, and the pollinators and nectar robbers consume a common limiting resource without interfering competition. My aim is to show a mechanism by which pollination-mutualism could persist when there exist nectar robbers. Through the dynamics of a plant-pollinator-robber model, it is shown that (i) when the plants alone (i.e., without pollination-mutualism) cannot provide sufficient resources for the robbers' survival but pollination-mutualism can persist in the plant-pollinator system, the pollination-mutualism may lead to invasion of the robbers, while the pollinators will not be driven into extinction by the robbers' invasion. (ii) When the plants alone cannot support the robbers' survival but persistence of pollination-mutualism in the plant-pollinator system is density-dependent, the pollinators and robbers could coexist if the robbers' efficiency in translating the plant-robber interactions into fitness is intermediate and the initial densities of the three species are in an appropriate region. (iii) When the plants alone can support the robbers' survival, the pollinators will not be driven into extinction by the robbers if their efficiency in translating the plant-pollinator interactions into fitness is relatively larger than that of the robbers. The analysis leads to an explanation for the persistence of pollination-mutualism in the presence of nectar robbers in real situations.

CircKRT14 upregulates E2F3 by interacting with miR-1256 to act as an oncogenic factor in esophageal cancer.

BACKGROUND: A growing number of studies have focused on the regulatory role of circular RNAs (circRNAs) in a variety of cancers. The purpose of this study was to investigate the effect of circRNA Keratin 14 (circKRT14) on the progression of esophageal cancer (EC). METHODS: The levels of circKRT14, miR-1256 and E2F transcription factor 3 (E2F3) were analyzed by real-time quantitative polymerase chain reaction (qRT-PCR) and western blot. The circular structure of circKRT14 was confirmed by RNase R digestion assay. Cell apoptosis, migration and invasion were detected by flow cytometry and transwell assay. The protein levels of related factors were determined by western blot. The relationship between miR-1256 and circKRT14 or E2F3 was verified by dual-luciferase reporter assay. The in vivo function of circKRT14 was studied by xenograft tumor assay. RESULTS: CircKRT14 was significantly increased in EC tissues and cells. CircKRT14 silencing inhibited EC cell proliferation, migration, and invasion, but promoted EC cell apoptosis in vitro. CircKRT1 acted as a sponge for miR-1256 in EC, and in-miR-1256 abolished the inhibitory effect of circKRT14 suppression on EC cell progression. E2F3 was a target of miR-1256 and functioned as an oncogene in EC cells. MiR-1256 curbed EC progression by downregulating E2F3. CircKRT14 could affect E2F3 expression by targeting miR-1256. CircKRT14 regulated EC progression in vivo through miR-1256/E2F3 axis. CONCLUSIONS: These results uncovered that circKRT14 up-regulated the expression of E2F3 and promoted the malignant development of EC through sponging miR-1256.

Persistence of pollination mutualisms in plant-pollinator-robber systems.

Interactions between pollinators, nectar robbers, defensive plants and non-defensive plants are characterized by evolutionary games, where payoffs for the four species are represented by population densities at steady states in the corresponding dynamical systems. The plant-robber system is described by a predator-prey model with the Holling II functional response, while the plant-pollinator system is described by a cooperative model with the Beddington-DeAngelis functional response. By combining dynamics of the models with properties of the evolutionary games, we show mechanisms by which pollination mutualisms could persist in the presence of nectar robbers. The analysis leads to an explanation for persistence of plant-pollinator-robber systems in real situations.