Permanence of single-species stage-structured models

In this paper, we consider population survival by using single-species stage-structured models. As a criterion of population survival, we employ the mathematical notation of permanence. Permanence of stage-structured models has already been studied by Cushing (1998). We generalize his result of permanence, and obtain a condition which guarantees that population survives. The condition is applicable to a wide class of stage-structured models. In particular, we apply our results to the Neubert-Caswell model, which is a typical stage-structured model, and obtain a condition for population survival of the model.The research is partially supported by the Ministry of Education, Science and Culture, Japan, under Grant in Aid for Scientific Research (A) 13304006.     

Movement behaviour determines competitive outcome and spread rates in strongly heterogeneous landscapes

Classical models for biological invasions were single-species models in homogeneous landscapes, but most invasions happen in the presence of interacting species and in heterogeneous environments. The combination of spatial variation and species interaction could alter the spreading process significantly. For example, the ‘environmental heterogeneity hypothesis of invasions’ posits that heterogeneity offers more opportunities for invaders and reduces the negative impact on native species. Environmental heterogeneity offers an obvious coexistence mechanism on the regional scale if two or more competing species have different spatial niches, i.e. if the local competitive advantage changes in space. We consider a more subtle mechanism of space use through individual movement behaviour when the local competitive advantage remains with the same species. Specifically, we model the densities of two species, diffusing and competing in an infinite landscape consisting of two types of patches. We include individual behaviour in terms of movement rate and patch preference. We consider the scenario that one of the species is the stronger local competitor in both patch types. We then uncover a number of mechanisms—based solely on movement behaviour—through which these two species can coexist regionally, how the inferior competitor can replace the superior competitor globally, or how a bistable situation can arise between the two. We calculate mutual invasion conditions as well as mutual spatial spread rates, and we show that spread rates may depend on movement parameters in unexpected ways.     

一个污染环境中的单种群模型的动力学性质

以脉冲微分方程为基础建立了一个污染环境中在固定时刻对污染净化处理的单种群模型,详细研究了此模型的动力学性质,给出了种群灭绝和持续生存的充分条件.结果表明,当脉冲作用的周期小于某个阈值时,种群将持续生存;否则,种群将趋于灭绝.     

Global asymptotic behavior in single-species discrete diffusion systems

We consider a single-species dynamical system which is composed of several patches connected by discrete diffusion. Based on recently developed cooperative system theory and the property of a cooperative matrix, we obtain sufficient and necessary conditions for the system with linear diffusion to be extinct and for one with nonlinear diffusion to be globally stable. We also obtain a critical patch number in the system with linear diffusion for the species to go extinct. These results extend some recent known ones for discrete diffusion systems.Research partly supported by the Ministry of Education, Science and Culture, Japan, under Grant 01540177     

Permanence of delayed population model with dispersal loss

Permanence of a dispersal single-species population model where environment is partitioned into several patches is considered. The species not only requires some time to disperse between the patches but also has some possibility to die during its dispersion. The model is described by delay differential equations. The existence of 'super' food-rich patch is proved to be sufficient to ensure partial permanence of the model. It is also shown that partial permanence implies permanence if each food-poor patch is chained to the super food-rich patch. Furthermore, it is proven that partial persistence is ensured if there exist food-rich patches and the dispersion of the species among the patches are small. When the dispersion is large, the partial persistence is realized under relatively small dispersion time.     

Non-Additive Increases in Sediment Stability Are Generated by Macroinvertebrate Species Interactions in Laboratory Streams

Previous studies have shown that biological structures such as plant roots can have large impacts on landscape morphodynamics, and that physical models that do not incorporate biology can generate qualitatively incorrect predictions of sediment transport. However, work to date has focused almost entirely on the impacts of single, usually dominant, species. Here we ask whether multiple, coexisting species of hydropsychid caddisfly larvae have different impacts on sediment mobility compared to single-species systems due to competitive interactions and niche differences. We manipulated the presence of two common species of net-spinning caddisfly (Ceratopsyche oslari, Arctopsyche californica) in laboratory mesocosms and measured how their silk filtration nets influence the critical shear stress required to initiate sediment grain motion when they were in monoculture versus polyculture. We found that critical shear stress increases non-additively in polycultures where species were allowed to interact. Critical shear stress was 26% higher in multi-species assemblages compared to the average single-species monoculture, and 21% greater than levels of stability achieved by the species having the largest impact on sediment motion in monoculture. Supplementary behavioral experiments suggest the non-additive increase in critical shear stress may have occurred as competition among species led to shifts in the spatial distribution of the two populations and complementary habitat use. To explore the implications of these results for field conditions, we used results from the laboratory study to parameterize a common model of sediment transport. We then used this model to estimate potential bed movement in a natural stream for which we had measurements of channel geometry, grain size, and daily discharge. Although this extrapolation is speculative, it illustrates that multi-species impacts could be sufficiently large to reduce bedload sediment flux over annual time scales in streams where multiple species of caddisfly are present.     

Mathematical analysis of a delayed stage-structured predator–prey model with impulsive diffusion between two predators territories

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete, but in reality, many species diffuse only during a single period, and diffusion often occurs in regular pulses. Further, in forest habitats, the highest-level predator species are restricted to a specific territory, but prey can impulsively move between territories. Therefore, in this paper, we consider a delayed stage-structured predator–prey model with impulsively diffusive prey between two patches; in the model, patches represent the territories of two different predator populations. Here, we analytically obtain the global attractivity condition of predator-extinction periodic solutions for the system by using the concepts of Hui and Chen (2005); a numerical simulation is also included to illustrate this result. Further, we establish permanence conditions for the coexistence of the species using the theory of impulsive delayed differential equations. Finally, we explore the possibilities of the permanence of the system by using the growth rates of immature predators and the impulse period as critical parameters, and we also obtain the parameters’ threshold limits using numerical experimentation.     

Qualitative permanence of Lotka–Volterra equations

In this paper, we consider permanence of Lotka-Volterra equations. We investigate the sign structure of the interaction matrix that guarantees the permanence of a Lotka-Volterra equation whenever it has a positive equilibrium point. An interaction matrix with this property is said to be qualitatively permanent. Our results provide both necessary and sufficient conditions for qualitative permanence.     

Larval interspecific competition in two flea species parasitic on the same rodent host

Abstract.  1. The fleas Xenopsylla conformis and Xenopsylla ramesis exploit the same rodent host, Meriones crassus , and replace each other between two different habitats situated at the opposite sides of a steep precipitation gradient. It was hypothesised that the reason for this paratopic distribution is competition between larvae of the two species for food resources.
2. This hypothesis was tested by studying the performance of larvae of the two species in terms of their developmental success in mixed-species and single-species treatments under different air temperatures, relative humidities, substrate textures, and food abundance.
3. The number of individuals of X. conformis that survived until emergence depended significantly on the presence of competing species, being, in general, lower in mixed-species compared with single-species treatments. The decrease in developmental success of X. conformis in mixed-species treatments was found mainly during food shortage. In contrast, presence of the competitor did not affect the number of X. ramesis that survived until emergence. No effect of the presence of the competitor on duration of development or sex ratio was found in either species.
4. The results of this study, together with the results of our previous studies, provide an explanation for the paratopic distribution of X. conformis and X. ramesis that exploit the same host species.     

Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment

A new single-species model disturbed by both white noise and colored noise in a polluted environment is developed and analyzed. Sufficient criteria for extinction, stochastic nonpersistence in the mean, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence of the species are established. The threshold between stochastic weak persistence in the mean and extinction is obtained. The results show that both white and colored environmental noises have sufficient effect to the survival results.     

Effect of aggregating behavior on population recovery on a set of habitat islands

We consider a single-species model which is composed of several patches connected by linear migration rates and having logistic growth with a threshold. We show the existence of an aggregating mechanism that allows the survival of a species which is in danger of extinction due to its low population density. Numerical experiments illustrate these results.     

The stage-structured predator-prey model and optimal harvesting policy

In this paper, we establish a mathematical model of two species with stage structure and the relation of predator-prey, to obtain the necessary and sufficient condition for the permanence of two species and the extinction of one species or two species. We also obtain the optimal harvesting policy and the threshold of the harvesting for sustainable development.     

Performance and scalability of discriminative metrics for comparative gene identification in 12 Drosophila genomes

Comparative genomics of multiple related species is a powerful methodology for the discovery of functional genomic elements, and its power should increase with the number of species compared. Here, we use 12 Drosophila genomes to study the power of comparative genomics metrics to distinguish between protein-coding and non-coding regions. First, we study the relative power of different comparative metrics and their relationship to single-species metrics. We find that even relatively simple multi-species metrics robustly outperform advanced single-species metrics, especially for shorter exons (≤240 nt), which are common in animal genomes. Moreover, the two capture largely independent features of protein-coding genes, with different sensitivity/specificity trade-offs, such that their combinations lead to even greater discriminatory power. In addition, we study how discovery power scales with the number and phylogenetic distance of the genomes compared. We find that species at a broad range of distances are comparably effective informants for pairwise comparative gene identification, but that these are surpassed by multi-species comparisons at similar evolutionary divergence. In particular, while pairwise discovery power plateaued at larger distances and never outperformed the most advanced single-species metrics, multi-species comparisons continued to benefit even from the most distant species with no apparent saturation. Last, we find that genes in functional categories typically considered fast-evolving can nonetheless be recovered at very high rates using comparative methods. Our results have implications for comparative genomics analyses in any species, including the human.     

Relative nonlinearity and permanence

We modify the commonly used invasibility concept for coexistence of species to the stronger concept of uniform invasibility. For two-species discrete-time competition and predator-prey models, we use this concept to find broad easily checked sufficient conditions for the rigorous concept of permanent coexistence. With these results, permanent coexistence becomes a tractable concept for many discrete-time population models. To understand how these conditions apply to nonpoint attractors, we generalize the concept of relative nonlinearity and use it to show how population fluctuations affect the long-term low-density growth rate (“the invasion rate”) of a species when it is invading the system consisting of the other species (“the resident”) at a single-species attractor. The concept of relative nonlinearity defines circumstances when this invasion rate is increased or decreased by resident population fluctuations arising from a nonpoint attractor. The presence and sign of relative nonlinearity is easily checked in models of interacting species. When relative nonlinearity is zero or positive, fluctuations cannot decrease the invasion rate. It follows that permanence is then determined by invasibility of the resident’s fixed points. However, when relative nonlinearity is negative, invasibility, and hence permanent coexistence, can be undermined by resident population fluctuations. These results are illustrated with specific two-species competition and predator-prey models of generic forms.     

Seven-Year Survival of Perennial Herbaceous Transplants in Temperate Woodland Restoration

Little is known about restoring the perennial herbaceous understory of Midwestern deciduous woodlands, despite the significant and widespread degradation of remnants due to human activities. Because many woodland understory species have reproductive characters that make reestablishment from seed slow or difficult, we investigated transplanting as a strategy for introducing 24 species to a degraded early-successional woodland in central Iowa, U.S.A. Plants were planted in single-species groups of generally four individuals, and then monitored for survival five times over a 7-year period, and for flowering during the first year. After 7 years, persistence of these groups was 57% averaged across species. Survival in years 5–7 does not reflect individuals that spread beyond the original planting units by self-sowing or vegetative spread and is therefore a minimum estimate of the abundance of many species at the site. Mean percent flowering was 72% across single-species groups for 15 species monitored. We consider these survival and flowering rates acceptable indicators of establishment success, especially given drought conditions at our site in the first few years and lack of weed control beyond the first year, and evidence that transplanted species were establishing outside the original planting locations. Additional work is needed to investigate regional differences in transplant success, and methods for sustainable production of species are not suitable for introduction by seed. We caution that our results do not necessarily apply to the restoration of rare species.     

Optimal foraging and predator-prey dynamics, II.

In this paper we consider one-predator-two-prey population dynamics described by a control system. We study and compare conditions for permanence of the system for three types of predator feeding behaviors: (i) specialized feeding on the more profitable prey type, (ii) generalized feeding on both prey types, and (iii) optimal foraging behavior. We show that the region of parameter space leading to permanence for optimal foraging behavior is smaller than that for specialized behavior, but larger than that for generalized behavior. This suggests that optimal foraging behavior of predators may promote coexistence in predator-prey systems. We also study the effects of the above three feeding behaviors on apparent competition between the two prey types.     

An exactly solvable model of population dynamics with density-dependent migrations and the Allee effect

We consider a single-species model of population dynamics allowing for migrations and the Allee effect. Two types of migration are taken into account: one caused by environmental factors (e.g., a passive transport with the wind or water current) and the other associated with biological mechanisms. While the first type is apparently density-independent, the speed of migration in the second one can depend on the population density. Mathematically, this model consists of a non-linear partial differential equation of advection-diffusion-reaction type. Using an appropriate change of variables, we obtain an exact solution of the equation describing propagation of travelling population fronts. We show that, depending on parameter values and thus on the relative intensity of density-dependent and density-independent factors, the direction of the propagation can be different thus describing either species invasion or species retreat.     

From antagonistic larvae to mutualistic adults: coevolution of diet niches within life cycles

Population structures largely affect higher levels of organization (community structure, ecosystem functioning), especially when involving ontogenetic changes in habitat or diet. Along life cycles, partners and interaction type may change: for instance Lepidopterans are herbivores as larvae and pollinators as adults. To understand variations in diet niche from larvae to adults, we model a community of two plant species and one stage‐structured insect species consuming plants as juvenile and pollinating them as adult. We model the coevolution of juvenile and adult diet specialization using adaptive dynamics to investigate when one should expect niche partitioning or niche overlap among life stages. We consider ecological and evolutionary implications for the coexistence of species. As predicted based on indirect effects among stages, we find that juvenile diet evolution increases niche overlap and favours the coexistence of plants, while the evolution of the adult diet decreases niche overlap and reduces plant coexistence, because of positive feedbacks emerging from the mutualistic interaction.     

Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment II

This is a continuation of our paper [Liu, M., Wang, K., 2010. Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment, J. Theor. Biol. 264, 934-944]. Taking both white noise and colored noise into account, a stochastic single-species model under regime switching in a polluted environment is studied. Sufficient conditions for extinction, stochastic nonpersistence in the mean, stochastic weak persistence and stochastic permanence are established. The threshold between stochastic weak persistence and extinction is obtained. The results show that a different type of noise has a different effect on the survival results.     

具有阶段结构的两种群竞争系统的周期解

本文研究了具有阶段结构的两种群竞争系统的渐近行为.我们得到了系统持续生存的条件.由Brouwer不动点定理和李亚普诺夫函数,我们证明相应的周期系统在满足一定的条件下,存在一个唯一的全局渐近稳定的正周期解.最后我们把没有阶段结构的系统与有阶段结构的系统进行了比较.