Search for: All records

In this research, we study the impacts of the traceable mobility in a two-patch environment when the population in each patch exhibits strong Allee effects. Traveling individuals are traced across patches by budgeting the average time spent in each patch while keeping their place of residency. Particularly, we focus on the impact that the effective population (residents and visitors) produces on regional dynamics.Our results show that low mobility across regions produces simple dynamics, where orbits converge to single or double extinction, or to a coexistence steady state. We derive mobility conditions under which an endangered population may benefit of the presence of a visitant one and avoid extinction -- the rescue effect. Nonetheless, increments in the visiting population would also lead the resident population to extinction -- the induced extinction effect.

 

The variation of nutrient supply not only leads to the differences in the phytoplankton biomass and primary productivity but also induces the long-term phenotypic evolution of phytoplankton. It is widely accepted that marine phytoplankton follows Bergmann's Rule and becomes smaller with climate warming. Compared with the direct effect of increasing temperature, the indirect effect via nutrient supply is considered to be an important and dominant factor in the reduction of phytoplankton cell size. In this paper, a size-dependent nutrient-phytoplankton model is developed to explore the effects of nutrient supply on the evolutionary dynamics of functional traits associated with phytoplankton size. The ecological reproductive index is introduced to investigate the impacts of input nitrogen concentration and vertical mixing rate on the persistence of phytoplankton and the distribution of cell size. In addition, by applying the adaptive dynamics theory, we study the relationship between nutrient input and the evolutionary dynamics of phytoplankton. The results show that input nitrogen concentration and vertical mixing rate have significant effects on the cell size evolution of phytoplankton. Specifically, cell size tends to increase with the input nutrient concentration, as does the diversity of cell sizes. In addition, a single-peaked relationship between vertical mixing rate and cell size is observed. When the vertical mixing rate is too low or too high, only small individuals are dominant in the water column. When the vertical mixing rate is moderate, large individuals can coexist with small individuals, so the diversity of phytoplankton is elevated. We predict that reduced intensity of nutrient input due to climate warming will lead to a trend towards smaller cell size and will reduce the diversity of phytoplankton.

 

In this paper, we investigate the dynamical behavior for a hybrid non-autonomous predator–prey system with Holling Type II functional response, impulsive effects and generalist predator on time scales, where our proposed model commutes between a continuous-time dynamical system and discrete-time dynamical system. By using comparison theorems, we first study the permanence results of the proposed model. Also, we established the uniformly asymptotic stability for the almost periodic solution of the proposed model. Finally, in the last section, we provide some examples with numerical simulation. 

Social insect colonies’ robust and efficient collective behaviors without any central control contribute greatly to their ecological success. Colony migration is a leading subject for studying collective decision-making in migration. In this paper, a general colony migration model with Hill functions in recruitment is proposed to investigate the underlying decision making mechanism and the related dynamical behaviors. Our analysis provides the existence and stability of equilibrium, and the global dynamical behavior of the system. To understand how piecewise functions and Hill functions in recruitment impact colony migration dynamics, the comparisons are performed in both analytic results and bifurcation analysis. Our theoretical results show that the dynamics of the migration system with Hill functions in recruitment differs from that of the migration system with piecewise functions in the following three aspects: (1) all population components in our colony migration model with Hill functions in recruitment are persistent; (2) the colony migration model with Hill functions in recruitment has saddle and saddle-node bifurcations, while the migration system with piecewise functions does not; (3) the system with Hill functions has only equilibrium dynamics, i.e. either has a global stability at one interior equilibrium or has bistablity among two locally stable interior equilibria. Bifurcation analysis shows that the geometrical shape of the Hill functions greatly impacts the dynamics: (1) the system with flatter Hill functions is less likely to exhibit bistability; (2) the system with steeper functions is prone to exhibit bistability, and the steady state of total active workers is closer to that of active workers in the system with piecewise function. 

Social hierarchies are ubiquitous in social groups such as human societies and social insect colonies; however, the factors that maintain these hierarchies are less clear. Motivated by the shared reproductive hierarchy of the ant species Harpegnathos saltator, we have developed simple compartmental nonlinear differential equations to explore how key life-history and metabolic rate parameters may impact and determine its colony size and the length of its shared hierarchy. Our modeling approach incorporates nonlinear social interactions and metabolic theory. The results from the proposed model, which were linked with limited data, show that: (1) the proportion of reproductive individuals decreases over colony growth; (2) an increase in mortality rates can diminish colony size but may also increase the proportion of reproductive individuals; and (3) the metabolic rates have a major impact in the colony size and structure of a shared hierarchy.