The formation, persistence and movement of self-organised biological aggregations are mediated by signals (e.g., visual, acoustic or chemical) that organisms use to communicate with each other. To investigate the effect that communication has on the movement of biological aggregations, we use a class of nonlocal hyperbolic models that incorporate social interactions and different communication mechanisms between group members. We approximate the maximum speed for left-moving and right-moving groups, and show numerically that the travelling pulses exhibited by the nonlocal hyperbolic models actually travel at this maximum speed. Next, we use the formula for the speed of a travelling pulse to calculate the reversal time for the zigzagging behaviour, and show that the communication mechanisms have an effect on these reversal times. Moreover, we show that how animals communicate with each other affects also the density structure of the zigzags. These findings offer a new perspective on the complexity of the biological factors behind the formation and movement of various aggregations.

The release of chemicals following herbivore grazing on primary producers may provide feeding cues to carnivorous predators, thereby promoting multitrophic interactions. In particular, chemicals released following grazing on phytoplankton by microzooplankton herbivores have been shown to elicit a behavioural foraging response in carnivorous copepods, which may use this chemical information as a mechanism to locate and remain within biologically productive patches of the ocean. In this paper, we use a 1D spatial reaction-diffusion model to simulate a tri-trophic planktonic system in the water column, where predation at the top trophic level (copepods) is affected by infochemicals released by the primary producers forming the bottom trophic level. The effect of the infochemical-mediated predation is investigated by comparing the case where copepods forage randomly to the case where copepods adjust their vertical position to follow the distribution of grazing-induced chemicals. Results indicate that utilization of infochemicals for foraging provides fitness benefits to copepods and stabilizes the system at high nutrient load, whilst also forming a possible mechanism for phytoplankton bloom formation. We also investigate how the copepod efficiency to respond to infochemicals affects the results, and show that small increases (2%) in the ability of copepods to sense infochemicals can promote their persistence in the system. Finally we argue that effectively employing infochemicals for foraging can be an evolutionarily stable strategy for copepods.

Habitat fragmentation is an important area of concern in species conservation. Habitat fragmentation can affect population distributions through reductions in suitable habitat, and through organism responses to different habitat types and the transitions between them. In earlier work, the effect of habitat fragmentation on cyclic populations was investigated in the context of populations that show no behavioural response to the interface between habitat types. In this paper, we extend the earlier work by adding edge-mediated behaviour to the models. That is, we investigate the dynamics that result when oscillatory predator and prey species also exhibit behavioural responses to habitat interfaces. Our results show generally that habitat loss decreases the amplitude and the average density of the prey and predator populations, but that most of the reponses observed in the two models exhibit marked differences. This work highlights the complexity of the interplay between population cycles, habitat fragmentation, and edge-mediated behaviour, and the need to study such systems in greater detail.

A recently proposed model for the investigation of diffusivity in planktonic systems containing toxin-producing phytoplanktons is here reconsidered. We show the existence of planktonic travelling waves. Numerical simulations validate the analytical findings, to elucidate the sensitivity of the results in dependence of the diffusion coefficients.

The introduction of the ragweed leaf beetle in the South of Russia in 1978–1989 was accompanied by a number of spectacular phenomena that determined the general success of the ragweed control and further dispersal and acclimatization of the beetles: (i) formation of solitary population waves (SPW), characterized by an extremely high density of the phytophage population at the narrow band of the front of a moving wave defoliating nearly all ragweed plants, and (ii) rapid, within 5-6 generations, development of flight in the leaf beetle species that in its homeland lost the ability to fly. We present here a demogenetic model capable of reproducing both these phenomena, assuming that the flight ability of a phytophage population is governed by a single diallelic locus with flight and flightless alleles that determine three genotypes of the ragweed leaf beetle. Simulation results agree well with the practical recommendation of retaining a high density of common ragweed in the release area in order to provide the necessary conditions for the initial increase of the leaf beetle population and the formation of the wave. The model confirms the earlier hypothesis that the SPW is the key factor that determines efficiency of weed biocontrol program. We demonstrate also that the formation of the wave has crucially accelerated the development of the beetles’ ability to fly.

Spatial heterogeneity greatly affects the population spread. Although the theory for biological invasion in heterogeneous spatially continuous habitats have received considerable attention, spatially discrete models have remained outside of the mainstream. In this study, we formulate and analyze a Coupled Map Lattice model for a single species population invading a two dimensional heterogeneous environment. The population growth rate and dispersal coefficient depend on the site quality. We first find an analytical criterium for the spread success in terms of the population growth rate and the dispersal coefficient in unfavorable regions. We then implemented our model for two distinct spatial configurations: periodical stripe-like and randomized environments. The spread rate is computed numerically and it shows a decrease with an increase of the fraction of the hostile sites. However, we observed that invasion success does not depend on the fraction of favorable sites but crucially depends on the connectivity of favorable regions.

In this work we review the aggregation of variables method for discrete dynamical systems. These methods consist of describing the asymptotic behaviour of a complex system involving many coupled variables through the asymptotic behaviour of a reduced system formulated in terms of a few global variables. We consider population dynamics models including two processes acting at different time scales. Each process has associated a map describing its effect along its specific time unit. The discrete system encompassing both processes is expressed in the slow time scale composing the map associated to the slow one and the k-th iterate of the map associated to the fast one. In the linear case a result is stated showing the relationship between the corresponding asymptotic elements of both systems, initial and reduced. In the nonlinear case, the reduction result establishes the existence, stability and basins of attraction of steady states and periodic solutions of the original system with the help of the same elements of the corresponding reduced system. Several models looking over the main applications of the method to populations dynamics are collected to illustrate the general results.

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fishes and boats movements between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that boats and fishes movements as well as prices variations occur at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model. We show that the aggregated model can have 1, 2 or 3 non trivial equilibria. We show that a variation of the total number of sites can induce a switch from over-exploitation to sustainable fisheries.

This work deals with the consequences on structural stability of Gause type predator-prey models, when are considered three standard functional responses and the prey growth rate is subject to an Allee effect.

An important consequence of this ecological phenomenon is the existence of a separatrix curve dividing the behavior of trajectories in the phase plane. The origin is an attractor for any set of parameters and the existence of heteroclinic curves can be also shown.

Conditions on the parameter values are established to ensure the existence of a unique positive equilibrium, which can be either an attractor or a repellor surrounded by one or more limit cycles.

The influence of the Allee effect on the number of limit cycles is analyzed and the results are compared with analogous models without this phenomenon, and which main features have been given in various above works. Ecological interpretations of these results are also given.

We develop a framework for analysing the outcome of resource competition based on bifurcation theory. We elaborate our methodology by readdressing the problem of competition of two species for two resources in a chemostat environment. In the case of perfect-essential resources it has been extensively discussed using Tilman’s representation of resource quarter plane plots. Our mathematically rigorous analysis yields bifurcation diagrams with a striking similarity to Tilman’s method including the interpretation of the consumption vector and the resource supply vector. However, our approach is not restricted to a particular class of models but also works with other trophic interaction formulations. This is illustrated by the analysis of a model considering interactively-essential or complementary resources instead of prefect-essential resources. Additionally, our approach can also be used for other ecosystem compositions: multiple resources–multiple species communities with equilibrium or oscillatory dynamics. Hence, it gives not only a new interpretation of Tilman’s graphical approach, but it constitutes an extension of competition analyses to communities with many species as well as non-equilibrium dynamics.