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

The release of chemicals following herbivore grazing on primary producers may providefeeding cues to carnivorous predators, thereby promoting multitrophic interactions. Inparticular, chemicals released following grazing on phytoplankton by microzooplanktonherbivores have been shown to elicit a behavioural foraging response in carnivorouscopepods, which may use this chemical information as a mechanism to locate and remainwithin biologically productive patches of the ocean. In this paper, we use a 1D spatialreaction-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 releasedby the primary producers forming the bottom trophic level. The effect of theinfochemical-mediated predation is investigated by comparing the case where copepodsforage randomly to the case where copepods adjust their vertical position to follow thedistribution of grazing-induced chemicals. Results indicate that utilization ofinfochemicals for foraging provides fitness benefits to copepods and stabilizes the systemat high nutrient load, whilst also forming a possible mechanism for phytoplankton bloomformation. We also investigate how the copepod efficiency to respond to infochemicalsaffects the results, and show that small increases (2%) in the ability of copepods tosense infochemicals can promote their persistence in the system. Finally we argue thateffectively employing infochemicals for foraging can be an evolutionarily stable strategyfor copepods.

Habitat fragmentation is an important area of concern in species conservation. Habitatfragmentation can affect population distributions through reductions in suitable habitat,and through organism responses to different habitat types and the transitions betweenthem. In earlier work, the effect of habitat fragmentation on cyclic populations wasinvestigated in the context of populations that show no behavioural response to theinterface between habitat types. In this paper, we extend the earlier work by addingedge-mediated behaviour to the models. That is, we investigate the dynamics that resultwhen oscillatory predator and prey species also exhibit behavioural responses to habitatinterfaces. Our results show generally that habitat loss decreases the amplitude and theaverage density of the prey and predator populations, but that most of the reponsesobserved in the two models exhibit marked differences. This work highlights the complexityof the interplay between population cycles, habitat fragmentation, and edge-mediatedbehaviour, and the need to study such systems in greater detail.

A recently proposed model for the investigation of diffusivity in planktonic systemscontaining toxin-producing phytoplanktons is here reconsidered. We show the existence ofplanktonic travelling waves. Numerical simulations validate the analytical findings, toelucidate 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 wasaccompanied by a number of spectacular phenomena that determined the general success ofthe ragweed control and further dispersal and acclimatization of the beetles:(i) formation of solitary population waves (SPW), characterized by anextremely high density of the phytophage population at the narrow band of the front of amoving wave defoliating nearly all ragweed plants, and (ii) rapid, within5-6 generations, development of flight in the leaf beetle species that in its homelandlost the ability to fly. We present here a demogenetic model capable of reproducing boththese phenomena, assuming that the flight ability of a phytophage population is governedby a single diallelic locus with flight and flightless alleles that determine threegenotypes of the ragweed leaf beetle. Simulation results agree well with the practicalrecommendation of retaining a high density of common ragweed in the release area in orderto provide the necessary conditions for the initial increase of the leaf beetle populationand the formation of the wave. The model confirms the earlier hypothesis that the SPW isthe key factor that determines efficiency of weed biocontrol program. We demonstrate alsothat 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 forbiological invasion in heterogeneous spatially continuous habitats have receivedconsiderable 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 speciespopulation invading a two dimensional heterogeneous environment. The population growthrate and dispersal coefficient depend on the site quality. We first find an analyticalcriterium for the spread success in terms of the population growth rate and the dispersalcoefficient in unfavorable regions. We then implemented our model for two distinct spatialconfigurations: periodical stripe-like and randomized environments. The spread rate iscomputed numerically and it shows a decrease with an increase of the fraction of thehostile sites. However, we observed that invasion success does not depend on the fractionof favorable sites but crucially depends on the connectivity of favorable regions.

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

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

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

An important consequence of this ecological phenomenon is the existence of a separatrixcurve dividing the behavior of trajectories in the phase plane. The origin is an attractorfor 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 uniquepositive equilibrium, which can be either an attractor or a repellor surrounded by one ormore limit cycles.

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

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