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The impact of the variation of the number of functional traits on functional diversity assessment is still poorly known. Although the covariation between these two parameters may be desirable in some situations (e.g. if adding functional traits provides relevant new functional information), it may also result from mathematical artefacts and lead to misinterpretation of the results obtained. Here, we have tested the behaviour of a set of nine indices widely used for assessing the three main components of functional diversity (i.e. functional richness, evenness and divergence), according to the variation in the number of functional traits. We found that the number of functional traits may strongly impact the values of most of the indices considered, whatever the functional information they contain. The FRic, TOP and n-hypervolume indices that have been developed to characterize the functional richness component appeared to be highly sensitive to the variation in the number of traits considered. Regarding functional divergence, most of the indices considered (i.e. Q, FDis and FSpe) also showed a high degree of sensitivity to the number of traits considered. In contrast, we found that indices used to compute functional evenness (FEve and Ru), as well as one of the indices related to functional divergence (FDiv), are weakly influenced by the variation in the number of traits. All these results suggest that interpretation of most of the functional diversity indices considered cannot only be based on their values as they are, but requires taking into account the way in which they have been computed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: Two distinguishing features characterize the population dynamic models considered in the present work. On the one hand, we consider several interacting organization levels associated to different time scales. On the other hand, the environment tends to be constant in the long term. The mathematical representation of these properties leads to slow-fast asymptotically autonomous systems. These characteristics add some realism in the models. However, the analytical study of this class of systems is generally hard to perform. Here we present a reduction technique that can be included among the so-called approximate aggregation methods. The existence of different time scales, together with the long term features, are used to build up a simpler system, which can be described by means of a lower number of state variables. The asymptotic behavior of the simplified model helps to study the original one. The reduction procedure is formulated in a general way. Following, two illustrations of asymptotically autonomous models with two time scales, in a gradostat, are given: a consumer–resource model and a competition model. Finally, a wider range of applications is suggested. [Copyright &y& Elsevier]

Abstract: Marine ecosystems are characterized by a strong influence of hydrodynamics on biological processes. The associated models involve the coupling of physical to biological models and therefore require a large number of state variables. The consequent high complexity limits our capacity to perform a complete and detailed study and even prevents any complete mathematical study of these models. It is also difficult to disentangle among all the processes involved, which ones actually drive the system at any moment. Hydrodynamics, among other consequences, affect the way under which the nutrients are supplied to marine ecosystems. The variability of nutrient input rate in marine systems generally results from runs-off in coastal systems and from physical processes (wind forcing and hydrodynamics) in open ocean. This paper is devoted to the study of the effects of the nutrient input rate variability on the dynamics and the functioning of trophic chains. In this context, we aim to provide an understandable study, based on simplified system models. We consider a periodic nutrient input rate and analyze how this variability modifies some system properties: its dynamics, its functioning and its structure. The dynamics is obtained by numerical simulations and when possible, enlighten by already published mathematical results. The functioning is measured by the time averaged state variables during the simulation period, and their variability. The structure concerns the number of surviving populations, a proxy of specific biodiversity. We show how these properties can be affected and provide some conditions under which the modifications can occur. We also highlight that, even if the physical process is the main driving force in the global dynamics, the choice of the biological model is important to understand the biological response of the system to physical forcing. [Copyright &y& Elsevier]

This work deals with the approximate reduction of a nonautonomous two time scales ordinary differential equations system with periodic fast dynamics. We illustrate this technique with the analysis of two models belonging to different fields in ecology. On the one hand, we deal with a two patches periodic predator-prey model with a refuge for prey. Considering migrations between patches to be faster than local interaction allows us to study a three-dimensional system by means of a two-dimensional one. On the other hand, a two time scales periodic eco-epidemic model is addressed by considering two competing species, one of them being affected by a periodic SIR epidemic process which is faster than inter-species interactions. The difference between time scales allows us to study the asymptotic behavior of the four-dimensional system by means of a planar, reduced one. Furthermore, we propose a methodology straightforwardly applicable to a very large class of two time scales periodic systems. [ABSTRACT FROM AUTHOR]

Abstract: In this work we consider a spatially distributed periodic multi strain SIS epidemic model. We let susceptible and infected individuals migrate between patches, with periodic migration rates. Considering that migrations are much faster than the epidemic process, we build up a less dimensional (aggregated) system that allows to study some features of the asymptotic behavior of the original model. In particular, we are able to define global reproduction numbers in the non-spatialized aggregated system that serve to decide the eradication or endemicity of the epidemic in the initial spatially distributed nonautonomous model. Comparing these global reproductive numbers with those corresponding to isolated patches we show that adequate periodic fast migrations can in many cases reverse local endemicity and get global eradication of the epidemic. [Copyright &y& Elsevier]

This paper assesses how considering variation in DOC availability and cell maintenance in bacterial models affects Bacterial Growth Efficiency (BGE) estimations. For this purpose, we conducted two biodegradation experiments simultaneously. In experiment one, a given amount of substrate was added to the culture at the start of the experiment whilst in experiment two, the same amount of substrate was added, but using periodic pulses over the time course of the experiment. Three bacterial models, with different levels of complexity, (the Monod, Marr-Pirt and the dynamic energy budget - DEB - models), were used and calibrated using the above experiments. BGE has been estimated using the experimental values obtained from discrete samples and from model generated data. Cell maintenance was derived experimentally, from respiration rate measurements. The results showed that the Monod model did not reproduce the experimental data accurately, whereas the Marr-Pirt and DEB models demonstrated a good level of reproducibility, probably because cell maintenance was built into their formula. Whatever estimation method was used, the BGE value was always higher in experiment two (the periodically pulsed substrate) as compared to the initially one-pulsed-substrate experiment. Moreover, BGE values estimated without considering cell maintenance (Monod model and empirical formula) were always smaller than BGE values obtained from models taking cell maintenance into account. Since BGE is commonly estimated using constant experimental systems and ignore maintenance, we conclude that these typical methods underestimate BGE values. On a larger scale, and for biogeochemical cycles, this would lead to the conclusion that, for a given DOC supply rate and a given DOC consumption rate, these BGE estimation methods overestimate the role of bacterioplankton as CO2 producers. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a predator-prey model in a patchy environment. The model represents the interactions between phytoplankton and zooplankton in the water column. Two patches are considered with respect to light availability: one patch is associated to the surface layer, the second patch describes the bottom layer. We show that this spatial heterogeneity may destabilize the predator-prey system, even in oligotrophic system where the nutrient is low enough to avoid "paradox-enrichment" phenomenon. Indeed, in this case, an heterogeneity index can be used as a bifurcation parameter, leading to a Hopf bifurcation. Moreover, we assume that individuals can be dispersed in both patches via hydrodynamism processes, like in a mixed layer. The effect of mixing intensity is analysed as well as interactions between dispersion and enrichment. We also show that, in some cases, spatial heterogeneity has a stabilizing effect. These contrasted results are examined by considering the non linear interaction between heterogeneity, dispersal and enrichment and some mechanisms leading to stabilization/destabilization are exhibited. [ABSTRACT FROM AUTHOR]

The merging of two independent populations of heterotrophs and autotrophs into a single population of mixotrophs has occurred frequently in evolutionary history. It is an example of a wide class of related phenomena, known as symbiogenesis. The physiological basis is almost always (reciprocal) syntrophy, where each species uses the products of the other species. Symbiogenesis can repeat itself after specialization on particular assimilatory substrates. We discuss quantitative aspects and delineate eight steps from two free-living interacting populations to a single fully integrated endosymbiotic one. The whole process of gradual interlocking of the two populations could be mimicked by incremental changes of particular parameter values. The role of products gradually changes from an ecological to a physiological one. We found conditions where the free-living, epibiotic and endobiotic populations of symbionts can co-exist, as well as conditions where the endobiotic symbionts outcompete other symbionts. Our population dynamical analyses give new insights into the evolution of cellular homeostasis. We show how structural biomass with a constant chemical composition can evolve in a chemically varying environment if the parameters for the formation of products satisfy simple constraints. No additional regulation mechanisms are required for homeostasis within the context of the dynamic energy budget (DEB) theory for the uptake and use of substrates by organisms. The DEB model appears to be closed under endosymbiosis. This means that when each free-living partner follows DEB rules for substrate uptake and use, and they become engaged in an endosymbiotic relationship, a gradual transition to a single fully integrated system is possible... [ABSTRACT FROM AUTHOR]

Sediment and water can potentially be altered, chemically, physically and biologically as they are sampled at the seafloor, brought to the surface, processed and analysed. As a result, in situ observations of relatively undisturbed systems have become the goal of a growing body of scientists. Our understanding of sediment biogeochemistry and exchange fluxes was revolutionized by the introduction of benthic chambers and in situ micro-electrode profilers that allow for the direct measurement of chemical fluxes between sediment and water at the sea floor and for porewater composition. Since then, rapid progress in the technology of in situ sensors and benthic chambers (such as the introduction of gel probes, voltammetric electrodes or one- and two-dimensional optodes) have yielded major breakthroughs in the scientific understanding of benthic biogeochemistry. This paper is a synthesis of discussions held during the workshop on sediment biogeochemistry at the “Benthic Dynamics: in situ surveillance of the sediment–water interface” international conference (Aberdeen, UK—March 25–29, 2002). We present a review of existing in situ technologies for the study of benthic biogeochemistry dynamics and related scientific applications. Limitations and possible improvement (e.g., technology coupling) of these technologies and future development of new sensors are discussed. There are countless important scientific and technical issues that lend themselves to investigation using in situ benthic biogeochemical assessment. While the increasing availability of these tools will lead research in yet unanticipated directions, a few emerging issues include greater insight into the controls on organic matter (OM) mineralization, better models for the understanding of benthic fluxes to reconcile microelectrode and larger-scale chamber measurements, insight into the impacts of redox changes on trace metal behavior, new insights into geochemical reaction pathways in surface sediments, and a better understanding of contaminant fate in nearshore sediments. [Copyright &y& Elsevier]

Two predator-prey model formulations are studied: the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to a singular perturbation problem. In contradiction to the RM-model, the resource for the prey is modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare. In both models the transcritical bifurcation, a threshold above which invasion of predator into prey-only system occurs, and the Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle occur. The slow-fast limit cycles are called relaxation oscillations which for increasing differences in time scales leads to the well known degenerated trajectories being concatenations of slow parts of the trajectory and fast parts of the trajectory. In the fast-slow version of the RM-model a canard explosion of the stable limit cycles occurs in the oscillatory region of the parameter space. To our knowledge this type of dynamics has not been observed for the RM-model and not even for more complex ecosystem models. When a bifurcation parameter crosses the Hopf bifurcation point the amplitude of the emerging stable limit cycles increases. However, depending of the perturbation parameter the shape of this limit cycle changes abruptly from one consisting of two concatenated slow and fast episodes with small amplitude of the limit cycle, to a shape with large amplitude of which the shape is similar to the relaxation oscillation, the well known degenerated phase trajectories consisting of four episodes (concatenation of two slow and two fast). The canard explosion point is accurately predicted by using an extended asymptotic expansion technique in the perturbation and bifurcation parameter simultaneously where the small amplitude stable limit cycles exist. The predicted dynamics of the MB-model is in a large part of the parameter space similar to that of the RM-model. However, the fast-slow version of MB-model does not predict a canard explosion phenomenon., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Over-parametrization in modelling is a well-known issue that makes it hard to identify which part of a model is responsible for a given behaviour. In line with that ascertainment, this work presents the outline of an empirical method to simplify models by decreasing the number of parameters. By using regression trees to classify outputs according to related input parameters, the method provides the modeller with an objective tool to reduce the range of the used parameters and, under certain conditions, to establish relations between them. Thereby, the complexity of the model is reduced on the basis of mathematical arguments. As an example, a dynamic energy budget-based model of a mesopelagic bacterial ecosystem is simplified using the presented method. The main benefits of such a method are thus highlighted: (i) more robust parameter estimations; (ii) less complex formulations; and (iii) fewer modelling assumptions. To conclude, the difficulties encountered are discussed, and several solutions are proposed to deal with them.

We present the state of the art of the development of dynamic energy budget theory, and its expected developments in the near future within the molecular, physiological and ecological domains. The degree of formalization in the set-up of the theory, with its roots in chemistry, physics, thermodynamics, evolution and the consistent application of Occam's razor, is discussed. We place the various contributions in the theme issue within this theoretical setting, and sketch the scope of actual and potential applications.

We try to answer the question of to what extent details in nutrient uptake and phytoplankton physiology matter for population and community dynamics. To this end, we study how two nutrients interact in limiting phytoplankton growth. A popular formulation uses a product-rule for nutrient uptake, which we compare with that on the basis of synthesizing units. We first fit different nutrient uptake models to a dataset and conclude that the quantitative differences between the models are small. Then we study the sensitivity of phytoplankton growth and zooplankton-phytoplankton interactions (ZPi) models to uptake formulations. Two population models are compared; they are based on different assumptions on the relation between nutrient uptake and phytoplankton growth. We find that the population and community models are sensitive to uptake formulations. According to the uptake formulation used in the ZPi models, qualitative differences can be observed. Indeed, although two models based on functions with similar shapes have close equilibria, these can differ in stability properties. Since stability involves the derivatives of formulas, even if two formulas provide close values, large numerical differences in the stability criterion may occur after derivation. We conclude that mechanistic details can be of importance for community modelling.

This paper provides a mathematical analysis of a virus-marine bacteria interaction model. The model is a simplified case of the model published and used by Middelboe (Middelboe, M. 2000 Microb. Ecol. 40, 114-124). It takes account of the virus, the susceptible bacteria, the infected bacteria and the substrate in a chemostat. We show that the numerical values of the parameters given by Middelboe allow two different time scales to be considered. We then use the geometrical singular perturbation theory to study the model. We show that there are two invariant submanifolds of dimension two in the four-dimensional phase space and that these manifolds cross themselves on the boundary of the domain of biological relevance. We then perform a rescaling to understand the dynamics in the vicinity of the intersection of the manifolds. Our results are discussed in the marine ecological context.

In the laboratory, marine worms were fed with a mixture of algae and several aliphatic hydrocarbons for 15 days. After ingestion by the worms, 34.9% of hydrocarbons are found in the faeces and only 3.1% accumulated in the gut. The comparison between the initial mixture and the faeces shows that the worm's digestive process lead to changes in the distribution of the n-alkane mixture. These changes are different from those only due to physical processes in the experimental conditions. In our experiment, no variation in the distribution of hydrocarbons in faeces with time and no microbial hydrocarbon biodegradation were evidenced. Our results suggest that marine worm feeding can substantially affect the fate of hydrocarbons in the sedimentary marine ecosystem by predominantly stimulating dissolution processes.

The aim of this work is to study the effects of different individual behaviours on the overall growth of a spatially distributed population. The population can grow on two spatial patches, a source and a sink, that are connected by migrations. Two time scales are involved in the dynamics, a fast one corresponding to migrations and a slow one associated with the local growth on each patch. Different scenarios of density-dependent migration are proposed and their effects on the population growth are investigated. A general discussion on the use of aggregation methods for the study of integration of different ecological levels is proposed.

We present aggregation and emergence methods in large-scale dynamical systems with different timescales. Aggregation corresponds to the reduction of the dimension of a dynamical system which is replaced by a smaller model for a small number of global variables at a slow timescale. We study the couplings between fast and slow dynamics leading to the emergence of global properties in the aggregated model. First, we study the case of a single population in a patchy environment. Growth rates are assumed to be linear on each patch. Individuals can migrate from one patch to another at a fast timescale. We choose different density dependent migration processes. In each case, we use aggregation methods to obtain the corresponding growth equation for the total density of the population at a slow timescale. We look for particular density dependent migration processes leading to an aggregated logistic-like equation. Second, we study the case of two interacting populations. A particular choice of density dependent migrations leads to an aggregated competition model.