Linking saturation,stability and sustainability in food webs with observed equilibrium structure

Stability of a dynamic equilibrium in a predator-prey system depends both on the type of functional response and on the point of equilibrium on the response curve. Saturation effects from Holling type II responses are known to destabilise prey populations, while a type III (sigmoid) response curve has been shown to provide stability at lower levels of saturation. These effects have also been shown in multi-trophic model systems. However, stability analyses of observed equilibria in real complex ecosystems have as yet not assumed non-linear functional responses. Here, we evaluate the implications of saturation in observed balanced material-flow structures, for system stability and sustainability. We first make the effects of the non-linear functional responses on the interaction strengths in a food web transparent by expressing the elements of Jacobian ‘community’ matrices for type II and III systems as simple functions of their linear (type I) counterparts. We then determine the stability of the systems and distinguish two critical saturation levels: (1) a level where the system is just as stable as a type I system and (2) a level above which the system cannot be stable unless it is subsidised, separating a stable materially sustainable regime from an unsustainable one. We explain the stabilising and destabilising effects in terms of the feedbacks in the systems. The results shed light on the robustness of observed patterns of interaction strengths in complex food webs and suggest the implausibility of saturation playing a significant role in the equilibrium dynamics of sustainable ecosystems.     

Period 7 in a line of trees

In a line of model trees the heights tend to vary with period 7 in many cases. This is the observable effect of an interesting structural reason: in the parameter space just beyond the border of the stability range of homogeneous heights stationary solutions with long spatial periods and irregularities can be observed before simpler short periodic solutions become stable. The model can be solved mainly analytically. The models ecological significance concerns the onset of patchiness in forest systems.     

Host-parasitoid spatial dynamics in heterogeneous landscapes

This paper explores the effect of spatial processes in a heterogeneous environment on the dynamics of a host-parasitoid interaction. The environment consists of a lattice of favourable (habitat) and hostile (matrix) hexagonal cells, whose spatial distribution is measured by habitat proportion and spatial autocorrelation (inverse of fragmentation). At each time step, a fixed fraction of both populations disperses to the adjacent cells where it reproduces following the Nicholson-Bailey model. Aspects of the dynamics analysed include extinction, stability, cycle period and amplitude, and the spatial patterns emerging from the dynamics.
We find that, depending primarily on the fraction of the host population that disperses in each generation and on the landscape geometry, five classes of spatio-temporal dynamics can be objectively distinguished: spatial chaos, spirals, metapopulation, mainland-island and spiral fragments. The first two are commonly found in theoretical studies of homogeneous landscapes. The other three are direct consequences of the heterogeneity and have strong similarities to dynamic patterns observed in real systems (e.g. extinction-recolonisation, source-sink, outbreaks, spreading waves).
We discuss the processes that generate these patterns and allow the system to persist. The importance of these results is threefold: first, our model merges into a same theoretical framework dynamics commonly observed in the field that are usually modelled independently. Second, these dynamics and patterns are explained by dispersal rate and common landscape statistics, thus linking in a practical way population ecology to landscape ecology. Third, we show that the landscape geometry has a qualitative effect on the length of the cycles and, in particular, we demonstrate how very long periods can be produced by spatial processes.     

The effect of spatial heterogeneity on the persistence of predator-prey interactions

The effect of spatially discontinuous environments on predator-prey systems is examined by using a computer simulation model. It is shown that increasing prey dispersal and decreasing predator dispersal do not necessarily have a stabilizing influence on the interaction, as had been concluded by previous workers. The stability of predator-prey interaction depends on the interaction of the dispersal process with normal reproduction and feeding of the predator and prey species.     

The effect of subinhibitory concentrations of antibiotics on the adhesion of enterobacteria

It is impossible to determine rigidly a net result of the influence of antibiotics on the interaction between parasite and host cells, as many factors participating in this process are not studied. Adhesion of microorganisms is one of the essential mechanisms of the above interaction. Antibiotics with a different mechanism of action in the subinhibitory concentrations affecting viability of microbes either slightly or nowise have been studied for their effect on adhesion on a model of the intestine section of human embryos and experimental animals. Most of antibiotics influenced differently adhesion of the microorganisms, that also depended on the species attribution of the latter. The accelerated selection of resistance during a successive passage via the suggested adhesion system was observed. The data obtained elucidated certain mechanisms of the effect of antibiotics on the microbial populations at the initial phase of the infectious process and under the primary contamination of mucosa.     

Functional composition of plant communities determines the spatial and temporal stability of soil microbial properties in a long‐term plant diversity experiment

Stable provisioning of ecosystem functions and services is crucial for human well‐being in a changing world. Two essential ecological components driving vital ecosystem functions in terrestrial ecosystems are plant diversity and soil microorganisms. In this study, we tracked soil microbial basal respiration and biomass over a time period of 12 years in a grassland biodiversity experiment (the Jena Experiment) and examined the role of plant diversity and plant functional group composition for the spatial and temporal stability of soil microbial properties (basal respiration and biomass) in bulk‐soil. Spatial and temporal stability were calculated as the inverse coefficient of variation (CV^?1) of soil microbial respiration and biomass measured from soil samples taken over space and time, respectively. We found that 1) plant species richness consistently increased soil microbial properties after a time lag of four years since the establishment of the experimental plots, 2) plant species richness had minor effects on the spatial stability of soil microbial properties, whereas 3) the functional composition of plant communities significantly affected spatial stability of soil microbial properties, with legumes and tall herbs reducing both the spatial stability of microbial respiration and biomass, while grasses increased the latter, and 4) the effect of plant diversity on temporal stability of soil microbial properties turned from being negative to neutral, suggesting that the recovery of soil microbial communities from former arable land‐use takes more than a decade. Our results highlight the importance of plant functional group composition for the spatial and temporal stability of soil microbial properties, and hence for microbially‐driven ecosystem processes, such as decomposition and element cycling, in temperate semi‐natural grassland.     

Spatial heterogeneity enhance robustness of large multi-species ecosystems

Understanding ecosystem stability and functioning is a long-standing goal in theoretical ecology, with one of the main tools being dynamical modelling of species abundances. With the help of spatially unresolved (well-mixed) population models and equilibrium dynamics, limits to stability and regions of various ecosystem robustness have been extensively mapped in terms of diversity (number of species), types of interactions, interaction strengths, varying interaction networks (for example plant-pollinator, food-web) and varying structures of these networks. Although many insights have been gained, the impact of spatial extension is not included in this body of knowledge. Recent studies of spatially explicit modelling on the other hand have shown that stability limits can be crossed and diversity increased for systems with spatial heterogeneity in species interactions and/or chaotic dynamics. Here we show that such crossing and diversity increase can appear under less strict conditions. We find that the mere possibility of varying species abundances at different spatial locations make possible the preservation or increase in diversity across previous boundaries thought to mark catastrophic transitions. In addition, we introduce and make explicit a multitude of different dynamics a spatially extended complex system can use to stabilise. This expanded stabilising repertoire of dynamics is largest at intermediate levels of dispersal. Thus we find that spatially extended systems with intermediate dispersal are more robust, in general have higher diversity and can stabilise beyond previous stability boundaries, in contrast to well-mixed systems.     

Effects of deterministic and random refuge in a prey-predator model with parasite infection

Most natural ecosystem populations suffer from various infectious diseases and the resulting host-pathogen dynamics is dependent on host's characteristics. On the other hand, empirical evidences show that for most host pathogen systems, a part of the host population always forms a refuge. To study the role of refuge on the host-pathogen interaction, we study a predator-prey-pathogen model where the susceptible and the infected prey can undergo refugia of constant size to evade predator attack. The stability aspects of the model system is investigated from a local and global perspective. The study reveals that the refuge sizes for the susceptible and the infected prey are the key parameters that control possible predator extinction as well as species co-existence. Next we perform a global study of the model system using Lyapunov functions and show the existence of a global attractor. Finally we perform a stochastic extension of the basic model to study the phenomenon of random refuge arising from various intrinsic, habitat-related and environmental factors. The stochastic model is analyzed for exponential mean square stability. Numerical study of the stochastic model shows that increasing the refuge rates has a stabilizing effect on the stochastic dynamics.     

Mesoscopic effects in an agent-based bargaining model in regular lattices

The effect of spatial structure has been proved very relevant in repeated games. In this work we propose an agent based model where a fixed finite population of tagged agents play iteratively the Nash demand game in a regular lattice. The model extends the multiagent bargaining model by Axtell, Epstein and Young modifying the assumption of global interaction. Each agent is endowed with a memory and plays the best reply against the opponent's most frequent demand. We focus our analysis on the transient dynamics of the system, studying by computer simulation the set of states in which the system spends a considerable fraction of the time. The results show that all the possible persistent regimes in the global interaction model can also be observed in this spatial version. We also find that the mesoscopic properties of the interaction networks that the spatial distribution induces in the model have a significant impact on the diffusion of strategies, and can lead to new persistent regimes different from those found in previous research. In particular, community structure in the intratype interaction networks may cause that communities reach different persistent regimes as a consequence of the hindering diffusion effect of fluctuating agents at their borders.     

Bacterial viability assessment by flow cytometry analysis in soil

Soil microhabitats and their heterogeneity are often considered to be among the most important factors affecting soil biotic communities. The microbial commu-nity has become one of the most important links in soil nutrient cycles and trophic components due to its role in biological processes, spatial and temporal dynamics, and physiological adaptation. Sandy-soil desert systems are characterized by fast water infiltration during the rainy season, high salinity, and low moisture availability in the upper soil layers. Plants have developed different ecophy-siological adaptations in order to cope with this harsh environment. The Tamarix aphylla is known to be one of the most commonly adapted plants, exhibiting a mechan-ism for secretion of excess salts as aggregates through its leaves. These leaves aggregate beneath the plant, creating 'islands of salinity'. Soil biotic components are, therefore, exposed to extreme abiotic stress conditions in this niche. The goal of this study was to examine the effect of T. aphylla on the live/dead bacterial population ratio on a spatial and temporal scale. The results emphasize the effect of abiotic factors, which changed on temporal as well as spatial scales, and also on the size of the active soil bacterial community, which fluctuated between 1.44% and 25.4% in summer and winter, respectively. The results of this study elucidate the importance of moisture availability and the 'island-of-salinity' effect on the active microbial community in a sandy desert system.     

Evolutionary basis and ecological role of toxic microbial secondary metabolites

This presentation develops a theory of the evolutionary origin and ecological implications of toxic microbial secondary metabolites. The theory is based on a model system that outlines cause—effect associations between pertinent biotypes in the aflatoxin contamination of developing maize kernels. The model suggests that the aflatoxin-producing fungi are natural digestive tract inhabitants of a number of insect species that feed on developing kernels. During feeding, the insect larvae introduce fungal propagules and provide infection sites on damaged kernels. The fungal association with insects exhibits extraordinary variability, ranging from symbiotic to pathogenic. Elaboration of aflatoxin by the fungus facilitates the pathogenic process in host insects. The theory contends that genetic information for secondary microbial metabolites evolved during ecosystem disequilibria. During periods of ecological stability, mechanisms evolved for repression of toxic secondary metabolite biosynthesis. The theory broadly suggests that contemporary agricultural activities presents the requisite milieu for production or toxic microbial secondary metabolites.     

Nutritional value of algae: a critical control on the stability of Daphnia-algal systems

In Daphnia–algal systems, the effect of nutrient enrichmenton stability is an important ecological issue. Here I considera system of Daphnia and two potential prey; one prey termedprimary algae, which are preferentially consumed, and the othersecondary algae, which yield less nutrition and are more resistantto the grazer. The presence of secondary algae is a key to thestability, but their nutritional value has not been clearlydefined in the previous theory and the actual value varies.Here I use a simple mathematical model defining explicitly thenutritional values of algae and examine the stability of thesystems as a function of phosphorus enrichment. Whether or notall three species can stably coexist depended on the combinationof the algal species used for simulation. In systems where allthe species coexist in a stable manner, in which enrichmentdoes not necessarily lead to destabilization, there is alwaysa critical nutritional value of the secondary algae. Empiricalwork supports the possibility that the unknown nutritional valueof secondary algae takes a value close to the critical one.Furthermore, at the critical nutritional value, the populationresponse in the systems to enrichment is consistent with theobserved trend in natural systems. This suggests that Daphnia–algalsystems in nature can maintain stability in the face of enrichment,without requiring specific assumptions such as spatial heterogeneity.     

Habitat Fragmentation can Modulate Drought Effects on the Plant-soil-microbial System in Mediterranean Holm Oak (<Emphasis Type="Italic">Quercus ilex</Emphasis>) Forests

Ecological transformations derived from habitat fragmentation have led to increased threats to above-ground biodiversity. However, the impacts of forest fragmentation on soils and their microbial communities are not well understood. We examined the effects of contrasting fragment sizes on the structure and functioning of soil microbial communities from holm oak forest patches in two bioclimatically different regions of Spain. We used a microcosm approach to simulate the annual summer drought cycle and first autumn rainfall (rewetting), evaluating the functional response of a plant-soil-microbial system. Forest fragment size had a significant effect on physicochemical characteristics and microbial functioning of soils, although the diversity and structure of microbial communities were not affected. The response of our plant-soil-microbial systems to drought was strongly modulated by the bioclimatic conditions and the fragment size from where the soils were obtained. Decreasing fragment size modulated the effects of drought by improving local environmental conditions with higher water and nutrient availability. However, this modulation was stronger for plant-soil-microbial systems built with soils from the northern region (colder and wetter) than for those built with soils from the southern region (warmer and drier) suggesting that the responsiveness of the soil-plant-microbial system to habitat fragmentation was strongly dependent on both the physicochemical characteristics of soils and the historical adaptation of soil microbial communities to specific bioclimatic conditions. This interaction challenges our understanding of future global change scenarios in Mediterranean ecosystems involving drier conditions and increased frequency of forest fragmentation.     

Costs and benefits of within-group spatial position: a feeding competition model

An animal's within-group spatial position has several important fitness consequences. Risk of predation, time spent engaging in antipredatory behavior and feeding competition can all vary with respect to spatial position. Previous research has found evidence that feeding rates are higher at the group edge in many species, but these studies have not represented the entire breadth of dietary diversity and ecological situations faced by many animals. In particular the presence of concentrated, defendable food patches can lead to increased feeding rates by dominants in the center of the group that are able to monopolize or defend these areas. To fully understand the tradeoffs of within-group spatial position in relation to a variety of factors, it is important to be able to predict where individuals should preferably position themselves in relation to feeding rates and food competition. A qualitative model is presented here to predict how food depletion time, abundance of food patches within a group, and the presence of prior knowledge of feeding sites affect the payoffs of different within-group spatial positions for dominant and subordinate animals. In general, when feeding on small abundant food items, individuals at the front edge of the group should have higher foraging success. When feeding on slowly depleted, rare food items, dominants will often have the highest feeding rates in the center of the group. Between these two extreme points of a continuum, an individual's optimal spatial position is predicted to be influenced by an additional combination of factors, such as group size, group spread, satiation rates, and the presence of producer-scrounger tactics.     

干湿交替对生物滞留系统中氮素功能微生物群落的影响

【目的】为探究生物滞留系统干湿交替下环境因子对氮素功能微生物群落的影响。【方法】应用高通量测序技术(Illumina MiSeq PE300),并以amoA和nirS功能基因为分子标记,对无植物型和植物型生物滞留系统在干湿交替下不同土壤空间位置(种植层、淹没层)的硝化和反硝化细菌的多样性和群落结构进行研究,并对微生物群落与环境因子的相互关系进行相关性分析。【结果】微生物种群的功能基因存在显著的空间差异,相比淹没层,种植层的功能细菌更丰富。种植层的OTUs高于淹没层,而进水再湿润促使两种功能基因在种植层和淹没层的OTUs占比差异性增大。群落组成分析表明,amoA型硝化细菌和nirS型反硝化细菌的优势细菌门均为变形菌门(Proteobacteria)。虽然植物根系对氮素功能微生物的多样性指数影响不显著,但在属水平上,植物系统种植层的反硝化菌群种类高于淹没层,而无植物系统则刚好相反。CCA/RDA分析表明,土壤空间位置是影响硝化和反硝化菌群结构的最重要环境因子。【结论】本研究证实干湿交替运行下生物滞留系统中的氮素功能微生物群落受土壤空间位置、水分含量和植物根系的共同调控,其机制有待进一步研究。     

Complex dynamics of microbial competition in the gradostat

We examine the conditions necessary for the emergence of complex dynamic behavior in systems of microbial competition. In particular, we study the effect of spatial heterogeneity and substrate-inhibition on the dynamics of such a system. This is accomplished through the study of a mathematical model of two microbial populations competing for a single nutrient in a configuration of two interconnected chemostats. Microbial growth is assumed to follow substrate-inhibited kinetics for both species. Such a system with sterile feed has been shown in a previous work to exhibit stable periodic states. In the present work we study the system for the case of non-sterile feed, i.e., when the two species are present in the feed of the chemostats. The analysis is done by numerical bifurcation theory methods. We demonstrate that, in addition to periodic states, the system possesses stable quasi-periodic states resulting from Neimark-Sacker bifurcations of limit cycles. Also, periodic states may undergo successive period doublings leading to periodic states of increasing period and indicating that chaotic states might be possible. Multistability is also observed, consisting in the coexistence of several stable steady states and possibly stable periodic or quasi-periodic states for given operating conditions. It appears that substrate-inhibition, spatial heterogeneity and presence of microorganisms in the inflow are all necessary conditions for complex dynamics to arise in a microbial system of pure and simple competition.     

The Role of Axonal Delay in the Synchronization of Networks of Coupled Cortical Oscillators

Coupled oscillator models use a single phase variable to approximate the voltage oscillation of each neuron during repetitivefiring where the behavior of the model depends on the connectivityand the interaction function chosen to describe the coupling. Weintroduce a network model consisting of a continuum of theseoscillators that includes the effects of spatially decaying coupling and axonal delay. We derive equations for determining the stability of solutions and analyze the network behavior for two different interaction functions. The first is a sine function, and the second is derived from a compartmental model of a pyramidal cell.In both cases, the system of coupled neural oscillators can undergo a bifurcation from synchronous oscillations to waves.The change in qualitative behavior is due to the axonal delay,which causes distant connections to encourage a phase shift between cells. We suggest that this mechanism could contribute to the behavior observed in several neurobiological systems.     

Antagonistic and Synergistic Interactions Among Predators

The structure and dynamics of food webs are largely dependent upon interactions among consumers and their resources. However, interspecific interactions such as intraguild predation and interference competition can also play a significant role in the stability of communities. The role of antagonistic/synergistic interactions among predators has been largely ignored in food web theory. These mechanisms influence predation rates, which is one of the key factors regulating food web structure and dynamics, thus ignoring them can potentially limit understanding of food webs. Using nonlinear models, it is shown that critical aspects of multiple predator food web dynamics are antagonistic/synergistic interactions among predators. The influence of antagonistic/synergistic interactions on coexistence of predators depended largely upon the parameter set used and the degree of feeding niche differentiation. In all cases when there was no effect of antagonism or synergism (a _ij =1.00), the predators coexisted. Using the stable parameter set, coexistence occurred across the range of antagonism/synergism used. However, using the chaotic parameter strong antagonism resulted in the extinction of one or both species, while strong synergism tended to coexistence. Whereas using the limit cycle parameter set, coexistence was strongly dependent on the degree of feeding niche overlap. Additionally increasing the degree of feeding specialization of the predators on the two prey species increased the amount of parameter space in which coexistence of the two predators occurred. Bifurcation analyses supported the general pattern of increased stability when the predator interaction was synergistic and decreased stability when it was antagonistic. Thus, synergistic interactions should be more common than antagonistic interactions in ecological systems.     

Bacterial viability assessment by flow cytometry analysis in soil

Soil microhabitats and their heterogeneity are often considered to be among the most important factors affecting soil biotic communities. The microbial community has become one of the most important links in soil nutrient cycles and trophic components due to its role in biological processes, spatial and temporal dynamics, and physiological adaptation. Sandy-soil desert systems are characterized by fast water infiltration during the rainy season, high salinity, and low moisture availability in the upper soil layers. Plants have developed different ecophysiological adaptations in order to cope with this harsh environment. The Tamarix aphylla is known to be one of the most commonly adapted plants, exhibiting a mechanism for secretion of excess salts as aggregates through its leaves. These leaves aggregate beneath the plant, creating ‘islands of salinity’. Soil biotic components are, therefore, exposed to extreme abiotic stress conditions in this niche. The goal of this study was to examine the effect of T. aphylla on the live/dead bacterial population ratio on a spatial and temporal scale. The results emphasize the effect of abiotic factors, which changed on temporal as well as spatial scales, and also on the size of the active soil bacterial community, which fluctuated between 1.44% and 25.4% in summer and winter, respectively. The results of this study elucidate the importance of moisture availability and the ‘island-of-salinity’ effect on the active microbial community in a sandy desert system.     

Spatial effects favour the evolution of niche construction

We present an individual-based, spatial implementation of an existing two-locus population genetic model of niche construction. Our analysis reveals that, across a broad range of conditions, niche-construction traits can drive themselves to fixation by simultaneously generating selection that favours ‘recipient’ trait alleles and linkage disequilibrium between niche-construction and recipient trait alleles. The effect of spatiality is key, since it is the local, resource-mediated interaction between recipient and niche-constructing loci which gives rise to gene linkage. Spatial clustering effects point to a possible mechanism by which an initially rare recipient trait whose selection depends on niche construction could establish in an otherwise hostile environment. The same mechanism could also lead to the spread of an established niche-constructing colony. Similar phenomena are observed in the spatial modelling of two species ‘engineering webs’. Here, the activities of two niche-constructing species can combine to drive a particular recipient trait to fixation, or in certain circumstances, maintain the presence of polymorphisms through the preservation of otherwise deleterious alleles. This may have some relevance to ecosystem stability and the maintenance of genetic variation, where the frequencies of key resources are affected by the niche-constructing activities of more than one species. Our model suggests that the stability of multi-species webs in natural populations may increase as the complexity of species–environment interactions increases.