Persistence in seasonally forced epidemiological models

In this paper we address the persistence of a class of seasonally forced epidemiological models. We use an abstract theorem about persistence by Fonda. Five different examples of application are given.     

Consequences of symbiosis for food web dynamics

Basic Lotka-Volterra type models in which mutualism (a type of symbiosis where the two populations benefit both) is taken into account, may give unbounded solutions. We exclude such behaviour using explicit mass balances and study the consequences of symbiosis for the long-term dynamic behaviour of a three species system, two prey and one predator species in the chemostat. We compose a theoretical food web where a predator feeds on two prey species that have a symbiotic relationships. In addition to a species-specific resource, the two prey populations consume the products of the partner population as well. In turn, a common predator forages on these prey populations. The temporal change in the biomass and the nutrient densities in the reactor is described by ordinary differential equations (ODE). Since products are recycled, the dynamics of these abiotic materials must be taken into account as well, and they are described by odes in a similar way as the abiotic nutrients. We use numerical bifurcation analysis to assess the long-term dynamic behaviour for varying degrees of symbiosis. Attractors can be equilibria, limit cycles and chaotic attractors depending on the control parameters of the chemostat reactor. These control parameters that can be experimentally manipulated are the nutrient density of the inflow medium and the dilution rate. Bifurcation diagrams for the three species web with a facultative symbiotic association between the two prey populations, are similar to that of a bi-trophic food chain; nutrient enrichment leads to oscillatory behaviour. Predation combined with obligatory symbiotic prey-interactions has a stabilizing effect, that is, there is stable coexistence in a larger part of the parameter space than for a bi-trophic food chain. However, combined with a large growth rate of the predator, the food web can persist only in a relatively small region of the parameter space. Then, two zero-pair bifurcation points are the organizing centers. In each of these points, in addition to a tangent, transcritical and Hopf bifurcation a global heteroclinic bifurcation is emanating. This heteroclinic cycle connects two saddle equilibria where the predator is absent. Under parameter variation the period of the stable limit cycle goes to infinity and the cycle tends to the heteroclinic cycle. At this global bifurcation point this cycle breaks and the boundary of the basin of attraction disappears abruptly because the separatrix disappears together with the cycle. As a result, it becomes possible that a stable two-nutrient–two-prey population system becomes unstable by invasion of a predator and eventually the predator goes extinct together with the two prey populations, that is, the complete food web is destroyed. This is a form of over-exploitation by the predator population of the two symbiotic prey populations. When obligatory symbiotic prey-interactions are modelled with Liebigs minimum law, where growth is limited by the most limiting resource, more complicated types of bifurcations are found. This results from the fact that the Jacobian matrix changes discontinuously with respect to a varying parameter when another resource becomes most limiting.Revised version: 21 July 2003     

Chaotic dynamics of a food web in a chemostat

We analyze a mathematical model of a simple food web consisting of one predator and two prey populations in a chemostat. Monod's model is employed for the dependence of the specific growth rates of the two prey populations on the concentration of the rate-limiting substrate and a generalization of Monod's model for the dependence of the specific growth rate of the predator on the concentrations of the prey populations. We use numerical bifurcation techniques to determine the effect of the operating conditions of the chemostat on the dynamics of the system and construct its operating diagram. Chaotic behavior resulting from successive period doublings is observed. Multistability phenomena of coexistence of steady and periodic states at the same operating conditions are also found.     

Rapid contemporary evolution and clonal food web dynamics

Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most readily explored in systems with short generations and simple genetics. Asexual and cyclically parthenogenetic organisms such as microalgae, cladocerans and rotifers, which frequently dominate freshwater plankton communities, meet these requirements. Multiple clonal lines can coexist within each species over extended periods, until either fixation occurs or a sexual phase reshuffles the genetic material. When clones differ in traits affecting interspecific interactions, within-species clonal dynamics can have major effects on the population dynamics. We first consider a simple predator–prey system with two prey genotypes, parametrized with data from a well-studied experimental system, and explore how the extent of differences in defence against predation within the prey population determine dynamic stability versus instability of the system. We then explore how increased potential for evolution affects the community dynamics in a more general community model with multiple predator and multiple prey genotypes. These examples illustrate how microevolutionary ‘details’ that enhance or limit the potential for heritable phenotypic change can have significant effects on contemporaneous community-level dynamics and the persistence and coexistence of species.     

群落水平食物网能流季节演替特征

稳定碳、氮同位素比值分析技术是研究生态系统中物质循环与能量流动的有效技术.δ13C可以用来判断食物网中不同生物的能量来源;δ15N主要用于确定生物在食物网中所处的营养位置.通常用δ13C—δ15N图来表征某一特定时间或空间的食物网结构,但是这种方法在比较不同时间和空间食物网结构中功效较差.同时这种定性描述食物网结构也无法满足食物网复杂变化下的假说验证.应用环形统计方法,以太湖梅梁湾鱼类群落为例,定量评价了群落水平食物网能流季节演替特征.结果表明太湖梅梁湾鱼类营养生态位移动的季节特征明显.进一步物种水平分析结果表明,各种鱼类角度和幅度随季节均有变化.Rayleigh检验结果表明,群落中不同种类在秋冬、冬春和夏秋均有显著的一致的方向变化;而春夏期间不显著.Watson-William检验结果表明,群落水平的鱼类营养生态位移动在秋冬和冬春季节转换中有显著差异.引起鱼类群落水平营养生态位在食物网空间中季节性移动的主要因素为可利用资源稳定同位素的季节变化和不同鱼类种群自身的食性季节性转变.同时,由于梅梁湾食物网鱼类群落杂食性水平高,季节性浮游初级生产力成为食物网能量流动的重要驱动作用.因此,在富营养化生态系统中,食物网群落水平营养生态位季节波动也暗示了系统稳定性的下降.定量评价食物网变化有助于认识和理解食物网结构与功能在生态学和生态系统管理等方面的重要.     

Successional dynamics of the cultivated kelp microbiome

Kelp are important primary producers that are colonized by diverse microbes that can have both positive and negative effects on their hosts. The kelp microbiome could support the burgeoning kelp cultivation sector by improving host growth, stress tolerance, and resistance to disease. Fundamental questions about the cultivated kelp microbiome still need to be addressed before microbiome-based approaches can be developed. A critical knowledge gap is how cultivated kelp microbiomes change as hosts grow, particularly following outplanting to sites that vary in abiotic conditions and microbial source pools. In this study we assessed if microbes that colonize kelp in the nursery stage persist after outplanting. We characterized microbiome succession over time on two species of kelp, Alaria marginata and Saccharina latissima, outplanted to open ocean cultivation sites in multiple geographic locations. We tested for host-species specificity of the microbiome and the effect of different abiotic conditions and microbial source pools on kelp microbiome stability during the cultivation process. We found the microbiome of kelp in the nursery is distinct from that of outplanted kelp. Few bacteria persisted on kelp following outplanting. Instead, we identified significant microbiome differences correlated with host species and microbial source pools at each cultivation site. Microbiome variation related to sampling month also indicates that seasonality in host and/or abiotic factors may influence temporal succession and microbiome turnover in cultivated kelps. This study provides a baseline understanding of microbiome dynamics during kelp cultivation and highlights research needs for applying microbiome manipulation to kelp cultivation.     

Environmental fluctuations can stabilize food web dynamics by increasing synchrony

Natural food webs are species-rich, but classical theory suggests that they should be unstable and extinction-prone. Asynchronous fluctuations in the densities of competing consumers can stabilize food web dynamics in constant environments. However, environmental fluctuations often synchronize dynamics in nature. Using the same 'diamond-shape' food web model first used to demonstrate the stabilizing effects of asynchrony in constant environments, we show that weak-to-moderate environmentally induced fluctuations in consumer mortality rates stabilize food webs while disrupting asynchrony. Synchrony actually promotes stability because: (i) synchronous declines in consumer density reduce the maximum abundance of top predators and (ii) resource competition quickly converts synchronous increases in consumer density into synchronous declines. These results are robust to details of food web topology and the implementation of environmental fluctuations. The fluctuation strengths that enhance stability are within the range experienced naturally by many species, suggesting that stabilization via environmental fluctuations is a realistic possibility.     

The effects of stochastic population dynamics on food web structure

We develop a stochastic, individual-based model for food web simulation which in the large-population limit reduces to the well-studied Webworld model, which has been used to successfully construct model food webs with several realistic features. We demonstrate that an almost exact match is found between the population dynamics in fixed food webs, and that the demographic fluctuations have systematic effects when the new model is used to construct food webs due to the presence of species with small populations.     

Plankton population dynamics: food web interactions and abiotic constraints

1. In this introduction, I try to follow some developments in plankton ecology, how they have led to current research topics, and how the contributions in this issue of Freshwater Biology are related to these fields of research.
2. Due to several favourable features, such as small size, short generation time and a relatively homogeneous habitat, planktonic organisms remain ideal subjects for theoretical and experimental population ecology.
3. Important current research topics involve: (1) the control of plankton communities by external abiotic factors; (2) bottom-up (limitation by resources) and top-down (control by predators) effects in the food web; (3) the importance of dormant resting stages and benthic–pelagic coupling in plankton dynamics; (4) costs and benefits of the mixotrophic strategy, i.e. the ability to combine a phototrophic and a phagotrophic mode of nutrition.     

Habitat structural complexity mediates food web dynamics in a freshwater macrophyte community

A considerable amount of research has investigated the influence of habitat structure on predator success, yet few studies have explored the implications for community structure and food-web dynamics. The relative importance of macrophyte structure and fish predation on the composition of the macroinvertebrate and periphyton communities in a lowland river was investigated using a multifactorial caging experiment. We hypothesised that: (1) fish predators are less effective in a more structurally complex macrophyte analogue; (2) strong direct and indirect effects of fish predators (e.g. trophic cascades) are less likely to occur in a structurally complex habitat; and (3) the strength of these patterns is influenced by the composition of the prevailing community assemblage. We measured the abundance and composition of the macroinvertebrate and periphyton communities associated with three different-shaped macrophyte analogues, under different fish predator treatments and at different times. Macrophyte analogue architecture had strong, consistent effects on both the macroinvertebrate and periphyton communities; both were most abundant and diverse on the most structurally complex plant analogue. In contrast, the fish predators affected only a subset of the macroinvertebrate community and there was a suggestion of minor indirect effects on periphyton community composition. Contrary to expectations, the fish predators had their strongest effects in the most structurally complex macrophyte analogue. We conclude that in this system, macrophyte shape strongly regulates the associated freshwater assemblage, resulting in a diverse community structure less likely to exhibit strong effects of fish predation.     

Seasonal subsidy stabilizes food web dynamics: Balance in a heterogeneous landscape

Resource subsidies from external habitats can substantially affect the food web dynamics of local habitats. In this paper, we explore a mathematical model that is tailored for a stream food web, studied by Nakano and colleagues, in which consumers, in situ prey and subsidies all show seasonal fluctuation. The model reveals that the food web dynamics are stabilized if subsidies increase in summer when in situ productivity is low. Consumer dynamics are stabilized because subsidies complement seasonal resource deficiency. In situ prey dynamics are stabilized because subsidies indirectly balance the predation pressure by consumers, with seasonal change in prey carrying capacity. In summer when prey carrying capacity is low, seasonally abundant subsidies indirectly decrease predation pressure, whereas in winter, with high prey carrying capacity, scarce subsidies increase the predation pressure. Our results suggest that temporal productivity differences between spatially linked habitats are important to promote the stability of food web dynamics in a landscape context.     

Simulating food web dynamics along a gradient: quantifying human influence

Realistically parameterized and dynamically simulated food-webs are useful tool to explore the importance of the functional diversity of ecosystems, and in particular relations between the dynamics of species and the whole community. We present a stochastic dynamical food web simulation for the Kelian River (Borneo). The food web was constructed for six different locations, arrayed along a gradient of increasing human perturbation (mostly resulting from gold mining activities) along the river. Along the river, the relative importance of grazers, filterers and shredders decreases with increasing disturbance downstream, while predators become more dominant in governing eco-dynamics. Human activity led to increased turbidity and sedimentation which adversely impacts primary productivity. Since the main difference between the study sites was not the composition of the food webs (structure is quite similar) but the strengths of interactions and the abundance of the trophic groups, a dynamical simulation approach seemed to be useful to better explain human influence. In the pristine river (study site 1), when comparing a structural version of our model with the dynamical model we found that structurally central groups such as omnivores and carnivores were not the most important ones dynamically. Instead, primary consumers such as invertebrate grazers and shredders generated a greater dynamical response. Based on the dynamically most important groups, bottom-up control is replaced by the predominant top-down control regime as distance downstream and human disturbance increased. An important finding, potentially explaining the poor structure to dynamics relationship, is that indirect effects are at least as important as direct ones during the simulations. We suggest that our approach and this simulation framework could serve systems-based conservation efforts. Quantitative indicators on the relative importance of trophic groups and the mechanistic modeling of eco-dynamics could greatly contribute to understanding various aspects of functional diversity.     

Biological vs. physical mixing effects on benthic food web dynamics

Biological particle mixing (bioturbation) and solute transfer (bio-irrigation) contribute extensively to ecosystem functioning in sediments where physical mixing is low. Macrobenthos transports oxygen and organic matter deeper into the sediment, thereby likely providing favourable niches to lower trophic levels (i.e., smaller benthic animals such as meiofauna and bacteria) and thus stimulating mineralisation. Whether this biological transport facilitates fresh organic matter assimilation by the metazoan lower part of the food web through niche establishment (i.e., ecosystem engineering) or rather deprives them from food sources, is so far unclear. We investigated the effects of the ecosystem engineers Lanice conchilega (bio-irrigator) and Abra alba (bioturbator) compared to abiotic physical mixing events on survival and food uptake of nematodes after a simulated phytoplankton bloom. The (13)C labelled diatom Skeletonema costatum was added to 4 treatments: (1) microcosms containing the bioturbator, (2) microcosms containing the bio-irrigator, (3) control microcosms and (4) microcosms with abiotic manual surface mixing. Nematode survival and subsurface peaks in nematode density profiles were most pronounced in the bio-irrigator treatment. However, nematode specific uptake (Δδ(13)C) of the added diatoms was highest in the physical mixing treatment, where macrobenthos was absent and the diatom (13)C was homogenised. Overall, nematodes fed preferentially on bulk sedimentary organic material rather than the added diatoms. The total C budget (μg C m(-2)), which included TO(13)C remaining in the sediment, respiration, nematode and macrobenthic uptake, highlighted the limited assimilation by the metazoan benthos and the major role of bacterial respiration. In summary, bioturbation and especially bio-irrigation facilitated the lower trophic levels mainly over the long-term through niche establishment. Since the freshly added diatoms represented only a limited food source for nematodes, the macrobenthic effect was more pronounced in niche establishment than the negative structuring effects such as competition.     

Spatiotemporal food web dynamics along a desert riparian–upland transition

Increased awareness of spatiotemporal variation in species interactions has motivated the study of temporally-resolved food web dynamics at the landscape level. Empiricists have focused attention on cross-habitat flows of materials, nutrients, and prey, largely ignoring the movement of predators between habitats that differ in productivity (and how predators integrate pulses in resource availability over time). We set out to study seasonal variation in food web interactions between mammalian carnivores and their rodent prey along a riparian–upland gradient in semi-arid southeastern Arizona which features both spatial and temporal heterogeneity in resource availability. Specifically, we tested whether mammalian carnivores spill over from productive, near-river habitats into adjacent, desert-scrub habitats; and if they do, to document the effects of this spillover on rodent communities. Furthermore, we examined seasonal variation in top-down effects by measuring changes in carnivore diet and distribution patterns and rodent populations over time. The results indicate that carnivores track seasonally-abundant resources across the landscape, varying both their diet and movement patterns. In turn, desert-scrub rodent population dynamics track seasonal shifts in carnivore habitat use but not resource availability, suggesting that predation plays a role in structuring rodent communities along the San Pedro River. Further evidence comes from data on rodent community composition, which differs between desert-scrub habitats near and far from the river, despite similarities in resource availability. Our data also suggest that seasonal omnivory helps predators survive lean times, increasing their effects on prey populations. Taken together, these results underscore the importance of spatiotemporal variation in species interactions, highlighting the complexity of natural systems and the need for further detailed studies of food web dynamics.     

The ecology of chytrids in aquatic ecosystems: roles in food web dynamics

Chytrids are very important components of freshwater ecosystems, but the ecological significance of this group of fungi is not well understood. This review considers some of the significant environmental factors affecting growth and population composition of chytrids in aquatic habitats. The physical factors include primarily salinity, dissolved oxygen concentration and temperature. The biological factors include the role of chytrids as saprobes and parasites and methods of dispersal of propagules throughout the ecosystem. Dispersal depends upon both zoospores for short range and whole thalli for long range dispersal. Five roles for chytrids in food-web dynamics are proposed: (1) chytrid zoospores are a good food source for zooplankton, (2) chytrids decompose particulate organic matter, (3) chytrids are parasites of aquatic plants, (4) chytrids are parasites of aquatic animals and (5) chytrids convert inorganic compounds into organic compounds. New molecular methods for analysis of chytrid diversity in aquatic environments have the potential to provide accurate quantitative data necessary for better understanding of ecological processes in aquatic ecosystems.     

The significance of partial migration for food web and ecosystem dynamics

Migration is ubiquitous and can strongly shape food webs and ecosystems. Less familiar, however, is that the majority of life cycle, seasonal and diel migrations in nature are partial migrations: only a fraction of the population migrates while the other individuals remain in their resident ecosystem. Here, we demonstrate different impacts of partial migration rendering it fundamental to our understanding of the significance of migration for food web and ecosystem dynamics. First, partial migration affects the spatiotemporal distribution of individuals and the food web and ecosystem-level processes they drive differently than expected under full migration. Second, whether an individual migrates or not is regularly correlated with morphological, physiological, and/or behavioural traits that shape its food-web and ecosystem-level impacts. Third, food web and ecosystem dynamics can drive the fraction of the population migrating, enabling the potential for feedbacks between the causes and consequences of migration within and across ecosystems. These impacts, individually and in combination, can yield unintuitive effects of migration and drive the dynamics, diversity and functions of ecosystems. By presenting the first full integration of partial migration and trophic (meta-)community and (meta-)ecosystem ecology, we provide a roadmap for studying how migration affects and is affected by ecosystem dynamics in a changing world.     

Modeling the microbial food web

Models of the microbial food web have their origin in the debate over the importance of bacteria as an energetic subsidy for higher trophic levels leading to harvestable fisheries. Conceptualization of the microbial food web preceded numerical models by 10–15 years. Pomeroy's work was central to both efforts. Elements necessary for informative and comprehensive models of microbial loops in plankton communities include coupled carbon and nitrogen flows utilizing a size-based approach to structuring and parameterizing the food web. Realistic formulation of nitrogen flows requires recognition that both nitrogenous and nonnitrogenous organic matter are important substrates for bacteria. Nitrogen regeneration driven by simple mass-specific excretion constants seems to overestimate the role of bacteria in the regeneration process. Quantitative assessment of the link-sink question, in which the original loop models are grounded, requires sophisticated analysis of size-based trophic structures. The effects of recycling complicate calculation of the link between bacteria or dissolved organic matter and mesozooplankton, and indirect effects show that the link might be much stronger than simple analyses have suggested. Examples drawn from a series of oceanic mixed layer plankton models are used to illustrate some of these points. Single-size class models related to traditional P-Z-N approaches are incapable of simulating bacterial biomass cycles in some locations (e.g., Bermuda) but appear to be adequate for more strongly seasonal regimes at higher latitudes.     

Nitrogen dynamics in seasonally flooded soils in the Amazon floodplain

Large areas of the Amazon are subject to seasonal flooding due to water level changes of the river. This flood pulse causes rapidly changing conditions for microorganisms living in the soils which affects the cycling of nitrogen in the ecosystem. An understanding of the nitrogen dynamics in the seasonally flooded soils is essential for the development of productive and sustainable management concepts. We measured nitrogen concentrations, denitrifier enzyme activity (DEA), cell numbers of nitrifying and denitrifying bacteria, respiration, pH and total carbon in the seasonally flooded soils over one entire annual hydrological cycle. By comparing three sites with different vegetation (forest, aquatic macrophyte stand and bare sediment with annual herbs) we assessed the effect of vegetation on soil nitrogen dynamics. Inorganic nitrogen was always dominated by ammonium indicating reduced conditions in the soil even during the terrestrial phase. Although conditions were generally poor for nitrification we observed high numbers of nitrifying bacteria between 10⁴ and 10⁷cells g^–1. Pulses of ammonium as well as high DEA were observed during the transition periods between aquatic and terrestrial phase. Thus the alternation between aquatic and terrestrial phase promotes nitrogen mineralization and denitrification in the soils. There were no plausible correlations between microbial activities and numbers with soil physical or chemical parameters except a relation between the numbers of nitrate reducing bacteria and soil moisture (R² = 0.81) and ammonium (R² = 0.92) at one site. This shows the complex regulation patterns in this habitat. Different vegetation did not alter the general patterns of nitrogen dynamics but the absolute extend of fluctuations. We conclude that both the soil physical and chemical changes directly caused by the flood pulse and the vegetation have a great impact on microbial nitrogen turnover in the soils. The effects of the flood pulse can be buffered by a fine soil texture or a litter layer which prevents desiccation of the soil during the terrestrial phase.     

The influence of predator--prey population dynamics on the long-term evolution of food web structure

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large-scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organized criticality.