Small-amplitude cycles emerge from stage-structured interactions in Daphnia-algal systems

Zooplankton as a model to study the effects of anthropogenic sounds on aquatic ecosystems

There is a growing interest in the impact of acoustic pollution on aquatic ecosystems. Currently, research has primarily focused on hearing species, particularly fishes and mammals. However, species from lower trophic levels, including many invertebrates, are less studied despite their ecological significance. Among these taxa, studies examining the effects of sound on holozooplankton are extremely rare. This literature review examines the effects of sound on both marine and freshwater zooplankton. It highlights two differences: the few used organisms and the types of sound source. Marine studies focus on the effects of very intense acute sound on copepods, while freshwater studies focus on less intense chronic sound on cladocerans. But, in both, various negative effects are reported. The effects of sound remain largely unknown, although previous studies have shown that zooplankton can detect vibrations using mechanoreceptors. The perception of their environment can be affected by sounds, potentially causing stress. Limited research suggests that sound may affect the physiology, behaviour, and fitness of zooplankton. Following this review, I highlight the potential to use methods from ecology, ecotoxicology, and parasitology to study the effects of sound at the individual level, including changes in physiology, development, survival, and behaviour. Responses to sound, which could alter species interactions and population dynamics, are expected to have larger-scale implications with bottom-up effects, such as changes in food web dynamics and ecosystem functioning. To improve the study of the effect of sound, to better use zooplankton as biological models and as bioindicators, researchers need to better understand how they perceive their acoustic environment. Consequently, an important challenge is the measurement of particle motion to establish useable dose-response relationships and particle motion soundscapes.

Thermal dependence of Daphnia life history reveals asymmetries between key vital rates

Temperature variation affects virtually every aspect of ectotherms' ecological performance, such as their foraging rate, reproduction, and survival. Although these changes influence what happens at higher levels of organizations, such as populations and communities, qualitative changes in dynamics usually require some degree of asymmetry between key vital rates, i.e. that different vital rates, such as growth, development, fecundity and mortality rates, respond differently to temperature. In order to identify possible asymmetries among vital rates and/or life stages, we characterized the thermal response of individuals a clone of Daphnia sinensis, drawn from a high-mountain environment in Taiwan, and examined the temperature dependence of growth, maturation, reproduction, and mortality rates, as well as fitness measures (r and R₀) at eight temperatures. Daphnia sinensis was able to maintain reproductive success over a broad range of temperatures, much wider than the one experienced in its environment. However, negative effects of temperature were perceptible at temperatures much lower than the highest one at which they can achieve reproductive success. Adult mortality greatly increased for temperatures above 23 °C, and other vital rates started to decelerate, resulting in a large drop in lifetime reproductive success. This finding implies that D. sinensis may be able to persist over a wide range of temperatures, but also that it may become more sensitive to the detrimental effect of species interactions at increased temperatures. Different vital rates responded relatively similarly at low temperatures, but the degree of asymmetry among these rates was much more pronounced at higher temperatures. In particular, rates associated with adult performance decelerated more strongly than juveniles' rates. These findings indicate that elevated temperatures affect the balance between juvenile and adult performance, which is known to have a crucial role in Daphnia population dynamics. We discuss the implications of these results for the dynamics of structured populations.

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

Environmental seasonality on predator-prey systems under nutrient and toxicant constraints

Bioaccumulation of toxicants in aquatic food webs can pose risks to ecosystem function and human health. Toxicant models of aquatic ecosystems can be improved by incorporating realistic environmental impacts such as nutrient availability and seasonality. It is well known that the carrying capacity of predator-prey systems can vary seasonally due to environmental cycles resulting from natural and human activities. As such, incorporating seasonal variation in the carrying capacity of a predator-prey system provides a better understanding of the underlying population dynamics bioaccumulation of toxicants. Here, we develop a seasonally varied predator-prey model subject to concurrent nutrient and toxicant stressors. We investigate the effects of seasonality on population dynamics to increase understanding of the complex governing processes of the trophic transfer of nutrients, energy, and toxicants. We observe that the strength of seasonality can shift solutions from periodic to quasi-periodic and models that neglect environmental seasonality may be under-predicting adverse effects of toxicity.

Effect of copper contamination on zooplankton epidemics

Infectious disease and chemical contamination are increasingly becoming vital issues in many ecosystems. However, studies integrating the two are surprisingly rare. Contamination not only affects the inherent host-resource interaction which influences the epidemic process but may also directly affect epidemiological traits via changes in host's behaviour. The fact that heavy metal such as copper is also an essential trace element for organisms, further increase complexity which make predicting the resultant effect of contamination and disease spread difficult. Motivated by this, we model the effect of copper enrichment on a phytoplankton-zooplankton-fungus system. We show that extremely deficient or toxic copper may have a destabilizing effect on the underlying host-resource dynamics due to increased relative energy fluxes as a result of low host mortality due to fish predation. Further, on incorporating disease into the system, we find that the system can become disease-free for an intermediate range of copper concentration whereas it may persist for very less copper enrichment. Also, we predict that there may exist vulnerable regions of copper concentration near the toxic and deficient levels, where the parasite can invade the system for a comparatively lower spore yield. Overall, our results demonstrate that, the effect of contamination may be fundamental to understanding disease progression in community ecology.

Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods

We consider a mathematical model describing the maturation process of stem cells up to fully mature cells. The model is formulated as a differential equation with state-dependent delay, where maturity is described as a continuous variable. The maturation rate of cells may be regulated by the amount of mature cells and, moreover, it may depend on cell maturity: we investigate how the stability of equilibria is affected by the choice of the maturation rate. We show that the principle of linearised stability holds for this model, and develop some analytical methods for the investigation of characteristic equations for fixed delays. For a general maturation rate we resort to numerical methods and we extend the pseudospectral discretisation technique to approximate the state-dependent delay equation with a system of ordinary differential equations. This is the first application of the technique to nonlinear state-dependent delay equations, and currently the only method available for studying the stability of equilibria by means of established software packages for bifurcation analysis. The numerical method is validated on some cases when the maturation rate is independent of maturity and the model can be reformulated as a fixed-delay equation via a suitable time transformation. We exploit the analytical and numerical methods to investigate the stability boundary in parameter planes. Our study shows some drastic qualitative changes in the stability boundary under assumptions on the model parameters, which may have important biological implications.

Assessing the direct and indirect effects of food provisioning and nutrient enrichment on wildlife infectious disease dynamics

Anthropogenic resource supplementation can shape wildlife disease directly by altering the traits and densities of hosts and parasites or indirectly by stimulating prey, competitor or predator species. We first assess the direct epidemiological consequences of supplementation, highlighting the similarities and differences between food provisioning and two widespread forms of nutrient input: agricultural fertilization and aquatic nutrient enrichment. We then review an aquatic disease system and a general model to assess whether predator and competitor species can enhance or overturn the direct effects of enrichment. All forms of supplementation can directly affect epidemics by increasing host population size or altering parasite production within hosts, but food provisioning is most likely to aggregate hosts and increase parasite transmission. However, if predators or competitors increase in response to supplementation, they could alter resource-fuelled outbreaks in focal hosts. We recommend identifying the traits of hosts, parasites or interacting species that best predict epidemiological responses to supplementation and evaluating the relative importance of these direct and indirect mechanisms. Theory and experiments should examine the timing of behavioural, physiological and demographic changes for realistic, variable scenarios of supplementation. A more integrative view of resource supplementation and wildlife disease could yield broadly applicable disease management strategies.This article is part of the theme issue 'Anthropogenic resource subsidies and host-parasite dynamics in wildlife'.

The impact of development on patterns of nutrient limitation

Development is often accompanied by major changes in an organism's functioning and in the way it interacts with its environment. We consider how developmental events such as allocation changes at maturity, ontogenetic diet shift or metamorphosis may affect the likelihood and nature of nutrient limitation and explore the consequences of these changes in nutrient limitation for individual life history and patterns of biomass production.To this purpose, we develop a general model for individual growth and reproduction that is based on the assumption that biomass production and metabolism require several nutrients and that individuals may require them in different proportion at different stages of their lives.We parameterize this model for Daphnia based on its physiological requirements for carbon (C) and phosphorus (P). Growth and reproduction have different nutrient requirements, and this affects the likelihood of C vs. P limitation of differently sized individuals. This translates into a size-dependent threshold elemental ratio (TER), with a difference of up to twofold between juveniles and adults, a difference comparable to measured interspecific differences.The main implications of these findings are that, at the population level, co-limitation of biomass production by several nutrients is likely to occur under a wide range of food qualities. In addition, different regimes of nutrient limitation strongly influence the relative difference in biomass production of differently sized individuals, which has been shown to be a major driver of population and community dynamics. Our results point to development as a key determinant of a population's response to food quality. A http://onlinelibrary.wiley.com/doi/10.1111/1365-2435.13101/suppinfo is available for this article.

Rapid evolution leads to differential population dynamics and top-down control in resurrected Daphnia populations

There is growing evidence of rapid genetic adaptation of natural populations to environmental change, opening the perspective that evolutionary trait change may subsequently impact ecological processes such as population dynamics, community composition, and ecosystem functioning. To study such eco‐evolutionary feedbacks in natural populations, however, requires samples across time. Here, we capitalize on a resurrection ecology study that documented rapid and adaptive evolution in a natural population of the water flea Daphnia magna in response to strong changes in predation pressure by fish, and carry out a follow‐up mesocosm experiment to test whether the observed genetic changes influence population dynamics and top‐down control of phytoplankton. We inoculated populations of the water flea D. magna derived from three time periods of the same natural population known to have genetically adapted to changes in predation pressure in replicate mesocosms and monitored both Daphnia population densities and phytoplankton biomass in the presence and absence of fish. Our results revealed differences in population dynamics and top‐down control of algae between mesocosms harboring populations from the time period before, during, and after a peak in fish predation pressure caused by human fish stocking. The differences, however, deviated from our a priori expectations. An S‐map approach on time series revealed that the interactions between adults and juveniles strongly impacted the dynamics of populations and their top‐down control on algae in the mesocosms, and that the strength of these interactions was modulated by rapid evolution as it occurred in nature. Our study provides an example of an evolutionary response that fundamentally alters the processes structuring population dynamics and impacts ecosystem features.

Continuous Structured Population Models for Daphnia magna

We continue our efforts in modeling Daphnia magna, a species of water flea, by proposing a continuously structured population model incorporating density-dependent and density-independent fecundity and mortality rates. We collected new individual-level data to parameterize the individual demographics relating food availability and individual daphnid growth. Our model is fit to experimental data using the generalized least-squares framework, and we use cross-validation and Akaike Information Criteria to select hyper-parameters. We present our confidence intervals on parameter estimates.

Integrating lipid storage into general representations of fish energetics

Fish, even of the same species, can exhibit substantial variation in energy density (energy per unit wet weight). Most of this variation is due to differences in the amount of storage lipids. In addition to their importance as energy reserves for reproduction and for survival during unfavourable conditions, the accumulation of lipids represents a large energetic flux for many species, so figuring out how this energy flux is integrated with other major energy fluxes (growth, reproduction) is critical for any general theory of organismal energetics. Here, we synthesize data from a wide range of fish species and identify patterns of intraspecific variation in energy storage, and use these patterns to formulate a general model of energy allocation between growth, lipid storage and reproduction in fishes. From the compiled data we identified two patterns: (1) energy density increases with body size during the juvenile period, but is invariant with body size within the adult size range for most species, and (2) energy density changes across seasons, with depletion over winter, but increases fastest in periods of transition between favourable and unfavourable conditions for growth (i.e. fall). Based on these patterns we propose DEBlipid, a simple, general model of energy allocation that is closely related to a simplified version of Dynamic Energy Budget theory, DEBkiss. The crux of the model is that assimilated energy is partitioned, with κ fraction of energy allocated to pay maintenance costs first, and the surplus allocated to growth, and 1 - κ fraction of assimilated energy is allocated to accumulating storage lipids during the juvenile phase, and later to reproduction as adults. This mechanism, in addition to capturing the two patterns that motivated the model, was able to predict lipid dynamics in a novel context, the migration of anadromous fish from low-food freshwater to high-food marine environments. Furthermore, the model was used to explain intra and interspecific variation in reproductive output based on patterns of lipid accumulation as juveniles. Our results suggest that many seemingly complex, adaptive energy allocation strategies in response to ontogeny, seasonality and habitat quality can emerge from a simple physiological heuristic.

A fitness trade-off between seasons causes multigenerational cycles in phenotype and population size

Although seasonality is widespread and can cause fluctuations in the intensity and direction of natural selection, we have little information about the consequences of seasonal fitness trade-offs for population dynamics. Here we exposed populations of Drosophila melanogaster to repeated seasonal changes in resources across 58 generations and used experimental and mathematical approaches to investigate how viability selection on body size in the non-breeding season could affect demography. We show that opposing seasonal episodes of natural selection on body size interacted with both direct and delayed density dependence to cause populations to undergo predictable multigenerational density cycles. Our results provide evidence that seasonality can set the conditions for life-history trade-offs and density dependence, which can, in turn, interact to cause multigenerational population cycles.

A paradox in individual-based models of populations

The standard dynamic energy budget model is widely used to describe the physiology of individual animals. It assumes that assimilation rate scales with body surface area, whereas maintenance rate scales with body volume. When the model is used as the building block of a population model, only limited dynamical behaviour, the so-called juvenile-driven cycles, emerges. The reason is that in the model juveniles are competitively superior over adults, because juveniles have a higher surface area-to-volume ratio. Maintenance requirements for adults are therefore relatively large, and a reduced assimilation rate as a result of lowered food levels will easily become insufficient. Here, an alternative dynamic energy budget model is introduced that gives rise to adult-driven cycles, which may be closer to what is often observed in reality. However, this comes at the price of a rather odd description of the individual, in that maintenance scales with body area and assimilation rate with body volume, resulting in unbounded exponential body growth. I make a plea to solve the paradox and come up with reliable descriptions at both the individual and the population level.

Identifying consumer-resource population dynamics using paleoecological data

Ecologists have long been fascinated by cyclic population fluctuations, because they suggest strong interactions between exploiter and victim species. Nonetheless, even for populations showing high-amplitude fluctuations, it is often hard to identify which species are the key drivers of the dynamics, because data are generally only available for a single species. Here, we use a paleoecological approach to investigate fluctuations in the midge population in Lake Mývatn, Iceland, which ranges over several orders of magnitude in irregular, multigeneration cycles. Previous circumstantial evidence points to consumer-resource interactions between midges and their primary food, diatoms, as the cause of these high-amplitude fluctuations. Using a pair of sediment cores from the lake, we reconstructed 26 years of dynamics of midges using egg remains and of algal groups using diagnostic pigments. We analyzed these data using statistical methods that account for both the autocorrelated nature of paleoecological data and measurement error caused by the mixing of sediment layers. The analyses revealed a signature of consumer-resource interactions in the fluctuations of midges and diatoms: diatom abundance (as inferred from biomarker pigment diatoxanthin) increased when midge abundance was low, and midge abundance (inferred from egg capsules) decreased when diatom abundance was low. Similar patterns were not found for pigments characterizing the other dominant primary producer group in the lake (cyanobacteria), subdominant algae (cryptophytes), or ubiquitous but chemically unstable biomarkers of total algal abundance (chlorophyll a); however, a significant but weaker pattern was found for the chemically stable indicator of total algal populations (β-carotene) to which diatoms are the dominant contributor. These analyses provide the first paleoecological evaluation of specific trophic interactions underlying high amplitude population fluctuations in lakes.

Host age modulates within-host parasite competition

In many host populations, one of the most striking differences among hosts is their age. While parasite prevalence differences in relation to host age are well known, little is known on how host age impacts ecological and evolutionary dynamics of diseases. Using two clones of the water flea Daphnia magna and two clones of its bacterial parasite Pasteuria ramosa, we examined how host age at exposure influences within-host parasite competition and virulence. We found that multiply-exposed hosts were more susceptible to infection and suffered higher mortality than singly-exposed hosts. Hosts oldest at exposure were least often infected and vice versa. Furthermore, we found that in young multiply-exposed hosts competition was weak, allowing coexistence and transmission of both parasite clones, whereas in older multiply-exposed hosts competitive exclusion was observed. Thus, age-dependent parasite exposure and host demography (age structure) could together play an important role in mediating parasite evolution. At the individual level, our results demonstrate a previously unnoticed interaction of the host's immune system with host age, suggesting that the specificity of immune function changes as hosts mature. Therefore, evolutionary models of parasite virulence might benefit from incorporating age-dependent epidemiological parameters.

Relating suborganismal processes to ecotoxicological and population level endpoints using a bioenergetic model

Ecological effects of environmental stressors are commonly evaluated using organismal or suborganismal data, such as standardized toxicity tests that characterize responses of individuals (e.g., mortality and reproduction) and a rapidly growing body of "omics" data. A key challenge for environmental risk assessment is relating such information to population dynamics. One approach uses dynamic energy budget (DEB) models that relate growth and reproduction of individuals to underlying flows of energy and elemental matter. We hypothesize that suborganismal information identifies DEB parameters that are most likely impacted by a particular stressor and that the DEB model can then project suborganismal effects on life history and population endpoints. We formulate and parameterize a model of growth and reproduction for the water flea Daphnia magna. Our model resembles previous generic bioenergetic models, but has explicit representation of discrete molts, an important feature of Daphnia life history. We test its ability to predict six endpoints commonly used in chronic toxicity studies in specified food environments. With just one adjustable parameter, the model successfully predicts growth and reproduction of individuals from a wide array of experiments performed in multiple laboratories using different clones of D. magna raised on different food sources. Fecundity is the most sensitive endpoint, and there is broad correlation between the sensitivities of fecundity and long-run growth rate, as is desirable for the default metric used in chronic toxicity tests. Under some assumptions, we can combine our DEB model with the Euler-Lotka equation to estimate longrun population growth rates at different food levels. A review of Daphnia gene-expression experiments on the effects of contaminant exposure reveals several connections to model parameters, in particular a general trend of increased transcript expression of genes involved in energy assimilation and utilization at concentrations affecting growth and reproduction. The sensitivity of fecundity to many model parameters was consistent with frequent generalized observations of decreased expression of genes involved in reproductive physiology, but interpretation of these observations requires further mechanistic modeling. We thus propose an approach based on generic DEB models incorporating few essential species-specific features for rapid extrapolation of ecotoxicogenomic assays for Daphnia-based population risk assessment.

Modeling the direct and indirect effects of copper on phytoplankton-zooplankton interactions

Predicting the effects of pollution at the community level is difficult because of the complex impacts of ecosystem dynamics and properties. To predict the effects of copper on a plant-herbivore interaction in a freshwater ecosystem, we built a model that focuses on the interaction between an alga, Scenedesmus sp., and a herbivore, Daphnia sp. The model assumes logistic growth for Scenedesmus and a type II functional response for Daphnia. Internal copper concentrations in Scenedesmus and Daphnia are calculated using a biodynamic model. We include two types of direct effects of copper on Scenedesmus and Daphnia that results from hormesis: a deficiency effect at low concentration and a toxic effect at high concentration. We perform a numerical analysis to predict the combined effects of copper and nutrient enrichment on the Scenedesmus-Daphnia interaction. Results show three types of outcomes depending on copper concentration. First, low (4 μg L(-1)) and high (50 μg L(-1)) copper concentrations cause deficiency and toxicity, respectively, leading to the extinction of all populations; for less extreme concentrations (between 4 and 5 μg L(-1) and between 16.5 and 50 μg L(-1)), only the consumer population becomes extinct. The two populations survive with intermediate concentrations. Second, when population dynamics present oscillations, copper has a stabilizing effect and reduces or suppresses oscillations. Third, copper, on account of its stabilizing effect, opposes the destabilizing effect of nutrient enrichment. Our model shows that (1) Daphnia is affected by copper at lower concentrations when community interactions are taken into account than when analyzed alone, and (2) counterintuitive effects may arise from the interaction between copper pollution and nutrient enrichment. Our model also suggests that single-value parameters such as NOEC and LOEC, which do not take community interactions into account to characterize pollutants effects, are unable to determine pollutant effects in complex ecosystems. More generally, our model underscores the importance of ecosystem-scale studies to predict the effects of pollutants.

Ecological resilience of population cycles: a dynamic perspective of regime shift

Studies of catastrophic regime shifts have mostly considered a simple equilibrium situation, in which there are two stable equilibria divided by an unstable equilibrium. However, populations and communities in nature often show more complex dynamics, and regime shifts in the complex dynamic systems have attracted limited attention so far. Understanding the division between alternative stable states in multispecies communities requires an extended perspective and the conventional analysis of a simple equilibrium situation cannot be applied as it is. What divides the alternative stable states can take complex structure rather than a point, and this division of alternative states is usually impossible to be obtained by analytical approaches. In this study, we developed a numerical method that can relatively easily provide the structure of the division of alternative stable states. We then applied the method to different three-species systems exhibiting oscillatory dynamics to understand their recoverability from perturbations that can bring out irreversible state change. Our results suggested that there is temporal variation of the recoverability that may not be understood straightforwardly because of the complex structure of the division of alternative stable states. Also, which of the alternative states is more vulnerable to perturbations and easier to show a regime shift can vary depending on the size of perturbation. These attributes of regime shifts have not been found in a simple equilibrium situation, suggesting the need of a dynamic aspect of the recoverability of ecological systems.

Host age modulates parasite infectivity, virulence and reproduction

Host age is one of the most striking differences among hosts within most populations, but there is very little data on how age-dependent effects impact ecological and evolutionary dynamics of both the host and the parasite. Here, we examined the influence of host age (juveniles, young and old adults) at parasite exposure on host susceptibility, fecundity and survival as well as parasite transmission, using two clones of the water flea Daphnia magna and two clones of its bacterial parasite Pasteuria ramosa. Younger D. magna were more susceptible to infection than older ones, regardless of host or parasite clone. Also, younger-infected D. magna became castrated faster than older hosts, but host and parasite clone effects contributed to this trait as well. Furthermore, the early-infected D. magna produced considerably more parasite transmission stages than late-infected ones, while host age at exposure did not affect virulence as it is defined in models (host mortality). When virulence is defined more broadly as the negative effects of infection on host fitness, by integrating the parasitic effects on host fecundity and mortality, then host age at exposure seems to slide along a negative relationship between host and parasite fitness. Thus, the virulence-transmission trade-off differs strongly among age classes, which in turn affects predictions of optimal virulence. Age-dependent effects on host susceptibility, virulence and parasite transmission could pose an important challenge for experimental and theoretical studies of infectious disease dynamics and disease ecology. Our results present a call for a more explicit stage-structured theory for disease, which will incorporate age-dependent epidemiological parameters.

Complex Daphnia interactions with parasites and competitors

Species interactions can strongly influence the size and dynamics of epidemics in populations of focal hosts. The "dilution effect" provides a particularly interesting type of interaction from a biological standpoint. Diluters - other host species which resist infection but remove environmentally-distributed propagules of parasites (spores) - should reduce disease prevalence in focal hosts. However, diluters and focal hosts may compete for shared resources. This combination of positive (dilution) and negative (competition) effects could greatly complicate, even undermine, the benefits of dilution and diluter species from the perspective of the focal host. Motivated by an example from the plankton (i.e., zooplankton hosts, a fungal parasite, and algal resources), we study a model of dilution and competition. Our model reveals a suite of five results: • A diluter that is a superior competitor wipes out the host, regardless of parasitism. Although expected, this outcome is an ever-present danger in strategies that might use diluters to control disease. • If the diluter is an inferior competitor, it can reduce disease prevalence, despite the competition, as parameterized in our model. However, competition may also reduce density of susceptible hosts to levels below that seen in focal host-parasite systems alone. • As they decrease disease prevalence, diluters destabilize dynamics of the focal host and their resources. Thus, diluters undermine the stabilizing effects of disease. • The four species combination can generate very complex dynamics, including period-doubling bifurcations and torus (Neimark-Sacker) bifurcations. • At lower resource carrying capacity, the diluter’s dilution of spores is 'helpful' to the focal host, i.e., dilution can elevate host density by reducing disease. But, as the resource carrying capacity increases further, the equilibrium density of the diluter increases while the density of the focal host decreases, despite competition. Namely, the negative effects of competition start to outweigh the positive effects of dilution from the perspective of equilibrium density of the focal host.

Form of an evolutionary tradeoff affects eco-evolutionary dynamics in a predator-prey system

Evolution on a time scale similar to ecological dynamics has been increasingly recognized for the last three decades. Selection mediated by ecological interactions can change heritable phenotypic variation (i.e., evolution), and evolution of traits, in turn, can affect ecological interactions. Hence, ecological and evolutionary dynamics can be tightly linked and important to predict future dynamics, but our understanding of eco-evolutionary dynamics is still in its infancy and there is a significant gap between theoretical predictions and empirical tests. Empirical studies have demonstrated that the presence of genetic variation can dramatically change ecological dynamics, whereas theoretical studies predict that eco-evolutionary dynamics depend on the details of the genetic variation, such as the form of a tradeoff among genotypes, which can be more important than the presence or absence of the genetic variation. Using a predator-prey (rotifer-algal) experimental system in laboratory microcosms, we studied how different forms of a tradeoff between prey defense and growth affect eco-evolutionary dynamics. Our experimental results show for the first time to our knowledge that different forms of the tradeoff produce remarkably divergent eco-evolutionary dynamics, including near fixation, near extinction, and coexistence of algal genotypes, with quantitatively different population dynamics. A mathematical model, parameterized from completely independent experiments, explains the observed dynamics. The results suggest that knowing the details of heritable trait variation and covariation within a population is essential for understanding how evolution and ecology will interact and what form of eco-evolutionary dynamics will result.

Bifurcation analysis in a stage-structured predator–prey model with maturation delay

In this paper, we investigate the impact of maturation delay on the positive equilibrium solutions in a stage-structured predator–prey system. By analyzing the characteristic equation we derive the conditions for the emergence of Hopf bifurcation. By applying the normal form and the center manifold argument, the direction as well as the stability of periodic solutions bifurcating from Hopf bifurcation is explored. Results show that maturation delay can change the nature of the positive equilibrium solutions, and the loss of equilibrium stability occurs as a consequence of Hopf bifurcation. When Hopf bifurcation takes place, periodic solution arises and is further demonstrated to be asymptotically stable. In addition, the periodic solutions appear only for intermediate maturation delay, that is, there exists a delay window, outside of which the positive equilibrium is locally stable. Furthermore, numerical analysis shows that Hopf bifurcation is favored by a superior competition for adult predators to juveniles, a smaller mortality on juvenile and/or adult predators, and a higher resource carrying capacity. Interestingly, increasing food carrying capacity can lead to the emergence of irregular chaotic dynamics and regular limit cycles.

Double trouble at high density: cross-level test of resource-related adaptive plasticity and crowding-related fitness

Population size is often regulated by negative feedback between population density and individual fitness. At high population densities, animals run into double trouble: they might concurrently suffer from overexploitation of resources and also from negative interference among individuals regardless of resource availability, referred to as crowding. Animals are able to adapt to resource shortages by exhibiting a repertoire of life history and physiological plasticities. In addition to resource-related plasticity, crowding might lead to reduced fitness, with consequences for individual life history. We explored how different mechanisms behind resource-related plasticity and crowding-related fitness act independently or together, using the water flea Daphnia magna as a case study. For testing hypotheses related to mechanisms of plasticity and crowding stress across different biological levels, we used an individual-based population model that is based on dynamic energy budget theory. Each of the hypotheses, represented by a sub-model, is based on specific assumptions on how the uptake and allocation of energy are altered under conditions of resource shortage or crowding. For cross-level testing of different hypotheses, we explored how well the sub-models fit individual level data and also how well they predict population dynamics under different conditions of resource availability. Only operating resource-related and crowding-related hypotheses together enabled accurate model predictions of D. magna population dynamics and size structure. Whereas this study showed that various mechanisms might play a role in the negative feedback between population density and individual life history, it also indicated that different density levels might instigate the onset of the different mechanisms. This study provides an example of how the integration of dynamic energy budget theory and individual-based modelling can facilitate the exploration of mechanisms behind the regulation of population size. Such understanding is important for assessment, management and the conservation of populations and thereby biodiversity in ecosystems.

The effect of temperature on Anopheles mosquito population dynamics and the potential for malaria transmission

The parasites that cause malaria depend on Anopheles mosquitoes for transmission; because of this, mosquito population dynamics are a key determinant of malaria risk. Development and survival rates of both the Anopheles mosquitoes and the Plasmodium parasites that cause malaria depend on temperature, making this a potential driver of mosquito population dynamics and malaria transmission. We developed a temperature-dependent, stage-structured delayed differential equation model to better understand how climate determines risk. Including the full mosquito life cycle in the model reveals that the mosquito population abundance is more sensitive to temperature than previously thought because it is strongly influenced by the dynamics of the juvenile mosquito stages whose vital rates are also temperature-dependent. Additionally, the model predicts a peak in abundance of mosquitoes old enough to vector malaria at more accurate temperatures than previous models. Our results point to the importance of incorporating detailed vector biology into models for predicting the risk for vector borne diseases.

Environmental feedbacks and engineered nanoparticles: mitigation of silver nanoparticle toxicity to Chlamydomonas reinhardtii by algal-produced organic compounds

The vast majority of nanotoxicity studies measures the effect of exposure to a toxicant on an organism and ignores the potentially important effects of the organism on the toxicant. We investigated the effect of citrate-coated silver nanoparticles (AgNPs) on populations of the freshwater alga Chlamydomonas reinhardtii at different phases of batch culture growth and show that the AgNPs are most toxic to cultures in the early phases of growth. We offer strong evidence that reduced toxicity occurs because extracellular dissolved organic carbon (DOC) compounds produced by the algal cells themselves mitigate the toxicity of AgNPs. We analyzed this feedback with a dynamic model incorporating algal growth, nanoparticle dissolution, bioaccumulation of silver, DOC production and DOC-mediated inactivation of nanoparticles and ionic silver. Our findings demonstrate how the feedback between aquatic organisms and their environment may impact the toxicity and ecological effects of engineered nanoparticles.

Symmetry breaking in ecological systems through different energy efficiencies of juveniles and adults

Ontogenetic development is a fundamental aspect of the life history of all organisms and has major effects on population and community dynamics. We postulate a general conceptual framework for understanding these effects and claim that two potential energetics bottlenecks at the level of the individual organism--the rate by which it develops and the rate by which it reproduces--form a fundamental route to symmetry-breaking in ecological systems, leading to ontogenetic asymmetry in energetics. Unstructured ecological theory, which ignores ontogenetic development, corresponds to a limiting case only, in which mass-specific rates of biomass production through somatic growth and reproduction, and biomass loss through mortality, are independent of body size (ontogenetic symmetry). Ontogenetic symmetry results in development and reproduction being limited to the same extent by food density. In all other cases, symmetry-breaking occurs. Ontogenetic asymmetry results in increases in juvenile, adult, or even total biomass in response to mortality. At the community level, this gives rise to alternative stable states via predator-induced shifts in prey size distributions. Ontogenetic asymmetry furthermore leads to two distinct types of cycles in population dynamics, depending on whether development or reproduction is most energy limited. We discuss the mechanisms giving rise to these phenomena and the empirical support for them. We conclude that the concepts of ontogenetic symmetry and ontogenetic asymmetry form a novel and general organizing principle on which future ecological theory should be developed.

Recurrent insect outbreaks caused by temperature-driven changes in system stability

Insects often undergo regular outbreaks in population density but identifying the causal mechanism for such outbreaks in any particular species has proven difficult. Here, we show that outbreak cycles in the tea tortrix Adoxophyes honmai can be explained by temperature-driven changes in system stability. Wavelet analysis of a 51-year time series spanning more than 200 outbreaks reveals a threshold in outbreak amplitude each spring when temperature exceeds 15°C and a secession of outbreaks each fall as temperature decreases. This is in close agreement with our independently parameterized mathematical model that predicts the system crosses a Hopf bifurcation from stability to sustained cycles as temperature increases. These results suggest that temperature can alter system stability and provide an explanation for generation cycles in multivoltine insects.

Mechanistic effect modeling for ecological risk assessment: where to go from here?

Mechanistic effect models (MEMs) consider the mechanisms of how chemicals affect individuals and ecological systems such as populations and communities. There is an increasing awareness that MEMs have high potential to make risk assessment of chemicals more ecologically relevant than current standard practice. Here we discuss what kinds of MEMs are needed to improve scientific and regulatory aspects of risk assessment. To make valid predictions for a wide range of environmental conditions, MEMs need to include a sufficient amount of emergence, for example, population dynamics emerging from what individual organisms do. We present 1 example where the life cycle of individuals is described using Dynamic Energy Budget theory. The resulting individual-based population model is thus parameterized at the individual level but correctly predicts multiple patterns at the population level. This is the case for both control and treated populations. We conclude that the state-of-the-art in mechanistic effect modeling has reached a level where MEMs are robust and predictive enough to be used in regulatory risk assessment. Mechanistic effect models will thus be used to advance the scientific basis of current standard practice and will, if their development follows Good Modeling Practice, be included in a standardized way in future regulatory risk assessments.

Armstrong-McGehee mechanism revisited: competitive exclusion and coexistence of nonlinear consumers

A number of mechanisms have been proposed to explain the coexistence of species engaging in exploitative competition. The Armstrong-McGehee mechanism relies on different levels of nonlinearity in functional response between competing consumers and their ability to avoid competitive exclusion through temporal resource partitioning during endogenously generated fluctuations. While previous studies have mainly focused on cases where one consumer has nonlinear functional response and the other consumer has linear functional response, our study assessed coexistence and competitive exclusion under a more realistic scenario with two nonlinear consumers. Using analytical and numerical methods we found that the potential of coexistence of the two consumers decreases with increasing nonlinearity in the more linear species; increasing nonlinearity in the more nonlinear species, however, resulted in non-monotonic changes in the parameter space allowing coexistence. When coexistence potential is quantified under the presupposition that each consumer must be able to persist with the resource by itself, coexistence becomes consistently less likely with increasing similarity of the functional responses of the two consumers. Our results suggest that the Armstrong-McGehee mechanism is unlikely to operate as the sole coexistence-promoting mechanism in communities with generally nonlinear consumer-resource interactions. However, its role as a module in more complex systems and in synergy with other factors remains to be established.

Ecological nanotoxicology: integrating nanomaterial hazard considerations across the subcellular, population, community, and ecosystems levels

Research into the health and environmental safety of nanotechnology has seriously lagged behind its emergence in industry. While humans have often adopted synthetic chemicals without considering ancillary consequences, the lessons learned from worldwide pollution should motivate making nanotechnology compatible with environmental concerns. Researchers and policymakers need to understand exposure and harm of engineered nanomaterials (ENMs), currently nanotechnology's main products, to influence the ENM industry toward sustainable growth. Yet, how should research proceed? Standard toxicity testing anchored in single-organism, dose-response characterizations does not adequately represent real-world exposure and receptor scenarios and their complexities. Our approach is different: it derives from ecology, the study of organisms' interactions with each other and their environments. Our approach involves the characterization of ENMs and the mechanistic assessment of their property-based effects. Using high throughput/content screening (HTS/HCS) with cells or environmentally-relevant organisms, we measure the effects of ENMs on a subcellular or population level. We then relate those effects to mechanisms within dynamic energy budget (DEB) models of growth and reproduction. We reconcile DEB model predictions with experimental data on organism and population responses. Finally, we use microcosm studies to measure the potential for community- or ecosystem-level effects by ENMs that are likely to be produced in large quantities and for which either HTS/HCS or DEB modeling suggest their potential to harm populations and ecosystems. Our approach accounts for ecological interactions across scales, from within organisms to whole ecosystems. Organismal ENM effects, if propagated through populations, can alter communities comprising multiple populations (e.g., plant, fish, bacteria) within food webs. Altered communities can change ecosystem services: processes that cycle carbon, nutrients, and energy, and regulate Earth's waters and atmosphere. We have shown ENM effects on populations, communities, and ecosystems, including transfer and concentration of ENMs through food chains, for a range of exposure scenarios; in many cases, we have identified subcellular ENM effects mechanisms. To keep pace with ENM development, rapid assessment of the mechanisms of ENM effects and modeling are needed. DEB models provide a method for mathematically representing effects such as the generation of reactive oxygen species and their associated damage. These models account for organism-level effects on metabolism and reproduction and can predict outcomes of ENM-organism combinations on populations; those predictions can then suggest ENM characteristics to be avoided. HTS/HCS provides a rapid assessment tool of the ENM chemical characteristics that affect biological systems; such results guide and expand DEB model expressions of hazard. Our approach addresses ecological processes in both natural and managed ecosystems (agriculture) and has the potential to deliver timely and meaningful understanding towards environmentally sustainable nanotechnology.

Predicting population dynamics from the properties of individuals: a cross-level test of dynamic energy budget theory

Individual-based models (IBMs) are increasingly used to link the dynamics of individuals to higher levels of biological organization. Still, many IBMs are data hungry, species specific, and time-consuming to develop and analyze. Many of these issues would be resolved by using general theories of individual dynamics as the basis for IBMs. While such theories have frequently been examined at the individual level, few cross-level tests exist that also try to predict population dynamics. Here we performed a cross-level test of dynamic energy budget (DEB) theory by parameterizing an individual-based model using individual-level data of the water flea, Daphnia magna, and comparing the emerging population dynamics to independent data from population experiments. We found that DEB theory successfully predicted population growth rates and peak densities but failed to capture the decline phase. Further assumptions on food-dependent mortality of juveniles were needed to capture the population dynamics after the initial population peak. The resulting model then predicted, without further calibration, characteristic switches between small- and large-amplitude cycles, which have been observed for Daphnia. We conclude that cross-level tests help detect gaps in current individual-level theories and ultimately will lead to theory development and the establishment of a generic basis for individual-based models and ecology.

Generation separation in simple structured life cycles: models and 48 years of field data on a tea tortrix moth

Population cycles have fascinated ecologists since the early nineteenth century, and the dynamics of insect populations have been central to understanding the intrinsic and extrinsic biological processes responsible for these cycles. We analyzed an extraordinary long-term data set (every 5 days for 48 years) of a tea tortrix moth (Adoxophyes honmai) that exhibits two dominant cycles: an annual cycle with a conspicuous pattern of four or five single-generation cycles superimposed on it. General theory offers several candidate mechanisms for generation cycles. To evaluate these, we construct and parameterize a series of temperature-dependent, stage-structured models that include intraspecific competition, parasitism, mate-finding Allee effects, and adult senescence, all in the context of a seasonal environment. By comparing the observed dynamics with predictions from the models, we find that even weak larval competition in the presence of seasonal temperature forcing predicts the two cycles accurately. None of the other mechanisms predicts the dynamics. Detailed dissection of the results shows that a short reproductive life span and differential winter mortality among stages are the additional life-cycle characteristics that permit the sustained cycles. Our general modeling approach is applicable to a wide range of organisms with temperature-dependent life histories and is likely to prove particularly useful in temperate systems where insect pest outbreaks are both density and temperature dependent.

Epidemic size determines population-level effects of fungal parasites on Daphnia hosts

Parasites frequently reduce the fecundity, growth, and survival of individual hosts. How often do these virulent effects reduce the density of host populations? Spectacular examples show that recently invaded parasites can severely impact host populations--but what about parasites persisting long-term in host populations? We have addressed this issue using a zooplankton host (Daphnia dentifera) that becomes infected with a fungal microparasite (Metschnikowia bicuspidata). We combined observations of epidemics in nine lakes over 6 years, fine-scale sampling of three epidemics, and a mesocosm experiment. Most epidemics remained small (<10% maximum prevalence) and exerted little influence on host densities. However, larger epidemics more severely depressed the populations of their hosts. These large/severe epidemics started and peaked earlier than smaller/benign ones. The larger epidemics also exerted particularly negative effects on host densities at certain lags, reflecting the delayed consequences of infection on fecundity reduction and host mortality. Notably, negative effects on the juvenile stage class manifested later than those on the adult stage class. The results of the experiment further emphasized depression of host density by the fungus, especially on the density of the juvenile stage class. Consequently, this common parasite reduces the density of host populations when conditions foster larger outbreaks characterized by an earlier start and earlier peak. Given these considerable effects on host density seen in a number of large epidemics, parasitism may sometimes rank highly among other factors (predation, resource availability) driving the population dynamics of these hosts.

Dynamic energy budget theory and population ecology: lessons from Daphnia

Dynamic energy budget (DEB) theory offers a perspective on population ecology whose starting point is energy utilization by, and homeostasis within, individual organisms. It is natural to ask what it adds to the existing large body of individual-based ecological theory. We approach this question pragmatically--through detailed study of the individual physiology and population dynamics of the zooplankter Daphnia and its algal food. Standard DEB theory uses several state variables to characterize the state of an individual organism, thereby making the transition to population dynamics technically challenging, while ecologists demand maximally simple models that can be used in multi-scale modelling. We demonstrate that simpler representations of individual bioenergetics with a single state variable (size), and two life stages (juveniles and adults), contain sufficient detail on mass and energy budgets to yield good fits to data on growth, maturation and reproduction of individual Daphnia in response to food availability. The same simple representations of bioenergetics describe some features of Daphnia mortality, including enhanced mortality at low food that is not explicitly incorporated in the standard DEB model. Size-structured, population models incorporating this additional mortality component resolve some long-standing questions on stability and population cycles in Daphnia. We conclude that a bioenergetic model serving solely as a 'regression' connecting organismal performance to the history of its environment can rest on simpler representations than those of standard DEB. But there are associated costs with such pragmatism, notably loss of connection to theory describing interspecific variation in physiological rates. The latter is an important issue, as the type of detailed study reported here can only be performed for a handful of species.

Never mind the length, feel the quality: the impact of long-term epidemiological data sets on theory, application and policy

Infectious diseases have been a prime testing ground for ecological theory. However, the ecological perspective is increasingly recognized as essential in epidemiology. Long-term, spatially resolved reliable data on disease incidence and the ability to test them using mechanistic models have been critical in this cross-fertilization. Here, we review some of the key intellectual developments in epidemiology facilitated by long-term data. We identify research frontiers at the interface of ecology and epidemiology and their associated data needs.

Complete compensation in Daphnia fecundity and stage-specific biomass in response to size-independent mortality

1. Recent theory suggests that compensation or even overcompensation in stage-specific biomass can arise in response to increased mortality. Which stage that will show compensation depends on whether maturation or reproduction is the more limiting process in the population. Size-structured theory also provides a strong link between the type of regulation and the expected population dynamics as both depend on size/stage-specific competitive ability. 2. We imposed a size-independent mortality on a consumer-resource system with Daphnia pulex feeding on Scenedesmus obtusiusculus to asses the compensatory responses in Daphnia populations. We also extended an existing stage-structured biomass model by including several juvenile stages to test whether this extension affected the qualitative results of the existing model. 3. We found complete compensation in juvenile biomass and total population fecundity in response to harvesting. The compensation in fecundity was caused by both a higher proportion of fecund females and a larger clutch size under increased mortality. We did not detect any difference in resource levels between treatments. 4. The model results showed that both stages of juveniles have to be superior to adults in terms of resource competition for the compensatory response to take place in juvenile biomass. 5. The results are all in correspondence with that the regulating process within the population was reproduction. From this, we also conclude that juveniles were superior competitors to adults, which has implications for population dynamics and the kind of cohort cycles seen in Daphnia populations. 6. The compensatory responses demonstrated in this experiment have major implications for community dynamics and are potentially present in any organisms with food-dependent growth or development.