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

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.

Cycles, phase synchronization, and entrainment in single-species phytoplankton populations

Complex dynamics, such as population cycles, can arise when the individual members of a population become synchronized. However, it is an open question how readily and through which mechanisms synchronization-driven cycles can occur in unstructured microbial populations. In experimental chemostats we studied large populations (>10(9) cells) of unicellular phytoplankton that displayed regular, inducible and reproducible population oscillations. Measurements of cell size distributions revealed that progression through the mitotic cycle was synchronized with the population cycles. A mathematical model that accounts for both the cell cycle and population-level processes suggests that cycles occur because individual cells become synchronized by interacting with one another through their common nutrient pool. An external perturbation by direct manipulation of the nutrient availability resulted in phase resetting, unmasking intrinsic oscillations and producing a transient collective cycle as the individuals gradually drift apart. Our study indicates a strong connection between complex within-cell processes and population dynamics, where synchronized cell cycles of unicellular phytoplankton provide sufficient population structure to cause small-amplitude oscillations at the population level.

Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators

It is shown that the dormancy of predators induces mixed-mode oscillations and chaos in the population dynamics of a prey-predator system under certain conditions. The mixed-mode oscillations and chaos are shown to bifurcate from a coexisting equilibrium by means of the theory of fast-slow systems. These results may help to find experimental conditions under which one can demonstrate chaotic population dynamics in a simple phytoplankton-zooplankton (-resting eggs) community in a microcosm with a short duration.

Stoichiometrically Explicit Food Webs: Feedbacks between Resource Supply, Elemental Constraints, and Species Diversity

A stoichiometrically explicit approach to food web ecology yields new insight into promotion and degradation of diversity, changes in species composition along environmental gradients, biomass partitioning among trophic levels, and limitation of primary production. These revelations emerge from food web modules that incorporate fundamental constraints imposed by mass balance and a key trait, stoichiometric body composition, into a species’ niche. These niche components involve a species’ requirements from its environment and its own impacts on its environment. More specifically, stoichiometric composition influences minimal nutrient requirements of consumers (perhaps especially grazers); this component becomes pertinent because large imbalances often arise between nutrient:carbon content of consumers relative to prey. Furthermore, these imbalances then modulate the impact of consumers on their own resources through nutrient recycling. Once these niche components become synthesized, their implications in shaping food webs provide powerful mechanisms linking changes in environmental gradients with community structure and ecosystem function.

Coupled predator-prey oscillations in a chaotic food web

Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles are coupled through competition between prey species. Here, we investigate predator-prey oscillations in a long-term experiment with a marine plankton community. Wavelet analysis of the species fluctuations reveals two predator-prey cycles that fluctuate largely in anti-phase. The phase angles point at strong competition between the phytoplankton species, but relatively little prey overlap among the zooplankton species. This food web architecture is consistent with the size structure of the plankton community, and generates highly dynamic food webs. Continued alternations in species dominance enable coexistence of the prey species through a non-equilibrium 'killing-the-winner' mechanism, as the system shifts back and forth between the two predator-prey cycles in a chaotic fashion.

Determining the functional form of density dependence: deductive approaches for consumer-resource systems having a single resource

Consumer-resource models are used to deduce the functional form of density dependence in the consumer population. A general approach to determining the form of consumer density dependence is proposed; this involves determining the equilibrium (or average) population size for a series of different harvest rates. The relationship between a consumer's mortality and its equilibrium population size is explored for several one-consumer/one-resource models. The shape of density dependence in the resource and the shape of the numerical and functional responses all tend to be "inherited" by the consumer's density dependence. Consumer-resource models suggest that density dependence will very often have both concave and convex segments, something that is impossible under the commonly used theta-logistic model. A range of consumer-resource models predicts that consumer population size often declines at a decelerating rate with mortality at low mortality rates, is insensitive to or increases with mortality over a wide range of intermediate mortalities, and declines at a rapidly accelerating rate with increased mortality when mortality is high. This has important implications for management and conservation of natural populations.

Daphnia revisited: local stability and bifurcation theory for physiologically structured population models explained by way of an example

We consider the interaction between a general size-structured consumer population and an unstructured resource. We show that stability properties and bifurcation phenomena can be understood in terms of solutions of a system of two delay equations (a renewal equation for the consumer population birth rate coupled to a delay differential equation for the resource concentration). As many results for such systems are available (Diekmann et al. in SIAM J Math Anal 39:1023-1069, 2007), we can draw rigorous conclusions concerning dynamical behaviour from an analysis of a characteristic equation. We derive the characteristic equation for a fairly general class of population models, including those based on the Kooijman-Metz Daphnia model (Kooijman and Metz in Ecotox Env Saf 8:254-274, 1984; de Roos et al. in J Math Biol 28:609-643, 1990) and a model introduced by Gurney-Nisbet (Theor Popul Biol 28:150-180, 1985) and Jones et al. (J Math Anal Appl 135:354-368, 1988), and next obtain various ecological insights by analytical or numerical studies of special cases.