Changes in sea floor productivity are crucial to understanding the impact of climate change in temperate coastal ecosystems according to a new size-based model.

The multifaceted effects of climate change on physical and biogeochemical processes are rapidly altering marine ecosystems but often are considered in isolation, leaving our understanding of interactions between these drivers of ecosystem change relatively poor. This is particularly true for shallow coastal ecosystems, which are fuelled by a combination of distinct pelagic and benthic energy pathways that may respond to climate change in fundamentally distinct ways. The fish production supported by these systems is likely to be impacted by climate change differently to those of offshore and shelf ecosystems, which have relatively simpler food webs and mostly lack benthic primary production sources. We developed a novel, multispecies size spectrum model for shallow coastal reefs, specifically designed to simulate potential interactive outcomes of changing benthic and pelagic energy inputs and temperatures and calculate the relative importance of these variables for the fish community. Our model, calibrated using field data from an extensive temperate reef monitoring program, predicts that changes in resource levels will have much stronger impacts on fish biomass and yields than changes driven by physiological responses to temperature. Under increased plankton abundance, species in all fish trophic groups were predicted to increase in biomass, average size, and yields. By contrast, changes in benthic resources produced variable responses across fish trophic groups. Increased benthic resources led to increasing benthivorous and piscivorous fish biomasses, yields, and mean body sizes, but biomass decreases among herbivore and planktivore species. When resource changes were combined with warming seas, physiological responses generally decreased species' biomass and yields. Our results suggest that understanding changes in benthic production and its implications for coastal fisheries should be a priority research area. Our modified size spectrum model provides a framework for further study of benthic and pelagic energy pathways that can be easily adapted to other ecosystems.

Spatial drivers of instability in marine size-spectrum ecosystems.

Size-spectrum models are a recent class of models describing the dynamics of a whole community based on a description of individual organisms. The models are motivated by marine ecosystems where they cover the size range from multicellular plankton to the largest fish. We propose to extend the size-spectrum model with spatial components. The spatial dynamics is governed by a random motion and a directed movement in the direction of increased fitness, which we call 'fitness-taxis'. We use the model to explore whether spatial irregularities of marine communities can occur due to the internal dynamics of predator-prey interactions and spatial movements. This corresponds to a pattern-formation analysis generalized to an entire ecosystem but is not limited to one prey and one predator population. The analyses take the form of Fourier analysis and numerical experiments. Results show that diffusion always stabilizes the equilibrium but fitness-taxis destabilizes it, leading to non-stationary spatially inhomogeneous population densities, which are travelling in size. However, there is a strong asymmetry between fitness-induced destabilizing effects and diffusion-induced stabilizing effects with the latter dominating over the former. These findings reveal that fitness taxis acts as a possible mechanism behind pattern formations in ecosystems with high diversity of organism sizes, which can drive the emergence of spatial heterogeneity even in a spatially homogeneous environment.

Sheldon spectrum and the plankton paradox: two sides of the same coin-a trait-based plankton size-spectrum model.

The Sheldon spectrum describes a remarkable regularity in aquatic ecosystems: the biomass density as a function of logarithmic body mass is approximately constant over many orders of magnitude. While size-spectrum models have explained this phenomenon for assemblages of multicellular organisms, this paper introduces a species-resolved size-spectrum model to explain the phenomenon in unicellular plankton. A Sheldon spectrum spanning the cell-size range of unicellular plankton necessarily consists of a large number of coexisting species covering a wide range of characteristic sizes. The coexistence of many phytoplankton species feeding on a small number of resources is known as the Paradox of the Plankton. Our model resolves the paradox by showing that coexistence is facilitated by the allometric scaling of four physiological rates. Two of the allometries have empirical support, the remaining two emerge from predator-prey interactions exactly when the abundances follow a Sheldon spectrum. Our plankton model is a scale-invariant trait-based size-spectrum model: it describes the abundance of phyto- and zooplankton cells as a function of both size and species trait (the maximal size before cell division). It incorporates growth due to resource consumption and predation on smaller cells, death due to predation, and a flexible cell division process. We give analytic solutions at steady state for both the within-species size distributions and the relative abundances across species.

Predation effects on mean time to extinction under demographic stochasticity.

Methods for predicting the probability and timing of a species' extinction are typically based on single species population dynamics. Assessments of extinction risk often lack effects of interspecific interactions. We study a birth and death process in which the death rate includes an effect of predation. Predation is included via a general nonlinear expression for the functional response of predation to prey density. We investigate the effects of the foraging parameters (e.g. attack rate and handling time) on the mean time to extinction. Mean time to extinction varies by orders of magnitude when we alter the foraging parameters, even when we exclude the effects of these parameters on the equilibrium population size. Conclusions are robust to assumptions about initial conditions and variable predator abundance. These findings clearly show that accounting for the nature of interspecific interactions is likely to be critically important when estimating extinction risk.

A stability analysis of the power-law steady state of marine size spectra.

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.

A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems.

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick-von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation, and the McKendrick-von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.

Scale-invariant model of marine population dynamics.

A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence that the population dynamics in the ocean is approximately scale-invariant. We use this invariance in the construction and solution of a size-structured dynamical population model. Starting from a Markov model encoding the basic processes of predation, reproduction, maintenance respiration, and intrinsic mortality, we derive a partial integro-differential equation describing the dependence of abundance on weight and time. Our model represents an extension of the jump-growth model and hence also of earlier models based on the McKendrick-von Foerster equation. The model is scale-invariant provided the rate functions of the stochastic processes have certain scaling properties. We determine the steady-state power-law solution, whose exponent is determined by the relative scaling between the rates of the density-dependent processes (predation) and the rates of the density-independent processes (reproduction, maintenance, and mortality). We study the stability of the steady-state against small perturbations and find that inclusion of maintenance respiration and reproduction in the model has a strong stabilizing effect. Furthermore, the steady state is unstable against a change in the overall population density unless the reproduction rate exceeds a certain threshold.