Michael Dowd

On predicting the growth of cultured bivalves

Abstract A simple, limited ecosystem model focused on bivalve growth in a coastal aquaculture site is presented. The model is based on a system of coupled, nonlinear ordinary differential equations which predict the temporal evolution of the following state variables: individual bivalve weight, bivalve numbers, zooplankton biomass, phytoplankton biomass and non-plankton seston. A limiting nutrient is also included to constrain the overall system. The equations are based on population mass budgets and allow for particle exchange with adjacent regions. The model structure is general and designed to be applicable to a variety of bivalve species or sites. In order to test the feasibility of the model for predicting growth, it is applied to a blue mussel Mytilus edulis culture site in a coastal inlet near Lunenburg, Nova Scotia, Canada. Idealized forcing functions for the annual cycles of light, temperature and the far-field concentrations of the state variables are used. It is shown that the model is able to reproduce the general features of observed mussel growth in the different regions of the inlet at the relatively low stocking densities found there. Numerical experiments with high stocking densities are carried out in order to estimate carrying capacity for the inlet. Sensitivity analysis shows that predicted mussel growth is highly influenced by small changes in the physiological parameters which describe the mussel energy budget. It is suggested that this feature may prove to be an important limitation in using such models as predictive tools for managing the development of shellfish aquaculture.

Perspectives on Field Studies and Related Biological Models of Bivalve Growth and Carrying Capacity

Marine bivalves are cultured throughout the world, and in many places such as Atlantic Canada and New Zealand, culture of mussels and other groups has grown exponentially in the last decade (Hickman 1989; Mallet 1989). Acceptable culture sites are limited due to habitat suitability, road access, and competing recreational or commercial use such as wild fisheries. As available culture space becomes filled up with stock, there may be a depression of individual bivalve growth rate and an increase in mortality caused by several factors associated with overcrowding. Suspension feeders have a remarkable capacity to filter the water column such that they are food limited at high culture density (Navarro et al. 1991). There are several indications that production maxima have been reached or exceeded as culture is continually expanded to the detriment of food supply (Mallet 1989; Hickman et al. 1991; Perez Comacho et al. 1991). This phenomenon is also documented for natural populations of both infaunal and epifaunal bivalves including mussel beds (Peterson and Black 1987; Frechette and Grant 1991; Smaal 1991; Bayne and Hawkins 1992). Moreover, culture research has demonstrated major site differences in growth rate (Mallet et al. 1986) confirming that environmental conditions can regulate shellfish production. Overcrowded culture conditions also lead to increased incidence of shellfish diseases (Dijkema and van Stralen 1989). Finally, high culture biomass may produce a negative feedback to the local environment through organic loading and anaerobic conditions beneath culture leases (Dahlback and Gunnarsson 1981), potentially leading to degradation of culture environments.

Predator decline leads to decreased stability in a coastal fish community

Fisheries exploitation has caused widespread declines in marine predators. Theory predicts that predator depletion will destabilise lower trophic levels, making natural communities more vulnerable to environmental perturbations. However, empirical evidence has been limited. Using a community matrix model, we empirically assessed trends in the stability of a multispecies coastal fish community over the course of predator depletion. Three indices of community stability (resistance, resilience and reactivity) revealed significantly decreasing stability concurrent with declining predator abundance. The trophically downgraded community exhibited weaker top-down control, leading to predator-release processes in lower trophic levels and increased susceptibility to perturbation. At the community level, our results suggest that high predator abundance acts as a stabilising force to the naturally stochastic and highly autocorrelated dynamics in low trophic species. These findings have important implications for the conservation and management of predators in marine ecosystems and provide empirical support for the theory of predatory control.

A Bayesian approach to the ecosystem inverse problem

This study investigates a probabilistic approach for the inverse problem associated with blending time-dependent ecosystem models and observations. The goal is to combine prior information, in the form of ecological dynamics and substantive knowledge about uncertain parameters, with available measurements. Posterior estimates of both the time-varying ecological state variables and the model parameters are obtained, along with their uncertainty. Ecological models of interacting populations are considered in the context of a nonlinear, non-Gaussian state space model. This comprises a nonlinear stochastic difference equation for the ecological dynamics, and an observation equation which relates the model state to the measurements. Complex error processes are readily incorporated. The posterior probability density function provides a complete solution to the inverse problem. Bayes’ theorem allows one to obtain this posterior density through synthesis of the prior information and the observations. To illustrate this Bayesian inverse method, these ideas are applied to a simple ecosystem box model concerned with predicting the seasonal co-evolution of a population of grazing shellfish and its two food sources: plankton and detritus. Observations of shellfish biomass over time are available. Lognormal system noise was incorporated into the ecosystem equations at all time steps. Ingestion and respiration parameters for shellfish growth are considered as uncertain quantities described by beta distributions. Stochastic simulation was carried out and provided predictions of the model state with uncertainty estimates. The Bayesian inverse method was then used to assimilate the additional information contained in the observations. Posterior probability density functions for the parameters and time-varying ecological state were computed using Markov Chain Monte Carlo methods. The ecological dynamics spread the measurement information to all state variables and parameters, even those not directly observed. Probabilistic state estimates are refined in comparison to those from the stochastic simulation. It is concluded that this Bayesian approach appears promising as a framework for ecosystem inverse problems, but requires careful control of the dimensionality for practical applications.

Changing recruitment capacity in global fish stocks

Significance Marine fish stocks play an important role in marine ecosystems and provide a source of protein for billions of people worldwide. Recent environmental changes have affected the distribution of many stocks, but it is yet unclear whether their productivity is affected as well. We show that recruitment capacity (the ability of stocks to produce surviving offspring) has been significantly altered by both environmental changes and biological changes brought about by overfishing. In total, these effects have reduced recruitment capacity by 3% of the historical maximum per decade, on average. This paper helps us to understand and track previously unrecognized changes in fish stock productivity during the early stages of their life cycle. Marine fish and invertebrates are shifting their regional and global distributions in response to climate change, but it is unclear whether their productivity is being affected as well. Here we tested for time-varying trends in biological productivity parameters across 262 fish stocks of 127 species in 39 large marine ecosystems and high-seas areas (hereafter LMEs). This global meta-analysis revealed widespread changes in the relationship between spawning stock size and the production of juvenile offspring (recruitment), suggesting fundamental biological change in fish stock productivity at early life stages. Across regions, we estimate that average recruitment capacity has declined at a rate approximately equal to 3% of the historical maximum per decade. However, we observed large variability among stocks and regions; for example, highly negative trends in the North Atlantic contrast with more neutral patterns in the North Pacific. The extent of biological change in each LME was significantly related to observed changes in phytoplankton chlorophyll concentration and the intensity of historical overfishing in that ecosystem. We conclude that both environmental changes and chronic overfishing have already affected the productive capacity of many stocks at the recruitment stage of the life cycle. These results provide a baseline for ecosystem-based fisheries management and may help adjust expectations for future food production from the oceans.

Seston dynamics in a tidal inlet with shellfish aquaculture: a model study using tracer equations

Abstract A process-oriented modelling study is used to examine biophysical control of the distribution of particulate organic matter, or seston, in a tidal embayment with shellfish aquaculture. The focus is on the spatio-temporal dynamics of seston as influenced by the processes of water motion and mixing, internal primary production of seston, and the clearance of the water volume by the grazing activity of a large bivalve population. A fluid dynamical framework is used wherein seston is treated as a non-conservative tracer in an advection–diffusion equation with additional source and sink terms. An idealized one-dimensional (1D) tidal inlet is first used to examine the sensitivity of tidally averaged seston concentration and flux to variations in tidal transport, internal production, and shellfish grazing. This model is then applied to Tracadie Bay, a tidal inlet off Canadas east coast, to illustrate temporal variability in seston level and flux for a more complex tidal regime. The results of this study suggest that seston flux is mainly under physical control, with its spatial distribution set by tidal transport processes. Seston level, on the other hand, is affected by both grazing and production, with the magnitude of these effects being spatially dependent as dictated by the tidal currents. Grazing and production effects on seston are most pronounced near the head of the inlet, which depends on internal, or local, processes. More seaward areas are buffered against these changes due the advection of seston from the adjacent open ocean. Variation in the spatial distribution of grazing activity demonstrates how local processes have inlet-wide effects. The temporal response of the inlet to tidal changes in the incoming far-field seston flux resembles a low-pass filter with a phase lag; temporal changes in seston at the head of the inlet are highly dampened and occur later than the forcing flux at the mouth. The implications of these results for marine bivalve aquaculture in terms of growth potential (seston level) and carrying capacity (seston flux) are discussed.

Probabilistic characterization of tidal mixing in a coastal embayment: a Markov Chain approach

Abstract Horizontal mixing by tidal streams and turbulent motions is modelled using a low-dimensional representation based on the theory of Markov Chains. Such a representation is expected to prove useful in the characterization of the bulk properties of mixing and exchange in coastal areas and thereby provide a basis for box, or reservoir, models of water quality and marine ecosystems. Irregular coastlines and complex bathymetry are common in many coastal environments and can cause highly structured tidal flows. Advective stirring by such flows, combined with the effect of turbulence, can give rise to complex mixing regimes and enhanced dispersion. The characterization of mixing proposed in this study is based on a discrete-time, finite-state Markov Chain model. We first provide a brief overview of Markov Chains and their use in modelling the ensemble effects of mixing in terms of the probability of a particle (or fluid parcel) making a transition from one region to another over a fixed number of tidal cycles. These ideas are then illustrated by examining tidal mixing in Passamaquoddy Bay, a tidally energetic coastal embayment close to the entrance of the Bay of Fundy off the east coast of Canada. The transition probabilities are estimated from the trajectories of order 10 5 particles calculated using tidal flow fields from a realistic numerical ocean model of the study region. Various quantities describing the tidal flushing, retention and exchange properties of Passamaquoddy Bay are determined from the Markov Chain model and shown to agree reasonably well with estimates based on the trajectories of the tracked particles.

Ocean wave extraction from RADARSAT synthetic aperture radar inter-look image cross-spectra

This study is concerned with the extraction of directional ocean wave spectra from synthetic aperture radar (SAR) image spectra. The statistical estimation problem underlying the wave-SAR inverse problem is examined in detail in order to properly quantify the wave information content of SAR. As a concrete focus, a data set is considered comprising six RADARSAT SAR images co-located with a directional wave buoy off the east coast of Canada. These SAR data are transformed into inter-look image cross-spectra based on two looks at the same ocean scene separated by 0.4 s. The general problem of wave extraction from SAR is cast in terms of a statistical estimation problem that includes the observed SAR spectra, the wave-SAR transform, and prior spectral wave information. The central role of the weighting functions (inverse of the error covariances) is demonstrated, as well as the consequence of approximate (based on the quasilinear wave-SAR transform) versus exact linearizations on the convergence properties of the algorithm. Error estimates are derived and discussed. This statistical framework is applied to the extraction of spectral wave information from observed RADARSAT SAR image cross-spectra. A modified wave-SAR transform is used to account for case-specific geophysical and imaging effects. Analysis of the residual error of simulated and observed SAR spectra motivates a canonical form for the SAR observation error covariance. Wave estimates are then extracted from the SAR spectra, including wavenumber dependent error estimates and explicit identification of spectral null spaces where the SAR contains no wave information. Band-limited SAR wave information is also combined with prior (buoy) spectral wave estimates through parameterization of the wave spectral shape and use of regularization.

Estimating behavioral parameters in animal movement models using a state‐augmented particle filter

Data on fine-scale animal movement are being collected worldwide, with the number of species being tagged and the resolution of data rapidly increasing. In this study, a general methodology is proposed to understand the patterns in these high-resolution movement time series that relate to marine animal behavior. The approach is illustrated with dive data from a northern fur seal (Callorhinus ursinus) tagged on the Pribilof Islands, Alaska, USA. We apply a state-space model composed of a movement model and corresponding high-resolution vertical movement data. The central goal is to estimate parameters of this movement model, particularly their variation on appropriate time scales, thereby providing a direct link to behavior. A particle filter with state augmentation is used to jointly estimate the movement parameters and the state. A multiple iterated filter using overlapping data segments is implemented to match the parameter time scale with the behavioral inference. The time variation in the auto-covariance function facilitates identification of a movement model, allows separation of observation and process noise, and provides for validation of results. The analysis yields fitted parameters that show distinct time-evolving changes in fur seal behavior over time, matching well what is observed in the original data set.

Patterns in Taxonomic and Functional Diversity of Macrobenthic Invertebrates Across Seagrass Habitats: a Case Study in Atlantic Canada

Functional diversity (FD) characterizes the role of species within communities based on their morphological, behavioural and life history traits. Taxonomic diversity is not always a surrogate for FD, and ecosystem functioning is more dependent on functional traits rather than species richness. Despite this, most diversity studies in seagrass ecosystems do not consider the functional trait landscape. Here, we compare and contrast the taxonomic and functional diversity and composition of macrobenthic invertebrates (infauna and small epifauna) across a gradient of seagrass habitats (bare sediment, bed edge and bed interior) at three sites in Nova Scotia, Canada. We also determine the relationship between taxonomic diversity and FD to gain insight into the consequences of species loss. At two sites, we found that taxonomic diversity (species number and Margalef and Simpson’s indices) increased from bare sediments to the bed interior, while FD (Rao index) did not or else showed a weaker pattern. At a third site, both taxonomic and functional diversity tended to increase across the seagrass gradient. Despite the differences in relationships between taxonomic and functional diversity, functional trait composition tended to be distinct across seagrass habitats at all sites. Regressions showed that FD increased either hyperbolically or linearly with taxonomic diversity. Our study suggests that for seagrass ecosystems similar to the ones sampled, the implications of species loss for ecosystem functioning may not be easily predicted from data of taxonomic diversity alone. This study provides some of the first data of taxonomic and functional diversity in seagrass ecosystems, which can be used to inform conservation objectives and management practices.