Mathematics & StatisticsCurrent Projects

Abstract: Atlantic salmon are the most economically important species of freshwater fish in Scotland. They also have a high conservation value, as demonstrated through numerous Natura designations under the EU Habitats Directive. The assessment of Atlantic salmon and other salmonids is a central part of the FRS FL mission on fisheries management for the SG. Scotland has a unique diversity of salmon run-timing which greatly enhances the commercial value of Scottish salmon fisheries.

Abstract: We aim to construct a spatial multi-species ecosystem model focused on commercially exploited fish in the northern European shelf (47 to 62 degrees N, and -12 to 10 degrees E). Species or functional groups within the model will be placed within a hierarchy of biological detail. At the highest, or "structured", level of detail the target species will be represented by interacting length-structured populations in which the processes governing individual growth, predation, reproduction, and mortality are fully specified. At an intermediate level will be "unstructured" ecosystem elements, such as benthic invertebrates and zooplankton, that are represented dynamically but without life history detail. At the lowest level of detail we will have the "drivers" of top predators (cetacean and seabird) and fishing mortality, which are not modelled but provide forcing functions to the rest of the ecosystem. The model will be run at various spatial scales, from a series of linked regional models through to medium-scale grid covering the entire domain. The physical environment will be obtained from an ocean circulation model, with temperatures used to drive temperature-dependent process such as growth rate, and flows determining the transport of plankton zooplankton and fish larvae. The model will be parameterised using fishing survey data, and estimates of zooplankton and benthic production, and estimates of consumption by top predators. Due to the potential for ecologically and commercially important impacts by top predators a joint proposal (for a tied studentship) will aim to produce improved spatial estimates for these drivers. Free parameters will be estimated by Markov chain Monte Carlo (MCMC) methods. We will draw on a range of computational innovations developed at Strathclyde University for dealing with explicitly spatial models of populations with life history structure and growth variability. We will use the Ecopath software as an aid to constructing regional budgets for mass transfer between the species in our system, and which can then be compared to those predicted by our model. Our modelling approach differs substantially from alternative ecosystem modelling methods, such as Ecopath with Ecosim (EwE), that are frequently advocated as the way forward for ecosystem-based management in fisheries. A key part of our proposal is therefore a comparative study involving EwE regional ecosystem models, with a view to identifying the strengths and weaknesses of alternative methodologies.

Abstract: Many global marine fisheries have collapsed, or are at record low levels of abundance. Continuing exploitation and the uncertain impacts of climate change are adding further pressures on fish resources. New strategies are therefore required to assist in our management and conservation efforts. One such development will be to incorporate the extent and dynamics of spatially-associated biological differences that exist among fish stocks into stock assessment.

Abstract: The aim of the project is to develop a high-spatial resolution ecosystem model of an inshore area of the west of Scotland focussing on secondary producers and their predators. We shall use a box-model approach to represent nutrients and primary production adapted from previous work, allied to a demographic representation of secondary producers and their principal predators adapted from a fish-focussed non-spatial ecosystem model currently under development (FRS funded) at the University of Strathclyde. The model will cover the region surveyed in the FRS 1991 Loch Linnhe programme (see diagram below) plus connecting waters; the Firth of Lorne from Luing northwards, the Sound of Mull and the whole of Loch Linnhe up to the narrows at the mouth of Loch Eil. The physical context of the ecosystem model will be set by the hydrodynamics of the system. These will be simulated using the POLCOMS model configured for the region of interest at a resolution of about 100m. Key drivers of the model will be freshwater inputs and winds. Although good fresh water run-in data are available for this area for both the 1991 hindcast period (Heath 1995) and for the present day, only rather generalized wind data exist. Since western Scottish inshore waters are located in mountainous terrain, wind circulation (and hence wind driven surface currents) show strong local heterogeneity, and it will be necessary to develop a local wind model, which can predict surface wind forcing in relation to local terrain. This model will be developed and validated against present-day behaviour observed as part of field data collection during this programme. The resulting validated wind model will then be used to drive POLCOMS under present day conditions, so that the flow predictions can be validated against observations. The combined models will be used to hindcast flow fields during the 1991 survey as drivers for the biological model. A key aspect of the biological modelling will be testing against the 1991 survey data. To this end the model will be designed to facilitate Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) methods. Such estimation not only locates a `best-fit' parameter combination, but also evaluates parameter uncertainty and correlation; an invaluable tool during model development. For this purpose we shall develop models at a variety of spatial resolutions, running from a high resolution model at 100m scale, which will be primarily used in prognostic mode, down to a low resolution model at approximately 1km resolution, which will be used mainly for extended parameter exploration. We expect that the parameter estimation models will use a well established vertical scheme which divides the water column into surface (above the pycnocline), intermediate (tidally flushed) and deep (i.e. flushed only at turnover events) layers. However, to investigate sub-tidal cycle events we shall also construct a high resolution model with full water column representation.

Abstract: Several of Scotland’s key fish stocks are being managed with reference to pre-determined strategies or harvest control rules. In order to provide advice on the likely utility of these plans, it is necessary to evaluate their effects, and the effects of potential subsequent revisions.

Scottish Government Marine Scotland project MF0767 (April 2009 – March 2012)

Abstract:The 5th North Sea Conference in 2002 agreed that an EcoQO should be developed and applied in the framework of OSPAR for the ecological quality element “changes in the proportion of large fish and hence the average weight and average maximum length of the fish community”. The EcoQO index is referred to as the “Large Fish Index” (LFI).

The justification given for this EcoQO is that in exploited fish assemblages, larger fish generally suffer higher fishing mortality than smaller individuals and the size distribution becomes skewed towards the smaller end of the size spectrum.The purpose of this project is provide the research framework for Marine Scotland and University of Strathclyde scientists to develop a fish community ecosystem model of the LFI, lead this work in ICES, and be at the forefront of developing the necessary advice at the North Sea scale to OSPAR.

The fish community model is a development of the partial ecosystem model of cod developed in project MF0762 (see “Recent projects”). Although the ‘proportion of large fish’ metric is expressed at the North Sea scale, the fish represented in the model are not distributed North Sea-wide, and so in reality do not have access to each other as predators and prey. Hence, the model needs elaboration if it is to deliver advice on the North Sea-wide community metric as a result of altering fishing patterns. One way to achieve this might be to parameterize the spatial overlap of the various component species. An alternative is to make the model more spatially explicit, by either setting up independent models for different sub-regions of the North Sea and aggregating the results, or to allow communication between the sub-regional models according to hydrodynamic and migration schemes, so that fishing on one sub-region has consequences for the fish community in other regions of the domain. The project will need to explore the pros and cons of each of these alternatives.