Scottish Marine and Freshwater Science Vol 6 No 6: Development of a Model for Predicting Large Scale Spatio-Temporal Variability in Juvenile Fish Abundance from Electrofishing Data

Introduction

Large scale models of juvenile fish abundance are required to understand and predict spatial variability in fish productivity. In fisheries management, such models can inform the development of juvenile assessment tools from which to interpret electrofishing data (Godfrey, 2005; SNIFFER, 2011) or provide an intermediate step in scaling stock-recruitment relationships between data rich and poor catchments for the development of conservation limits (Wyatt and Barnard, 1997).

Fish productivity is known to vary at a range of spatial scales depending on water quality, food availability, hydraulic and sedimentary characteristics (Fausch et al., 1988; Armstrong et al., 2003). However, not all these variables can be adequately characterised at large spatial scales suitable for the development of regional or national models. Under such circumstances, it is necessary to substitute process based predictors for mechanistically plausible Geographical Information System ( GIS) derived surrogates to make spatial predictions of abundance. These surrogates typically take the form of landscape characteristics ( e.g., channel slope) that can be defined using a GIS, thereby allowing covariates to be readily obtained for sampling sites and predictions to be made for un-monitored locations.

In addition to the issues of scale and environmental characterisation, the development of juvenile density models is affected by technical challenges in two main areas: Firstly, the need to obtain density estimates from electrofishing observations, where catch probability likely varies with a range of factors including habitat, sampling equipment, procedures and personnel; and secondly, the need to model spatial variability in density where this is influenced by habitat, but is also spatially correlated.

Recent attempts to model spatial variability in juvenile fish abundance at large spatial scales have attempted to combine models of capture probability and spatial prediction using hierarchical Bayesian models (Wyatt, 2002, 2003; Rivot et al., 2008). Hierarchical Bayesian models can readily accommodate complicated model structures and are well suited for modelling electrofishing data. As such, these models provide joint distributions of the estimates of capture probability and abundance, integrating uncertainty across multiple sites. However, such complex models often require considerable time (days) to fit. In addition, because they are tailored for specific analyses, model exploration and comparison is time consuming and thus limiting. Likelihood based alternatives could offer significant benefits in terms of rapid fitting. Furthermore where generalised additive models can be used, this provides model flexibility (Wyatt et al., 2007b) and ease of implementation using standard software e.g., mgcv (Wood, 2011).

Unfortunately, between site variability in densities and capture probabilities cannot be estimated simultaneously using GAMs because the resulting likelihood is not an exponential family distribution (Wood, 2006). However, where capture probability is estimated separately, GAMs can be used to model density. Consequently, many previous approaches have estimated capture probability independently for individual site visits (Otis et al., 1978; Lanka et al., 1987; Huggins and Yip, 1997) or at the other extreme assumed a constant capture probability (Bohlin et al., 2001). Approaches that focus on individual site visits can result in poorly defined capture probabilities (and thus density estimates) or provide very uncertain estimates of density in the case where no fish are caught. Conversely, an assumption of constant capture probability across all sites is potentially an over simplification and could lead to an under-estimate of uncertainty or to model bias where estimates of density are fed into subsequent spatial habitat models. Improvements in density estimates could be made if capture probability were to be modelled in a flexible framework where it was allowed to vary with mechanistic covariates.

In contrast to terrestrial and marine spatial models, data collected on rivers have specific spatial structuring that is not directly related to the distance between sampling points, but instead to the combined effects of geographical (as the crow flies or Euclidian distance) and network distance. There have been a large number of statistical developments in recent years that could improve models of fish densities on river networks. For example, geostatistical approaches (Cressie et al., 2006; Peterson et al., 2013), or the use of Gaussian Markov random fields (Wyatt, 2003; Rue and Held, 2005). However, at present, there is no single software package that allows ready specification of models that could include variation at different spatial scales, on river networks, over time and in relation to landscape covariates. Such models would be desirable in the context of fish abundance studies.

This report describes the development of a two stage modelling approach that can be used to characterise, understand and predict spatio-temporal variability in fish abundance at the Scottish scale. This was achieved by developing models to (1) predict capture probability from removal electrofishing data and (2) to understand and predict spatio-temporal variability in fish abundance using GIS derived landscape characteristics and fish abundances estimated from the catch probability model.

As a first step, development and application of the models was undertaken using a single species and life stage: Atlantic salmon fry.

The report is structured according to the following specific objectives:

1. Identify, request and collate electrofishing data from internal ( MSS) and external sources including SFCC and SEPA.

2. Identify a set of GIS covariates that could plausibly influence fish abundance or capture probability and calculate these for each electrofishing site. Describe the processes involved and technical difficulties associated with the generation of covariates.

3. Develop models for estimating capture probability from depletion electrofishing data.

4. Develop models for estimating spatio-temporal variability in salmonid abundance.

5. Produce an R software package to fit the models identified in 4 & 5 and describe the process of model specification and selection.

6. Demonstrate model application using a case study of Atlantic salmon fry and interpret findings.

7. Make recommendations for future data collection, data processing, software development and modelling.