Marine Research Findings of the VECTORS Project

This website provides access to the research results of the VECTORS project, which can be used to support marine management decisions, policies and governance as well as future research and investment. VECTORS was a large scale project that brought together more than 200 expert researchers from 16 different countries. It examined the significant changes taking place in European seas, their causes, and the impacts they will have on society.

Statistical analysis of changes in species distributions

Changes in the spatial distribution of marine animals may be indicative of ecological or environmental changes or reflect the impact of anthropogenic drivers. In order to correctly identify the cause of a distributional change it is necessary to use statistical models to account for sampling error and bias. In this project we have studied the statistical problems in separating overall abundance changes from changes in distribution. We have also developed a novel single species geo-statistical model that can be used to describe survey and fisheries data characterised by irregular sampling, many zeros and changing species distributions over time. The new model is a generic tool that can easily be adapted to any area for which time series of spatially explicit count data (numbers per sample) are available.

The relationship between abundance and commonly used indices of changes in fish distribution were studied by means of simulated sampling. Many of the common indices were found to generate relationships between abundance and distribution even when no such relationships existed. 

The relationship between abundance and distribution is a key issue in the management of marine ecosystems, as a population that contracts into a small area at low abundance becomes highly vulnerable to e.g. exploitation. The relationship between abundance and distribution is often investigated by using indices reflecting one of the three aspects of distribution: proportion of area occupied, aggregation, and geographical range. Using simulations and analytical derivations, we examine whether these indices provide unbiased estimates of the relationship when estimated from count data. Using simulations we found that many of the indicators generate relationships between abundance and distribution even when no such relationships exist. Selecting indices of spatial distribution that are unaffected by changes in overall abundance is important for analysing changes in distribution due to climate change and fishing. We show that a number of frequently used indices of distribution are intrinsically linked to the mean number of individuals observed per sample when the mean is small. Using such indices may lead to the erroneous conclusion that a change in distribution has occurred when in fact abundance is the only variables that changed. Apart from the effect that these erroneous conclusions may have on the understanding of the ecology of individual species, it may lead to inefficient conservation of natural populations if conservation management is based on the assumption that species aggregate at low stock sizes.


We have combined models of spatio-temporal correlations with models of population dynamics to make a complete estimation of the spatio-temporal dynamics of size structured populations. The new model can be used to assess the efficiency of closed areas and seasons, and to assess how environmental variables affect species distributions.

Spatial distributions of age or size-structured populations are usually modelled by fitting abundance surfaces for each stage and at each point of time separately, ignoring correlations that emerge from the growth of individuals. We have developed a new statistical model, the Log Gauss Cox Process (LGCP) model, that combines spatio-temporal correlations with simple stock dynamics to estimate simultaneously how size distributions and spatial distributions develop in time. The LGCP model uses space and time correlations to model the number of individuals caught per sample. Assuming the numbers caught to follow a Poisson distribution the spatio-temporal correlations and population parameters are estimated by maximum likelihood and used to predict abundance continuously through time and space. The method has been applied to a cod (Gadus morhua) population sampled by trawl surveys. Particular attention is paid to correlation between size classes wit hin each trawl haul due to clustering of individuals with similar size. The model estimates growth, mortality, and reproduction, after which any aspect of size structure, spatio-temporal population dynamics, as well as the sampling process can be probed. The new method improves the possibilities for testing hypothesis about the influence of environmental variables and anthropogenic drivers on the spatial distribution of population. It demonstrates that it is possible to combine stock assessment models and spatio-temporal dynamics; however, this comes at a high computational cost.

Relevance for Policy:
  • Common Fisheries Policy
  • Directive on Maritime Spatial Planning and Integrated Coastal Management (forthcoming)
  • Environmental Impact Assessment Directive
  • Marine Strategy Framework Directive


Lead Author:

Kasper Kristensen & Henrik Gislason
Danmarks Tekniske Universitet (DTU-Aqua)
Date of research: July 2014

Related articles:

Could MPAs mitigate the effects of fishing? 

Ecology - Economy interactions in fisheries 

Fishing vessels interactions with other activities 

Modelling hotspots of change in the North Sea 

Population dynamics of sprat in the Baltic Sea 

Saprobity in coastal lagoons

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The content of this website may be subject to copyright, if you wish to use any of the information or figures please contact the attributed author(s).
This project has received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement no 266445
© Vectors 2015. Coordinated by Plymouth Marine Laboratory.