A multivariate indicator to monitor changes in spatial patterns of age-structured fish populations

Quantitative analysis of the spatial patterns in age-structured fish populations provides a useful complement to stock assessment methods. The spatial distribution of an age-structured population is characterized by indicators for location, dispersion and aggregation, which are estimated from survey data. The times series of spatial indicators are organised in a 3D data structure with dimensions along indicators, age classes and years. Multi factor analysis (MFA) is applied to quantify the reproducibility in time of the multivariate structure between age classes and indicators. MFA computes the mean annual pattern over the age classes. The deviation around that pattern in each year is also quantified. A multivariate indicator that characterise the spatial pattern over all age classes is developed. Its variation in time is evaluated with quality control methods. The multivariate indicator is shown to be $\chi ^{2}$ distributed and a CUSUM control chart is used to detect any significant changes in time. Software for implementing the method is presented and described. To illustrate this new method, North Sea cod data are analysed, and changes in the spatial patterns of the age-structured population are detected and interpreted