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.