Testing for simple structure in a spatial time series with an application to the distribution of Alexandrium resting cysts in the Gulf of Maine

We describe a test of the goodness of fit of a simple model for the mean of a spatial time series. Under this model, the mean consists of a temporally varying scaling of a fixed spatial map. The test is applied to the distribution of cysts of the harmful algal bloom organism Alexandrium fundyense in the top 1 cm of sediment in the Gulf of Maine over the period 2004 to 2012. The analysis, which was motivated by a practical problem encountered when designing an annual cyst survey, supports this simple model. The test has broad applicability in marine ecology and related fields.