Statistical models for biological growth curves.

The problems of selecting and fitting models to data collected on the growth of an organism or population are considered. The ways of identifying suitable models are reviewed and some suggestions made using smoothed growth rates. The problems in fitting non-linear models to growth data are considered. Use is made of measures of non-linearity and new methods developed to take into account the effects of non-linearity and also the possible presence of auto correlated errors. Stochastic dynamic models for growth are examined and parameter estimators found. Extensive use is made of the Kalman filter. For multivariate situations two methods by which phase plane solutions can be fitted in the bivariate case are developed. The use of the Kalman filter is also considered.The study also considers the role of statistical modelling. A possible methodology is presented. Examples from two areas are presented: plant growth and child growth.