Estimator of upgrowth transition rates for size-classified matrix from small samples

Matrix models can incorporate demographic, environmental or sampling stochasticity. The first two have intensively been studied, and we shall focus on the latter. It comes from the uncertainty on the estimation of vital rates, that generates an uncertainty on the model predictions. When dealing with size-classified models, the continuous information brought by the size may or may not be taken into consideration to estimate vital rates. The proportion estimator is obtained in the former case, whereas the increment estimator is obtained in the latter case. We compared these two estimators on the basis of their bias, variance and probability of being null, and applied the results to a tropical rain forest in French Guiana. The proportion estimator is unbiased, whereas the increment estimator is generally biased. We specified some conditions under which the increment estimator is also unbiased. However, the increment estimator generally has a lower asymptotic variance than the proportion estimator. As a consequence, the increment estimator is generally more efficient than the proportion estimator for small samples. Moreover, the increment estimator cannot bring null estimates, contrary to the proportion estimator, which reinforces its suitability for small samples.