Definition and estimation of vital rates from repeated censuses: Choices, comparisons and bias corrections focusing on trees

1. Mortality and recruitment rates are fundamental measures of population dynamics. Ecologists and others have defined and estimated these vital rates in various ways. We review these alternatives focusing on tree population census data in fixed area plots, though many aspects have wider application when similar data characteristics and assumptions apply: our goal is to guide choices and facilitate comparisons. 2. We divide our estimates into instantaneous and annual rates, corresponding to continuous or discrete time dynamics, respectively. In each case, vital rate estimates can be further divided into those based on population density (per-capita rates) and those based on census area (per-area rates). We also examine how all such rate estimates relate to each other and can thus be interconverted and compared. 3. In a heterogeneous population (e.g. trees in a forest stand) comprising subpopulations (e.g. species, locations, exposure classes), estimates of vital rates that assume homogeneity (equal likelihood of mortality and equal likelihood of recruitment for all individuals) are biased towards lower vital rates in stable mixed populations (due to survivorship bias) and towards lower absolute values of population change rate (due to changing-frequency bias). 4. We describe and illustrate an individual-based Bayesian procedure for estimating vital rates that reduces biases by accounting for demographic heterogeneity and sampling errors among and within subpopulations.