Estimating Timing of Life-History Events With Coarse Data

Populations often are sampled with a coarse scale of measurement. As scale becomes increasingly coarse, the variance estimate can become biased; Sheppard's method has been used to correct that bias. Sheppard's correction, however, also becomes inadequate when the scale of measurement is too coarse. We develop a rule to decide how coarse a scale should be for a particular population variance. In addition, we propose a generalization of Sheppard's correction that allows for divisions of the scale to be unequal. Divisions of a measurement scale (intervals or bins) should be no larger than twice the population SD (σ). When the population variance (σ2) is small, a large amount of variation in interval size can produce inaccurate results. As σ2 becomes large, more variation in interval size can be allowed without producing large inaccuracies. This new methodology has wide application for estimating timing of life-history events for mammals where dates must be pooled into intervals. We demonstrate this method with computer simulations and with an example for estimating mean and variance of birth date in Dall's sheep (Ovis dalli).