Derzhavin's Biostatistical Method of Population Analysis

Abstract

Derzhavin's biostatistical method, as modified by Boiko and others, uses annual age censuses and catch statistics to compute the utilized stock (virtual population), Vi, of year-class i in a given year as the sum of all members of that year-class that are caught in the current and future years. The sum of Vi values for all year-classes present in a given year is the total utilized population, V. The biostatistical rate of exploitation for individual ages (Ci/Vi), or for the stock as a whole (C/V), is the catch divided by the utilized stock. If ages of the fish in the stock are read too low, values of Ci/Vi and C/V are too large. For fully recruited fish, Ci/Vi is an unbiased estimate of the total mortality rate, A, bat for incompletely recruited ages, it differs progressively from A and has no simple interpretation. Variations in abundance of successive year-classes do not affect the interpretation of Ci/Vi or C/V for fully recruited ages, but changes in rate of fishing, F, are disturbing. When incompletely recruited ages are included in a biostatistical computation (as has usually been done), C/V does not have any precise interpretation in terms of population parameters. In addition, variations in year-class strength affect the value of C/V even when F does not change from year to year. It is possible to use C/V for the whole catch as an "arbitrary" index that reflects the direction and magnitude of changes in intensity of fishing over a period of years. However, even for this purpose the same minimum age must be used in all years. When data for a long series of years are available, the utilized year-class strength (ΣCi) of the year-class hatched in year i can be compared with the total utilized stock (or the utilized mature stock) present in year i, in order to examine parent–progeny relations. Incompletely recruited as well as fully recruited ages can be used in this comparison, but adjustments are necessary if mortality rate (natural or fishing) changes from year to year. The biostatistical method does not provide separate estimates of natural and fishing mortality rates. If the possibility of a moderate or large natural mortality is disregarded, serious errors of interpretation may result.