DeMoNS (Determining Mortality rates from Nonequilibrium Size frequency data):

An Excel spreadsheet for estimating total mortality rates from a time series of estimates of mean length.

This spreadsheet was developed by Clay Porch of the National Marine Fisheries Service Miami Laboratory to implement the method described by Gedamke and Hoenig (2006).

Click here to download the Excel spreadsheet.

Background

It has been known since the time of Baranov (1918) that mean length in a fish population goes down as the total mortality rate increases. Beverton and Holt developed the following simple estimator for the total mortality rate:

where Z is the total instantaneous mortality rate (per year), k and are parameters of the von Bertalanffy growth equation (k has units of yr^-1), is the mean length of those animals above the size L_c, and L_c is the size at which animals are first caught (assuming knife-edge recruitment)

This estimator is attractive because of its minimal data requirements. However, it requires some important assumptions, principally that recruitment is constant over time and that mortality rate is constant over age and over time.

Recently, Gedamke and Hoenig (2006) generalized the approach of Beverton and Holt to allow mortality rate to change at one or more discrete points in time. Then, given a series of annual observations of mean length over time it is possible to estimate the original total mortality rate, the year in which it changed, and the new mortality rate (and, possibly, the year the next change in mortality rate occurred, the newer mortality rate, and so forth).

Below is an example pertaining to goosefish (monkfish, Lophius americanus) taken in the National Marine Fisheries Service groundfish trawl survey in the Mid-Atlantic Bight. The sample sizes for each year are quite low and the mean size is highly variable from year to year. Nonetheless, there is a clear downward trend in the mean length over time suggesting an increase in mortality rate. The data give rise to the following estimates: Z was 0.33 up until 1977 when it rose to 0.58 per year.