What Can We Learn about Mortality from Sex Ratio Data? A Look at Lumpfish in Newfoundland

Abstract

Sex ratio data can provide information about mortality rates, which may be especially useful for sex-specific fisheries when little other information is available. In this paper, we develop a theory and methods relating sex ratio to mortality rates and apply them to data for lumpfish Cyclopterus lumpus on the southern Newfoundland Shelf. If the sexes have different mortality rates, and the rates as well as recruitment are constant with age and time, the sex ratio of the population provides an estimate of the ratio of the instantaneous mortality rates of the sexes. If a cohort can be followed over time, changes in the sex ratio provide an estimate of the ratio of the survival rates of the sexes or the difference in the instantaneous mortality rates. With the latter approach, it is not necessary for the sexes to have equal catchabilities in the survey nor for recruitment to be constant over time. This approach involves fewer assumptions and is of greater general interest, but it requires that cohorts be identified either by aging or tagging the fish. For lumpfish, we used sex ratio data from a research survey to estimate the change in the mortality rate of females, which are the subject of a sex-specific roe fishery. Unfortunately, it is not possible to follow cohorts of lumpfish over time because lumpfish caught in the survey are not aged. Nonetheless, the sex ratio (females : males) decreased progressively from approximately 2.24 in 1985 to 1.09 in 1994. We attribute the decline to a doubling of the mortality rate of female lumpfish caused by the fishery, and our analysis probably underestimates the true change because of failures of assumptions. Our results are consistent with those of other work on lumpfish in Newfoundland and indicate that there is cause for serious concern about the effects of the fishery on lumpfish stocks.