Abstract. — Determining absolute 

 survival rates for larval fishes is ex- 

 tremely difficult. However, many eco- 

 logical questions concern relative sur- 

 vival of two groups. For example, we 

 might ask: (1) Do older larvae have 

 higher survival than younger larvae? 

 and (2) Do faster growers have high- 

 er survival than slower growers? We 

 present a simple model and several 

 estimation schemes for the ratio of 

 survival rates based on monitoring 

 relative abundance of the two groups 

 over time. When the logarithm of the 

 ratio of abundances is regressed on 

 time, the resulting estimate of slope 

 is an estimate of the difference in in- 

 stantaneous mortality rates. An esti- 

 mate of the ratio of survival rates is 

 obtained by exponentiating the slope. 

 The model is shown to be a logistic 

 model and can be fitted by maximum 

 likelihood methods. 



Estimating Relative Survival Rate for 

 T\A/o Groups of Larval Fishes from 

 Field Data: Do Older Larvae 

 Survive Better Than Young? 



John M. Hoenig 

 Pierre Pepin 



Science Branch, Department of Fisheries and Oceans 



PO Box 5667. St John's. Newfoundland, AlC 5X1, Canada 



William D. Lawing 



Departments of Statistics and Industrial Engineering 

 University of Rhode Island, Kingston, Rhode Island 02881 



Manuscript accepted Ki April 1990. 

 Fishery Bulletin. U.S. 88:485-491. 



Determining absolute survival rates 

 for larval fishes is extremely difficult, 

 even when cohorts can be accurate- 

 ly identified by means of daily growth 

 rings in the otoliths. For example, 

 survival between times 1 and 2 might 

 be estimated by catch/tow at time 2 

 -^ catch/tow at time 1. Due to ran- 

 dom sampling error alone, this esti- 

 mate may be nonsensical (>1), and 

 the chances of obtaining nonsensical 

 estimates increases with increasing 

 patchiness in the distribution of lar- 

 vae over space. 



In some cases, it may not be neces- 

 sary to estimate absolute survival 

 rates. Estimates of relative survival 

 rate may be sufficient and easier to 

 obtain. Many ecological questions 

 concern the relative survival rates of 

 two or more groups. For example, at 

 a given point in time, the older lar- 

 vae present should be larger than the 

 yotmger larvae and, hence, may have 

 a higher survival rate (Peterson and 

 Wroblewski 1984, McGurk 1986). On 

 the other hand, it has been suggested 

 that larvae born later (i.e., younger 

 larvae) may have a higher survival 

 than larvae born earlier (Victor 1983, 

 Methot 1983, Crecco and Savoy 1985, 

 Rice et al. 1987). Also, it has been 

 suggested that faster-growing larvae 

 survive better than slower-growing 

 ones (Rosenberg and Haugen 1982). 



In this paper, we consider how rela- 

 tive survival rates can be estimated 

 for two groups occurring at the same 

 time and place from field data con- 

 sisting of the composition of the catch 

 at two or more times. The intuitive 

 basis for the method is this: Changes 

 in the relative abundance of two 

 groups over time reflect differences 

 in mortality rates (assuming no emi- 

 gration or immigration occurs). The 

 methods we present allow for catch- 

 ability to differ for the two groups 

 and to vary over time. However, the 

 relative catchability (ratio of the catch- 

 ability coefficients) of the groups can- 

 not change over the time period con- 

 sidered. Thus, if factors such as wind, 

 currents, boat speed, or net clogging 

 vary among sampling periods, then 

 the same proportional change in the 

 catchability coefficient must occur 

 for both groups. This is less restric- 

 tive than assuming constant catch- 

 ability over time (as when estimating 

 absolute survival rate by the decline 

 in catch-per-unit-sampling-effort 

 over time). 



Development of the model 



Suppose that at time t, a sample of 

 larvae is obtained and that examina- 

 tion of the otoliths reveals that all lar- 

 vae are of the same (approximate) 



485 



