Wade Population size of Stenella longirosths orientalis 



783 



a: 



0.06 



Figure 6 



Point estimates and 95 f r confidence limits for relative 

 population size for the eastern spinner dolphin 

 {Stenella longirostris orientalist, as a function of the 

 maximum net recruitment rate (/?.„). for the estimate 

 of the maximum net productivity level (MNPL=0.60i 

 currently used for management under the U.S. Ma- 

 rine Mammal Protection Act. 



tend to cancel itself, as over-estimates of kill in 

 some years would be balanced by under-estimates 

 in other years. However, systematic bias in the 

 kill estimates would lead to a poor estimate of 

 relative population size, creating a relatively 

 precise yet inaccurate estimate. The same 

 would be true for bias due to the use of an 

 inappropriate model, or in the estimate of N,.. 

 Potential biases in these three areas must 

 therefore be considered. 



Bias 



Two major sources of bias may have existed in 

 the fisheries kill estimates from 1972 to the 

 present. One source of bias, that of observer 

 effects, has been demonstrated and implies that 

 less dolphin kill occurred on observed trips due 

 to modifications in fishing behavior in response 

 to the observer's presence (Wahlen and Smith, 

 1985). Unfortunately, there is no way to esti- 

 mate the magnitude of the effect. The second 

 potential source of bias was the lack of partici- 

 pation in data collection by some countries dur- 

 ing some years, especially if significant differ- 

 ences in kill rates existed between countries. 

 Most important may have been the lack of 



1979-1986 data from Mexico (Edwards, 1989), a major 

 component of the fishery whose kill rates may have been 

 higher than average during that time period. These bi- 

 ases would lead to under-estimates of kill and thus over- 

 estimates of relative population size. 



Additional sources of bias existed in the pre-1972 kill 

 estimates, because of both a lack of observations of mor- 

 tality-per-set (MPS) in many years and because the MPS 

 data prior to 1971 were not collected as part of a system- 

 atic observer program. Data on the number and types of 

 sets were collected in every year, starting in 1959 (Punsly, 

 1983), but an observer program for collecting MPS data 

 was not started until 1971 and random placement of ob- 

 servers until 1972 (Edwards, 1989). The moderate amount 

 of MPS data collected in 1971 was potentially biased be- 

 cause most of the boats with observers were smaller and 

 older, and may have had a higher MPS (Edwards, 1989; 

 Lo and Smith, 1986, table 1). Most of the pre-1971 data 

 were from scientists who were on the tuna boats for the 

 purpose of collecting dolphin specimens, but who also re- 

 corded MPS data on their own initiative (Smith and Lo. 

 1983). There is no obvious reason why tuna vessels that 

 agreed to allow scientists to collect specimens during their 

 fishing operations would tend to have different mortality 

 rates, but in a strict sense these were not random samples 

 of fishing trips. Data from one fishing trip in 1964 were 

 recorded and reported by a fisherman, who may have done 

 so because of the magnitude of the kill, making those 

 data potentially biased (Smith and Lo, 1983). However, 

 the MPS data did not differ greatly in those years from 

 the data collected in 1972 (Lo and Smith, 1986, table 1). 

 Because of this and the greater quantity of MPS data 

 available from 1972, estimates of 1959-1972 fisheries kill 

 made by multiplying the average 1972 MPS rate by the 

 number of sets in each year would not differ greatly from 

 the estimates used here from Lo and Smith (1986), which 

 were made by using the pooled 1964-1972 MPS rate. 



Therefore, the fisheries kill would only have been over- 

 estimated if the MPS in the pre-1971 unobserved years was 

 lower than in 1972. However, MPS has consistently declined 

 over time, declining most rapidly following the passage of 

 the Marine Mammal Protection Act in 1972 (Smith 1983). 

 No evidence exists that MPS could have been lower from 

 1959 to 1970 than it was in 1971-72. MPS may have been 

 higher, especially before use of the back-down procedure had 

 become widespread and well practiced (Perrin, 1969; 

 Edwards, 1989). If it is assumed that MPS has only declined 

 since the beginning of the fishery, the 1959-1970 kill esti- 

 mates of Lo and Smith ( 1986) were likely under-estimates of 

 the true kill. Thus, the major sources of bias in fisheries kill 

 estimates all suggest that kill estimates were negatively 

 biased. 



Bias in the estimate of abundance could also bias the 

 estimate of relative population size. Wade and Gerrodette 



