COLLECTION OF EGGS AND LARVAE 



Eggs and larvae were collected with a hydraulic 

 sampler (McNeil, 1962a) from small enclosed 

 quadrat or circular areas (sampling units) of known 

 area. Area of sampling units varied from 0.2 

 to 0.9 m. 2 



Samples preserved in the field were examined 

 later to determine the number of live and dead 

 eggs and alevins collected. Eggs were preserved 

 in a clearing solution (Stockard's solution). 



ESTIMATION OF MORTALITY 



Data on egg and larval populations were 

 analyzed by three methods to obtain information 

 on temporal changes and spatial differences in 

 mortality levels. Although the methods have 

 been described (McNeil, 1962a), they will be 

 reviewed briefly here. 



Ratio of Dead to Total Eggs and Larvae 



Mortality has commonly been estimated from 

 ratios of dead to total e^<i's and larvae collected 



in k samples; 



.e..° 



dead 

 live + dead 



(3) 



An estimate of mortality based on such ratios 

 underestimates true total mortality where the 

 number of eggs and larvae present in the spawning 

 bed at the time of sampling is less than the number 

 of eggs originally available for deposition. Des- 

 pite this limitation, estimates of M r are very 

 helpful in establishing time of mortality where 

 mortality is caused by factors not associated with 

 the direct removal of eggs and larvae from the 

 spawning bed and are sometimes useful in setting 

 lower limits to total mortality. 



Actual and Potential Abundance 



Total mortality ( M ,) can be estimated from 

 statistics on potential egg deposition and abun- 

 dance of live eggs and larvae at the time of 

 sampling. In this study, estimates of M, were 

 calculated from the double inequality 



1— gv<M«<l- -., 



(4) 



In double inequality (4), the value a and a are 

 the upper and lower confidence limits respectively 

 of the estimated number of live eggs and larvae 

 per m. 2 of spawning bed, and E' is the expected 

 number per m. 2 Values for a and a were cal- 

 culated with the standard error of the mean 

 obtained from either arithmetic or log-transformed 

 counts of live eggs and larvae. Log-transformed 

 counts are used only if the efficiency of the esti- 

 mate of Mi is increased without introducing 

 significant bias. 



Wliere the logarithmic transformation is used. 

 each observed count is transformed by the equa- 

 tion 



6,=log 10 (n t +P) (5) 



In equation (5), 6, is the transformed variate 

 and iii is the number of live eggs and larvae 

 collected at the i th point. The term /3is a constant 

 which describes the degree of contagion in a nega- 

 tive binomial distribution. A value of /3 is calcu- 

 lated from the expected frequency of zero observa- 

 tions in a negative binomial distribution. The 

 method, described by Anscombe (1949) and Bliss 

 (1953), requires an iterative solution of the 

 equation 



ilog !0 (l+j8SS) = 



og l0 (p) 



(6) 



'The value M, estimates the population parameter M,. The circumflex 

 : di ill be used to Identify estimators ofother population parameters. 



where k is the total number of observations, k' is 

 the number of zero observations, and n is the 

 sample arithmetic mean. 



To set confidence limits to estimates of abun- 

 dance of eggs and larvae with log-transformed 

 data, the mean log values must be corrected so 

 that the arithmetic mean will result from the 

 antilog. A correction term is required because 

 the mean of log-transformed data is geometric 

 rather than arithmetic (Ricker, 195S, ch. 11). 

 Jones (1956) developed the correction term and 

 described the method used here to calculate 

 confidence limits with log-transformed counts. 

 The equation used to obtain an arithmetic mean 

 (n) from the log-transformed counts is 



n=antilog (b+1.1518sl)-p, (") 



where b is the logarithmic mean value and s] 

 is the sample variance of the log-transformed 

 counts. The term 13 is subtracted to correct for 

 its addition to the counts before making the 

 transformation in equation (5). 



504 



D.S. FISH AND WILDLIFE SERVICE 



