Strain and maturation effects on female spawning time in diallel ...

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interaction of sire strain k <strong>and</strong> <strong>maturation</strong> year l; (DSM) jkl is the interaction of dam strain j,
sire strain k <strong>and</strong> <strong>maturation</strong> year l; <strong>and</strong> eijklm is the residual error associated with
observation ijklm. A similar analysis was done by Friars et al. (1979) for diallel crosses
of Atlantic salmon.
Least squares means for strain <strong>effects</strong> were estimated from Models 1 <strong>and</strong> 2 <strong>and</strong>
compared with Tukey’s test for pairwise comparisons. Heterosis, defined as a significant
difference between the average spawn date of two pure strains <strong>and</strong> the average spawn date
of their hybrids, was tested with Model 2 contrasts.
Contrasts between G1 reciprocal crosses were inestimable from Model 2, therefore each
strain combination was considered a separate fixed effect. Model 3 contrasted 3 <strong>and</strong> 4
years of age spawn dates among reciprocal crosses,
yijkl ¼ l þ Yi þ Cj þ Mk þðCMÞ jk þ eijkl
where y ijkl is the 3-year old or 4-year old spawn date for individual l in year class i with
strain combination j; C j is the fixed effect of strain combination j ( j=1,..., 9); (CM) jk is the
interaction of strain combination j with <strong>maturation</strong> year k; e ijkl is the residual error
associated with observation ijkl; <strong>and</strong> remaining variables are as described for Model 2.
2.3.3. Repeatability
Repeatability is the correlation between repeated measurements on the same individual,
<strong>and</strong> is used to predict future performance (Falconer <strong>and</strong> Mackay, 1996). In this study,
spawn date repeatability was estimated on 4R females only because these fish had two
spawn date measurements each. The repeatability estimate for each generation was the
partial correlation between spawn dates calculated from analysis of variance. The analysis
removed <strong>effects</strong> of having different strains to find a pooled within-strain correlation value
for each generation. Model 1 was used for G0 <strong>and</strong> Model 2 was used for G1, where the
dependent variable was the 3 or 4 years of age spawning dates <strong>and</strong> other variables were as
previously described.
To predict future performance, it is also practical to know if the entire spawning
season of a population can shift in time over years. The overall time shift in days
between the first <strong>and</strong> the second spawning seasons was examined using general mixed
linear models. This estimated the difference in time, in days, from the first spawning
season to the second spawning season. In this case, all the spawning data were used, but
a r<strong>and</strong>om individual effect was added to distinguish maiden from repeat spawners. In the
first spawning season, all females were maidens, but in the second spawning season,
females could be either repeat or maiden spawners. The spawning season number effect
accounts for permanent environmental <strong>effects</strong> of having spawned previously. Model 4
was used for G0,
yijkl ¼ l þ Pi þ Tj þðPTÞ ij þ Ik þ eijkl
where yijkl is the 3- or 4-year old spawn date for individual k in pure strain i <strong>and</strong>
spawning season j; Tj is the fixed effect of the spawning season number j ( j=1, 2); (PT)ij
is the interaction of pure strain <strong>and</strong> spawning season number; Ik is the r<strong>and</strong>om effect of
ð3Þ
ð4Þ