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In our second approach, we used ANCOVA with standard deviation as the dependent variable, sample date as the treatment, and mean brood weight and colony size as covariates.
Residuals were saved and then regressed onto colony size to determine if colony size contributed to the SD independently of mean brood weight.
The magnitude of β here suggests a substantial negative effect of colony size on the standard deviation once the effects of mean brood weight are taken into account, while the positive β value for the initial regression indicates that the standard deviation increases with mean brood weight, as expected.
We then pooled the two samples and regressed the standard deviation of brood weight for each colony size-sample date combination onto mean brood weight (F1,10 = 25.387, P = 0.001, β = 0.847) and saved the residuals.
For this procedure we calculated the SD of total brood weight for each colony size for each sample date, and then regressed the SD onto mean brood weight, taking sample dates into account.
For our species, the CLT predicts that deviations from mean brood weight should decrease with increasing numbers of foraging trips, and therefore with both time and with number of foragers in the colony (colony size).
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Most importantly, if sex ratios are constant for different sized colonies, this would be equivalent to changing the total weight of each colony by a set amount and this would not affect our analyses since we used the CV (see above), which removes the effect of mean colony brood weights.
Therefore, the relationship between the mean and SD of brood weight was analysed using an ANCOVA.
For each site and field collection, the mean and standard deviations in the number of brood per capita and brood weight were calculated for 1-female, 2-female, 3-female, and 4 (or more -female colonies.
"The de Menils are a mean brood.
The mean brood size of the 1-year old pairs in the 1st birth was 85.4±56.9 per brood, which was significantly smaller than that in the 6th birth (465.9±136.4 per brood) (P<0.001).
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