Calhim & Birkhead. Testis Compensation
SUPPLEMENTARY MATERIAL
TESTING OBSERVED AGAINST NULL DISTRIBUTIONS
We used fixed-x bootstrap regression techniques to generate new sets of y values (i.e. novel scatters based on the observed relationship between left
and right testis size for each species). Within each bootstrap scatter, demarcation lines were computed: the 99% CLs based on SMA regression, and
medians for x, y and x+y. Three criteria were used to test whether the observed scatter between right and left testis size is different form random
(i.e. bootrap estimate probability distribution based on 1000 repeats):
(i)
the proportion of points lying outside the 99% CL of the relationship which lie in area C is significantly higher than random,
(ii)
the overall relationship between datapoints in area C (upper and lower combined) has a more negative slope than expected by random
(using Type II regression),
(iii)
the correlation coefficient calculated for the observed points in area C (upper and lower separately) is more negative than expected by
random.
Criteria (ii) and (iii) were based on the fact that males showing testis compensation will show a negative right-to-left size relationship. Since we
use 99% CL to exclude a large central area of the plot, we artificially create two scatter areas which are intrinsically negatively associated.
Therefore, we use criterion (iii) as an additional step to criterion (ii): compensation is considered more pronounced when a negative (cf. random)
relationship is observed within each of the upper and lower C areas (bootstrap restricted to minimum n=5 data points). Analyses were conducted
using R v.2.3.1 (R Development Core Team 2006).
Table S2. Bootstrap analysis results.
Original estimate
Bootstrap estimate (± s.e.)
Criteria met? (one-tailed Wilcoxon test)
SUPPLEMENTARY MATERIAL
Criterion (i): Proportion of data points outside 99% CL that occur in area C (upper & lower combined) is greater than expected by chance.
Red-billed quelea
0.75
0.65 (±0.073)
Yes (p<0.0001)
Zebra finch
0.88
0.71 (±0.15)
Yes (p<0.0001)
Criterion (ii): Slope across data points across areas C (using Type II regression) is more negative than expected by chance.
Red-billed quelea
-1.09
1.05 (±0.45)
Yes (p<0.0001)
Zebra finch
-0.93
0.63 (±0.80)
Yes (p<0.0001)
Criterion (iii): Correlation coefficient across area upper and lower areas C, separately, is more negative than expected by chance.
Red-billed quelea
Zebra finch
(upper)
-0.32
0.17 (±0.23)
Yes (p<0.0001)
(lower)
-0.48
0.23 (±0.21)
Yes (p<0.0001)
(upper)
0.39
0.19 (±0.43)
No (p>0.99) *
(lower)
0.86
0.26 (±0.39)
No (p>0.99) *
* Data points are mostly parallel to the line defining relationship between left and right testes, hence the positive association observed in the original data. In
addition, there was a non-significant trend for higher degree of compensation in the red-billed quelea cf. zebra finch (mean |residuals| across both upper and lower
C areas, controlling for species-specific GSI: Kolmogorov-Smirnov test, D=0.40, p=0.094).
Calhim & Birkhead. Testis Compensation
SUPPLEMENTARY MATERIAL
Figure S2. Histograms of the bootstrap estimate distributions. The red solid lines represent original data estimate, the dashed lines refer to the
standard error interval of mean bootstrap estimates. See Table S2 for statistical analyses.