Evolutionary Ecology

Submitted: 21 January 2014

Supplementary Information:

The shape of selection: Using alternative fitness functions to test predictions for selection on flowering time

Arthur E. Weis  Susana M. Wadgymar Michael Sekor Steven J. Franks

TABLE S1. Analysis of variance of flowering time, by population and season length.

Source / df / Sum of Squares / Mean Square / F / P
Population / 1 / 30,861 / 30,861 / 374.63 / <0.0001
Season Length / 1 / 1,537 / 1,537 / 18.66 / <0.0002
Pop  Season / 1 / 1,503 / 1,503 / 18.24 / <0.0003
Residual / 1135 / 93,496 / 82

TABLE S2. Parameter estimates for fitness functions in the short season environment. Parameter estimates in bold were significantly different from zero beyond the P = 0.001 level.

Back Bay / Arboretum
Parameter / Estimate / (Std. Error) / Estimate / (Std. Error)
Exponential Decay
a / 8.40 / (0.004) / 5.704 / (0.0049)
m / -0.09 / (0.0001) / -0.026 / (0.0001)
Piecewise Linear
a / 410.73 / (44.33) / 166.67 / (38.18)
mL / -11.30 / (1.92) / -15.63 / (5.86)
mR / -1.68 / (2.65) / -0.29 / (0.94)
v / 48.63 / (3.87) / 41.31 / (2.10)

TABLE S3. Parameter estimates for fitness functions in the long season environment, assuming a normally distributed error. Estimates indicated in bold are nominally different from null expectation at the 0.05 significance level.

Back Bay / Arboretum
Parameter / Estimate / (Std. Error) / Estimate / (Std. Error)
Generalized Epsilon-Skew-Normal
a / 6.98 / (1.50) / 7.30 / (0.0001)
p / 41.99 / (0.0003) / 61.78 / (0.002)
b / 121.95 / (6.70) / 50.99 / (0.040)
s / 0.96 / (0.0001) / -0.59 / (0.0002)
k / 0.46 / (0.0006) / 0.78 / (0.0006)
Piecewise Linear
a / 309.05 / (171.83) / 370.04 / (293.87)
mL / 14.06 / (4.05) / 16.52 / (6.13)
mR / -1.05 / (0.38) / -43.88 / (8.74)
v / 42.73 / (1.94) / 61.35 / (2.08)

Figure S1 Distribution of flowering times for the two populations under the two season length treatments. Dates at which watering was stopped are indicated.

FIGURE S2 SiZer analysis graphs showing the sign of the second derivatives of locally weighted ploynomial regression, evaluated at the observed flowering times, over a range of bandwidths. Blue regions indicate significantly positive curvature (convex) of the fitness function, red indicates a negative (concave) curvature. Purple regions indicate curvature is indistinguishable from zero, while gray indicates regions with insufficient data for analysis. The diverging curves though the center of the space indicate band size at each horizontal slice though the space.

Figure S3. Estimated fitness functions for the Back Bay (a & c) and Arboretum (b& d) populations of Brassica rapa.,assuming normally distributed error. Short season environment. Exponential decay function depicted in blue, and the piecewise regression in black. Estimated coefficients in Table S2. Note that while a 3-segmented lines fit best under the poisson error assumption, a 2-segments line fit best assuming a normal error distribution. The quadratic function plotted for comparison. Continued…

Figure S3, Continued. c & d): Long season environment. Generalized Epsilon-Skew-Normal function depicted in blue, while the segmented linear regression is depicted in blacb. Parameter estimates and their standard errors ad given in Table S3. The quadratic regression is plotted in red for comparison.

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