Fig. S1. Cohen’s (1966) model of bet hedging under “good” (green bars) or “bad” (red
bars) years offers a simple way to distinguish between geometric- and arithmetic-mean
fitness. The geometric-mean fitness is maximized by a dormancy fraction equal to the
frequency of bad years, whereas the arithmetic-mean fitness is always maximized by
complete germination (zero dormancy) when the probability of a bad year is <0.5. In this
example, an organism must allocate its ten propagules to immediate germination (green
numbers) or dormancy (red numbers) under 0%, 20% and 40% “bad” years. The
geometric mean of the number of successful offspring across generations reflects true
reproductive success, and cannot be improved upon with any alternative strategy.
r2 = 0.20
P = 0.0001
0.5
0.4
Observed evolu on
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Expected evolu on
Figure S2. Regression of observed on expected evolutionary change in ascospore
dormancy fraction with the zero bad-year treatment omitted from the dataset. Data points
represent replicate evolutionary trials of each genetic lineage. For the regression using the
entire dataset, see inset of Figure 1 of main document.
Table S1. The five year-type sequences (G=“good”, B=“bad”) within each selection line.
Each sequence was replicated for each of twelve genetic lineages. The term “year” is
used to parallel Cohen’s model and corresponds to one sexual cycle and the scale on
which selection is imposed. It should not be confused with the much larger number of
“generations” associated with mitotic nuclear divisions that occur within an ascospore-toascospore cycle. Note that different numbers of mitotic generations among treatments
resulted because the duration of good years is longer than bad years: the priority was to
manipulate the proportion of good vs. bad years while maintaining a constant number of
rounds of selection. This was constrained by the need to conduct all treatments over the
same time period so as not to confound temporal environmental effects with treatment
effects. Dormancy tests were conducted simultaneously at the termination of the
experiment; thus, the total number of cycles of selection increases with the frequency of
“bad” years in a sequence.
“Bad”
year
selection
line
0%
25%
30%
40%
50%
1
2
3
4
5
“Year” Number
6
7
8
9
G
B
G
G
G
G
B
G
B
G
G
B
G
B
B
B
B
G
G
G
G
G
G
G
B
G
G
G
G
B
G
G
G
G
G
B
G
G
G
G
B
G
B
G
G
B
G
G
B
B
B
G
G
G
B
G
G
G
B
G
G
G
G
B
B
G
G
G
G
B
G
G
G
G
G
G
G
B
G
G
G
G
B
B
B
G
G
G
G
G
B
G
G
B
G
G
B
G
B
G
G
G
G
G
B
G
B
G
G
B
G
B
B
G
B
G
B
B
B
G
G
G
B
G
B
G
G
B
G
G
G
G
G
G
G
G
G
G
B
G
B
G
G
G
G
B
B
B
B
B
B
B
B
10
11
12
13
14
G
G
G
B
G
B
G
G
G
G
G
G
G
G
G
G
G
G
B
G
B
G
B
G
G
B
B
B
B
B
G
B
B
G
G
G
G
G
G
B
G
G
G
G
G
G
G
G
G
B
G
G
G
B
B
B
B
B
G
B
G
G
G
G
G
G
G
G
G
G
G
Table S2. Results of preliminary study showing intermediate ascospore dormancy
fractions under experimental conditions (55°C for 45 minutes) for all genetic crosses
used in selection experiment. Dormancy is measured as the fraction of viable ascospores
that germinate only following a second heat treatment at 55°C for 45 minutes.
Cross
Mean Dormancy
Fraction (SE)
4832 x 4827
0.325 (0.177)
4712 x 4835
0.320 (0.070)
4712 x 4714
0.424 (0.054)
10654 x 4837
0.363 (0.084)
10654 x 4711
0.296 (0.104)
4712 x 2225
0.352 (0.077)
4828 x 4714
0.279 (0.041)
4828 x 4827
0.502 (0.054)
4831 x 4834
0.233 (0.087)
4831 x 4837
0.232 (0.070)
8876 x 4837
0.266 (0.089)
Table S3. Analysis of variance results for final dormancy fraction for bad-year categories
treated individually (a) and for various biologically motivated groupings: 40% and 50%
treatments grouped because of near identity between one 40% and the 50% sequences
(b); grouping low and high bad-year categories (two possible ways: c and d); and
grouping the similar 25% and 30% treatments to construct low, medium and high
categories (e).
% Bad-year
Source
df
SS
F
P
a)
Bad-year frequency
4
0.342
2.90
0.027
0, 25, 30, 40, 50
Within
82
2.420
b)
Bad-year frequency
3
0.333
3.79
0.013
0, 25, 30, (40, 50)
Within
83
2.430
c)
Bad-year frequency
1
0.226
7.57
0.007
(0, 25, 30) (40, 50)
Within
85
2.537
d)
Bad-year frequency
1
0.301
10.40
0.002
(0, 25) (30, 40, 50)
Within
85
2.461
e)
Bad-year frequency
2
0.301
5.13
0.008
0, (25, 30) (40, 50)
Within
84
2.462
categories
Text S1
If the probability of a particular outcome is p, the probability Pk of observing k or more
occurrences of this outcome given n independent events is:
Pk =
n!
p k (1- p)n-k .
k!(n - k)!
The binomial distribution may be used to test the statistical null hypothesis of no
relationship between frequency of bad years and the evolution of dormancy fraction for
the 12 genetic lineages used in the selection experiment where power precludes tests for
positive regression slopes in each genetic lineage. The one-tailed probability of
observing 11 or more positive nominal slopes of 12 for final dormancy fraction is given
by P11 + P12 = 0.00317, and the observation of 10 positive nominal slopes of 12 for the
regression of observed vs. expected evolution of dormancy fraction is given by P10 + P11
+ P12 = 0.0193.