1
SUPPORTING FIGURE
2
3
Fig. S1 Mean weekly temperatures derived from the Lake Model FLake (a), and
4
photoperiods including morning and evening civil twilights (b) for the three studied regions.
5
The x-axis shows time (weeks), for start and end of experiemnt, where 0 indicates the start of
6
the experiment for northern, central and southern regions. The shaded square indicates
7
mean daily temperature measured at the northern site on 8 August 2013 (week 11).
8
9
SUPPORTING TABLES
10
Table S1
11
Coordinates for sampled populations, estimated population size, number of days within a year when the shallow water temperature exceeds
12
10°C, mean shallow water temperature within a growth season, number of degree days for each of the studied populations. Degree days were
13
calculated by multiplying number of days by mean daily temperature during the time when shallow water temperature exceeded 10 °C.
14
Temperatures were derived using the FLake model (Lake Model Flake 2009).
15
16
17
Locality
Coordinates
Estimated population
size (flying adults)
No. of days when
temperature exceeds 10 °C
Mean temperature (°C)
within a growth season
Degree days
France
43°29' N, 4°48' E
> 1000
254
19.0
4660.6
France
43°31' N, 4°46' E
> 1000
254
19.0
4660.6
Poland
53°29' N, 16°30' E
> 1000
175
16.6
2898.7
Poland
53°38' N, 16°22' E
300-1000
175
16.6
2898.7
Sweden
65°36' N, 22°7' E
300-1000
112
15.4
1722.0
Sweden
66°36' N, 19°52' E
50-100
112
15.0
1578.7
18
Table S2
19
Mean (±1 SE) values of egg volume, egg development time, larval development time, larval head width and larval growth rate across studied
20
populations.
Locality
Coordinates
Egg volume
(mm3)
Egg development
time (days)
Larval development
time (days)
Larval head width
(mm)
Larval growth rate
(mm/day)
France
43°29' N, 4°48' E
0.070 ±0.0003
35.668 ±0.8168
88.983 ±0.9144
3.594 ±0.0060
0.041 ±0.0004
France
43°31' N, 4°46' E
0.069 ±0.0004
46.633 ±1.4594
86.087 ±1.2103
3.578 ±0.0098
0.042 ±0.0006
Poland
53°29' N, 16°30' E
0.062 ±0.0003
30.762 ±0.5942
86.785 ±0.6594
3.485 ±0.0067
0.041 ±0.0003
Poland
53°38' N, 16°22' E
0.064 ±0.0003
33.765 ±0.6717
85.334 ±0.882
3.493 ±0.0085
0.041 ±0.0004
Sweden
65°36' N, 22°7' E
0.079 ±0.0003
9.691 ±0.0996
78.944 ±0.6269
3.330 ±0.0076
0.043 ±0.0003
Sweden
66°36' N, 19°52' E
0.081 ±0.0005
9.862 ±0.2491
76.107 ±0.7719
3.311 ±0.0102
0.044 ±0.0004
21
Table S3
22
Comparisons of linear mixed models with various constrained (C) and unconstrained (U)
23
structures for respective random effects (S – sire, D – dam, R – residual). Only traits
24
exhibiting significant genetic variance were included.
25
Model no.
Trait
S
D
R
logLik
Models comp.
P
26
1.1
Growth rate
C
C
C
3436.45
‒
‒
27
1.2
U
U
U
3456.62
1.2 vs. 1.1
<0.0001
28
1.3
U
U
C
3438.84
1.2 vs. 1.3
<0.0001
29
1.4
U
C
U
3455.72
1.2 vs. 1.4
0.41
30
1.5
C
C
U
3454.85
1.4 vs. 1.5
0.34
31
1.6
U
C
C
3455.71
1.6 vs. 1.1
<0.0001
1.4 vs. 1.6
0.99
32
C
C
C
‒3825.13
‒
‒
2.2
U
U
U
‒3287.07
2.2 vs. 2.1
<0.0001
35
2.3
U
U
C
‒3802.10
2.2 vs. 2.3
<0.0001
36
2.4
U
C
U
‒3303.14
2.2 vs. 2.4
<0.0001
37
2.5
C
C
U
‒3323.02
2.4 vs. 2.5
<0.0001
38
2.6
U
C
C
‒3303.80
2.6 vs. 2.1
<0.0001
2.4 vs. 2.6
0.98
33
2.1
34
Devel. time (e)
39
40
3.1
41
3.2
Egg volume
C
C
C
6592.33
‒
‒
U
U
U
6617.90
3.2 vs. 3.1
<0.0001
4
42
3.3
U
U
C
6595.82
3.2 vs. 3.3
<0.0001
43
3.4
U
C
U
6615.93
3.2 vs. 3.4
0.14
44
3.5
C
C
U
6614.28
3.4 vs. 3.5
0.20
45
3.6
U
C
C
6600.18
3.6 vs. 3.1
0.0004
3.4 vs. 3.6
<0.0001
46
C
C
C
-299.47
‒
‒
4.2
U
U
U
-273.22
4.2 vs. 4.1
<0.0001
49
4.3
U
U
C
-296.32
4.2 vs. 4.3
<0.0001
50
4.4
U
C
U
-273.77
4.2 vs. 4.4
0.58
51
4.5
C
C
U
-274.51
4.4 vs. 4.5
0.63
52
4.6
U
C
C
-297.26
4.6 vs. 4.1
0.11
4.4 vs. 4.6
<0.0001
47
4.1
48
Devel. time (l)
53
54
C
C
C
-40.06
‒
‒
5.2
U
U
U
-37.22
5.2 vs. 5.1
0.22
57
5.3
U
U
C
-38.08
5.2 vs. 5.3
0.42
58
5.4
U
C
U
-39.28
5.2 vs. 5.4
0.12
59
5.5
C
C
U
-39.28
5.4 vs. 5.5
0.39
60
5.6
U
C
C
-40.05
5.6 vs. 5.1
0.98
5.4 vs. 5.6
0.46
55
5.1
56
61
Head width
62
5
63
Table S4
64
Comparisons of linear mixed models with various constrained (C) and unconstrained (U)
65
structures for respective random effects (D – dam, R – residual). Only traits exhibiting
66
significant genetic variance were included.
67
Model no.
Trait
D
R
logLik
Models comp.
P
68
1.1
Growth rate
C
C
3806.91
‒
‒
69
1.2
U
U
3830.01
1.2 vs. 1.1
<0.0001
70
1.3
U
C
3807.95
1.2 vs. 1.3
<0.0001
71
1.4
C
U
3829.83
1.2 vs. 1.4
0.84
1.4 vs. 1.1
<0.0001
72
C
C
‒4231.66
‒
‒
2.2
U
U
‒3615.17
2.2 vs. 2.1
<0.0001
75
2.3
U
C
‒4194.71
2.2 vs. 2.3
<0.0001
76
2.4
C
U
‒3665.85
2.2 vs. 2.4
<0.0001
2.4 vs. 2.1
<0.0001
73
2.1
74
Devel. time (e)
77
C
C
7322.98
‒
‒
3.2
U
U
7357.62
3.2 vs. 3.1
<0.0001
80
3.3
U
C
7324.85
3.2 vs. 3.3
<0.0001
81
3.4
C
U
7356.01
3.2 vs. 3.4
0.14
78
3.1
79
82
Egg volume
3.4 vs. 3.1
83
6
C
C
-2202.30
‒
4.2
U
U
-2169.11
4.2 vs. 4.1
<0.001
86
4.3
U
C
-2199.18
4.2 vs. 4.3
<0.001
87
4.4
C
U
-2169.37
4.2 vs. 4.4
0.77
4.4 vs. 4.1
<0.001
‒
84
4.1
85
Devel. time (a)
88
‒
C
C
1897.65
‒
5.2
U
U
1899.10
5.2 vs. 5.1
0.58
91
5.3
U
C
1898.13
5.2 vs. 5.3
0.38
92
5.4
C
U
1898.50
5.2 vs. 5.4
0.55
5.4 vs. 5.1
0.43
89
5.1
90
93
Head width
94
7
95
APPENDIX 1
96
Study species
97
The damselfly L. sponsa is characterized by a range distribution across central and northern
98
Europe. Being obligatorily univoltine (one generation per year), it is seasonally time-stressed
99
in temperate regions, where it must complete larval development, emerge and mate before
100
the season ends (Dijkstra 2006b; Śniegula & Johansson 2010). Females insert their eggs
101
into plant tissues and the eggs enter winter diapause about two weeks later (Corbet 1956a).
102
Eggs overwinter either above (in plant stems) or below (lake bottom) water surfaces. Winter
103
diapause terminates during winter and post-overwintering egg development (hereafter called
104
egg development) proceeds during the following spring. Larval hatching starts when the
105
water temperature reaches 10°C (Corbet 1956a; Van Doorslaer & Stoks 2005). Spring egg
106
development is, to a great extent, regulated by photoperiod (Śniegula & Johansson 2010).
107
Larval development time is dependent on temperature and photoperiod and takes about two
108
to three months (Corbet 1956b; Pickup, Thompson & Lawton 1984; Pickup & Thompson
109
1984; Śniegula & Johansson 2010; Johansson, Śniegula & Brodin 2010). Although there is
110
no data available on L. sponsa, studies on damselflies in general indicate that the proportion
111
of a female’s offspring that is sired by the last male with which she copulated rarely falls
112
below 95% (Corbet 1999). However, it has been shown that in some species the proportion
113
may vary from 44% to over 90% (Fincke 1984; Cooper, Miller & Holland 1996).
114
115
Field sampling
116
To estimate growth and development in the egg and larval stages, we collected eggs from
117
adult females in three geographic regions covering a distance of 2,730 km: northern Sweden
118
(66°N, alt. 220 mamsl and10 mamsl), north-western Poland (54°N, alt. 140 mamsl) and
119
southern France (43°N, alt. 0 mamsl), hereafter northern, central and southern populations or
120
regions. Estimated number of flying individuals at each sampling site is presented in Table
8
121
S1. One of the northern population was situated beyond the species’ northern geographic
122
distribution shown in Dijkstra (Dijkstra 2006a) and hence can be regarded as a peripheral
123
population. The number of flying individuals during the peak of the flying season (Table S1)
124
as well as our visits in previous years (Śniegula et al. 2014; unpublished data) suggests that
125
the peripheral population is at least several years old. The southern populations are not
126
peripheral, since the species distribution extends further south. We sampled two populations
127
within each study region. The distance between northern sites was 151 km. The central
128
populations were separated by 18 km, the southern by 5 km. We sampled two populations in
129
each study region to consider possible intraregional, cross-population variation in study traits.
130
Our results show that the two sampled populations in northern, central and southern
131
populations did not differ in genetic variance. One sampling site in the northern, two in central
132
and two in southern regions supported fish populations. We have no information on the
133
status of fish in the second site in northern region. Field sampling started with the southern
134
and ended with the northern populations (southern population 29 June and 2 July, central
135
23‒28 July, and northern 6‒10 August). We collected paternal half-sibling egg clutches from
136
the one northern, two central and two southern populations. This enabled us to estimate
137
additive genetic variance, taking into account potential maternal effects (Lynch & Walsh
138
1998). We collected these paternal half-sibs by separating the initially copulating pairs and
139
saving females for egg laying. The male mating with the first female was thereafter enclosed
140
in a small insectary together with a new single female. Using this method we produced the
141
following number of paternal half-sib families: northern site, 10 males, each of which mated
142
with two females, resulting in a total of 20 families; central sites, 16 and four males, each of
143
which mated with two females, resulting in a total of 32 and eight families, respectively; and
144
southern sites, 18 and nine males, each of which mated with two females, resulting in a total
145
of 36 and 18 families, respectively. In addition, from the populations where we sampled full-
146
sibs, the northern, one central and one southern population we sampled the following
147
numbers of adult females that produced full-sib families: eight, nine and one respectively.
148
These families were also included in the variance partitioning analysis (see below). The less
9
149
numerous northern population did not allow us to collect half sibs. However, we obtained 16
150
full-sib families from this northern population.
151
After copulation, females were individually placed in plastic jars with moist filter
152
papers as oviposition substrates and transported to ‘research stations’ situated up to 16 km
153
away from the sampling sites. These females were kept in room conditions (temperature
154
22°C) by a window, i.e. with a natural photoperiod at the sampling site. We kept females in
155
this condition until they oviposited eggs, an event which occurred within 48 hours after field
156
sampling. Egg clutches were stored in these conditions for up to five days (i.e. until all
157
females laid eggs). Then we placed the clutches, embedded in filter paper, in dark conditions
158
(Styrofoam boxes with an interior temperature of 22°C) and transported them by car to the
159
laboratory (Cracow, Poland). Transport of egg clutches took from one (central populations) to
160
three (northern populations) days. Our previous experiments indicated that such transport
161
has little or no effect on damselfly development (Śniegula & Johansson 2010; Śniegula et al.
162
2014); therefore we feel confident that this method excludes unwanted effects on life history
163
traits.
164
165
Experimental set-up
166
Estimates of growth and development of eggs and larvae were carried out at the Institute of
167
Nature Conservation PAS in Cracow, Poland, in climate chambers. In three separate
168
chambers, we reared the northern, central and southern populations at programmed
169
temperatures and photoperiods (thermo-photoperiods) simulating the thermo-photoperiods
170
experienced by the damselflies in their natural conditions (experiment 1, Fig. S1). A fourth
171
chamber, with a mean thermo-photoperiod averaged over all sampled regions and growth
172
seasons, was used to rear all four study regions (experiment 2). Upon the arrival of eggs at
173
the laboratory, the clutches were placed in plastic containers (12x8 cm, 5 cm high) filled with
174
250 ml of mixed dechlorinated tap water and filtered pond water. We thereafter simulated the
175
progress of summer, winter and spring conditions as described below.
10
176
Experiment 1
177
In this experiment we determined genetic variance in life history traits simulating natural
178
temperature and photoperiod regimes by using a half-sib design based on the northern,
179
central and southern populations. One of the northern population was excluded from this
180
analysis, since we could not produce half-sib families. However, it is included in summary
181
statistics and experiment 2. Containers with eggs from each of the study regions were put
182
into three climate chambers with programmed temperatures and photoperiods (thermo-
183
photoperiods) mimicking natural changes in these variables in natural conditions in each
184
sampling region. Two separate models for calculation of water temperature at the two
185
northern sites showed statistically identical mean weekly temperatures during the growth
186
season for L. sponsa larvae (results not shown). To follow the natural progress of the
187
thermo-photoperiod through the season, we changed it every Friday (Fig. S1). The exception
188
was the period of winter simulation (described below).
189
To apply a realistic surface water temperature for each region, we used an extension of
190
the lake model FLake (Lake Model Flake 2009) constructed by (Nilsson-Örtman et al. 2012)
191
to calculate temperatures throughout the season at each sampling location. We thereafter
192
used the mean weekly values for the populations at each region as our temperature
193
treatment (Fig. S1a). The following parameters were included in the model: surface thermal
194
radiation, solar radiation, wind speed, dew point temperature, and air temperature. However,
195
the model did not take temperature inversion, which becomes less frequent at progressively
196
higher temperate latitudes, into account. This can strongly ameliorate harsh environmental
197
conditions, especially near the bottom of the shallow, dark bottom bodies of water that are
198
frequent in boreal regions (Corbet 2003). The northern individuals originated from such
199
bodies of water. We found that water temperatures in the northern region were 1‒2 degrees
200
higher than that derived from the model, supporting stronger temperature inversion in the
201
north. We therefore increased the mean weekly temperatures in chambers holding the
202
northern and central individuals by 2°C (Fig. S1a).
11
203
The applied photoperiodic regimes used for each latitudinal region included morning
204
and evening civil twilights (Fig. S1b). Insects, including odonates, are known to be very
205
sensitive to light intensity and the threshold at which they register light is very low (Lutz &
206
Jenner 1964; Saunders 2002). Note that in natural conditions populations from the northern
207
regions experience the same photoperiods during the larval growth season, i.e. from the end
208
of May to mid-July (24 hours of daylight, including civil twilight). These temperatures and
209
photoperiods were initiated once larvae had overwintered in the laboratory (see below).
210
Upon arrival at the laboratory, the northern, central, and southern eggs were given the
211
following hours of light-dark conditions ‒ L 20:57 and D 3:03, L 17:38 and D 6:22, L 16:31
212
and D 7:29, respectively ‒ along with corresponding temperatures ‒ 19.2°C, 21°C, and
213
24.8°C, respectively ‒ simulating late summer conditions. After three weeks, when eggs had
214
begun diapause (Corbet 1956a), we initiated winter conditions by lowering the temperature to
215
15°C. The next day we changed the temperature to 5°C and switched off the light. This
216
procedure was applied to the northern and central populations. For the southern individuals
217
we used only two weeks of late summer conditions, because some eggs from several
218
clutches started to hatch nearing the end of the second week of their development. The
219
northern, central, and southern eggs were kept dark at 5°C, simulating winter conditions for
220
28±1.5, 28±1, 28±1.5, and 28±1.5 days, respectively (the variation is due to differences
221
between females in ovipositing dates).
222
To simulate spring conditions we set thermo-photoperiods to match the dates when
223
temperatures exceeded 12°C at the origin of the populations. For the northern regions this
224
corresponded to 30 May (temp. 14°C), for the central region 25 April (temp. 13.3°C), and for
225
the southern region 4 April (temp. 13.8°C) (Fig. S1a). These temperatures correspond to the
226
first week after 12°C was reached. We chose these temperatures (and hence photoperiods)
227
for the initiation of spring, since egg hatching in L. sponsa starts when the water temperature
228
exceeds 10°C (Corbet 1956a). Thereafter, we simulated natural (weekly) changes in
229
temperature until 25 July in the chamber housing the northern populations (week 9), 15
12
230
August in the chamber housing the central populations (week 17) and 12 September in the
231
chamber housing the southern populations (week 24). On these dates, when the temperature
232
in nature starts to slowly decline, there were still individuals that had not emerged. We
233
therefore maintained the temperature that the larvae experience at these dates until all
234
individuals had emerged in the northern populations (Fig. S1a). The photoperiod followed
235
weekly changes until the end of the experiment (Fig. S1b). We terminated the experiment on
236
7 February 2014, which corresponded to 17 Oct (northern regions), 26 Sept (central region)
237
and 3 Sept 2014 (southern region) under natural conditions. None of the northern larvae
238
remained on this date (all had emerged), whereas nine central and eight southern outliers
239
were still in the larval stage. We terminated the experiment because from these dates
240
forward the climatic conditions are unlikely to be beneficial for emergence, although it is
241
common to record aged flying individuals at this date in central Europe (Wendzonka 2005).
242
Eggs started to hatch soon after spring conditions were initiated. When this happened,
243
larvae from each family were individually placed in round plastic containers (diameter 7 cm,
244
height 4 cm) and fed daily with a mean of 350 SE: 26.8 laboratory-reared brine shrimp,
245
Artemia salina. Ten larvae were taken from each female, resulting in 440 northern, 490
246
central and 550 southern individuals, for a total of 1,480 individuals at the start of the
247
experiment.
248
We estimated the following life history traits: egg volume, egg development time, larval
249
development time, larval size at last instar (F0) and larval growth rate. After the spring
250
initiation, we photographed 10 randomly chosen eggs from each clutch with a Moticam 3MP
251
digital camera mounted on a Motic SMZ168 microscope. These ten eggs correspond to the
252
ten larvae used for the larval growth experiment. We estimated ellipsoid egg shape volume
253
with the image analysis program Motic Image Plus 2.0 by using the equation V=1/6 x 3.14 x
254
L x W 2, where L is egg length and W is egg width. We calculated egg development time as
255
the number of days from the initiation of spring conditions until hatching. When the larvae
256
reached the last instar, we photographed the larvae to estimate their size. We calculated
13
257
larval size as head width, using the ImageJ v.1.36b image analysis program (see Śniegula
258
2012a, b for details). The larval development time was estimated as the number of days
259
between hatching and emergence. The larval growth rate was estimated as final instar larval
260
head width divided by the number of days needed for larval development, i.e. between
261
hatching and emergence dates. We used head widths for growth rate estimates as this
262
measure significantly correlates with other body size traits and is commonly used for adult
263
size and growth rate estimates (Corbet 1999). In addition, using head width instead of weight
264
at emergence allowed us to use a larger sample size for growth rate, since it was impossible
265
to accurately determine the dry weight of some emerging individuals.
266
14
267
Statistical methods, experiment 1
268
We employed a full-sib/half-sib design, where each sire was mated with two dams and
269
offspring were measured in each full-sib family. Thus, full sibs for each dam were also
270
paternal half sibs. In such a breeding design, the covariance between paternal half sibs
271
(PHS) is equal to the variance between sires (V(s)) and approximates one-quarter of the total
272
additive genetic variance V(a) (Lynch & Walsh 1998). Observed variance between dams V(d)
273
is the sum of several components: ¼ additive genetic variance, ¼ dominance variance, plus
274
several terms related to epistatic effects and maternal effects if present (both genetic and
275
environmental). The remaining sources of variation (e.g. environmental) form the
276
unexplained residual component of the variance (V(e)). Heritability can thus be approximated
277
as 4tPHS, where the intra-class correlation between paternal half sibs (tPHS) is defined as
278
V(s)/V(z), i.e. the fraction of total phenotypic variance V(z)=V(s)+V(d)+V(e) explained by sire
279
effects (V(s)).
280
Data was analyzed using the linear mixed model in ASReml-R v. 3.0 (Butler et al.
281
2009) and the R computing environment (R Development Core Team 2012). Prior to analysis
282
all response variables were standardized (to mean = 0 and SD = 1). In all analyses we
283
inspected residual plots to ensure that the models fitted the data correctly. In all models we
284
included sire and dam identity as random effects, and the region of sampling as a fixed
285
effect. Preliminary analyses, including population identities, indicated no population-related
286
differences in estimated parameters within regions. We thus decided to remove the
287
population effect from all models to increase the power of comparisons. We included
288
offspring sex (male/female/unknown) as a fixed variable; however, we later removed it, as it
289
proved insignificant. In total we analyzed five response variables: egg volume, embryonic
290
developmental time, larval developmental time, last instar (F0) larval head width, and larval
291
growth rate.
292
293
To test for the presence of genetic variance and its partitioning among regions, we
employed a hierarchy of mixed models of successively greater complexity. A detailed
15
294
description of the testing procedure and results can be found in Supporting Information 2, but
295
in short, we relaxed constraints placed on the covariance matrices and fitted all random
296
effects as square 3×3 covariance matrices. Testing of respective variances and their
297
differences was performed using the likelihood-ratio test.
298
In half-sib/full-sib cases heritabilities (h2) were calculated as 4(V(s)/V(z)), except in
299
cases where the between-sires and between-dams variances were approximately equal. In
300
the latter case heritability was calculated as 4((V(s)+V(d))/V(z)) (i.e. using the covariance
301
between full sibs as the proxy of ¼Va; Lynch & Walsh 1998). We also calculated fractions of
302
total variance explained by the dam effect m2 = V(d)/V(z). Standard errors of all variance
303
functions were calculated using the delta method (Lynch & Walsh 1998). All values of h2 and
304
m2 were calculated from models with the highest likelihood.
305
Due to logistic constraints it was impossible to gather data on half sibs in the one of
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the two northern populations. As all these individuals were full sibs it was impossible to
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separately estimate dam and sire components of variance with these individuals included
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(these two components are fully confounded in full sibs). Hence, data on individuals from this
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population were included in summary statistics, overall phenotypic variance analysis and full-
310
sib analyses, but not in the half-sib variance analysis described above. In the analysis based
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on full-sib design, we have treated the two northern populations as coming from one region.
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The structure of random effects in these models was different as it did not include sire effect.
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Broad-sense genetic variance was approximated in those models by the dam (i.e. family)
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effect. In purely full-sib analyses broad-sense heritabilities for all traits were calculated as
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2*V(d)/V(z) (Lynch & Walsh 1998).
316
To estimate regional phenotypic differences in egg volume, embryonic and larval
317
development time, F0 larval size and larval growth rate (larval size/larval development time in
318
days), we used a linear mixed model function implemented in the package for R nlme, where
319
full-sib families and populations were random effects.
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321
Experiment 2
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In this experiment we determined genetic variance in life history traits using a constant
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temperature and photoperiod and a full-sib design. We used this design because space
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limitation in the climate chamber did not allow for a half-sib design with enough replicates;
325
hence half sibs were not included. The main aim was to compare the difference in genetic
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variance expressed in non-native, average conditions and at the simulated natural
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temperature and photoperiod used in experiment 1. When the winter simulation in
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experiment 1 was terminated (see above), we randomly chose six eggs from eight randomly
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chosen full-sib families from northern, central and southern regions. This resulted in a total of
330
144 larvae, which were then placed in a chamber with a constant temperature of 21.9°C and
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a photoperiod corresponding to the longest day length during the growth season (summer
332
solstice, June 21) at a mid-latitude along the transect of our study regions (55°N, 10°E), L
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19:25, D 04:35. We set this temperature because (1) earlier studies indicated that larvae are
334
characterized by the lowest mortality when reared at this temperature (Johansson et al.
335
2001; Stoks, De Block & McPeek 2006; Śniegula & Johansson 2010) and (2) this
336
temperature is experienced by all study regions in natural conditions for at least several
337
hours within a day during the peak in the growth season. We used a constant temperature
338
and photoperiod because we wished to estimate whether the amount of genetic variance in
339
the studied traits changed as the individuals were grown in a constant and changing native
340
temperature and photoperiod. In this experiment we estimated the same life history
341
parameters as in experiment 1, except we did not measure egg volume.
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343
Statistical methods, experiment 2
344
In this experiment we used a full-sib design. All sampled populations, including the two
345
northern ones, were used for estimations. To test whether family effects (i.e. broad-sense
346
genetic effects, G) are correlated between two contrasting environments (E): simulated
17
347
natural thermo-photoperiods (experiment 1) and a constant mean thermo-photoperiod for all
348
regions (experiment 2), we fitted an additional set of mixed models in which, for each
349
response variable, we included region and experimental group (simulated vs. constant
350
conditions) as a fixed effect. The random family effect was fitted in the form of four different
351
(co)variance structures:
352
1) Homogenous (equal) variances
353
2) Heterogeneous variances and family-wise correlation between treatments equal to unity
354
3) Heterogeneous variances and family-wise correlation between treatments equal to zero
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4) Heterogeneous variances and family-wise correlation unconstrained
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All models were fitted in ASReml-R (Butler et al. 2009). Significance of the interaction of
357
genetic effects and conditions (i.e. the presence or absence of genetic correlation between
358
simulated and constant conditions) was tested using a likelihood-ratio test. Comparison of
359
model 1 and 2 tests the presence of G×E interaction due to uneven genetic variances;
360
comparison of models 2-3 and 3-4 tested for G×E due to cross-environmental correlations of
361
genetic effects being less than one. For visualization purposes we extracted BLUPs (best
362
linear unbiased predictors) of the genetic family effect (Robinson 1991) from all best-fitting
363
models. BLUPs were used solely for graphing purposes
18
364
APPENDIX 2
365
Genetic variance and its partitioning among regions
366
To test for the presence of genetic variance and its partitioning among regions, we employed
367
a hierarchy of models of successively greater complexity. To test for the presence of
368
significant genetic variance we have compared the model with the sire, dam and residual
369
effects to the model with the sire effect excluded. Further analyses comprised a combination
370
of various (co)variance structures defined for the three random effects (sire, dam and
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residual) and structured according to the three studied regions. All models were first fitted
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assuming a homogenous covariance structure for regions, i.e. assuming equal variances in
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all random effects in separate regions. We then tested whether the variance could be
374
partitioned with respect to regions – i.e. whether different regions exhibited different genetic
375
variances. In these analyses we relaxed constraints placed on the covariance matrices and
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fitted all random effects as square 3×3 covariance matrices. The covariances between
377
regions with respect to each random effect were fixed at zero. We compared the following
378
sets of models (constrained (C) – one variance in all three regions; unconstrained (U) –
379
separate heterogeneous variance in three regions):
380
1) all random effects unconstrained vs. all random effects constrained
381
2) all random effects unconstrained vs. residual variance constrained
382
3) all random effects unconstrained vs. dam variance constrained
383
4) all random effects unconstrained vs. dam and sire variance constrained
384
5) sire variance unconstrained vs. all random effects constrained
385
6) sire and residual variance unconstrained vs. sire variance unconstrained
386
Comparisons 1, 5 and 6 directly tested the hypothesis of ‘no differences in sire’ (hence
387
genetic) variance between regions, employing various constraints on the remaining random
19
388
effects. The rationale behind these comparisons stems from the fact that the model allowing
389
for unconstrained (i.e. differing) genetic variances between regions should fit the data worse
390
than the constrained, equal-variances model if genetic variances in different regions are
391
identical. The degree of this lack-of-fit can be measured by the difference of the likelihoods of
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the two models, asymptotically distributed as a chi-squared variate with degrees of freedom
393
equal to the number of additional parameters varying in the unconstrained model. The
394
remaining comparisons were performed in order to further study heterogeneity in other
395
random effects and possibly account for their confounding influence on differences observed
396
in genetic variance. The applied hierarchy of models (see Table S3) reflects the logical order
397
of testing in search for significant region-specific variances: in the first step we ask whether
398
the variances differ at all, then we verify that this difference stems from the sire effect
399
(holding all the remaining random effects constrained), and finally we test whether residual
400
variance alone is not the confounding factor generating the observed differences in region-
401
specific sire variances.
402
Full-sib data analyses were performed in the same way with one modification: the sire
403
effect was absent in all models and hence only two random effects were tested (dam and
404
residual effect). Consequently, the number of different models to compare is reduced (see
405
Table S4).
406
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407
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