RESULTS
GF outlier detection – Simulations: Testing GF
without any correction for population structure (equivalent to GF-Raw)
against simulated scenarios of 1D isolation-by-distance showed that
under linear selection, GF had good power (>0.8 at 𝛼 =
0.05) to detect loci under moderate to strong selection for most
migration scenarios, although power was reduced somewhat under moderate
selection with high migration (s = 0.1, u = 8) (Fig. S2a).
Under weak selection (s = 0.01), GF was under-powered to detect
selection under all migration scenarios. Under non-linear selection
(Fig. S2b), power was also generally low (<0.5) for all but
strong selection (s = 0.2) and low to moderate migration
(u = 2 or 4). However, the false positive rate was well
calibrated between 0.04-0.06 for 𝛼 = 0.05 (Fig. S2c). Thus, under this
specific scenario of 1D isolation by distance, GF had good power to
detect moderate to strong linear selection or strong nonlinear selection
with low frequencies of false positives.
GF outlier detection – Empirical : Out of 107,309
high-quality SNPs, 23 (0.02%) were identified as statistical outliers
by all four outlier detection methods (Fig. 1). GF-X detected the
fewest number of outliers (120), had the smallest number of outliers
unique to that method (22), and therefore shared the largest proportion
(98/120=81.67%) of statistical outliers with one or more of the other
outlier detection methods. In contrast, Bayenv detected the largest
number of statistical outliers (320) and GF-Raw had the largest
proportion (234/291=80.41%) of detected outliers unique to that method.
GF modeling of SNP outliers - Of the 320 outlier SNPs
detected using Bayenv, 242 (75.62%) had an R 2greater than zero in the GF model. This compares to 146 of 310 (47.1%)
outlier SNPs for LFMM and 42 of 71 (59.2%) outlier SNPs for Bayenv-LFMM
(note that by definition all (100%) GF-Raw and GF-X outliers had
an R 2 greater than zero). On average 49.64 of
500 (9.93%) SNPs had an R 2 greater than zero
in the 999 GF models fitted to randomly selected SNPs.
Latitude was the most important predictor for all sets of SNPs (both
outliers and random), followed by winter temperature (bio11), whereas
elevation and diurnal range (bio2) were the least important variables
(Supplementary Fig. S3). GF-Raw had the strongest associations (highestR 2 of all models) with all variables, and
therefore the aggregate turnover functions for GF-Raw attained the
greatest maximum height for all variables (Fig. 2). Random SNPs had the
weakest associations (lowest R 2 of all models)
for all variables except elevation and diurnal range (bio2), for which
Bayenv-LFMM had a lower R 2. Although the
aggregate turnover functions differed in their maximum height,
reflecting differences in variable importance, most of the aggregate
turnover functions based on outlier SNPs had a similar shape, with
thresholds falling in the same general region of the gradients (Fig. 2).
The GF-Raw and GF-Random turnover functions were notable exceptions to
this pattern. Unlike the aggregate turnover functions for the five sets
of outlier SNPs, which exhibited pronounced thresholds, the turnover
functions for SNPs selected at random largely lacked thresholds and
instead turnover tended to be relatively constant along the seven
environmental gradients. For GF-Raw, SNP turnover was more rapid at the
colder and drier portions of the temperature and precipitation gradients
than other sets of outlier SNPs, reflecting the substantial differences
in patterns of turnover in the individual outlier SNPs uniquely detected
by GF-Raw (Fig. 3, Supplementary Fig. S4). Integrating across all
environmental predictors, the total R 2distribution across SNPs showed marked differences among different
outlier detection methods (1-way ANOVA: F = 152.18; df = 3, 823;P < 0.0001), with the highestR 2 values coming from GF-Raw and GF-Xand lower R 2 values from outliers detected bybayenv2 and lfmm (Supplementary Fig. S5).
Spatial patterns of genomic variation - The GF models
fit to different sets of SNPs produced different predicted patterns of
genomic variation (Fig. 4). The most similar mapped predictions were
between GF models fitted to outlier SNPs from Bayenv, LFMM, Bayenv-LFMM,
and GF-X . Differences in predicted spatial patterns were greatest
between GF-Raw and all other sets of outlier SNPs, followed by GF fit to
SNPs selected at random, with the largest range-wide differences being
between GF-Raw and GF-X . Differences in mapped patterns were
generally greatest in the southern third of balsam poplar’s range and
for most comparisons reached a maximum in a latitudinal band centered
near 50° N and in trailing range edge populations in the Rocky
Mountains.
Genetic offsets & climatic transfer distances - Because
GF-X had the largest proportion of outliers that overlapped with
other detection methods (and conversely, the smallest proportion of
unique SNPs), here we report results for GF-X only.
Northwesternmost populations, most distant from VT were predicted to
have the largest genetic offsets associated with transplanting
populations from their home environment to the VT common garden (Fig.
5a). The pattern of predicted genetic offsets was largely reversed for
transplanting populations to the IH common garden: populations in the
southeasternmost portion of the range, farthest from IH, were predicted
to have the largest genetic offsets (Fig. 5c). This resulted in a highly
significant negative correlation for the genetic offsets between the two
garden sites (r = 0.897, df = 40, P <0.0001;
Supplementary Fig. S6). In contrast, climate-only transfer distances
(i.e., genetically-naive climate distances based on Mahalanobis
distance) showed no clear cline with distance from the common gardens
(Fig. 5b, d), and in fact climate-only distances showed a weak but
positive correlation across gardens (r = 0.380, df = 40, P= 0.013; Supplementary Fig. S6).
Plotting the populations and the common gardens in the transformed
multidimensional genomic space and the untransformed multidimensional
environmental space reveals the locations of populations relative to the
common gardens in terms of expected genomic similarity (Fig. 6a) and
climatic similarity (Fig. 6b), thereby providing a means to
conceptualize genetic offsets and climate transfer distances (though in
only two of the seven dimensions as variation along additional axes is
not shown). Consistent with variable importance ranking, latitude (y)
and winter temperature (bio11) have the strongest contribution to
variation in the multidimensional genomic space (as indicated by the
length of the vectors in Fig. 6a). Shading indicates the degree of
expected similarity of genetic patterns, with locations with similar
shading being expected to have similar genomic composition. Numerous
populations are predicted to have similar genomic patterns as those for
the climate of the VT common garden. These populations plot near the VT
common garden in the transformed genomic space and therefore have lower
predicted genetic offsets for movement to VT common garden climate. In
contrast, all seven variables have roughly equal contribution to
variation in the untransformed environmental space (Fig. 6b) and the
locations of populations and their distances from the common gardens
reflects climatic similarity rather than underlying genomic patterns.
For example, SSR is located within the unique higher elevation climate
space (Fig. 6b), despite having predicted genetic composition similar to
some eastern populations (Fig. 6a).
Genetic offset prediction of common garden performance -
Genetic offset was significantly associated with the realized
performance of populations transferred to the novel environments of the
common gardens. Genetic offset models explained >60% of
the variation in height increment growth (Table 1). Consistent with
predictions, height growth was highest for populations experiencing the
lowest values of genetic offset and declined with larger values of
offset (Fig. 7). The shape of the height-offset relationship was
non-linear, represented by a significant quadratic effect (Table 1), and
exhibited the steepest decline as offset increased above zero followed
by a flattening out at larger genetic offset values. Surprisingly, the
estimates of genetic offset made from the random selection of SNPs from
the genomic background were just as good or slightly better
(R 2 = 0.66) than genetic offsets based on
outlier loci (R 2 = 0.61-0.63). Climate-only
distance had a negative linear association with height growth, but was a
weaker predictor overall, explaining a bit more than half the variance
in growth compared to genetic offset models (R 2= 0.34).
For the subset of populations that were phenotyped in both VT and IH
(N=9 of 41), we observed a clear rank order change and crossing reaction
norms in the genetic offset predictions, indicative of a tradeoff in the
locally adaptive gene-climate relationship across sites (Fig. 8).
Consistent with the prediction of a tradeoff, the height growth of
populations tended to increase or decrease in a trend that was inverse
to the change in genetic offset across sites, although without
consistent change in the rank-order of populations. Accordingly, the
per-population difference in height growth between sites (VT minus IH)
was negatively correlated with difference in offset (Spearman’s rho =
-0.6, P 1-tailed = 0.048), although with only 9
populations statistical power was limited.