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Supplemental Material
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Plant traits and plant-soil feedback (PSF)
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The magnitude and the sign of PSF tells us little about a plant's ability to change soil values
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(construct a niche) or how adapted it is to unconditioned soil. Therefore, to illustrate this
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somewhat complex dependence of PSF on the model parameters, Figures S1 and S2 show the
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values and magnitude of PSF for two cases, when a plant is and is not adapted to soil
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conditions. In Fig. S1 a plant performs best in unconditioned soil (x1 = θ0), and in Fig. S2 a
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plant performs poorly in unconditioned soil to indicate the importance of niche construction.
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To visualize positive and negative feedbacks, we chose a “home” plant with a particular
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ecological trait (x1) living in a particular unconditioned soil (θ0) and plotted how the sign and
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magnitude of PSF vary with respect to different values of the ability of the “home” and
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“away” genotype to change the soil ( f(y1) and f(y2) ). We chose f(y1) and f(y2) rather than y1
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and y2 because f(y1) and f(y2) represent how much a soil changes due to niche construction
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and can be measured in empirical studies, while y1 and y2 are the values of niche construction
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traits themselves and are usually hard to measure.
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Fig. S1 shows a plot in a case when x1 = θ0. In that case a “home” plant's ecological
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trait perfectly matches the unconditioned soil value. Figure S1A shows combinations of f(y1)
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and f(y2) for which PSF will be negative (grey areas) or positive (white areas), while figures
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S1B, S1C and S1D show the magnitude of PSF for a specific f(y1) value. If f(y1) = 0, (Figure
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S1C) the “home” plant does not change the soil and the germination probability of the “home”
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plant in “home” soil will be the highest possible. If the “away” genotype can change an
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unconditioned soil value ( f(y2) ≠ 0), the “away” soil will differ from “home” soil and there
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will be mismatch between the “home” genotype and the “away” soil which will cause lower
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germination probability of the“home” seed in “away” soils. As a result the sign of PSF will
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be positive. The magnitude of PSF will depend on how much the “away” genotype changed
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the soil. If the “home” plant can change the soil ( f(y1) ≠ 0 ), PSF can be positive or negative
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(Figure S1B and S1D). Because f(y1) ≠ 0, the “home” plant will mismatch the “home” soil (x1
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≠ f(y1) + θ 0). If the mismatch between the “home” plant and the “home” soil is bigger than
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between the “home” plant and the “away” soil, the “home” plant will have a higher
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germination probability in the “away” soil, which will result in negative PSF. A smaller
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mismatch between “home” plant and “home” soil than “home” plant and “away” soil will
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create positive PSF.
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Fig. S2 shows an example when x1 = 0.1 and θ0 = 0.7. Since x1 ≠ θ0, this case
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corresponds to a situation when the “home” plant is not adapted to the (unchanged) soil value
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in the cell. Having the ability to change a soil value might increase the germination rate of
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seed if the soil change is in the right direction, and when tested, such a plant would display
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strong PSF, most of which would be positive (Figure S2D). Having the ability to change a
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soil might also further decrease the germination rate (Figure S2B), and such a plant would
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also display strong PSF, most of which would be negative.
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Figure S1. Strength of plant-soil feedback (PSF) when the x trait of the “home” plant (with
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genotype x1, y1) perfectly matches the unconditioned soil (x1 = 0.5, 0 = 0.5,  = 1.0,  =0.05).
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The sign of PSF is shown on S1A. For some combinations of f(y1) and f(y2) the sign of PSF
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is negative (grey areas), while for others it is positive (white areas). Other plots show the
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magnitude of PSF when the “away” plant can change soils by 0.4 (B), 0 (C) or -0.2 (D).
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Figure S2. Strength of plant-soil feedback (PSF) when the x trait of the “home” genotype
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does not match an unconditioned soil (x1 = 0.1, 0 = 0.7,  = 1.0,  =0.05). As is the case
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with Figure S1, for some combinations of f(y1) and f(y2), PSF are negative (grey areas), while
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for others they are positive (white areas). The other panels show the magnitude of PSF when
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the “away” plant can change soils by 0.4 (B), 0 (C) or -0.2 (D).
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Individual-based Simulations
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We built a spatially explicit individual-based model to examine the roles of niche
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construction, selection and seed dispersal on the divergence of plant traits. In particular, we
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examined if and under what circumstances plant-soil feedbacks would lead to divergence of
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both the niche construction and ecological traits. Equations and model descriptions (not in
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main text) describing each parameter are described below. Plant-soil feedback in this model
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appears because soil change affects the fitness of a genotype that will be present in the cell
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map in the next generation.
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Detailed Model Description
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Space
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We modelled evolution on a 2D square grid (map). The map consists of L by L cells, where
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each cell can contain at most one adult plant. Each cell is characterized by a “soil value” (θ0)
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which creates a linear gradient ranging from 0 to 1 with respect to width of the map. Different
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values of θ0 represent one or multiple soil features that are related to seed germination (e.g.,
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soil pH, moisture, concentration of limiting nutrients, etc.).
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Plants
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Each plant is characterized by two independently evolving quantitative traits, an ecological
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trait (x) and niche construction trait (y). Trait x is a trait responsible for seed germination
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probability (e.g., pH sensitivity), and is under stabilizing selection, while trait y is the trait
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related to the ability of plant to modify its soil (construct a niche).
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Life cycle
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Generations are overlapping (effectively, this is same as simulating annual plants). During
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one generation: 1) each seed disperses to a neighbouring cell with probability ms or lands in
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the cell with a parent plant with probability 1 – ms; 2) seed germinates with the probability
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that depends on how well their ecological trait matches the soil value; 3) if multiple seed
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germinates in one cell, seedlings within the cell compete for survival, and only one (randomly
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chosen) survives to adulthood; 4) adult plants produce hermaphroditic flowers; 5) flowers are
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pollinated by either neighbouring plants or by self-pollination; 7) adult plant produces seed;
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and 8) adult plants change the soil based on the strength of its niche construction (y) trait.
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Germination probability
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For each cell, there is an optimal value of x, for which a seed will have the highest chance to
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germinate in that cell, and departing from optimal value will result in a lower germination
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probability (Figure S3).
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The probability to germinate (pg) in a cell with soil type θ (which depends on 0 and y trait,
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see Niche construction section below) is given by a bell-shape curve:
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pg = exp( - (x – θ)2/)
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(1)
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By changing the parameter  we can change how severely departures from optimum reduce
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the pg. When  is small, small differences in the value of x will have a large effect on the
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probability of germination, while if  is large, even large differences in the value of x will
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have small differences on the probability of germination.
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Figure S3. Seed germination probability (pg) for seeds with different x trait values in cells
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where soil value () is 0.5 (top) and 0.3 (bottom). When selection on x is strong (full line,  =
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0.05) germination probability decreases more as x departs from the optimal value (which is
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equal to ) than when selection is weak (dashed line,  = 1).
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Niche construction
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The soil value for each generation in each cell can change due to the fact that the effect of
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niche construction depends both on the plant's y trait and the unconditioned soil value. The
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soil value after niche construction () is equal to:
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θ = θ0 + f(y)
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(2)
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Where θ0 is the unconditioned soil value (soil value of cell that had no plants growing in it)
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and f(y) is the effect of niche construction. We use a linear function to model the dependence
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of f(y) on y:
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f(y) = β (y – ½)
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(3)
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Parameter β determines how much the soil is changed by changing y ( is the slope of the
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line), as well as the maximum amount the soil can be changed due to y. Since y ranges from 0
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to 1, values of f(y) range from - β /2 to β /2. Table S1 shows f(y) for several values of β and
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y.
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Table S1. Change of soil due to niche construction (function f(y) = β (y – ½)) for different
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values of y and β . If β is small, even extreme genotypes (genotypes close to 0 or 1) won't be
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able to significantly change a soil.
Values of β
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Values of y
0.1
0.5
1
2
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0.1
-0.04
-0.2
-0.4
-0.8
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0.5
0
0
0
0
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1
-0.05
0.25
0.5
1
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Flower production, pollen dispersal, pollination and seed production
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Each plant produces a number of flowers according to a Poisson distribution with mean . To
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model pollination, we assume that pollen can land on a flower stigma in home and adjacent
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cells with probability pp. If pollen from multiple plants land on the same stigma, only pollen
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from one (randomly chosen) plant fertilizes the flower. Self-pollination is allowed. A flower
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can produce seed only if it has been pollinated. The values of the x and y traits of each seed
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are equal to the mean value of their parent's x and y plus a small number taken from a normal
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distribution with mean 0 and standard deviation 0.01. Adding this small number represents
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the effect of mutation. We also assume that trait x or y can experience a mutation of large
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effect with probability . If such mutation happens, a trait value of a seed is equal to the
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mean parent's value plus a number taken from a normal distribution with mean 0 and standard
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deviation 0.1.
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Parameter choice
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We manipulated selection on trait x (), parameter  in f(y) that controls how the
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value of the y trait affects the change in soil ( Eq. 3) and seed dispersal probability (ms). The
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following parameters were constant in the simulations: the grid size was 100 x 100 cells, pp =
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1.0,  = 10-4 and  = 4. The soil gradient was linear with respect to the x axis (all cells with
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the same x coordinate had the same θo value), and the difference between environmental
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values of two adjacent cells was 1/99. With this design the first column had θ0 = 0 and the
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last θ0 = 1, while all the other columns had θ0 ranged between 0 and 1.
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For each manipulated parameter we ran 100 individual based simulations for three
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different values (low, intermediate, high):  = { 0.05, 0.1, 0.2},  = { 0.0, 1.0, 2.0} and ms =
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{0.1, 0.5, 1.0}. The value  = 0.05 represents strong selection, 0.1 intermediate and 0.2 weak.
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β = 0.0 corresponds to the case of no niche construction ability, while β = 2.0 corresponds to
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strong niche construction ability. We begin the simulation by filling the right most column of
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the grid (θ 0 = 1.0) with plants that have x = 1.0 and y = 0.5. Such plants are perfectly adapted
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to the right of the cell and they cannot modify the soil value. With this initial condition, we
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are simulating introduction of a small population to a new geographical region. By making
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individuals perfectly adapted to the right of most cells, we start the simulation under
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conditions that do not necessarily favour the evolution of a niche construction trait, since
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plants are perfectly adapted to their soil value (x1 = θ 0) and having a y value different from
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0.5 decreases germination rate. The results reported in the paper are based on the mean values
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of 100 runs for each parameter set collected at generation 1,000 and 10,000.
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Population dynamics.
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During the course of simulation with niche construction, plants spread from the point of
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introduction (right part of the map) across the map, and by generation 1,000 the whole map is
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populated by plants that differ with respect to their x and y traits (Figure S4). Plants can
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spread across the map only if they are able to germinate in soils of different values (local
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adaptation). Adaptation can be accomplished by a change in x only, by changing the soil
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value to look more similar to the soil where the seed originated or by a combination of those
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two. Simulations suggest that adaptation is driven by a combination of both changing y and x
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traits. Figure S5 shows a single simulation run when there is no niche construction (β = 0.0),
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in which case plants' spread across the map is accomplished only by adapting an ecological
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trait to local soils.
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Figure S4. Snapshots of 100 x 100 map showing the spatial distributions of x, y and soil θ
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traits at three time steps during the simulation (at generations 1, 500 and 1,000), with niche
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construction. Top row: ecological trait (x). Middle row: niche construction trait (y). Bottom
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row: soil value (θ). Different colours represent different mean soil gradient values, ranging
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from 0 (dark grey) to 1 (white). Divergence on an ecological trait is larger than divergence on
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a niche construction trait. Plant-soil feedbacks are more likely to be observed between plants
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with more different y values than between genotypes with similar y values.
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Figure S5. Snapshots of 100 x 100 map showing the spatial distributions of x, y and soil θ
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traits at three time steps during the simulation (at generations 1, 500 and 1,000), with niche
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construction. Top row: ecological trait (x). Middle row: niche construction trait (y). Bottom
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row: soil value (θ). Different colours represent different mean soil gradient values, ranging
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from 0 (dark grey) to 1 (white). Labels and parameters are the same as on Figure S4, except 
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= 0. The distribution of x follows the soil gradient () more closely than on Figure S4, when
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there is niche construction. Trait y is less diverged and it evolves neutrally.
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Fig S6. The mean trait x value across the soil gradient after 10,000 generations is very similar
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to the situation after 1,000 generations (Fig. 2 in text) suggesting that differences in
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divergence between cases with and without niche construction can persist over time. See
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Figure 2 for complete description.
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Figure S7. The mean trait y value across the soil gradient after 10,000 generations is very
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similar to the situation after 1,000 generations (Fig. 3 in text) suggesting that differences in
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divergence between cases with and without niche construction can persist over time. See
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Figure 3 for complete description.
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