Process overview and scheduling

The model proceeds with overlapping generations running with discrete annual time steps. Within each time step, the following processes take place in order (Figure 4.3.).

i. Annual climatic optimum generation

The annual climatic optimum in each patch is generated as the local mean climatic optimum plus a single random number drawn from a normal distribution with mean of 0 and a standard deviation set by climSD, which has a default value of 0.05.

ii. Reproduction, recombination, dispersal and selection

Recruitment of new trees is only permitted in gaps, i.e. grid cells not currently occupied by a living tree. Following Savolainen et al. (2004), we generate a pool of up to ten seedlings in each gap. Each of these seedlings has an opportunity to become established.

We assume spatially localised seed dispersal, so that seedling mothers are randomly selected from living individuals of reproductive age in the eight (Moore neighbour) cells immediately surrounding the gap, if such a candidate can be found. We assume the trees are entirely self- incompatible but that their pollen is highly dispersive, so that these mothers have been pollinated by any other living tree of reproductive age which is in the same patch as the mother, or by long-distance dispersed pollen from reproductive-age trees in other patches. The frequency of long distance dispersal events varies for each patch, because of loss of pollen dispersing out of the species’ range. We assume that long-distance-dispersed pollen is more likely to come from a neighbouring patch than from further afield and that peripheral patches receive less pollen from other patches than the interior patches (Figure 4.2). To model this we calculate an index for the relative ‘connectivity’ of a patch i to all the other patches 𝑠(𝑖) = ∑ |𝑖 − 𝑗|−1

𝑗≠𝑖 , where i and j are integers coding the patches position in the cline. The central interior patch has the highest connectivity, so the proportion of mating events involving the contribution of pollen from other patches is expressed as

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𝐦𝐚𝐱𝐏𝐫𝐨𝐩𝐏𝐨𝐥𝐥𝐞𝐧𝐋𝐃𝐃 𝑠(𝑖) 𝑠(6)⁄ , where maxPropPollenLDD is the maximum proportion of matings from long-distance pollen and has a default value of 0.05.

As with local pollen dispersal, the location of the individual contributing long-distance dispersed pollen within its local patch is not considered.

Figure 4.2. Graphical representation of the dispersal weighting functions applied in the model indicating a). Inverse

distance weighted pollen dispersal kernel and b). Proportion of mating events involving extra-patch pollen weighted by home patch.

The genotype of each seedling is determined by randomly combining the maternal and paternal alleles. There is no linkage among loci and so inheritance is independent. Mutation occurs at a rate prMutation, with a default setting of 10-7 _{per allele per generation, which,}

following Schiffers et al (2012), represents average published mutation rates for Arabidopsis thaliana (Schultz et al., 1999; Hoffman et al., 2004; Ossowski et al., 2010). Only point mutations are considered and these have the effect of substituting a 1 with a 0 and vice versa. After fertilisation and mutation have been accounted for, the genotype of the seedlings is generated and thus the phenotype score can be calculated.

We assume strong density-dependent selection on recruitment of seedlings to the adult tree population, based on the combined degrees of mismatch between their phenotypes and the local values of climate and habitat in that patch and year. Of the ten candidate seedlings, individuals with higher fitness values have a greater probability of becoming established (Savolainen et al. 2004). A seedlings’ fitness 𝑊_𝑐,ℎ(ɀ) relative to the environment is calculated by a bivariate Gaussian fitness function:

𝑊_𝑐,ℎ(ɀ) = 𝑒𝑥𝑝 [−(ɀ𝑐− 𝜃𝑐)2

0.01 −

ℎ𝑆 × (ɀℎ− 𝜃ℎ)2

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In which ɀ is the observed phenotype of the individual for c climate and h habitat, θ is the local phenotypic optimum at the time and 0.01 is a parameter that scales the relative strength of selection. Parameter hS (‘habitat strength’) allows the selective importance of habitat relative to climate to be varied. The pool of seedlings is then sampled stochastically with the probability of establishment related to the fitness condition of each individual.

iii. Mortality

To create canopy gaps, mortality of the standing population occurs randomly with Bernoulli trials at an annual rate prMort, with the default setting of 1/150 (following Savolainen et al., 2004). Therefore, the median lifespan is 104 years.

iv. Updating attributes

Live status of individuals (alive/dead) is updated, individuals are aged by one year and output summaries of each patch are generated. These summaries include the mean and standard deviation of the phenotype values for all individuals in each patch; the number of live individuals in each patch and the median age of live individuals in each patch. When the full experiments were conducted, these summary values were recorded and saved during the selection phase for the years 0 (prior to felling the locally adapted plantingPatch), 5, 25, 50, 75, 100, 125, 150, 175 and 200. Results presented will be based on the summary values for these years.

84 Figure 4.3. Flow diagram illustrating the scheduling of processes in the simulations. The annual schedule takes

place each year that the model is running.

4.2.3. Simulations

4.2.3.1. Equilibration

An equilibration or ‘burn-in’ phase, in which climate does not change over the long term is simulated to allow populations to adapt to the starting environment. From the initially diverse population, stabilising selection causes asymptotic decline in the standard deviation of the mean phenotype. The equilibration phase of the model is ended once the phenotypic standard deviation has reached the asymptote and the simulation has been running for at least 1000 years. To test for this each year, linear regression is used to estimate the temporal trend in phenotypic standard deviation over the previous 500 years. The populations are

considered to have reached equilibrium on the first occasion when the regression slope in phenotypic standard deviation is >0. At this point, the asymptote has been reached but stochasticity in the simulations means a very slightly positive slope is estimated.

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