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. 2016 Sep 5;113(36):10210–10214. doi: 10.1073/pnas.1605626113

Table S3.

Parameters of the simplified model and their values (range) used in the simulations

Genotype L* b θ d§ s ρ# γ|| W**
C. maritima 0.08 0.0001 1,195 0.1 0.01 [1300120] [16] 7.5
C. edentula 0.03 0.0001 906 0.1 0.8 [1300120] [16] 4.25
Hybrid 0.055 0.0001 1,486 0.1 0.2 [1300120] [16] 1
*

L is the fraction of the seedbank that results in mature plants. The average survival to flowering (across a foredune and open beach habitats) was ∼8 and 3% for C. maritima and C. edentula, respectively, in California (15). For hybrids, we assumed the average of the two parental species.

b is the density-dependent mortality parameter, assumed to be constant across the three genotypes. A b value of 0.0001 would result in a carrying capacity ∼500 adult plants (regardless of the genotype).

θ is the number of flowers produced by a single plant in the absence of competition and was obtained from our common garden experiment of five, six, and two populations of C. maritima, C. edentula, and putative hybrids.

§

d indicates the proportional reduction in the number of flowers as the population density increases. This coefficient was estimated from the data of Keddy (40) for C. edentula. There are no similar data for C. maritima or hybrids, so we assumed that the three genotypes exhibit the same response to density.

s is the fraction of flowers that produce seeds through selfing. Selfing rates for the three genotypes were obtained from our hand-crossing experiment.

#

ρ is a coefficient in the pollination foraging submodel (Eq. S6): the coefficient’s reciprocal is the population size at which the probability of pollination is 50%. Because there are no empirical data, a range of values was tested for this parameter. For the simulation presented in Fig. 4 and Fig. S5, we used a ρ value of 0.035 corresponding to a population size of ∼30 plants for 50% pollination. The results of simulations using the given range in the Table S3 is shown in Fig. S7.

||

γ is a shape parameter in the pollination foraging model (Eq. S6). Because there are no empirical data, a range of values was tested. For the simulation presented in Fig. 4 and Fig. S5, we used a γ value of 3.5, which results in a sigmoid response [type III functional response (30, 41)]. The results of simulations using the given range in the Table S3 is shown in Fig. S7.

**

W is a weighting parameter that adjusts the relative frequency of genotypes according to their attractiveness to pollinators. These values were obtained from our field observations in a mixed population. For hybrid genotypes, we assumed the average of the two parental species.