Functional Ecology
Appendix S4: Sensitivity analyses.
Compared with the results presented in the main text (scenarios with constrained generation
time, see Fig.2 of the main text), we changed several parameters in additional simulations to
assess their impact on our results. Specifically, we changed the carrying capacity (Fig. 1 of
the present appendix), the mean fecundity (by modifying the mean number of capitula γ, Fig.
2 of the present appendix), the distribution of the expected number of capitula per flowering plant
in year y (γy, Figs. 4 and 6), and the distribution of the number of capitula of any reproducing
individual j in a given year y (γy,j, Figs. 3 to 7).
These changes led to quantitative differences in the extinction risk from the main
model, with sometimes less differences among scenarios due to a saturation effect when all
extinction probabilities were close to unity, and sometimes even more differences among
scenarios than in the main model (e.g. when the carrying capacity or the mean fecundity were
increased, see Figs. 1b and 2b, respectively, to be compared with Fig. 2c of the main text).
Concerning the distribution of fecundities among years and among individuals, changing the
law caused little or no differences in extinction probabilities, which could be expected given
that these laws are similar in their general form. On the contrary, decreasing the variance led
to a decreased probability of extinction.
However, in any case these changes did not modify the qualitative differences in
population viability between heterogeneous and homogeneous populations done in the main
text
1
Heterogeneity of reproductive age increases the viability of semelparous populations
P. Acker, A. Robert, R. Bourget and B. Colas
Functional Ecology
Figure 1. Sensitivity analysis with changes in the carrying capacity. Effect of heterogeneity in
age at flowering on extinction probability with a constrained generation time from simulations
with demographic and environmental stochasticity and density dependence, with an initial
population size of 25 and carrying capacity (a) K=150, (b) K=350, instead of K=250 in the
main model (compare with Fig. 2c in the main text).
2
Heterogeneity of reproductive age increases the viability of semelparous populations
P. Acker, A. Robert, R. Bourget and B. Colas
Functional Ecology
Figure 2. Sensitivity analysis with changes in the mean fecundity. Effect of heterogeneity in
age at flowering on extinction probability with a constrained generation time from simulations
with demographic and environmental stochasticity and density dependence (carrying capacity
K=250), with an initial population size of 25. The expected number of capitula per flowering
plant in year y (γy) was drawn from a normal distribution with a mean (a) γ=24, (b) γ=28,
instead of γ=26 in the main model (compare with Fig. 2c in the main text).
3
Heterogeneity of reproductive age increases the viability of semelparous populations
P. Acker, A. Robert, R. Bourget and B. Colas
Functional Ecology
Figure 3. Sensitivity analysis with changes in the distribution of the number of capitula
among individuals. Effect of heterogeneity in age at flowering on extinction probability with a
constrained generation time from simulations with demographic stochasticity alone and
where, for each individual i flowering at year y, the number of capitula γy,j was randomly
taken from (a) a Poisson distribution, (b) a log-normal distribution with a variance equal to
the mean γy, instead of a variance fixed at 23² in the main model (compare with Fig. 2a in the
main text).
4
Heterogeneity of reproductive age increases the viability of semelparous populations
P. Acker, A. Robert, R. Bourget and B. Colas
Functional Ecology
Figure 4. Sensitivity analysis with changes in the distribution of the expected number of
capitula per flowering among years. Effect of heterogeneity in age at flowering on extinction
probability with a constrained generation time from simulations with demographic and
environmental stochasticity with an initial population size of 25 (no density dependence). The
expected number of capitula per flowering plant in year y (γy) was drawn from a normal
distribution, instead of a log-normal distribution in the main model. For each individual γy,j
was randomly taken from (a): a Poisson distribution, (b): a realistic log-normal distribution
(compare with Fig. 2b in the main text).
5
Heterogeneity of reproductive age increases the viability of semelparous populations
P. Acker, A. Robert, R. Bourget and B. Colas
Functional Ecology
Figure 5. Sensitivity analysis with changes in the distribution of the number of capitula
among individuals. Effect of heterogeneity in age at flowering on extinction probability with a
constrained generation time from simulations with demographic and environmental
stochasticity with an initial population size of 25 (no density dependence). γy was drawn from
a log-normal distribution. For each individual γy,j was randomly taken from (a): a Poisson
distribution, (b): a log-normal distribution with a variance equal to the mean γy, instead of a
variance fixed at 23² in the main model (compare with Fig. 2b in the main text).
6
Heterogeneity of reproductive age increases the viability of semelparous populations
P. Acker, A. Robert, R. Bourget and B. Colas
Functional Ecology
Figure 6. Sensitivity analysis with changes in the distribution of the expected number of
capitula per flowering among years. Effect of heterogeneity in age at flowering on extinction
probability with a constrained generation time from simulations with demographic and
environmental stochasticity and density dependence (carrying capacity K=250), with an initial
population size of 25. The expected number of capitula per flowering plant in year y (γy) was
drawn from a normal distribution, instead of a log-normal distribution in the main model. For
each individual γy,j was randomly taken from (a): a Poisson distribution, (b): a realistic lognormal distribution (compare with Fig. 2c in the main text).
7
Heterogeneity of reproductive age increases the viability of semelparous populations
P. Acker, A. Robert, R. Bourget and B. Colas
Functional Ecology
Figure 7. Sensitivity analysis with changes in the distribution of the number of capitula
among individuals. Effect of heterogeneity in age at flowering on extinction probability with a
constrained generation time from simulations with demographic and environmental
stochasticity and density dependence (carrying capacity K=250), with an initial population
size of 25. γy was drawn from a log-normal distribution. For each individual γy,j was randomly
taken from (a): a Poisson distribution, (b): a log-normal distribution with a variance equal to
the mean γy, instead of a variance fixed at 23² in the main model (compare with Fig. 2c in the
main text).
8
Heterogeneity of reproductive age increases the viability of semelparous populations
P. Acker, A. Robert, R. Bourget and B. Colas