Population growth rate
We calculated population growth rates by incorporating vital rates into
the following classic equation for an annual plant population model
(Cohen 1966), with an additional plant survival parameter:
\(\frac{N_{i,\ t+1}}{N_{i,\ t}}=s_{i}\left(1-g_{i}\right)+f_{i}z_{i}g_{i}\)Equation 1
where \(\frac{N_{i,\ t+1}}{N_{i,\ t}}\) is the per capita growth rate
of a given population i , si is seed
survival probability (proportion of seeds that remain viable in the soil
over summer, see Supplementary Methods), gi is
emergence probability, fi is the number of viable
seeds produced per emergent and zi is survival
probability of emerged plants (the proportion of emerged plants that
produced at least one viable or inviable seed).
Population growth rate was calculated twice for each plot; with and
without neighbours (the latter being intrinsic growth rate, λ). For
these calculations, species-specific seed survival and plot-level
emergence probabilities were held constant, while plant survival and
seed production were calculated with and without neighbours. Plot-level
seed production (fi ) was calculated as the
exponentiated average of log-transformed viable seed production per
focal plant that produced at least one viable seed.