Keep on growing or change direction? Dependence of clonal plant survival on the probability of side-branching

In clonal organisms, the genetic individual (genet) may consist of several physiological individuals (ramets). Clonal plants typically grow horizontally by means of stolons or other clonal growth organs. Some species grow linearly for several ramet generations, while others produce side branches frequently. We hypothesize that the probability of side-branching ($b$) affects genet survival ($G$) depending on the ramets' ratio of birth to death rates ($λ$). We used a spatially explicit model of ramet population dynamics to compare three growth strategies. In the neutral case, growing forward and side-branching were equally probable, whereas forward-growing and side-branching plants had lower and higher $b$, respectively. We found that the genet's survival threshold (the critical $λ_c$) strongly depended on the branching probability. The lowest threshold, and hence the broadest range of survival, occurred in moderately forward-growing plants, in which the average length of linear (non-branching) intervals was $1.89$ units. Above the threshold, the $G(b)$ relationship strongly depended on $λ$. Genet survival was promoted by forward growth in sparse ramet populations (low $λ$). However, this advantage gradually disappeared as $λ$ increased, and branching probability became effectively neutral across a broad parameter range encompassing both forward-growing and side-branching plants. This suggests strong selection for low branching intensity in unfavorable habitats, but weak or negligible selection in favorable habitats.