A spatially explicit model for flowering time in bamboos: long rhizomes drive the evolution of delayed flowering

1. Clonal plants produce semi-autonomous modules (ramets). The spatial distribution of ramets affects lifetime reproductive success via self-pollination, kin competition and competition among genotypes over space and nutrients. These, in turn, influence the evolution of the timing of flowering in monocarps (flowering is fatal), such as bamboos. 2. The vegetative growth period (flowering interval) in bamboos shows a geographic cline from tropical (short-interval) to temperate (long-interval) regions. However, the mechanisms underlying the emergence of this geographic trend in flowering interval remain elusive. 3. We hypothesized that differences in flowering interval are determined by ecological features that affect the spatial arrangement of ramets and the degree of kin competition. Using a spatially explicit mathematical model, we examined the effects of rhizome elongation, seed and pollen dispersal ranges and inbreeding depression on the evolution of flowering interval. 4. Flowering interval became longer as rhizome length increased but was shorter as seed dispersal range increased. However, flowering interval was less affected when these ranges were extremely large. These results could be caused by intragenet competition due to the spatial structure of genets. If the rhizome is short, each genet forms a clumping structure by vegetative growth and is subject to high intragenet competition. Early flowering may reduce this competition. When seed dispersal range is shorter, kin competition among seeds becomes greater and delayed flowering is a better strategy. When these parameters are extremely large, the effects of this type of competition are reduced, and flowering interval does not change. 5. The effect of inbreeding depression depends on the spatial distribution of ramets formed by vegetative growth. Inbreeding depression reduces reproductive success, and hence, delayed flowering is selected for when both rhizome length and pollen dispersal range are short, and inbreeding with neighbouring siblings is unavoidable. 6. Synthesis. The evolutionary consequences of flowering interval in clonal plants are affected by the spatial distribution of genets. Geographic patterns in flowering interval of bamboos can be explained by differences in rhizome length. Interspecific comparisons among species with different rhizome lengths should be examined by collecting long-term demographic data on the spatial arrangement of ramets.