Figure 1.
Schematic representation of the main model components.
The foraging cycle (A) is iterated over 10,000 time units. Steps indicted in boxes with dark-blue outline require time, during which moths spend energy at a rate that increases with the length of their proboscis (as indicated in the box at the upper-left corner). The energy is recovered through nectar consumption (box with green background). The decision whether to exploit the flowers of a plant is probabilistic, and the probability of accepting a plant depends on the corolla depth of its flowers (box in the lower-left corner). When a moth exploits a flower, pollen can be transferred from the flower to the moth and from the moth to the flower, with different probabilities (B). At the end of the season, ovules are fertilised (C). The probability that a pollen grain fertilises an ovule depends on whether it arrived to the stigma early or late. Pollen grains from the same plant have a lower probability of fertilisation, and heterospecific pollen grains can prevent ovule fertilisation.
Figure 2.
Change in time of proboscis length (triangles) and corolla-tube depth (circles). The simulation was run ten times and, for each run, the mean values of proboscis length or corolla-tube depth were calculated for each species. In all figures, symbols represent the means (and bars the standard errors) of the ten species means.
Figure 3.
At evolutionary equilibrium (following 20,000 generations) (A) there is little overlap in the frequency distribution of corolla-tube depth of the two plant species and (B) virtually no overlap in the frequency distribution of proboscis length.
Figure 4.
(A) When the distribution of proboscis lengths is kept fixed, with no difference between the two moth species, corolla-tube depth does not evolve. (B) Proboscis length diverges when the distribution of corolla-tube depth is kept fixed, provided that there is variability in corolla-tube depth, but (C) there is hardly any divergence when all corolla tubes have the same depth.
Figure 5.
Asymmetries in pollination effectiveness (defined as per visit probability of pollen transfer) hardly affect the divergence of proboscis length (triangles) and corolla-tube depth (circles) after 20,000 generations.
Figure 6.
Pollination effectiveness and evolutionary rates.
Asymmetries in pollination effectiveness (defined as per visit probability of pollen transfer) affect the speed of evolutionary change. When each moth species is a much better pollinator of one plant species than of the other (large δ), evolution proceeds much faster than when moths are equally good pollinators of the two plant species (δ = 0).
Figure 7.
At low population densities of moths there is little divergence in proboscis length (triangles) and no divergence of corolla-tube depth (circles).
Figure 8.
While proboscis length diverges for all values of nectar secretion rate (triangles), divergence of corolla- -tube depth is only observed for low and intermediate values of nectar secretion rate (circles).
Figure 9.
Cost of increasing proboscis length.
The model assumes a linear relationship between the cost of producing a proboscis and its length. For the baseline model, the slope of this relationship is 0.05 for X moths and 0.1 for Y moths. Divergence of proboscis length (triangles) and corolla-tube depth (circles) disappears when the cost of producing a proboscis of a given length is equal for the two moth species, whether (A) we increase the cost for species X letting the cost for species Y fixed, or (B) we decrease the cost for species Y letting the cost for species X fixed.
Figure 10.
The relationship between maintenance cost and equilibrium proboscis length depends on whether the competitor moth species has higher (empty triangles) or lower (black triangles) maintenance cost.
Figure 11.
As the magnitude of perceptual errors (indicated by the coefficient of variation of the noise term) increases, equilibrium differences in proboscis length (triangles) and corolla-tube depth (circles) decrease. The effect is more pronounced when there are few flowers per plant (solid line = one flower per plant; dashed line = two flowers per plant) than when each plant has several flowers (dotted line = five flowers per plant).