Fig 1.
Schematic of the modeled C. marinus behavior.
A simulated generation begins with the adults emerging during low tide on the lunar day determined by their internal circalunar clock. The height of low tide for different lunar emergence days T (i.e., the timing phenotype) is plotted on the lower right. Males and females find each other, and the male takes the female to the waterline for oviposition. The larvae hatch and compete with each other for resources while dispersing throughout the intertidal zone. The dispersal rate is denoted by and the competition kernel width Cw determines the strength of competition. The overall fitness of an individual
is the product of the environmental fitness component
, determined by the depth where the individual lives in the intertidal zone, and the competition component
, which is based on the level of competition an individual experiences as a larva. These fitness functions are plotted on the lower left of the schematic.
Fig 2.
A single simulation run of a population showing how branching occurs after only a few generations, resulting in one chronotype reproducing during a spring tide and another reproducing just off of the adjacent neap tide.
A: The green bars indicate the number of individuals with each phenotype at generation 500, and the black line denotes the height of low tide for each day in the lunar month. B: Each row is the distribution of phenotypes present at that generation, with brighter green indicating a larger number. Phenotypic divergence was observed after just a few generations. C: This divergence was accompanied by a separation in the depth at which larvae lived in the intertidal zone, with each column now representing one generation. This pattern of separation in depth follows what has been observed for C. marinus in the wild. The parameter values used for the simulation are given in Table 1.
Table 1.
Parameters values used for all simulations of the simple version of the model, unless stated in the text.
Fig 3.
Exploring how dispersal rate and competition strength Cw affect divergence in our model of C. marinus’ reproductive ecology.
A: The average number of chronotypes after 500 generations for 1000 simulations across Cw/ parameter space. Areas where divergence occurs are in yellow and white, and constitute a significant portion of parameter space. Black indicates the region of parameter space in which the population went extinct. B: Single simulation runs under three different parameter combinations of Cw/
showing how changing these parameters affects the dynamics of branching, if it occurs at all.
Table 2.
Parameter values used for all simulations of the model with the genetic extension, unless otherwise stated in the text.
Fig 4.
Divergence across /Cw parameter space after extending the model to including realistic sexual reproduction, recombination, and an additive genetic basis A: The average number of chronotypes after 1500 generations for 1000 simulations across Cw/
parameter space, with areas of divergence in lilac and white.
Despite the extensions, we still find divergence occurring over a range of parameter values. B: Single simulation runs under three different parameter combinations of Cw/. Branching dynamics are conserved despite the model’s extensions, except for low values of Cw/
, where sexual reproduction, recombination, and an additive genetic basis result in more phenotypic stability for chronotypes.
Fig 5.
Divergence across genetic parameter space.
A: A 3D scatter plot of parameter space for the genetic parameters ,
, and
. Divergence was observed via an increase in the proportion of intermediate frequency alleles (between 0.3 and 0.7) in the population over the simulation run. Therefore, the color of each dot represents the average over 1000 simulation runs of this value at generation 3000. Each dot has been additionally sized by the average proportion of intermediate frequency alleles so that parameter combinations that did not result in divergence do not obscure ones that did. B,C,D: Slices of the genetic parameter space at three values of
exemplify how
and
affect divergence.