Table 2.

Summary of simulation parameters

Parameter	Description	Parameter space
Initial abundance	When a new cell is colonised, it is seeded with an initial abundance (whereafter the abundance returns to 1 with each time step).	0.11–1. From the minimum value before extinction to full abundance on colonisation.
Thermal optimum	The thermal optimum of the root species at the start of the simulation was varied across the entire temperature range present in all habitable cells across the entire simulation.	17–31.4 °C. Values from [77].
Dispersal distance	The distance a species can disperse from cell-to-cell at each time step. This determines inter-population connectivity and colonisation events. These values are taken from a Weibull distribution approximating the probability distribution of dispersal events.	The scale of the Weibull dispersal kernel was varied from 100 to 5000 km based on long-term movement observations reported by [81] for non-pelagic coral reef fishes. The shape was set to 2.5.
Speciation threshold	The divergence threshold at which two populations will speciate.	12–600 timesteps, equivalent to between 20 ka and 1 ma. The divergence required for two populations to allopatrically speciate is complex [49]. Here, we simply explore as wide a range of values as possible.
Mutation rate	The standard deviation of the normal distribution around the thermal and competitive nice traits from which new trait values are picked at each time step.	0.01 to 0.15. These values were based on estimation based on preliminary simulations.
Competitive niche width	The amount of competitive space around the competitive niche trait value within which other species will compete.	0.02 to 0.50. The competitive niche width was varied from 0.02 to 0.50 based on preliminary simulations.