Transition Matrix Models, Crown-of-Thorns and Corals

Abstract

Transition matrix models have been used to investigate a number of questions regarding long and short term affects of crown-of-thorns starfish on coral communities and populations. The characteristics of damage to massive Porites corals at 21 sites on 5 reefs were expressed as ‘disturbance’ matrices containing the proportions of corals in each of 5 size classes which were killed, or had their living surface area reduced by various amounts. ‘Normal’ matrices were developed to describe recruitment, growth and regeneration between outbreaks. The long term (200 y) effects of outbreaks on the field populations were simulated by introducing the ‘disturbance’ matrix once every 8–30 iterations (= years) among 200 iterations of ‘normal’ matrix x vector multiplications. The matrices were also used to develop indices of the severity of starfish impact and vulnerability to additional outbreaks. Finally, trajectories of total coral cover (all species) over the next 20 y were predicted using ‘normal’ matrices based on 4 logistic coral growth functions, and population vectors based on field estimates of density and size frequency.