In typical treatments, environmental perturbations cause ecological populations to fluctuate around carrying capacity or even experience large sojourns in state space leading to extinction. Ecological theory has overlooked that, in some extreme cases, environmental noise causes the stable equilibrium at carrying capacity to disappear altogether and a stable equilibrium at extinction to appear. This phenomena, a noise-induced extinction is easily observable and just one type of noise-induced phase transition (NIPT). To better understand NIPT in ecology, we are developing a model system amenable to both theoretical analysis and experimentation. The system uses fluctuating light intensity as a stochastic environmental driver of growth for the freshwater, filamentous cyanobacteria Aphanizomenon flos-aquae. Importantly, Aphanizomenon flos-aquae exhibits photo-inhibition that is overcome by self shading, a form of positive density dependence (Allee effect) that increases the likelihood of observing a NIPT. The model was parameterized with previously published values and evaluated using an Euler integration scheme with a step of 0.02 days. Environmental noise treatments were created by drawing incident light conditions (PAR; photosynthetically active radiation) from a normal distribution with constant mean but differing standard deviation.
Results/Conclusions
Model analysis predicts that a constant light intensity of 600 PAR maximized growth rate of a population starting at an intermediate density (10 μmol photons m-1; units of vertical light attenuation), which is above the critical density (6.98 μmol photons m-1) that is generally required to escape photo-inhibition. Simulated population with these conditions (PAR μ = 600, sd=0) increased towards the upper equilibrium at 22.9 μmol photons m-1. When light intensity varied, simulated populations exposed to light regimes with a standard deviation above 281 PAR had an increased probability of a substantially lower population density than the upper equilibrium. Numerically, this pattern is reflected in the bimodal quasi-stationary probability density of states with modes at the upper and emerging lower equilibriums at 22.9 and 2.5 μmol photons m-1, respectively. As noise increased (sd≥290 PAR) the probability density of states flattened around the upper equilibrium while becoming more peaked at the lower equilibrium indicating that the upper equilibrium disappears with increasing environmental noise. This work has produced testable predictions that will be used to explore the plausibility of NIPT in ecological systems. An experimental apparatus is currently under development to validate these predictions.