In stochastic population dynamics, one form of non-demographic noise is extrinsic noise which introduces uncertainty over time with respect to the reaction rates and is known for its dramatic influence on the population's dynamics [1]. Here, we present a different type of non-demographic noise, reaction-step-size noise (SN), which introduces uncertainty over time in the step size of a given reaction. That is, the step size of a given reaction is assumed to fluctuate in time with given correlation time and statistics. Apart from specific examples, this type of noise has not been systematically investigated in the past.

 In this work we focus on static SN by considering a general problem of switching or escape in stochastic populations which include SN in the influx process. That is, particles or individuals arrive in groups or bursts, which are sampled from an arbitrary distribution. Applications for this scenario are found in a variety of fields including cell biology (bursty production of proteins), ecology (complex migration patterns), and evolutionary biology (punctuational bursts of speciation). We show that bursty influx exponentially decreases the mean escape time from a metastable state compared to the "usual" case of single-step influx. In particular, close to bifurcation we find a simple analytical expression for the mean escape time, which solely depends on the mean and variance of the step-size distribution [2].

[1] - E. Roberts, S. Be'er, C. Bohrer, R. Sharma, M. Assaf, The dynamics of simple gene network motifs subject to extrinsic fluctuations. arXiv: 1509:01083

[2] - S. Be'er, M. Heller-Algazi, M. Assaf, Effect of bursty influx on the switching dynamics of stochastic populations. arXiv:1509.03820.