Impact of environmental colored noise in single-species population dynamics

Abstract

Variability on the external conditions has important consequences for the dynamics and organization of biological systems, and, in many cases, the characteristic timescale of environmental changes as well as their correlations play a fundamental role in the way living systems adapt and respond to it. A proper mathematical approach to understand population dynamic, thus, requires of approaches more refined than e.g. simple white-noise approximations. To shed further light onto this problem, in this paper we propose a unifying framework based on different analytical and numerical tools available to deal with "colored" environmental noise. In particular, we employ a "unified colored noise approximation" to map the original problem into an effective one with white noise, and then we apply a standard path integral approach to gain analytical understanding. For the sake of specificity, we present our approach using as a guideline a variation of the contact process -which can also be seen as a birth-death process of the Malthus-Verhulst class-where the propagation/birth rate varies stochastically in time. Our approach allows us to tackle in a systematic manner some of the relevant questions concerning population dynamics under environmental variability such as, for instance, determining the stationary population density, establishing the conditions under which a population may become extinct, and estimating extinction times. More in general, we put the focus on the emerging phase diagram and its possible phase transitions, underlying how these are affected by the presence of environmental noise time-correlations.

Mean growth rate when rare is not a reliable metric for persistence of species

“…In this case one expects an N-independent extinction time, as discussed in detail in Dean & Shnerb (2019). This distinction between positive and negative E½r was demonstrated explicitly in many studies of stochastic-logistic (and logistic-like) systems (Lande et al, 2003;Spanio et al, 2017;Wada et al, 2018;Yahalom & Shnerb, 2019).…”

The effects of food level and social density on reproduction in the Least Killifish, Heterandria formosa

“…Interactive effects between density and resource levels, or other environmental conditions that affect energetic demand, play large roles in a variety of ecological issues, including population regulation (Dennis & Otten, 2000;Fowler & Pease, 2010;Gamelon et al, 2017;Spanio, Hidalgo, & Munoz, 2017), pairwise species interactions (Dallalio, Brand, & Grant, 2017;Dunson & Travis, 1991), and theories for the role of competition in structuring multi-species assemblages (Grime & Pierce, 2012;Tilman, 1988). Interactive effects between density and resource levels, or other environmental conditions that affect energetic demand, play large roles in a variety of ecological issues, including population regulation (Dennis & Otten, 2000;Fowler & Pease, 2010;Gamelon et al, 2017;Spanio, Hidalgo, & Munoz, 2017), pairwise species interactions (Dallalio, Brand, & Grant, 2017;Dunson & Travis, 1991), and theories for the role of competition in structuring multi-species assemblages (Grime & Pierce, 2012;Tilman, 1988).…”

“…Regardless of whether these experiments under-or overestimated the relative importance of social density, they demonstrated that social density exerts a substantial, measurable effect on reproduction, independently of the effects food level. Interactive effects between density and resource levels, or other environmental conditions that affect energetic demand, play large roles in a variety of ecological issues, including population regulation (Dennis & Otten, 2000;Fowler & Pease, 2010;Gamelon et al, 2017;Spanio, Hidalgo, & Munoz, 2017), pairwise species interactions (Dallalio, Brand, & Grant, 2017;Dunson & Travis, 1991), and theories for the role of competition in structuring multi-species assemblages (Grime & Pierce, 2012;Tilman, 1988). The extent to which these interactions reflect changes in the balance between nutrient acquisition and metabolic demand has only just begun to be explored (Ghedini, White, & Marshall, 2017).…”

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

“…where in each time window there is a preference for a randomly chosen species. Different works have recently analyzed this type of models, showing that time-dependent habitat preference greatly improves predictions of empirical ecological patterns with respect to purely neutral theories [31,[85][86][87]. In particular, it has been claimed that these models provides more realistic estimates of dynamical quantities, such as average species persistence times and distributions of species turnover [88], compared with their neutral counterparts.…”