Conservation of population size is required for self-organized criticality in evolution models

Abstract

We study models of biological evolution and investigate a key factor to yield self-organized criticality (SOC). The Bak-Sneppen (BS) model is the most basic model that shows an SOC state, which is developed based on minimal and plausible assumptions of Darwinian competition. Another class of models, which have population dynamics and simple rules for species migrations, has also been studied. It turns out that they do not show an SOC state although the assumptions made in these models are similar to those in the BS model. To clarify the origin of these differences and to identify a key ingredient of SOC, we study models that bridge the BS model and the dynamical graph model, which is a representative of the population dynamics models. From a comparative study of the models, we find that SOC is found when the fluctuations of the number of species N are suppressed, while it shows off-critical states when N changes according to its evolutionary dynamics. This indicates that the assumption of the fixed system size in the BS model plays a pivotal role to drive the system into an SOC state, and casts doubt on its applicability to actual evolutionary dynamics.

Out of Africa by spontaneous migration waves

“…The observed power-law relation is a hallmark of the self-organised criticality (SOC) model of Bak et al [78] (but also see [79]) that has been used [74,80] to explain punctuated equilibria [73]. The classical SOC model is the (numerical) sand pile in which grains are randomly sprinkled on a stage.…”

“…One redistribution event can lead to neighbouring sites reaching the criterion for redistribution, sometimes leading to large "avalanches". Sizes of these avalanches typically follow power-law distributions [79,81], as the critical state has no intrinsic time or length scale [78]. The current model is similar to the classical sand-pile model, as mutations are "sprinkled" on the map of demes.…”

“…Considering a combination of semi-stasis periods alternating with replacement sweeps as a result of large-scale and many smaller expansions may contribute to understand the current biological distribution of human populations, as well as the variation in the hominin fossil record. For this reason we suggest an integration of concepts coming from punctuated equilibrium theory [72,74,79–80], multiregional postulates [25,66– 67,70,93], and current out-of-Africa migration models. Any migration wave that spanned the whole world is most likely to have come from Africa.…”

Motif Dynamics in Signed Directional Complex Networks

“…We apply this setup to both a theoretical model network and empirical data. The model network is of mimicking the ecological system [13,[20][21][22][23][24], and the empirical data are collected from KONECT [25], which contains many kinds of network data sets in a variety of domains. We find that particular motifs mainly devote to the network growth, and that the motif dynamics can be interpreted in various contexts depending on networks.…”