LAUSR

The authors of the review paper [1] consider several examples of extreme statistics applications in the context of molecular and cell biology. This paper is very important because it focuses on nature’s strategy to select the shortest paths (the mean of the first among many particles instead of the mean arrival time of a single particle). As a result, “the statistics of the minimal time set kinetic laws in biology, which can be very different from the ones associated to average times” [1]. This interesting approach should be developed by applying it to new problems in biology and ecology. At the same time, the presented approach certainly requires additional substantiation and agreement with other fundamental principles in science. In this regard, we would like to mention two points that the authors may find interesting and relevant in developing their idea. 1. S-shaped (or sigmoid) kinetic curves, F(t), are very often observed in biology (e.g., the number of reproducing bacteria in a substrate) and chemistry (e.g., the dependence of reaction products’ mass on time) [2–6]. Such a behavior is often demonstrated by nonequilibrium systems; during their development to equilibrium, some quasi-particles (molecules, cells, etc.) originate that attempt to remove this nonequilibrium. The appearance of a single quasi-particle out of a countable set can be often treated as a stochastic process where the appearance time of the selected quasiparticle can be considered a random quantity (see, e.g., [6]). The function F(t) describes the number of quasi-particles in time. Let us normalize F(t) by dividing it by the limit number of quasi-particles that is achievable in the process at hand. In this case, F(t) can be seen as the probability of appearance of a quasi-particle (cumulative distribution function) over a time less than or equal to t . As shown specifically in [6], the explicit form of the normalized F(t) can be described rather accurately by the Weibull distribution. It is well known from mathematical statistics (see, e.g., [7]) that the distribution of minimums of a random quantity belongs to this distribution type. By applying abductive inference (as interpreted by Ch. Peirce), we can conclude that, since the distribution of F(t) agrees with the distribution of minimums of a random quantity, the appearance time of the quasi-particle is the shortest possible. In other words, the quasi-particle appears at the highest rate possible. Normally, the appearance rate of quasi-particles