Minimum size limit for useful locomotion by free-swimming microbes

Formulas are derived for the effect of size on a free-swimming microbe’s ability to follow chemical, light, or temperature stimuli or to disperse in random directions. The four main assumptions are as follows: (i) the organisms can be modeled as spheres, (ii) the power available to the organism for swimming is proportional to its volume, (iii) the noise in measuring a signal limits determination of the direction of a stimulus, and (iv) the time available to determine stimulus direction or to swim a straight path is limited by rotational diffusion caused by Brownian motion. In all cases, it is found that there is a sharp size limit below which locomotion has no apparent benefit. This size limit is estimated to most probably be about 0.6 μm diameter and is relatively insensitive to assumed values of the other parameters. A review of existing descriptions of free-floating bacteria reveals that the smallest of 97 motile genera has a mean length of 0.8 μm, whereas 18 of 94 nonmotile genera are smaller. Similar calculations have led to the conclusion that a minimum size also exists for use of pheromones in mate location, although this size limit is about three orders of magnitude larger. In both cases, the application of well-established physical laws and biological generalities has demonstrated that a common feature of animal behavior is of no use to small free-swimming organisms.

Empirical laws of survival and evolution: Their universality and implications

Presented analysis of human and fly life tables proves that with the specified accuracy their entire survival and mortality curves are uniquely determined by a single point (e.g., by the birth mortality q0), according to the law, which is universal for species as remote as humans and flies. Mortality at any age decreases with the birth mortality q0. According to life tables, in the narrow vicinity of a certain q0 value (which is the same for all animals of a given species, independent of their living conditions), the curves change very rapidly and nearly simultaneously for an entire population of different ages. The change is the largest in old age. Because probability to survive to the mean reproductive age quantifies biological fitness and evolution, its universal rapid change with q0 (which changes with living conditions) manifests a new kind of an evolutionary spurt of an entire population. Agreement between theoretical and life table data is explicitly seen in the figures. Analysis of the data on basic metabolism reduces it to the maximal mean lifespan (for animals from invertebrates to mammals), or to the maximal mean fission time (for bacteria), and universally scales them with the total number of body atoms only. Phenomenological origin of this unification and universality of metabolism, survival, and evolution is suggested. Their implications and challenges are discussed.