There has been some confusion concerning the animal group size: an exponential distribution was deduced by maximizing the entropy; lognormal distributions were practically used; as power-law decay with exponent 3/2 was proposed in physical analogy to aerosol condensation. Here I show that the animal group-size distribution follows a power-law decay with exponent 1, and is truncated at a cut-off size which is the expected size of the groups an arbitrary individual engages in. An elementary model of animal aggregation based on binary splitting and coalescing on contingent encounter is presented. The model predicted size distribution holds for various data from pelagic fishes and mammalian herbivores in the wild.

An excess of low-frequency mutations is a ubiquitous characteristic of many marine species, and may be explained by three hypotheses. First, the demographic expansion hypothesis postulates that many species experienced a post-glacial expansion following a Pleistocene population bottleneck. The second invokes some form of natural selection, such as directional selection and selective sweeps. The third explanation, the reproductive skew hypothesis, postulates that high variation in individual reproductive success in many marine species influences genetic diversity. In this study, we focused on demography and reproductive success and the use of coalescent theory to analyse mitochondrial DNA sequences from the Japanese sardine. Our results show that population parameters estimated from both the site-frequency spectrum and the mismatch distribution of pairwise nucleotide differences refute the demographic expansion hypothesis. Further, the observed mismatch distribution, compared with the expectations of the reproductive skew hypothesis, supports the presence of multiple mergers in the genealogy. Many short external branches but few long terminal branches are found in the sardine genealogy. Model misspecification can lead to misleading contemporary and historical estimates of the genetically effective population sizes in marine species. The prevalence of reproductive skew in marine species influences not only the analysis of genetic data but also has ecological implications for understanding variation in reproductive and recruitment patterns in exploited species.

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Universal scaling in the power-law size distribution of pelagic fish schools is established. The power-law exponent of size distributions is extracted through the data collapse. The distribution depends on the school size only through the ratio of the size to the expected size of the schools an arbitrary individual engages in. This expected size is linear in the ratio of the spatial population density of fish to the breakup rate of school. By means of extensive numerical simulations, it is verified that the law is completely independent of the dimension of the space in which the fish move. Besides the scaling analysis on school size distributions, the integrity of schools over extended periods of time is discussed.

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