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The spreading of evolutionary novelties across populations is the central element of adaptation. Unless populations are well mixed (like bacteria in a shaken test tube), the spreading dynamics depend not only on fitness differences but also on the dispersal behavior of the species. Spreading at a constant speed is generally predicted when dispersal is sufficiently short ranged, specifically when the dispersal kernel falls off exponentially or faster. However, the case of long-range dispersal is unresolved: Although it is clear that even rare long-range jumps can lead to a drastic speedup--as air-traffic-mediated epidemics show--it has been difficult to quantify the ensuing stochastic dynamical process. However, such knowledge is indispensable for a predictive understanding of many spreading processes in natural populations. We present a simple iterative scaling approximation supported by simulations and rigorous bounds that accurately predicts evolutionary spread, which is determined by a trade-off between frequency and potential effectiveness of long-distance jumps. In contrast to the exponential laws predicted by deterministic "mean-field" approximations, we show that the asymptotic spatial growth is according to either a power law or a stretched exponential, depending on the tails of the dispersal kernel. More importantly, we provide a full time-dependent description of the convergence to the asymptotic behavior, which can be anomalously slow and is relevant even for long times. Our results also apply to spreading dynamics on networks with a spectrum of long-range links under certain conditions on the probabilities of long-distance travel: These are relevant for the spread of epidemics.

Under harsh Pleistocene climates, migration and other forms of seasonally patterned landscape use were likely critical for reproductive success of mastodons (Mammut americanum) and other megafauna. However, little is known about how their geographic ranges and mobility fluctuated seasonally or changed with sexual maturity. We used a spatially explicit movement model that coupled strontium and oxygen isotopes from two serially sampled intervals (5+ adolescent years and 3+ adult years) in a male mastodon tusk to test for changes in landscape use associated with maturation and reproductive phenology. The mastodon's early adolescent home range was geographically restricted, with no evidence of seasonal preferences. Following inferred separation from the matriarchal herd (starting age 12 y), the adolescent male's mobility increased as landscape use expanded away from his natal home range (likely central Indiana). As an adult, the mastodon's monthly movements increased further. Landscape use also became seasonally structured, with some areas, including northeast Indiana, used only during the inferred mastodon mating season (spring/summer). The mastodon died in this area (>150 km from his core, nonsummer range) after sustaining a craniofacial injury consistent with a fatal blow from a competing male's tusk during a battle over access to mates. Northeast Indiana was likely a preferred mating area for this individual and may have been regionally significant for late Pleistocene mastodons. Similarities between mammutids and elephantids in herd structure, tusk dimorphism, tusk function, and the geographic component of male maturation indicate that these traits were likely inherited from a common ancestor. [ABSTRACT FROM AUTHOR]

It is thought that the adaptive immune system of immature organisms follows a more deterministic program of antibody creation than is found in adults. We used high-throughput sequencing to characterize the diversifying antibody repertoire in zebrafish over five developmental time points. We found that the immune system begins in a highly stereotyped state with preferential use of a small number of V (variable) D (diverse) J (joining) gene segment combinations, but that this stereotypy decreases dramatically as the zebrafish mature, with many of the top VDJ combinations observed in 2-wk-old zebrafish virtually disappearing by 1 mo. However, we discovered that, in the primary repertoire, there are strong correlations in VDJ use that increase with zebrafish maturity, suggesting that VDJ recombination involves a level of deterministic programming that is unexpected. This stereotypy is masked by the complex diversification processes of antibody maturation; the variation and lack of correlation in full repertoires between individuals appears to be derived from randomness in clonal expansion during the affinity maturation process. These data provide a window into the mechanisms of VDJ recombination and diversity creation and allow us to better understand how the adaptive immune system achieves diversity. [ABSTRACT FROM AUTHOR]