8,819 research outputs found

    Dynamics for infinite dimensional games

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    Lunar cycles of reproduction in the clown anemonefish Amphiprion percula: individual-level strategies and population-level patterns

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    Lunar cycles of reproduction are a widespread phenomenon in marine invertebrates and vertebrates. It is common practice to infer the adaptive value of this behavior based on the population level pattern. This practice may be flawed if individuals within the population are employing different reproductive strategies. Here, we capitalize on a long-term field study and a carefully controlled laboratory experiment of individually identifiable clown anemonefish, Amphiprion percula, to investigate the individual reproductive strategies underlying population-level patterns of reproduction. The field data reveal that A. percula exhibit a lunar cycle of reproduction at the population level. Further, the field data reveal that there is naturally occurring variation among individuals and within individuals in the number of times they reproduce per month. The laboratory experiment reveals that the number of times individuals reproduce per month is dependent on their food availability. Individuals are employing a conditional strategy, breeding once, twice or thrice per month, depending on resource availability. Breaking down the population level pattern by reproductive tactic, we show that each reproductive tactic has its own non-random lunar cycle of reproduction. Considering the adaptive value of these cycles, we suggest that all individuals, regardless of tactic, may avoid reproducing around the new moon. Further, individuals may avoid breeding in synchrony with each other, because of negative frequency dependent selection at the time of settlement. Most importantly, we conclude that determining what individuals are doing is a critical step toward understanding the adaptive value of lunar cycles of reproduction

    Evidence for chaotic behaviour in pulsar spin-down rates

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    We present evidence for chaotic dynamics within the spin-down rates of 17 pulsars originally presented by Lyne et al. Using techniques that allow us to re-sample the original measurements without losing structural information, we have searched for evidence of a strange attractor in the time series of frequency derivatives for each of the 17 pulsars. We demonstrate the effectiveness of our methods by applying them to a component of the Lorenz and R\"ossler attractors that were sampled with similar cadence to the pulsar time series. Our measurements of correlation dimension and Lyapunov exponent show that the underlying behaviour appears to be driven by a strange attractor with approximately three governing non-linear differential equations. This is particularly apparent in the case of PSR B1828−-11 where a correlation dimension of 2.06\pm0.03 and a Lyapunov exponent of (4.0±0.3)×10−4(4.0\pm0.3)\times10^{-4} inverse days were measured. These results provide an additional diagnostic for testing future models of this behaviour.Comment: 15 pages, 18 figures, 2 tables, Accepted to MNRA
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