Abstract
We propose a method to model the physiological link between somatic survival and reproductive output that reduces the number of parameters that need to be estimated by models designed to determine combinations of birth and death rates that produce historic counts of animal populations. We applied our Reproduction and Somatic Survival Linked (RSSL) method to the population counts of three species of North Pacific pinnipeds (harbor seals, Phoca vitulina richardii (Gray, 1864); northern fur seals, Callorhinus ursinus (L., 1758); and Steller sea lions, Eumetopias jubatus (Schreber, 1776))—and found our model outperformed traditional models when fitting vital rates to common types of limited datasets, such as those from counts of pups and adults. However, our model did not perform as well when these basic counts of animals were augmented with additional observations of ratios of juveniles to total non-pups. In this case, the failure of the ratios to improve model performance may indicate that the relationship between survival and reproduction is redefined or disassociated as populations change over time or that the ratio of juveniles to total non-pups is not a meaningful index of vital rates. Overall, our RSSL models show advantages to linking survival and reproduction within models to estimate the vital rates of pinnipeds and other species that have limited time-series of counts.
Highlights
Significant declines of pinnipeds in the Gulf of Alaska and Bering Sea have focused attention on the need to know birth and survival rates to determine why these populations have declined and why they are not recovering [1,2,3]
Our data came from life tables published for northern fur seals [31] and Steller sea lions [32] and published rates of survival, ovulation and pregnancy for harbor seals [2,22]
We investigated many mortality functions including the Gompertz, Gompertz-Makeham and logistic for the fur seal and harbor seal data, but none of them provided a satisfactory fit because the Gompertz and Weibull are strictly decreasing functions while our data indicated a continued slight increase in survival through the early years of adulthood prior to the expected decrease associated with senescence
Summary
Significant declines of pinnipeds (seals and sea lions) in the Gulf of Alaska and Bering Sea have focused attention on the need to know birth and survival rates to determine why these populations have declined and why they are not recovering [1,2,3]. One challenge in fitting age- or stage-structured models to count data to determine vital rates is that the ratio of parameters to data is relatively high, and results in large confidence intervals on the estimated birth and survival rates as well as the fitted model to count data. This shortage of data is often the case for difficult to observe species, and those that are rare and endangered. One means of reducing the number of parameters is to combine or link parameters that are correlated or influenced by common factors
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