Fitting state–space models to seal populations with scarce data

ICES Journal of Marine Science ICES Journal of Marine Science (2015), 72(5), 1462– 1469. doi:10.1093/icesjms/fsu195 Original Article Fitting state – space models to seal populations with scarce data Tor Arne Øigård 1 * and Hans J. Skaug 1,2 1 Institute of Marine Research, PO Box 6404, NO-9294 Tromsø, Norway Department of Mathematics, University of Bergen, PO Box 7800, NO-5020 Bergen, Norway 2 Øigård, T. A., and Skaug, H. J. Fitting state– space models to seal populations with scarce data. – ICES Journal of Marine Science, 72: 1462 –1469. Received 13 June 2014; revised 18 September 2014; accepted 14 October 2014; advance access publication 16 November 2014. We estimate temporal variation in fecundity, the reproduction rate, for Barents Sea and Greenland Sea harp seals using a state – space approach. A stochastic process model for fecundity is integrated with an age-structured population dynamics model and fit to available data for these two harp seal populations. Owing to scarceness of data, it is necessary to “borrow strength” from the Northwest Atlantic harp seal population in form of prior distributions on autocorrelation and variance in fecundity. Comparison is made to a simpler deterministic population dynamics model. The state– space model is more flexible and is able to account for the variations in the data. For Barents Sea harp seals, the state –space model gives a higher estimate of current population size but also a much higher associated uncertainty. In the Greenland Sea, the differences between the stochastic and deterministic models are much smaller. Keywords: age-structured population model, borrowing strength, fecundity, harp seals, state-space model. Introduction Three different harp seal populations (Pagophilus groenlandicus) inhabit the Arctic part of the North Atlantic Ocean (Sergeant, 1991; Nordøy et al., 2008; Kovacs et al., 2009). The Northwest Atlantic population whelps (gives birth) on the pack ice off Newfoundland and in the Gulf of St Lawrence, the Greenland Sea population breeds on the drift ice off the east coast of Greenland, and the Barents Sea population congregates in the White Sea to breed (Figure 1). During spring, harp seals perform a fixed sequence of activities: they whelp in March–April and then moulting of adults and subadults takes place north of each whelping location after a lapse of 4 weeks (Kovacs et al., 2009). For the Greenland Sea populations, these events occur primarily in the fringes of winter ice that lies on the seaward side of the thicker ice off the east Greenland pack and for the Barents Sea population in the White Sea and southeastern Barents Sea. When the moult is over, the seals disperse in small herds, feeding heavily to restore their blubber reserves. Their summer distribution is mainly dependent on the distribution of the drifting pack-ice. The Greenland Sea population spreads on the drift ice along the east coast of Greenland, from the Denmark Strait or further south, towards Spitsbergen and eastwards into the Barents Sea. The Barents Sea population follows the receding ice edge, gradually moving north into the Barents Sea. Both in summer and autumn, the Greenland Sea and the Barents Sea populations partly overlap. The southward migration towards the breeding areas begins in November–December (Kovacs et al., 2009). All populations have been subject to commercial hunt for centuries (Sergeant, 1991). Management of Barents Sea and Greenland Sea harp seals is based on assessments performed by the Joint ICES/NAFO working group on harp and hooded seals (WGHARP) and advice is provided by ICES (ICES, 2013; Øigård et al., 2014). The assessments are currently based on a deterministic population dynamics model that estimates the total population size based on historical catch data from commercial hunt, estimates of pup production, and available reproductive data such as the proportion of females that are mature at age and the proportion of mature females that are pregnant. The pup production estimates are obtained from dedicated surveys during the whelping season in March (Øigård et al., 2010, 2014) and all biological parameters are sampled in commercial hunt during the moulting period in April/May. The Barents Sea population was previously assessed to be around 2 million seals (Skaug et al., 2007), and as an abundant predator, they have an important role in the Barents Sea ecosystem (Bogstad # International Council for the Exploration of the Sea 2014. All rights reserved. For Permissions, please email: *Corresponding author: e-mail: 1463 Fitting state – space models to seal populations et al., 2000; Nilssen et al., 2000). For future integrated ecosystem management and, not the least, to understand the underlying process governing the dynamics of the Barents Sea ecosystem, we need multispecies or ecosystem models (e.g. Lindstrøm et al., 2009). The estimated population trajectory of harp seals is a crucial input in these models (Bogstad et al., 1997). Current census techniques only provide estimates of pup production, and hence knowledge of female reproductive rates is vital for inferring total population size and predicting future changes. Population regulation through density-dependent changes in fecundity is the result of a complex interaction between intrinsic factors related to changes in population and extrinsic factors involving environmental variability (de Little et al., 2007). Monitoring changes like this is difficult for most species as extensive measurements over long periods are required. Unfortunately, available data on biological parameters such as age-specific proportions of mature females and fecundity are scarce for both the Barents Sea and the Greenland Sea populations. This is a common problem when trying to estimate historical trends of marine mammal populations. In such situations, “borrowing strength” from other populations (Myers and Mertz, 1998) may provide a way forward if relevant and representative populations can be identified. Russian aerial surveys to assess pup production of the Barents Sea stock of harp seals indicate a sudden decline in pup production after 2003 (ICES, 2013). Reduced female fertility, rather than declining population size, has been suggested as the mechanism behind the observed change in pup production. Body condition measurements of Barents Sea harps seals in 2006 and 2011 were significantly lower than similar measurements conducted before the pup production declined, and a positive correlation between pup abundance and Material and methods Data The model uses historical catch records, fecundity rates, age-specific proportions of mature females, and estimates of pup production to estimate the total population trajectory. The catch records come from commercial hunt and distinguish between the number of pups (0-group) and the numbers of older animals (1+) caught per year, but contain no additional information about the age composition of the catches (...truncated)