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As the peak of the breeding season is in the austral autumn, hatching is assumed to take place on 1 April.
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Most juvenile penguins moult into adult plumage at the end of the following year. The first adult moult usually takes place around the beginning of the following December, in the third year of a penguin's life. As most penguins moult during spring and summer, the annual moult season is taken to run from 1 July until 30 June the following year. The Supplementary material provides model inputs related to the major oil spills as well as the parameter values that are fixed on input to the model. Note that this is the age at which the penguins become potential breeders in the model, and no explicit assumptions are made about the proportion of pairs that actually attempt breeding each season.
Both the rate of natural mortality M y and the annual reproductive success H y are assumed to depend on some function of prey biomass the deterministic effect , but to be influenced also by some noise random effects. For adult survival, the alternative approach below was developed.
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The series I H is taken to be the anchovy recruit biomass west of Cape Infanta estimated in the May survey. These choices are considered biologically reasonable for the following reasons Crawford et al. Anchovy biomass remained high during this period. The selection of November survey strata to include only those west of Cape Agulhas is appropriate considering the foraging range of non-breeding penguins which spend several weeks at a time at sea. Although breeding penguins have a limited foraging range as they must return to their nests every day or two, the choice of the anchovy recruit biomass series west of Cape Infanta is appropriate because most of the fish covered by this survey probably migrate past Robben Island from West Coast spawning grounds during autumn and winter Crawford et al.
As the Robben Island colony is clearly not a closed population, immigration must be considered. The inclusion of tag—recapture information allows, in principle, for the estimation of immigration in the model as it may resolve the confounding between estimates of natural mortality and of immigration. All immigrants are assumed to be pre-breeders in adult plumage Whittington et al.
Initially, a separate estimate was made for the number of birds immigrating to Robben Island each year, but there was not support for the addition of so many estimable parameters. Therefore, years were grouped together and an appropriately parsimonious model was selected using the Akaike information criterion AIC. There was no support for immigration from the year onwards.
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The model is fitted to counts of adult and juvenile moulters as well as to tag-resighting data by maximizing a likelihood. The standard assumption of distribution lognormality is used for fitting to the moult data. For the tag data, standard capture—mark—recapture modelling techniques are applied Lebreton et al. For more details, see the Supplementary material , Additional information about model fitting.
The main results reported in this paper are in the form of joint posterior modes and of posterior medians and probability intervals obtained from a Bayesian approach implemented using the Markov-chain Monte Carlo MCMC method. Convergence was checked using the Gelman—Rubin and Heidelberger—Welch diagnostics. For reasons discussed in the Supplementary material, Objective function minimized , this gives rise to numerical difficulties. Certain of the results in the figures following show joint posterior mode values as well as various posterior percentiles. A key aspect to the penguin—sardine model is the assumed relationship between adult penguin annual mortality and sardine abundance.
Future sardine abundance depends on future fishing mortality. Distributions of plausible future sardine abundances under different candidate MPs i. The management procedure adopted in December for the South African sardine and anchovy resources, known as Interim OMP de Moor and Butterworth, b , has been used to generate a large set of plausible projected sardine survey abundances.
The details of the harvest control rule are described in the Supplementary material, Sardine harvest control rule. Note that it is assumed that the link between projected sardine biomass and penguin abundance is unidirectional. Under this assumption discussed further in Supplementary material, Additional information about projections , a change in penguin abundance does not substantially affect sardine mortality as a result of increased or decreased predation.
The set of projected sardine abundances for any particular management option can thus be calculated independently of the penguin population dynamics. The reason for calculating projected penguin numbers is to evaluate which potential OMPs for sardine and anchovy satisfy the objective of an EAF of not having an excessively negative impact on penguins. In addition to the total annual abundance of sardine over the projection period, the proportion of sardine located to the west of Cape Agulhas is required for the calculation of future adult penguin annual mortalities.
As described above, plausible future sardine biomass trajectories are obtained from the operating model for sardine population dynamics, assuming future catches are generated using Interim OMP The sardine resource is currently managed as a single stock. As such, the operating model used when developing the OMP provides a single overall sardine abundance for each year with no spatial disaggregation. This means that an assumption is required concerning the proportions of sardine biomass located to the west of Cape Agulhas in future years.
The proportion of sardine observed to the west of Cape Agulhas has been variable over the history of the small pelagic hydroacoustic surveys Coetzee et al. In the simulations that follow, two alternatives regarding the future spatial distribution of sardine biomass are considered. Historical proportions of sardine biomass observed west of Cape Agulhas in the November hydroacoustic surveys are split into two sets: — and — This essentially provides two scenarios for penguin population projections.
In the more optimistic scenario, sardine is assumed to return immediately to a spatial distribution similar to that observed before , resulting in a larger proportion of sardine being available to the penguins on average. In the alternative scenario, the sardine distribution is assumed to remain similar to that observed thus far in the twenty-first century. For each year of each of the simulated projections, a value is chosen at random from the relevant set of proportions observed historically.
This value then multiplies the total sardine abundance for that year.
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The first scenario — proportions clearly results in a higher biomass of sardine available on average to Robben Island penguins than the second scenario — proportions; Figure 3. The thick lines are for projections assuming catches taken as specified by the sardine-anchovy management procedure adopted for use in Interim OMP , while the thin lines are for projections assuming no future fishing.
A distribution of year penguin population trajectories is calculated from plausible future sardine abundance trajectories for a particular fishery management option, given an assumption regarding the proportion of sardine to the west of Cape Agulhas in the future. From an ecological perspective, the most conservative fishery management decision is when fishing is suspended entirely.
The calculations for the projected penguin population dynamics are analogous to Equation 2. Major oil spills are not taken into account explicitly in the future, and no immigration term is included in the projection equations. The reproductive success factor H for each year in a projection was resampled with replacement from the posterior mode estimates of H y values over the years of the model fit.
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Future penguin mortality is assumed to depend on the projected sardine biomass according to the relationship fitted Figure 4. When viewed overall the model fits the data very well, with the one exception of the systematic trend of more observed than expected re-sightings of tagged penguins from to Figure 5. It is possible to force the expected numbers of re-sightings to match the observed data exactly, which results in higher re-sighting probabilities over this period. Although the fit to the moult data remains acceptable when this is done, the tag—recapture likelihood suffers considerably Supplementary Table S This suggests that it is the re-sighting histories of the birds that are not compatible with some assumptions of the recapture model being used; consideration of either or both of age-dependent mortality and of heterogeneous re-sighting probability factors might improve the fit of the model to the re-sighting numbers.
Importantly though, the key result relating the penguin projections is insensitive to forcing the model fit in this way see Supplementary Table S12 and Figure S Comparison of observed and expected posterior mode numbers of banded penguins re-sighted each year.
The model applied prefers the relationship to flatten as the biomass index approaches zero. In contrast, the probability intervals for the estimated number of penguins immigrating to Robben Island are rather wide. Time-series of estimated adult penguin annual survival rates for Robben Island at the joint posterior mode black circles.
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Time-series of female moulting penguins at Robben Island from observations black circles. The thick dashed line indicates the median trajectory for the same demographic parameter estimates had the immigration estimated by the model not occurred. The estimates for transient-related first year after banding apparent mortality rates are comparatively large in the years — and — Supplementary Figure S5 ; note that these transient rates for the first year of tagging differ from the natural mortality rates in subsequent years which are shown in Figure 6.
This may suggest that penguins were emigrating from Robben Island in those years, or that a large proportion of the birds tagged were visitors rather than residents. Alternatively, poor quality of either the tagging or the tags in those years might be the cause. Figure 8 shows annual predictions by the model of penguin reproductive success plotted against the anchovy recruit index, illustrating the somewhat surprising lack of any dependence as mentioned in the Reproductive success section.
Estimated posterior mode and predicted values of penguin reproductive success plotted against an index of anchovy recruitment prey abundance. A notable result is the large number of penguins estimated to immigrate to Robben Island from to Figure 9. This warrants further investigation to determine compatibility with data for the most likely source of these immigrants the Dyer Island colony. The model predicts that the Robben Island population would scarcely have been self-sustaining without immigration Figure 7 , showing only a moderate increase in abundance during the years of high sardine biomass — This suggests that most increases in the size of the Robben Island colony during the s are attributable to immigrants.
This observation has implications for future expectations of penguin abundance at Robben Island. Because penguins have apparently stopped immigrating to the colony in large numbers, it may be overly optimistic to assume that numbers at the colony will increase rapidly in the future, even if sardine biomass in the region increases substantially. Twenty-year projections for penguin abundance have been calculated for two different assumptions concerning the spatial distribution of future sardine biomass Figure 10 , reflecting proportions west of Cape Agulhas similar to those observed in, alternatively, — or — A key statistic of interest is the median year projection of the number of observable adult penguins, which is comparable with the historical adult moult count time-series to which the model is fitted.
The ratio of this statistic to the most recent adult penguin moult count as predicted by the model gives the proportional change in penguin numbers over the projection period Table 3.