D. Thompson, NERC Sea Mammal Research Unit, University of St Andrews, St Andrews KY16 8LB, UK (fax +44 1334462632; e-mail firstname.lastname@example.org).
1Harbour seals Phoca vitulina in eastern England were heavily exploited in the 1960s and 1970s, and affected by phocine distemper virus (PDV) epidemics in 1988 and 2002. Information on their historical and current status is required for their management. To maximize the effectiveness of limited population survey effort we need to both estimate and minimize error.
2Presented here are data from annual aerial surveys of the population. Sporadic, synoptic surveys in The Wash, England, were used with more frequent counts of subpopulations in the Moray Firth, Scotland, to determine optimum timing of surveys.
3We developed models that explicitly account for variability in both observation and population growth processes to show that the proportion of animals observed is much more variable than the annual growth rates. The latter can therefore be treated as constant within each period, and estimated along with the epidemic mortalities during the study and the precision of the survey results.
4The Wash population increased at around 3·1% per annum (pa) [95% confidence interval (CI) 2·1–4·1] between 1973 and 1988. It fell by approximately 52% (95% CI 44–59) as a result of the 1988 PDV epidemic, and subsequently increased at 5·7% pa (95% CI 4·8–6·7). These growth rates were below those reported for European mainland populations, but showed no indication of density-dependent effects.
5The recurrence of PDV in 2002 caused approximately 22% mortality (95% CI 9–33), significantly less than the 1988 epidemic and less than half that in European mainland populations in 2002.
6Synthesis and applications. Combining sparse, systematic survey data with sporadic counts produced robust estimates of growth rates and epidemic mortality. The results indicate the value of even limited and sporadic survey effort for monitoring populations. The study has highlighted significant differences in both population dynamics and the severity of disease events between English and European harbour seal populations.
In general, harbour seal population monitoring programmes have been designed to track and detect medium- to long-term changes in population size. As it is difficult to estimate absolute abundance, monitoring programmes have usually been directed towards obtaining indices of population size. If consistent, such time series are sufficient to describe population dynamics. For harbour seals, these indices are based on the numbers of individuals observed hauled out on land, so their utility depends on this being constant over time and unaffected by any changes in population density or structure.
The harbour seal is abundant over much of its range, although some local populations have been severely affected by hunting (Bonner, Vaughan & Johnston 1973; Vaughan 1978), loss of habitat, effects of human disturbance and pollution (Reijnders 1986; Reijnders 1992a; de Swart et al. 1994), as well as other phenomena such as the PDV epidemics. The Wash, which is the largest estuary in Britain (see the Appendix, Fig. A1), has traditionally been thought to hold one of the largest and most dense concentrations of harbour seals in Europe (Vaughan 1978). The dynamics of The Wash (England) harbour seal population have been influenced by a series of bounty hunts between 1915 and 1952, a programme of pup hunting between 1965 and 1973 (Sergeant 1951; Vaughan 1978) and the mass mortality as a result of PDV (Hall, Pomeroy & Harwood 1992).
We have used a series of aerial survey counts to investigate the dynamics of The Wash harbour seal population from 1968 to 2003, a period of growth interrupted by the 1988 and 2002 PDV outbreaks. We show how the numbers of animals observed varies through the year. We have constructed and compared models incorporating uncertainty in both the annual population growth rates and the proportions of individuals hauled out and therefore observed in the surveys. These demonstrate the differences in growth rates and epidemic mortalities during the study; provide estimates of the magnitude of the differences, the population trajectory and the precision of the survey results; and indicate the relative impact of the two forms of uncertainty considered.
The harbour seal population in The Wash has been monitored since the 1960s, using counts of animals hauled out as indices of population size. The initial impetus for monitoring was to investigate the effects of intensive pup hunting. When this hunt ceased in 1973 the monitoring programme was reduced, with only single counts in 1978, 1980 and 1988. More frequent counts were resumed after the 1988 epizootic. Population counts were obtained by aerial survey. Since 1988 the surveys have used a fixed-wing aircraft and covered the entire tidal region of The Wash together with the coastline for 50 km either side of the estuary. All groups of more than 10 animals are photographed using colour reversal film in a vertically mounted 5 × 4 inch format image motion-compensated camera (Hiby, Thompson & Ward 1987). Prior to 1988, surveys were conducted using either fixed-wing aircraft or helicopters and a combination of visual counts and oblique 35 mm or 70 mm photography (Vaughan 1978). Both methods provided synoptic censuses of the number of seals hauled out, with little or no counting error. Prior to 1988, few surveys included areas outside The Wash. The analysis of population trends therefore concentrates on The Wash population. Only complete censuses, in which all haul-out sites were surveyed during a single low tide period, were included in the analysis.
timing of surveys
Before 1988 there was no systematic monitoring of the harbour seal population on the English east coast. Sporadic surveys had been conducted during the 1960s and early 1970s to provide point estimates of population size. Traditionally, the highest number of seals counted in any year was used as a minimum estimate of the population (Summers & Mountford 1975; Vaughan 1978). A regular annual survey programme was established in 1988, but because of financial constraints it was restricted to only one or two flights per annum. Monitoring population trends with such sparse data requires that the counts provide a consistent index of abundance. Maintaining compatibility with the previous management regime requires that counts represent the annual maximum count. We therefore aimed to survey the population at a time of year when the counts represented the highest proportion of the population and had the lowest coefficient of variation. The timing of the annual surveys was determined by examining the seasonal and daily distributions of the numbers of seals hauled out on particular sand banks. As the haul-out sites in The Wash are remote and difficult to observe, haul-out patterns were also monitored in a similar but accessible habitat in the Moray Firth in eastern Scotland (see the Appendix, Fig. A1). We present an analysis of these data that supports the less objective decisions previously made on survey timing.
As most of the haul-out sites in The Wash are tidal, the timing of surveys within the tidal cycle had to be constrained to make counts comparable. The numbers of seals on six selected haul-out sites, on sand banks in the Inner Moray Firth in Scotland, were recorded at 10-min intervals throughout the tidal cycle to determine the best time window for surveying.
During the 1960s and 1970s, surveys of The Wash population were conducted throughout the year. These were used to investigate variation in the numbers of animals hauling out. A series of counts from land-based observation points overlooking tidal sand banks were also made in the Beauly Firth, one of the estuaries within the Inner Moray Firth. At least one low tide count was obtained on most days during the 11-month period March 1985 to January 1986.
Haul-out behaviour may also be affected by the time of day at which low tide occurs. The Beauly Firth counts were used to examine this.
Generalized additive modelling is an extension of generalized linear modelling (GLM) that provides a means of investigating the relationships between variables without knowing their exact functional form. The approach attempts to fit a spline function to the data by penalized regression, using generalized cross validation to decide how to best balance accuracy of fitted values against the ‘wigglyness’ of the result. An implementation for R is available as the mgcv library and contains examples and introductory material (Wood & Augustin 2002). Using a log-link function with constant error variance, gives a model of the form:
( eqn 1 )
where cj is the number of animals observed during a survey on Julian day j, a is a constant and e is a draw from a normal distribution with mean zero. The smooth, s(j), used is a cyclic cubic regression spline with 9 degrees of freedom, meaning that the annual pattern is modelled as 10 sections of cubic functions, continuous up to the second derivatives and with the ends joined. The parameters of s, along with a and the variance of the error distribution, are found by minimizing:
( eqn 2 )
where ci is the ith count, fi is the model's fitted value at the time ci was made, and the summation is over all the counts. The second term is a multiple, m, of the integral of the square of the second derivative of the fitted values with respect to date evaluated over the whole year. The relative weighting of the two terms is controlled by m, which is set automatically by the cross-validation method that fits the model with different values of m to subsets of the data and chooses the value for which the resultant predictions for the excluded data points are most accurate.
As the data from The Wash were collected over several years, an additional term was required to capture this trend, giving a model of the form:
( eqn 3 )
This model suggests an annual growth rate during the period of 2·5%[95% confidence interval (CI) 1–4%] and captures 59% of the deviance of the model. The smooth of date is also significantly different from zero (P < 0·001) and effectively has 4·8 degrees of freedom after smoothing. Figure 2 shows the modelled seasonal pattern, and that there is no strong pattern in the residuals.
The Beauly Firth data were collected at low tides that fell at various times of day, but within a single year, so a slightly different model was used:
( eqn 4 )
Here s(h) is another cyclic cubic spline of hours in the day. It has only a small effect on the model, although it is significantly non-flat (P < 0·05) and effectively uses 9·3 out of the 15 degrees of freedom available to it. Figure 3a shows the resultant fit, which captures 71% of the deviance, and that the error variances may increase through the year. This makes it especially important not to over-interpret the precise shape of the curve, although the tight CI allow the basic pattern to be clearly made out.
population growth model
Noisy exponential growth provides a simple and intuitive model of population development (McCallum 2000), and can be represented with:
( eqn 5 )
where Nt is the population in year t and rt is the log of the growth rate, a random variable. The numbers seen in a survey Mi carried out in year t is then given by:
( eqn 6 )
with pi another random variable. This formulation explicitly models two types of uncertainty: the interannual environmental variability that modifies the growth rate, and therefore has persistent effects on the population; and observation error, the shorter term changes that influence individual surveys separately. It neglects density dependence, stochasticity and the possible effects of changes in age structure on long-lived species.
makes the growth rate distribution log-normal, and allows its mean to change, from g1 to g2, after the 1988 epidemic. The mortalities as a result of the two epidemics, exp(m1) and exp(m2), are also potentially different, while the expected proportion of the population seen, q, variance of the growth rate, , and observation error, , are constant for the whole time. The normal approximation for p is adequate provided 1 − q > 3sd2, which appears plausible given that previous studies estimate q at or below 0·7 (Thompson & Harwood 1990; Thompson et al. 1997; Ries, Hiby & Reijnders 1998) and this study puts the coefficient of variation of p below 0·12 (see below).
The model was fitted using WinBUGS (Spiegelhalter et al. 1996), a package that implements Bayesian Markov Chain Monte Carlo methods for finding parameters and fitting models. These involve iteratively refitting to the data until the distributions of parameter estimates converge. Multiple parallel chains of estimates can be fitted simultaneously to enable checking of model convergence. All other data manipulation was carried out in R. We used the bugs.r functions to call WinBUGS from within the R environment (http://www.stat.columbia.edu/~gelman/bugsR, June 2004).
The count data provide little information for estimating the expectation of the proportion of the population observed during surveys. Any such estimate would be sensitive to deviations from normality in the tails of the error distributions. Instead of directly estimating this proportion, we used the expected number seen during surveys in a year as an index of population size. Fitting the model only required a way of tying this in to the data. Both visual inspection and GLM fits suggested that the results of the 1996 count lay close to the trend line, so, for numerical convenience, we used an index that took the observed value, 2151, in that year and set a relatively uninformative prior on the ratio of that figure to the expectation of that year's count, saying that this was at least 0·5.
Four variants of the model were fitted and compared (Table 1). As well as the full model described above, code for which is given in the Appendix, versions with a single mean growth rate throughout both periods and/or noiseless growth rates were constructed. In every case the model-fitting process produced an estimate of the ratio of the 1996 count to its expectation that was very close to unity (Table 1). The deviance information criterion (Spiegelhalter et al. 2002) was used to select the ‘best’ model. This suggested that a model with two separate noiseless growth rates provided the best balance of accuracy and parsimony. Figure 4 shows this model's estimates of the population trajectory, along with its uncertainty.
Table 1. Mean (%) and 95% CI for the population model parameter estimates. Fitting method WB indicates Bayesian models fitted using WinBUGS; GLM, frequentist GLM. The priors column contains the priors used within the Bayesian model fitting. Growth rates are presented as mean annual percentage increases for convenience, as the values are small enough for exp(x) ≈ 1 + x. Asterisks indicate significant differences between growth rates within models ( * P < 0·05, ** P < 0·001, pairwise comparisons of randomly reordered parameter estimates). No estimates of the uncertainty in the growth rate SD or observation error CV were available for the GLM. The deviance information criterion is a Bayesian measure of how well models fit data. As with AIC, lower numbers indicate better models and differences greater than five are unlikely to arise by chance. The model preferred by this measure is in bold
Equivalent models to those containing a single source of uncertainty can also be constructed within the frequentist paradigm. Models incorporating only observation error were fitted as GLM, with Gaussian errors, to the logged data. Their results agree closely with the WinBUGS equivalents (Table 1). Inspection of the residuals did not show any patterns or trends indicative of autocorrelation that would have suggested population swings resulting from environmental changes. The lower of the two counts made in 1991 appeared to be the only potential outlier, but removing it had little effect on the parameter estimates. Adding in quadratic terms in time to the GLM versions of the models increased the Akaike's Information Criterion (AIC), confirming that neither density dependence nor long-term changes in the population's age structure were having a large effect.
The differences between pairs of counts made in a single year require the inclusion of observation error in all models that use this data set. However, for completeness, and to investigate the modelling of populations where repeated counts are unavailable, models that only had uncertainty in the growth rates were fitted to a reduced data set produced by replacing repeated counts by their means and weighting them appropriately. These were fitted as GLM, using that function within R, and are labelled as such in Table 1, although they only involved estimating four constants and an error variance for the ratio of consecutive estimates. Similar models constructed within WinBUGS did not converge sufficiently well to produce meaningful results.
Timing of surveys
The numbers of seals hauled out throughout individual tidal cycles were recorded on six selected sand banks in the Moray Firth (Fig. 1). On each occasion, seals were present in the water around and above the haul-out site before the banks were exposed. The numbers ashore increased steadily as the banks were exposed, reached a plateau and then declined as the banks were submerged. To investigate the effects of conducting surveys at different stages of the tide, we combined the six sets of counts and plotted the sum of the individual counts, expressed as a percentage of the sum of the maximum counts, against time relative to low water (Fig. 1). As counts were not usually coincident, we linearly interpolated between consecutive counts to estimate the number ashore at half hourly intervals. The estimated number ashore exceeded 90% of the maximum count during the period 1·5 h before to 2 h after low water. In practice synoptic surveys require 3–4 h to be carried out reasonably efficiently, so the flights were restricted to this 3·5 h window.
Thirty-nine surveys were carried out at irregular intervals within The Wash estuary between 1968 and 1982. Initially these occurred throughout the year, although later on they were concentrated in summer (Fig. 2a). These produced counts varying between 500 and 2200 seals (Fig. 2b). After removal of long-term temporal trends, a clear pattern became apparent, with a peak in early August, approximately 50% higher than that in winter (Fig. 2c). The residuals from this model suggest that the variability of counts made at this time are unlikely to be higher than at other times of year (Fig. 2d), and therefore their coefficients of variation are likely to be lower, although there are not really enough data points to make very strong statements about the details of these patterns. Similar patterns were observed in the Beauly Firth, although with more variation around them (Fig. 3a) and a suggestion that the lowest variability might occur earlier (Fig. 3c). These correspond with those reported in another study (Thompson et al. 1997). The greater variability is at least partly the result of stochastic effects within the smaller population and many of the counts being made under conditions in which aerial surveys would be impractical. Differences in the precision of ground and aerial surveys may also have some effect. Both studies suggest that maximum counts will be obtained in August, supporting the decision to carry out all subsequent surveys in the first half of August.
The Beauly Firth model suggests that there may be a small, but statistically significant (P < 0·05, mgcv model diagnostics), effect of time of day, with possibly up to 20% more animals being observed at low tides in the early afternoon (Fig. 3b) than at other times. There is no indication of diurnal patterns in the variability of counts.
One or two complete surveys of The Wash were carried out in the first half of August in each year from 1988 to 2003. The results were combined with counts made at approximately the same time of year in the period 1968–82 (Fig. 4). The best Bayesian and frequentist models produced encouragingly similar population trajectories and CI (Fig. 4). It seems that the population was increasing at a little over 3% pa until 1988 [95% CI 2·1–4·1 (WinBUGS), 2·5–4·5 (GLM)]. The 1988 count was obtained approximately 1 week before the first reports of sick and dead seals being washed up on the UK coast. The number hauling out fell by approximately 50% between 1988 and 1989 [95% CI 44–59 (WinBUGS), 48–62 (GLM)], coincident with the PDV epidemic. After 1989 the number of seals increased again, at almost 6% pa [95% CI 4·8–6·7 (WinBUGS), 5·1–6·8 (GLM)]. The post-epidemic rate of increase was significantly higher than the pre-epidemic rate (P < 0·001, pairwise comparison of parameter estimates). The population was affected by a recurrence of the PDV epidemic in August 2002. The first indications of morbidity as a result of the epidemic were reported in early August, shortly after the 2002 survey. The dates of the surveys and the disease outbreak in 2002 were almost exactly the same as in 1988. However, mortality was lower than in 1988, at around 22%[95% CI 9–33 (WinBUGS), 11–33 (GLM)].
Pre- and post-1988-epidemic growth rates in The Wash were much lower than those observed in the Wadden Sea, which is the adjacent population in the southern North Sea. The initial effect of the 1988 epidemic was similar in the two populations, i.e. approximately 50% reduction in subsequent count. However, the rates of increase in the Wadden Sea, both before (8·8% pa) and after (12·7% pa) the epidemic, were much higher than the upper bounds of all the 95% CI calculated in this study for the growth of The Wash population (Tougaard 1999). The pre-epidemic rate of increase in the Wadden Sea was higher than the post-epidemic rate in The Wash. The populations within the Kattegat-Skagerrak area also grew more rapidly (12% before and after the 1988 epidemic) and have been reported to have suffered higher mortalities on both occasions (Heide-Jørgensen & Härkönen 1988; Harding, Härkönen & Caswell 2002; Härkönen, Harding & Heide-Jørgensen 2002).
Markov Chain Monte Carlo (MCMC) model-fitting techniques allow almost arbitrarily complicated models to be parameterized, and work particularly naturally within a Bayesian context. They also provide estimates of the uncertainty in error variances. A more traditional GLM-based approach would require bootstrapping or similar techniques to be applied, and this can be problematic for small data sets. However, MCMC techniques are newer, more computationally intensive and less immediately intuitive, and so less straightforward to evaluate. The deviance information criterion measures model appropriateness. It is especially convenient in its similarity in use to AIC, and ability to compare non-nested models as well as those containing non-independent parameters (Spiegelhalter 2002). In this analysis, the posterior distributions of all the parameter estimates were less diffuse than the priors supplied, suggesting that the results are driven mainly by the data. Removing the uncertainty in the annual growth rates had very little effect on the observation error variances, supporting the suggestion that it was relatively unimportant.
However, until we gain more experience with such methods it is comforting to be able to compare the results with more standard methods. The results of the pairs of equivalent models under the two approaches are not inconsistent. Observed differences result from the different assumptions and fitting criteria associated with them. It appears that in this case the observation error dominates to such an extent that the uncertainty in the growth rates can be neglected, and models that do this are perfectly adequate. However, models that assumed that all the noise was the result of interannual variations in growth rates predicted that such variations were quite dramatic, because of their misinterpretation of the effects of observation error. The model estimates of uncertainty in the counts suggest that they are generally accurate to within 20%, although the selection of good weather conditions for surveying will mean that this is an underestimate of the variation in numbers of animals hauling out over the season.
The population of harbour seals in The Wash was increasing during the period 1970–88. The impact of the 1988 PDV epidemic is clear, with counts falling by approximately 50%. Similar declines were noted in the adjacent European populations in the Wadden Sea and the Kattegat-Skagerrak (Dietz, Heide-Jørgensen & Härkönen 1989; Reijnders 1992b). After the epidemic, The Wash population showed evidence of a gradual recovery, with a post-epidemic growth rate significantly higher than the pre-epidemic rate. The population was then clearly impacted, but to a lesser extent, by the recurrence of the PDV epidemic in 2002.
Heavy seal pup hunting between 1968 and 1973 and earlier bounty schemes must have had some effect on the population trajectory. However, hunting pressure in the Wadden Sea was probably higher than in The Wash. Reijnders (1992b) estimated that, between 1900 and 1960, annual catches, which included adult females, ranged from 800 to 1700. Hunting continued in areas outside the Dutch section of the Wadden Sea until 1976, and pup production was further depressed after 1960, possibly because of the effects of pollution. Despite these restrictions, pre-epidemic growth in the Wadden Sea population exceeded that in The Wash. There is no indication of density-dependent effects constraining the growth rate within The Wash. It is clear that either there has been continual net emigration or survival, and/or fecundity rates in The Wash must have been lower than elsewhere in Europe since the 1970s.
It is also not clear why post-1988 epidemic rates of increase are higher than pre-epidemic rates. Before the epidemic, both The Wash and the Wadden Sea populations were apparently recovering from the effects of intensive hunting pressure (Reijnders 1992b). Despite reduced reproductive performance, apparently the result of high organochlorine (OC) burdens (Reijnders 1980; Anonymous 1988), the Wadden Sea population increased by 8·8% pa before the epidemic. It has been suggested that the increased growth rate after the epidemic was because of higher mortality in animals with below-average reproductive output, possibly associated with reduced immune system capacity (Reijnders et al. 1997). If OC-induced reproductive suppression was restricting growth rate in the Wadden Sea pre-1988, our results may imply a similar effect in the English east coast population. Hall et al. (1992) showed that The Wash harbour seals that died during the epidemic had higher OC burdens than those that survived. However, these levels were much lower than those recorded in the Wadden Sea seals (Reijnders 1980).
Härkönen, Harding & Lunneryd (1999) demonstrated that age- and sex-specific haul-out patterns, combined with the uneven sex and age distribution of mortality during the PDV epidemic, might partly explain the higher post-epidemic rates of increase observed in continental Europe. They suggest that uncorrected post-epidemic counts would have underestimated population size by around 13–16% in 1989–90 and that the negative bias would have decreased to around 2·6% by 1996. The observed trend in uncorrected survey counts would therefore have overestimated the population growth rate by around 3% pa in the first 6–7 years after the epidemic. If such an effect were operating in the English harbour seal population, we would expect growth rates to be inflated in the early post-epidemic period and then to decrease as the population age structure converged on the pre-epidemic structure. However, our population trend model does not indicate any long-term effect of change in population age structure. Mortality in 1988 appears to have been more evenly distributed with respect to age and sex in The Wash population than in the European mainland population (Hall, Pomeroy & Harwood 1992), possibly because the epidemic struck after the pupping season. Thus the observed trend may be expected to be less biased.
The effects of the two epidemics are clear from the trend data. The level of mortality in 1988 was similar to that seen throughout the European population. However, the 2002 mortality was apparently lower, approximately half the level suggested for the Wadden Sea (0·47) (Reijnders, Brasseur & Brinkman 2002) and Kattegat-Skagerrak (0·49) populations (Harding, Härkönen & Caswell 2002). As the population estimates and the timings of the epidemics in The Wash were similar in 1988 and 2002, it is not clear why the mortality rate should have been lower in 2002. It is interesting to note that PDV-linked mortality in other British harbour seal populations was also much lower in 2002 than in 1988 (Lawson & Jepson 2003).
The analytical method we used allowed us to combine sparse but regular monitoring data with sporadic observations from older data sets to produce robust estimates of growth rates and epidemic mortality rates for the English harbour seal population. The method highlights the value of structuring data collection strategies to ensure compatibility with previous data sets. The confidence limits on both the growth and mortality rates are tight enough to allow meaningful comparisons between different growth phases and epidemics both within and between populations. Clearly increasing the survey effort would improve the predictive value of the data set. However, the results may indicate that any available additional effort may be better deployed to investigate other more sensitive aspects of the population dynamics in parallel with the long-term monitoring. For example, combining the heavily damped population index provided by moult counts with estimates of the annual pup production may provide a more sensitive and responsive index of population status that would have greater value for population management.
We thank Tony Martin, Kevin Nicholas, Colin Hunter, Gilly Banks and many others for acting as camera operators, and Chris Francis, Pete Treadaway and Richard Davies for flying us around and around and around. Thanks to Lex Hiby, Phil Hammond, Ailsa Hall and John Harwood for reviews of earlier drafts. The work was funded by the Natural Environment Research Council.
The following supplementary material is available for this article online.
Appendix S1. WinBUGS model code.
Fig. S1. Map of Great Britain, showing locations of the study sites, with expanded maps showing the approximate locations of the main haul-out sites in The Wash and Moray Firth.