evaluation of the alaska harbor seal (phoca vitulina) population survey: a simulation study

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MARINE MAMMAL SCIENCE, 19(4):764-790 (October 2003) 0 2003 by the Society for Marine Mammalogy EVALUATION OF THE ALASKA HARBOR SEAL (PHOCA VITULINA) POPULATION SURVEY A SIMULATION STUDY MILO D. ADKISON TERRANCE J. QUINN I1 Juneau Center, School of Fisheries and Ocean Sciences, 11120 Glacier Hwy, Juneau Alaska 99801, U.S.A. ROBERT J. SMALL Alaska Department of Fish & Game, 1255 West 8th Street, Juneau, Alaska 99802, U.S.A. ABSTRACT We used simulation to investigate robust designs and analyses for detecting trends from population surveys of Alaska harbor seals. We employed an operating model approach, creating simulated harbor seal population dynamics and haul-out behavior that incorporated factors thought to potentially affect the performance of aerial surveys. The factors included the number of years, the number of haul- out sites in an area, the number and timing of surveys within a year, known and unknown covariates affecting haul-out behavior, substrate effects, movement among substrates, and variability in survey and population parameters. We found estimates of population trend were robust to the majority of potentially confounding factors, and that adjusting counts for the effects of covariates was both possible and beneficial. The use of mean or maximum counts by site with- out covariate correction can lead to substantial bias and low power in trend determination. For covariate-corrected trend estimates, there was minimal bias and loss of accuracy was negligible when surveys were conducted 20 d before or after peak haul-out attendance, survey date became progressively earlier across years, and peak attendance fluctuated across years. Trend estimates were severely biased when the effect of an unknown covariate resulted in a long-term trend in the fraction of the population hauled out. A key factor governing the robustness and power of harbor seal population surveys is intersite variability in trend. This factor is well understood for sites within the Prince William Sound and Kodiak trend routes for which at least 10 consecutive annual surveys have been conducted, but additional annual counts are needed for other areas. The operating model approach proved to be an effective means of evaluating these surveys and should be used to evaluate other marine mammal survey designs. Key words: harbor seal, Phoca vztulzna, survey design, aerial count, Gulf of Alaska, simulation, population. 764

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Page 1: EVALUATION OF THE ALASKA HARBOR SEAL (PHOCA VITULINA) POPULATION SURVEY: A SIMULATION STUDY

MARINE MAMMAL SCIENCE, 19(4):764-790 (October 2003) 0 2003 by the Society for Marine Mammalogy

EVALUATION OF THE ALASKA HARBOR SEAL (PHOCA VITULINA) POPULATION SURVEY

A SIMULATION STUDY MILO D. ADKISON

TERRANCE J. QUINN I1 Juneau Center, School of Fisheries and Ocean Sciences,

11120 Glacier Hwy, Juneau Alaska 99801, U.S.A.

ROBERT J. SMALL Alaska Department of Fish & Game,

1255 West 8th Street, Juneau, Alaska 99802, U.S.A.

ABSTRACT

We used simulation to investigate robust designs and analyses for detecting trends from population surveys of Alaska harbor seals. We employed an operating model approach, creating simulated harbor seal population dynamics and haul-out behavior that incorporated factors thought to potentially affect the performance of aerial surveys. The factors included the number of years, the number of haul- out sites in an area, the number and timing of surveys within a year, known and unknown covariates affecting haul-out behavior, substrate effects, movement among substrates, and variability in survey and population parameters. We found estimates of population trend were robust to the majority of potentially confounding factors, and that adjusting counts for the effects of covariates was both possible and beneficial. The use of mean or maximum counts by site with- out covariate correction can lead to substantial bias and low power in trend determination. For covariate-corrected trend estimates, there was minimal bias and loss of accuracy was negligible when surveys were conducted 20 d before or after peak haul-out attendance, survey date became progressively earlier across years, and peak attendance fluctuated across years. Trend estimates were severely biased when the effect of an unknown covariate resulted in a long-term trend in the fraction of the population hauled out. A key factor governing the robustness and power of harbor seal population surveys is intersite variability in trend. This factor is well understood for sites within the Prince William Sound and Kodiak trend routes for which at least 10 consecutive annual surveys have been conducted, but additional annual counts are needed for other areas. The operating model approach proved to be an effective means of evaluating these surveys and should be used to evaluate other marine mammal survey designs.

Key words: harbor seal, Phoca vztulzna, survey design, aerial count, Gulf of Alaska, simulation, population.

764

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ADKISON ET AL.: POPULATION SURVEY SIMULATION 765

Estimating abundance and detecting trends in an animal population can be problematic when only a fraction of the population is visible, and that fraction varies over time (Mansfield and St. Aubin 1991, Thomas 1996, Udevitz 1999). The fraction of the population visible may vary due to sex- and age-specific behavior, as well as environmental conditions at the time of the survey (Garrott et al. 1994, Dunn et a/. 1997, Galimbierti and Sanvito 2001, Huber et al. 2001). These dif- ficulties particularly apply to pinnipeds, where censuses usually count only those animals ashore (“hauled out”) (Eberhardt et al. 1979).

In Alaska, harbor seal (Phoca vitzllina) population abundance and trends in abundance are primarily assessed using aerial counts obtained during the August molt period. Photographs of all seals at a haul-out are taken from an aircraft, and precise counts are obtained when the images are later examined in the lab (Frost et al. 1999, Boveng et al. 2003, Small et a/. 2003). Logistical and weather related factors preclude surveys from being conducted under constant environmental conditions, most of which vary asynchronously, thereby resulting in difficulties inferring harbor seal abundance and population trends from these aerial counts. For example, not all seals haul out at any one time, and the number hauled out varies by date, time of day, stage of the tide, etc. (Frost et al. 1999, Small et al. 2003). The timing of the molt period may also vary across years (Harkonen et al. 1999, Daniel et al. 2003) resulting in temporal variation in haul-out attendance and thus the fraction of seals counted during surveys.

To monitor trends in harbor seal populations, a consistent set of trend sites are surveyed annually within each of several regions of Alaska (Frost et al. 1999, Small et al. 2003). Sophisticated statistical methodologies have been used to standardize these counts to comparable units by estimating the effects of covariates such as date, stage of tide, rime of day, etc. on the number of animals seen (Frost et al. 1999, Small et al. 2003, Ver Hoef and Frost 2003). These standardized counts are usually not translated to an estimate of absolute abundance; i.e., the fraction of the popula- tion in the water under standard conditions is unknown and not all haul-ours are censused.

This attempt at standardization may suffer from being based on observational rather than experimental data, in that there may be little contrast in the values of certain covariates and/or similar patterns in two or more covariates. In theory, such data could result in poor estimates of the effects of some covariares, reducing rather than enhancing precision (Lebreton et al. 1992). Similarly, in one instance counts had been obtained progressively earlier in the year across a 5-yr period (Hoover-Miller et al. 2001), potentially confounding a change in the fraction of the population hauled out due to date with an underlying true trend in the population.

To estimate absolute abundance, there are periodic aerial counts of seals over their entire range in Alaska. Both the maximum and mean count for each site are calculated and summed across sites, and mark-recapture methods are applied to presencelabsence data obtained from VHF radio-tagged animals to estimate the fraction in the water (Withrow and Loughlin 1997, Huber et al. 2001, Simpkins et al. 2003). Based on this fraction, a single “correction factor” is applied to the mean count to estimate absolute abundance. However, the correction factor that should be applied to estimate absolute abundance necessarily varies with the state of the covariates during each particular count. Further, radio tags ate applied at only a few locations, but the effects of a covariate can vary both within and among survey areas (Small et al. 2003, Ver Hoef and Frost 2003). Covariate data has been collected

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766 MARINE MAMMAL SCIENCE. VOL. 19. NO. 4. 2003

during surveys, and methodologies for incorporating this information into pop- ulation estimates are being investigated (Boveng et al. 2003).

Other concerns about the hatbot seal surveys have arisen in recent years. In the Prince William Sound (PWS) region, the number of animals killed by the Exxon Valdez oil spill (Frost et al. 1994) has been disputed, based on the premise that seals may have moved to locations outside of the survey area, and that the current survey sites may not be representative of the entire PWS area (Hoover-Miller et al. 2001). Problematically, the areas that the seals have purportedly moved to contain glacially dominated fiords, where it is suspected that both haul-out behavior and visibility of the seals may differ (Mathews and Kelly 1996, Hoover-Miller et al. 2001). In addition, recent evidence indicates that seals separated by relatively short distances may have significant genetic differences (Westlake and O’Corry-Crowe 2002), and thus population trends could differ over small spatial scales.

Here, we examine harbor seal population surveys in that portion of the Gulf of Alaska affected by the Exxon Valdez oil spill (EVOS) using computer simulation. We use this approach to evaluate the effects of animal movement, variation in molt period timing, intersite variability in trends, and other factors thought to affect the surveys and, thus, harbor seal population estimates. We compare the robustness of alternative survey designs and analyses to the biological factors that might affect our ability to estimate population trends. Based on these analyses, we provide guidance on how to improve existing surveys.

METHODS

Operating Model Approach

The operating model approach (also known as operational management pro- cedure) is an emerging technology that is becoming widely used in evaluating the robustness of natural resource management strategies. Pioneered by the Scientific Committee of the International Whaling Commission (Kirkwood 1997), it has found use in fisheries management, particularly in South Africa (Butterworth and Bergh 1993, Butterworth et al. 1997, Cochran et al. 1998). The goal is to find a management procedure that achieves resource conservation objectives by conduct- ing simulations over a wide variety of operating conditions and hypotheses (Cooke 1999).

In our context, the management strategy is the search for robust designs (low bias and variability in estimates of abundance and trend) for the Gulf of Alaska harbor seal population surveys. The operating model allows us to examine many known and hypothesized factors affecting the population and the survey, and to compare the performance of alternative methods for analyzing the resulting data (Thomas 1996).

To ensure relevancy, many features of the operating model are drawn directly from observations of Gulf of Alaska harbor seal populations. We use many years of detailed count data from Tugidak Island to estimate the day-to-day variability in the number of animals hauled out, as well as the variation among years in which the peak numbers occur. We use an intensely surveyed set of 25 haul-out sites in Prince William Sound to estimate variability in trends in abundance among sites within the same region. We also use these data to examine how variable are the effects of factors, such as tide and date, from site to site.

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ADKISON ET AL.: POPULATION SURVEY SIMULATION 7 67

Harbor Seal Biology and Distribution

Harbor seal haul-outs in Alaska range from the tip of Southeast Alaska through the Gulf of Alaska and Aleutian Islands, and through Bristol Bay and Kuskokwim Bay (Rice 1998). Maximum observed population growth rates in harbor seals rend to be slightly above 10% per year (Olesiuk et al. 1990), as females produce a single pup and typically do not reproduce before age 3 or 4 (Bigg 1969). Satellite tagging studies in Alaska indicate limited movements among haul-out sites by all age classes (Lowry e t al. 2001; Small, unpublished data), particularly in the month before molting (most tagging methods do not permit studies during molting). Recent genetics research reveals divisions at small spatial scales, suggesting limited gene flow (Stanley et al. 1996, Goodman 1998, Westlake and O’Corry-Crowe 2002).

Haul-outs are used throughout the year, but peak usage occurs in summer, associated with pupping and molting (Jemison and Kelly 2001, Daniel etul. 2003). Different demographic components of the population differ in the timing of these activities (Thompson and Rothery 1987, Harkonen et al. 1999, Daniel et ul. 2003). Other factors such as tide, weather, and disturbance events affect the fraction of the population hauled-out at any particular time (Schneider and Payne 1983, Watts 1996).

Analysis of Tugidah Island Counts

From Tugidak Island in the Gulf of Alaska, six years of almost daily counts of hauled-out harbor seals have been obtained (Jemison and Kelly 2001). These data allowed us ro empirically estimate a couple of key parameters of our simulation model; i e . , how much counts vary from day to day and how much the timing of annual peaks in counts varies from year to year.

The sex and age composition of seals hauled out at a particular site is dynamic, driven by a complex suite of life history requirements (Jemison and Kelly 2001, Daniel et ul. 2003). The net result is usually two distinct peaks in the number of animals hauled out each year, the first associated with pupping and the second with molting Uemison and Kelly 2001).

We approximated the complicated biological processes affecting the seasonal magnitude of the counts using the sum of two bell-shaped curves:

The shape of each of these curves was a normal distribution multiplied by a scalar. Cxr refers to the count on day t in year y. The subscripts 1 and 2 refer to the pupping and molting periods, respectively. The scalar ( H ) and mean date (p) of each curve differed among years and periods, but the width parameter (0) was assumed constant to achieve parameter stability.

Curves were fitted to the daily peak count data from Tugidak Island by maximum likelihood, assuming lognormal error (Fig. 1). The estimated peak dates (p) for the pupping and molting periods fluctuated with standard deviations of 13.7 and 12.0 d, respectively. The residuals of the log-transformed data had a standard deviation of approximately 0.36 with an autocorrelation of approximately 0.42. Because we fit a crude model to these data, the residuals were taken as conservatively large estimates of the day-to-day variability in counts unrelated to explanatory

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7 68 MARINE MAMMAL SCIENCE, VOL. 19, NO. 4, 2003

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Figure 1. Harbor seal counts from Tugidak Island, Alaska, collected during six separate years during between 1976 and 1999 (diamonds). The solid line denotes the sum of the two bell-shaped curves fit to the pupping and molting peaks within each year. The residuals of this “fit” were used to estimate conservatively large values for random variation and auto- correlation in count data for use in the simulation model.

covariates. We used these values to generate day-to-day fluctuations in counts in our simulation studies (details below).

Reanalysis of Prince William Sound Trend Route “A” Sites

To obtain estimates of the variation among sites within the same region in both trends in abundance and in the effect of covariates on counts, we used data from the 1 2 consecutive annual counts (1988-1999) from the Prince William Sound trend route A, the longest time-series of annual surveys available in the Gulf of Alaska. We found that the Bayesian hierarchical model of Ver Hoef and Frost (2003) provided a logical starting point for development of our simulation model. Knowing that this model would be too complex to use for large-scale simulations, we reanalyzed the raw count data and came up with a general linear model formulation to approximate results from the Bayesian model.

In our reanalysis, the dependent variable was In (count + l), assumed to be normally distributed. As predictors, we used a categorical variable for year and covariates for date, time of day, time relative to low tide (hereafter referred to as “tide”), and water height at the nearest low tide. Following Ver Hoef and Frost (2003), we fit linear and quadratic terms to each covariate. Because our analyses showed that tide height and time of day were the least significant variables, we

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ADKISON ET AL.; POPULATION SURVEY SIMULATION 769

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Figwe 2. Deviations of estimated trends from the average trend across sites for the 25 sites in the Prince William Sound Trend A survey, based on reanalysis of the raw data. These deviations were used to generate among site variability in trends in simulations.

dropped those variables and performed a second analysis. Results were fairly similar to those of Ver Hoef and Frost (2003), so we used parameters from the reduced model in subsequent work.

The exponential trend in abundance at each site was estimated by fitting a simple linear regression to the estimated year effects at each site. The estimated deviation of the trend at each site from the average trend of-0.11 (corresponding to a 10% annual rate of decline) indicated large among-site trend variability, with deviations ranging from -0 .28 to 0.22 (Fig. 2). For simulations (below), these deviations were randomly sampled to simulate the variability in trend among sites in the same region.

The estimated effects of date on In (count + 1) among sites and averaged across sites (Fig. 3a) ranged from about -1 to 1 from 10 d before the mean survey date of 28 August to 20 dafter that date (corresponding to the range in the data). The effects also range from minimal (flat) to concave downward (the expected effect) to concave upwards (somewhat counterintuitive). Averaged across sites, the overall effect is concave downward. The peak cannot be seen on the graph, but occurs about 15 d before 28 August (standardized date = -0.15). For simulations (below), these 25 curves were randomly sampled to represent the variability in the effect of date among sites.

The estimated effects of tide on In (count + 1) among sites and averaged across sites (Fig. 3b) ranged from about -2 to 1 from 3 h before low tide to 3 h after low tide (corresponding to the range in the data). The effects ranged mainly from minimal (flat) to concave downward (the expected effect). Averaged across sites, the overall effect is concave downward with a peak about low tide. For simulations (below), these 25 curves were randomly sampled to represent the variability in the effect of tide among sites.

Spatial Structure of the Operating Model

We delineated five geographic regions: PWS, Kodiak, Alaska Peninsula, Cook Inlet, and Kenai (Fig. 4). All potential haul-out sites within each region were

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770 MARINE MAMMAL SCIENCE. VOL. 19, NO. 4. 2003 ~~ ~

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Standardized Time Relative to Low Tide F i g w e 3, Estimated effects of (a) survey date and (b) time relative to low tide on

In(abundance) for the 25 sites in the Prince William Sound Trend A survey, from reanalysis of the raw data. The average effect across sites is also shown (circles). Standardized date is (Date - 28 August)/100. The range of the observed data was used for the range of the x-axis, which corresponds to 10 d before 28 August to 20 d after 28 August. Standardized tide is (Time relative to low tide)/l00. The range of the observed data was used for the range of the x-axis, which corresponds to 2.5 h before low tide to 2.5 h after low tide.

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ADKJSON ET AL.: POPULATION SURVEY SIMULATION 77 1

Figure 4. The 244 haul-out locations included in this simulation study (triangles) and the subdivision of the study area into five geographic regions (dark lines).

identified from the 1996 NMFS survey and the ADF&G Kodiak and PWS trend routes, and categorized as either an ice or non-ice substrate. We pooled all sites within 2 km of each other to minimize the complication of animals moving among adjacent sites during the survey period; this resulted in a total of 244 sites (Fig. 4). The sites were sorted, mainly by decreasing longitude (west to east), and classified into eight survey subareas within the five main regions (Table 1). The size of survey subareas was chosen to approximate those areas actually surveyed during the 1996 NMFS survey. With the exception of survey subarea 8, these survey routes cor- respond to entire areas or subdivisions of areas as defined for population dynamics (see below).

Simulated Population Dynamics

The model generated the abundance of harbor seals at all sites over the course of the 12-yr simulation period. Because the survey design was the key factor in this study, we kept the model’s population dynamics simple and deterministic; true abundance increased (or decreased) at a constant exponential rate. For our purposes, we defined “abundance” as the count of animals that would occur on the date of peak attendance during the molt period at low tide if no unknown covariate affected counts. By doing so, we avoided the complication of estimating the relationship between peak counts and the true population abundance. This scaling factor, while important for some purposes, was not necessary to our examination of the ability of different survey schemes to detect trends. We consider some implications of scaling counts to absolute abundance in our discussion.

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772 MARINE MAMMAL SCIENCE, VOL. 19, NO. 4 , 2003

Table I , simulations.

Survey subarea Region Number of haul-out sites

The number of harbor seal haul-out sites in eight survey subareas used in model

1 Alaska Peninsula 53 2 Kodiak 37 3 Kodiak 35 4 Cook Inlet 34 5 Kenai 1 2 6 PWS A 19 7 PWS B 27 8 Area 5 (PWS C + Copper River) 27

Movement-Movement data are unavailable for the August molt period when population surveys are typically conducted in Alaska. However, mean distance moved by non-pups between haul-outs was <5 km during June and July in PWS (Lowry et al. 200 l) , and cumulative monthly distance traveled among haul-outs by non-pups was lowest (<25 km) in the Kodiak and Southeast Alaska regions during July and September (Small, unpublished data). We believe these data indicate movement is likely minimal during the molt period, particularly in relation to the temporal duration and spatial extent ofannual surveys within subareas, and thus we assumed no short-term movement among sites. Interannual movement among sites was incorporated in studies of differing substrate preferences (see below), as follows. Using all sites, a matrix 0 of movement proportions was constructed: e,,, was the probability that an animal at si tej would be at site i the next year, so that the “from” region was in columns and the “to” region was in rows. For simplicity it was assumed that movement declined linearly with distance between sites at rate z , up to a distance d,, so that O,,, = z , (1 - d/d,), where d was the distance between sites i and j .

Trend in abundance-We used a hierarchical structure for the trend parameter z1 at each site, which was defined as the log ratio of abundance in two successive years:

~1 = ln(Nt+l/Nt) = p + L k , where

p = overall trend

Lb = site-specific deviation from regional trend

We assumed that substrate did not affect trends in abundance; rather i t affected behavior of the seals through movement ot attendance parameters. Note that the value of z1 is negative when the population at a site is decreasing. We assumed that intersite variability in trend from PWS was representative of all sites in the overall study area. The site adjustments ( L k ) of all 244 locations in the simulation were thus sampled with replacement from the 25 estimated deviations (Fig. 2) in PWS site trends. Various values for the overall trend (p) were explored, depending upon the specific purpose of each simulation.

Initial conditions-We used the counts from the 1996 NMFS database (Withrow and Loughlin 1997) to set initial conditions for abundance in the first year. If the NMFS count was <10 in 1996, we replaced it with 10 so that all sites would start with some animals.

Population abundance-Abundance at the start of year t was written in vector notation as Nt. It was assumed that movement among sites (if any) occurred

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ADKISON ET AL.: POPULATION SURVEY SIMULATION 773

immediately after the beginning of the year, so that abundance after movement was f i 8 = ON,. The population trend was accounted for thereafter from the equation N,,8+l = f i2 ,8 exp(Tl,), where f l r is the site-specific trend. Because our main interest was to determine the ability of the survey to detect a trend in abundance, our simple population dynamics model had site-specific trends only.

Simulated Attendance at Haul-out Sites (Covariate Effects)

Covariates-Many factors (covariates) including survey date, time of day, time relative to low tide, and height of the nearest low tide may affect the number of seals present at a site (i.e,, attendance) (Ver Hoef and Frost 2003, Small et al. 2003). Survey date is one of the main survey design features and must be included in our operating model. For simplicity, we subsumed the remaining known influences on attendance into a single factor. In addition, we included an additional factor in the model that was assumed unknown or unmeasured to examine how abundance and trend estimates might be affected. Therefore, we assumed that attendance was related to:

variable x: date relative to the mean PWS survey date of August 28, variable y, a known covariate: a variable that affects attendance within a day, which we took from the variable “time relative to low tide” in the Ver Hoef and Frost (2003) analysis and our reanalysis,

(3) variable z , an unknown covariate: a lurking variable not related to time of low tide, and

(4) random events.

Date and tide were modeled as quadratic effects, and the unknown covariate was modeled as a linear effect. The expected overall effect E, of the these three variables for each site i was loglinear:

El = eXP(P1,Xz + P 2 P ; + P3,YZf P4,Y; + P S d

(labeling differs from Ver Hoef and Frost {20031). Effects that differed at sites with different substrates were included for some scenarios.

Based on our analysis of data from Tugidak Island counts (above), random variation in counts was modeled as lognormal error with a standard deviation sd = 0.35, and successive counts within a site and year were assumed to be autocorrelated with c = 0.40. The random effect and the annual abundance at each site were then multiplied to obtain the simulated number of animals present on survey day k (i.e., the count on that day):

C,,t,k = N , t R ( E z , t , k , Jd, c),

where R is the lognormal random generator. Simulated valzles of covariates-Variable x, survey day: for each of the eight survey

subareas in the five regions, our base case was a 10-d survey period starting with a random date 0-10 d before the mean survey date (28 August). Flights were conducted on seven days chosen randomly from these 10. Variable y, tide, was modeled after standardized time relative to low tide. It was drawn for each site and survey as a uniformly distributed random variable between -1.5 and 1.5. This range is slightly shorter than the range found in actual surveys (-1.9 to 120, but helped to simplify the modeling. Variable z , as an unmeasured covariate, would have the greatest impact if the value of the variable fluctuated from year to year. Two

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774 MARINE MAMMAL SCIENCE, VOL. 19, NO. 4, 2003

such scenarios were considered: (1) unknown trend was assumed to have a linear positive trend from -1.5 to 1.5 over the 12 yr. In addition, for each site and survey a uniformly distributed random value between -1.5 to 1.5 was added to the resultant annual value to provide realistic within-year variability of the same magnitude as the tide covariate. ( 2 ) unknown fluctuation was assumed to have a random uniformly distributed mean between -1.5 to 1.5 that differed among the 12 yr. In addition, for each site and survey a uniformly distributed random value between -1.5 to 1.5 was added to the resultant annual value to realistically represent within-year variability. A realization of possible values of covariates y and z for a single site surveyed seven times in each of 12 yr is shown in Figure 5.

Attendance parameters-For each of the 244 sites, each pair of coefficients (p) specifying a covariate effect was randomly drawn with replacement from the 25 pairs of site-specific parameters estimated in the reanalysis of PWS Trend A data (described above).

For the unknown covariates 1 and 2, the central tendency of the linear parameter (there was no quadratic coefficient) was chosen to give a mean adjustment in the dependent variable of 0.5 at a covariate value of -1.5 and of 4 . 5 at 1.5, similar in magnitude to the average effect estimated for the covariate tide in PWS (described above). This criterion resulted in a coefficient of 4 . 3 2 . Each site-specific coefficient was drawn from a normal distribution with mean -0.32 and standard deviation 0.16 on the assumption that a 50% CV would be a reasonable amount of intersite variability. This was translated into an annual effect for unknown covatiate 1, which had a linear trend over rime.

Based on daily count data from Tugidak Island (Fig. l) , the peak date of attendance has an interannual fluctuation with a standard deviation of about 10 d. Because our base model assumed that peak date of attendance was constant, we ran an alternative set of simulations to investigate the effect of incorporating variability in the peak date.

For the purposes of this study, we did not have an additional parameter for the overall lack of attendance of animals not present given optimal conditions (molt peak, low tide). We were more interested in results related to optimal survey design rather than exact estimation of the population. We addressed survey issues related to this overall lack of attendance based on first principles rather than these simulations.

Counting errors-We assumed that animals hauled out were counted without error. We believe that the aerial survey probably does have some measurement error in counts due to weather conditions, glare, pelage color, and so on, but that the magnitude of this error is small relative to the effects of attendance factors.

Estimation ModelJ

Raw count estimates (RCE)-In this estimation procedure the average count for each site and year across replicate surveys was calculated and totaled. No adjustments for covariates were made. The trend was calculated as the slope of an ordinary linear regression of In(average count) us. year. In a sensitivity analysis the maximum count was substituted for the average count.

Covariate-corrected estimates (CCE)-We approximated the Bayesian estimation approach used by Ver Hoef and Frost (2003), in which counts are adjusted to account for the effects of covariates on the fraction of seals hauled out, with the simpler general linear model procedure described above. The rationale for this

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ADKISON ET AL.: POPULATION SURVEY SIMULATION 775

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1.5 1 -

-3

Figure 5. An example of randomly generated values of covariates for a single site surveyed seven times each year. In (a), the expected value is zero each year but random sampling still results in annual differences in the realized average and the range of values observed. In (b), the expected value also fluctuates among years, while in (c) there i s a linear trend in the expected value across years. Graph (a) is a typical realization of our known covariate "tide," while ( b x ) are typical of values generated for studying the effect of an unknown covariate.

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replacement was that we needed a computationally non-intensive method to approximate the technique of adjusting for covariates. Since the goal was to compare relative rather than absolute performance, we felt that the general linear model was acceptable for this purpose. Variables used in the general linear model were year, standardized date, standardized tide, and their quadratic counterparts. The unknown covariate, if present, was assumed not to be available to this estimation procedure. The trend was calculated by regression of the estimated annual effects from the general linear model us. year.

Simulation Trials to Test Alternative Survey Designs and Analysis Methods

The algorithm used for conducting simulations was:

1. Generate the population dynamics and hold fixed for each survey design, 2. Simulate the survey to obtain counts, 3. Use the estimation models to get estimates of trend, 4. Repeat steps 2 and 3 many times (100-1,000), 5 . Compare trend estimates from step 4 with the known values from step 1 to

determine bias, accuracy, and power to detect trends, and 6. Repeat steps 1 to 5 for various scenarios of interest.

The “base case” simulation contained the following assumptions: the survey was conducted annually at all sites over 12 yr, seven replicate counts at each site were obtained over a 10-d period roughly centered about the peak of attendance, net movement of seals among haul-outs was negligible during both the 10-d survey period and across years, the average trend was zero, the values of covariates affecting attendance were known, and there was no difference in behavior due to the substrate at the haul-out. Modifications of this base case were explored to test the sensitivity of estimates of trend to characteristics of the survey and the seal populations. Performance was defined as the bias (defined as the difference between the average estimate and the true value) and accuracy (defined as the square root of the mean squared residual) of estimates of trends and of the effects of covariates.

Modifcations of the survey-The first set of simulations looked at obvious modifications of the survey design related to sample size and timing (Table 2). We also looked at changes that had been recorded during previous surveys, such as a linear trend in the survey date (Hoover-Miller e t al, 2001).

Unknown covariates-The next set of simulations looked at the effect of a “lurking covariate”; i . e . , some unknown factor that affected the fraction of animals available to be counted from one year to the next. We simulated both annual fluctuations in the mean value of this covariate and a temporal trend in the mean value (details above).

Substrate ejjficts and movement among substrates-We investigated the effect of differing covariate relationships between haul-outs with different substrates. These simulations were run only for the 46 sites in Prince William Sound, where a particular concern has been expressed about differences between behavior at ice haul-outs and at other locations (Hoover-Miller et al. 2001). We simulated a systematic difference between ice and rock substrate types by removing the effect of “tide” in all ice sites and applying a single “average” tide effect at all other sites. As there are relatively few ice sites in Prince William Sound, we ran some simulations in which we assigned an ice designation to a random half of the 46 sites.

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Table 2. Modifications to the base case model simulation of Alaska harbor seal population surveys investigated through the operating model approach.

Scenario Values investigated Years of data available Replicate counts at each site wiin a year

(and number of days selected from) Timing relative to peak attendance

Linear trend in survey data

4, 8 , 12 2 (4), 4 (6), 7 (lo), 14 (20)

20 d before, at peak, 20 d after, split survey

First survey centered -10 d after peak, survey is with 4 counts at peak and 3 counts 20 d later

2 d earlier each year ~~ ~~ ~ . . .~ ~ ~

We also looked at the effect of annual movement among haul-outs in Prince William Sound outside of the survey period; in particular, directed movement to particular substrates. In one scenario, in each year up to 20% of the population was assumed to move from rock to ice sites or vice uersa. The percentage and direction of this movement was a random, uniformly distributed variable that varied from year to year. The second scenario was a gradual deterministic shift of the population on rocky haul-outs to icy haul-outs, 2% every year for each of the 1 2 yr of the simulation.

Power t o Detect Individual Site Trends

In application to the harbor seal survey, power is the probability of detecting a trend in population abundance when one is present. In conducting a power analysis, it is necessary to have an unbiased procedure; otherwise detection of a trend may be confused with bias in the estimation.

Trends at a single site-In our simulation, the trend at site R over time was the combination of an overall trend and the site-specific deviation:

T~ = ln(iVt+l/Nt) = p + Lk, where

p = overall trend

Lk = site-specific deviation

The random site-effects ( L k ) used in our simulation complicate the determination of power, because the realized trend at any site differs from the magnitude of the overall trend being evaluated. The power calculation we used adjusted for the random effects by rewriting the confidence statement as:

In our power analyses we set p to the trend magnitude we were interested in detecting and calculated confidence intervals. For calculating site-specific power, this approach is equivalent to setting Lb to zero. However, actually doing so would have provided misleading confidence in our ability to detect area-wide trends (see below).

If the confidence interval did not contain 0, then we concluded that a significant trend had been detected. Over 300 replications, the proportion of significant trends was counted, which equals power. The power values for the 244 sites were averaged as a summary statistic.

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Power t o Detect Area-wide Trends

Determining the power to detect a trend across sites in an area is more complicated. Intuitively, one would sum up abundance estimates by site using either the CCE or RCE approach and then estimate the trend using these sums. This procedure would effectively weight each site by its abundance. Unfortunately, when summing two sites with exponential growth rates of equal magnitude but opposite sign, the summed abundance will increase over time. This effect is the typical back-transformation bias found in the lognormal distribution. Thus, the lognormal error structure of the counts induces a bias in abundance weighting that we were unable ro correct for.

Alternatively, we averaged the trend estimates for each site (which were on a log scale), preserving the unbiased nature of the results. As before, we set p to the trend magnitude we were interested in detecting. We calculated confidence intervals as before, except we subtracted the average Lh across all sites in the area to compensate for the difference between the area average trend and the trend for which we wanted to calculate power. The operating model was run with a set of pseudoareas having from 2 to 75 sites.

Sensitivity Analyses on Power

A final power study looked at the effects of various other factors on the power of the survey. For the first of these, a base run with intersite trend deviations (Lg.) drawn from the PWS trend residuals was contrasted with runs assuming no intersite variability and with intersite variability twice as high as the base case (achieved by multiplying randomly drawn deviations by the square root of 2). In another trial the number of counts per site was reduced from 7 (base) to 3. In another trial, the number of years was reduced from 1 2 (base) to 5 . Finally, the RCE method was evaluated using the maximum count instead of average counts. All sensitivity analyses were conducted using 25 sites in a single hypothetical survey area, and both average site power and average area power were evaluated for true annual trends ranging from 0 to -0.1.

RESULTS

Modiflcations of the Suwey

Accuracy declined dramatically as the number of years of data available decreased, whereas bias was only slightly affected (Fig. ba, b). The number of replicate counts obtained each year was not so important, as accuracy increased only modestly as the number of replicates increased from 2 to 14 (Fig. bc, d). The effect of the date of the survey was mixed. Trend estimates were relatively insensitive to the particular dare surveyed, although accuracy was slightly improved for raw count-based trends when surveying at the peak (Fig. be, f). However, although the trend across years was well estimated, the estimated effect of date (the seasonal pattern in the fraction of seals hauled out) was very sensitive to when the survey was conducted. Surveying 20 d before or after the peak greatly affected the quality of estimates of this seasonal pattern, particularly of the linear component (Fig. 7). Splitting the survey so that some counts were taken 20 d apart had a negligible effect on estimates of trend (Fig. be, f) , but improved the estimate of the effect of date (Fig. 7 ) .

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R CCE bias

-0.001

0.m5 Base 6yean 4years

-0.001

0.003 -0.005 iE+ Zdays 4days Base 14days

0.005

0.003 1 I----- 0.001

0.001

-0.005 Date20 Base Date+ZO Split

0.03 3

0.025 0.02 0.015 0.01 0.005

0 -0.005 j

Base Fluctuate DateTrend

0.005

0.015

0.035 0.055

0.075

-0.095 Base Linear Random

RCCE accuracy b

Base 6years *years

d

0.04

0.02

0 Zdays 4days Base 14days

f

0.06 O M .

0.02

0 Date-20 Base Date+PO Split

h 0.1 , 0.06

0.06

0.04

0.02

0 Base Fluctuate DateTrend

0.1

0.08

0.06

0.04 0.02

0 Base Linear Random

Figwe 6. The performance of trend estimates as a function of survey characteristics, for both a covariate-corrected estimator (CCE) and an estimator based on the average count (RCE). Graphs on the left shows bias, graphs of the right show accuracy (smaller bars indicate better accuracy), based on results from 100 simulations with 244 haul-out sites. Figures a-b compares surveys over differing number of years, c-d over differing number of replicate counts within years, e-f the effect of survey date, g-h the effect of changes in the mean date of attendance, and i-j the effect of unknown covariates.

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0 6 - a 100 betal accuracy (x10) b 0 beta2 accuracy

40 30 20 10 h7

0 4 - 0 2 -

0-

-0 2 - - 0 4 -

-06 -

mbetal bias (x10) 0 beta2 bias

Date-20 Base Date+20 Split Date-20 Bare Date+M Split

Figure 7. The performance of estimates of the covariate effect as a function of the average date of the survey relative to 28 August (base case), for both the linear (betal) and quadratic (beta2) effects. Results for betal were multiplied by ten to aid visibility. Left graph shows bias, right accuracy. Results from 100 simulations with 244 haul-out sites.

When the date of the survey evolved over time, the covariate-corrected trend estimates lost little accuracy. However, the raw count-based trend estimate lost substantial accuracy and was severely biased (Fig. bg, h). The estimated bias of 0.022 equates to estimating an annual growth rate of more than 2% whereas the simulated populations were not growing at all. In contrast, natural fluctuations in the date of peak attendance resulted in no bias, but some loss of accuracy for both trend estimates.

Unknown Covariates

Including an unknown covariate that randomly fluctuated from year to year had only a minor effect on the accuracy of trend estimates (Fig. 6i, j). With 12 yr of data, the trend component of the counts was easily distinguishable from the additional noise due to this covariate. However, we would expect a larger impact if fewer years of data were available. A much more striking result occurred when the lurking covariate had a linear trend over time: both trend estimates were highly biased with substantially decreased accuracy (Fig. 6i, j). The estimated bias of -0.087 for both methods equates to estimating an annual rate of decline of more than 8%, whereas the simulated populations were not declining at all.

Substrate Eflects and Movement among Substratej

Including a systematic difference in the effects of the “tide” covariate between ice and rock sites in Prince William Sound did not appreciably affect the performance of the survey, even if half of the 46 sites were assumed to be ice type. However, in these scenarios only the covariate effects differed from site to site. As covariate effects are estimated fairly well under the base case survey, this result is not surprising.

Movement among sites did increase bias and decrease the accuracy of area-wide trend estimates. Directed movement of 2% per year from the 40 rock substrate sites to the six ice substrate sites resulted in a negative bias. This was because this movement resulted in more sites declining than increasing.

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100%

90%

80%

70%

60% -u 50% 8 40%

30%

20%

10%

0%

4

0 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 -0 1

Trend F i g w e 8. Power to detect site-specific trends of various magnitudes using covariate-

corrected estimates (CCE) or raw count estimates (RCE). The power for the RCE method is shown using both maximum counts and average counts at a site. Results from 300 simulations with 244 haul-out sites.

The randomly directed movement scenario resulted in an even greater negative bias. This is somewhat counterintuitive, as for any given year movement was as likely to be away from ice sites as to them. The bias resulted because we assumed that a fraction of each site’s population, rather than a fixed number of animals, would move each year, and the number of sites of each habitat type was unequal. Under these conditions, the loss of animals from the 40 rock substrate sites was not balanced by immigration of fewer animals from only six ice substrate sites when the direction of movement changed.

Power to Detect Individual Site Trends

Covariate correction increased the power to detect trends at individual sites (Fig. 8). Power for the CCE approach was approximately 0.79 for an annual trend of 4 . 0 5 . With the RCE approach, power was only about 0.65, and this decreased to 0.47 if maximum rather than average counts were used (Fig. 8).

Power to Detect Area-wide Trends

Power increased with the number of sites in the survey area for both the CCE and RCE methods (Fig. 9). Differences between the CCE and RCE methods were much smaller for detecting an area-wide trend than for detecting a trend at a single site; in some circumstances the RCE method was estimated to have slightly higher power (Fig. 9). No matter which method is used, one should survey at least 25 sites in order to detect a trend of -0.05 with at least 50% power.

When the true annual trend was small, the power to detect an area-wide trend was generally smaller than the power to detect a site-specific trend of similar magnitude, because intersite variability is the major determinant of area-wide

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0 -0.02 -0.04 -0.06 -0.08 -0.1

Trend

- _I

, RCE I

100%

90%

80%

70%

60% '11 0 50% !! 40%

a

b

30%

20%

10%

0% 0 -0.02 -0.04 -0.06 -0.08 -0.1

Trend Figure 9. Power to detect area-wide trends of various magnitudes (solid lines), for

areas containing various numbers of sites (number above each line), using (a) covariate- corrected estimates (CCE) or (b) raw count estimates (RCE). Results from 300 simu- lations.

power (Fig. 10a, b, base case). W h e n the trend was large the power to detect an area-wide trend tended to be larger, because the averaging over sites reduced estimator variance sufficiently to counteract intersite variability. For example, using a CCE approach, the power to detect an annual trend of magnitude -0.05 at a single

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,-yu-.l-f-u+---.---. 100%

80%

-Base I B 8 - a - ncOUntS=3 i 40% a

c - % - years=5 I - - novariance - 4 - 2X variance

20% A' ~ *.-• I 0%

100%

80%

60% g

40% 0. is

20%

0% 0 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 -0.07 -0.08 -0.09 -0.1

Trend

Figure 10. Sensitivity of power to detect area-wide (a) and site-specific (b) trends of various magnitudes to changing the number of replicate counts or the number of years in the survey, or (for area-wide trends) to changes in the intersite variability in trend. Results from 300 simulations using covariate-corrected estimates.

site was 0.79, but power for detecting an area-wide trend of the same magnitude in survey routes comprised of 25 sites was only 0.47 (Fig. 10a, b, base case).

Sensitivity Analyses on Power

Area-wide power was substantially affected by intersite variability in trend, decreasing as variability increased (Fig. 10a). Reducing the number of replicate counts from seven to three decreased area-wide power only slightly. Reducing the number of years from 12 to five actually increased area-wide power when the true trend was less than -0.05, but decreased power when the true trend was greater than or equal to -0.05. The increases were due to increased variability in the bounds of the confidence intervals when less data were available ( i e . , the variance among sites was poorly estimated), such that more of them excluded zero. Power for a single site (Fig. lob) uniformly decreased as less data (either fewer years or fewer counts per year) became available. Also, in contrast to what was seen with 12 yt of available data, power was higher for an area than for single sites when only 5 yr of data were available.

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DISCUSSION

Performance of Trend Estimates

Estimates of population trend for Alaska harbor seals in the Exxon Valdez oil spill area are robust to the majority of potentially confounding factors, based on simulations using our operating model approach. For covariate-corrected trend estimates, there was minimal bias and negligible loss of accuracy when surveys were conducted 20 d before or after peak attendance, when survey date became progressively earlier across years, or when peak attendance fluctuated across years. Similar performance was observed for trend estimates not corrected for covariates (i.e., raw-count estimates), except for substantial bias and decreased accuracy if the date of the survey evolved over time. Both covariate-corrected and raw-count trend estimates performed well when the influence of an unknown “lurking” covariate fluctuated across years, but were severely biased with decreased accuracy when the value of the lurking covariate had a linear trend over time. One candidate for such a phenomenon would be a trend in the availability of food such that the time spent foraging increased or decreased. Monitoring programs designed to detect temporal trends in haul-out behavior should be considered.

DeJining Area- Wide Trend

The intuitive definition of an area-wide population trend for harbor seals is the trend in the sum of counts from each haul-out site within the area. Alternatively, the average of each site-specific trend also represents another sort of area-wide population trend. Arguments could be made for using either measure for man- agement and conservation. A population trend estimate based on summed counts provides an index of the overall population status within an area and is important for basic population monitoring. In contrast, the average of site-specific trends gives the average state of all sites, weighting small sites as much as large sites. We chose the average of site-specific exponential growth rate (or “trend”) because i t was more suitable to how we modeled population changes at each site. Both of the current management models that estimate area-wide population trend of harbor seals give more weight to sites with a greater abundance of seals. Specifically, the Bayesian hierarchical model used by Ver Hoef and Frost (2003) estimates site-specific trends, and then determines the area-wide trend by using an abundance-weighted average of the trend at each individual site. The model-averaging approach used by Small et al. (2003) combines corrected counts at different sites when estimating trends.

Efects of Movement Among Sites

Our decision to use the average of the site-specific estimated trend rates and our modeling of movement did result in some artifacts in our assessment of the effects of movement among sites. For example, if there were three sites of 100 seals each and 20% of the seals at two sites (20 + 20 = 40) moved to the third, the third would have 140 animals. If 20% of the seals at the third site (28) returned the next year equally split (14) between the first two sites, then the first two sites would have declined and the third one increased. This explains the negative bias in area-wide trend we saw when we modeled seals randomly moving between 40 rock substrate

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and six ice substrate sites. In contrast to the difficulties movement caused in estimating area-wide trends, there was little effect on the estimate of site-specific trends. This was true even when animals exhibited directional movement towards sites with systematically differing relationships between covariates and counts. In retrospect, we realize that even eliminating the effect of the major covariate “tide” resulted in differences between ice and rock sites that were no larger than the differences among rock sites (Fig. 3). As these differences in covariate effects were adequately estimated in the base case, we should not expect to see any degradation in the performance of the survey solely from differences in the effects of the covariates.

However, our results do not eliminate the possibility that movement could result in biased estimates of trend. If two types of sites differ in average visibility rather than how visibility is affected by a covariate, a substantial redistribution of animals could well cause large biases.

Survey Design and Power

Power is a principal consideration in designing a survey and interpreting the results (Peterman 1990, Taylor and Gerrodette 1993). In the case of the Alaska harbor seal survey, the number of replicate counts needed each year to yield an unbiased and relatively accurate area wide trend estimate appears to be smaller than previously thought. Current surveys typically take 5-7 replicate counts during the annual molt period, yet our simulations suggest robust estimates of area wide trend could be obtained with 2 - 4 replicates with negligible loss of power. The accuracy of trend estimates declined as the number of years of surveys was reduced. The power to detect trends at individual sites also declined sharply, in accord with similar simulations (Galimbierti 2002). However, the change in power to detect area-wide trends was more complicated. When the length of the survey was reduced from 12 yr to 5 yr, there was a substantial reduction in the power to detect area-wide trends of -5% to -7%; power differences at other trend rates were negligible.

In our modeling, surveys occurred annually. In current practice, several trend routes are surveyed annually while the majority of sites get surveyed only every five years. Some power is necessarily lost by having fewer surveys. Larger changes in population abundance may occur between abundance surveys, somewhat mitigating this effect. However, such a large interval between surveys makes timely detection of a population trend unlikely.

Our simulations demonstrated that a key factor decreasing the robustness and power of area wide harbor seal surveys is increased intersite variability in trend (Fig. 10a); this variability has a larger influence than the number of replicates or years surveyed. This variability is well estimated for sites within the Prince William Sound and Kodiak trend routes, but additional information is needed for other sites in the EVOS area to determine its potential impact on trend.

The existing survey design seems to provide enough information to simul- taneously estimate both population trend and the effects of covariates at the spatial scale of individual haul-out sites. This was not obvious to us before this study, as surveys are typically conducted to minimize the range of values of the covariates; e.g., flying surveys during the molt period every year, within 2 h of low tide, etc. It was plausible that the covariate effects would be so poorly estimated for individual sites that the corrections would do more harm than good (Lebreton et al. 1992). In addition, the power to detect site-specific annual trend estimates < -5% appears

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greater than for area-wide trend estimates, except that a relatively large (-10) num- ber of annual surveys are needed.

Unexplored Issues

Several important issues were not addressed in our simulation studies, particularly the conversion of counts to absolute abundance. Boveng et al. (2003) have developed one approach to estimating absolute abundance from counts, and another approach underway at Tugidak Island uses a photographic mark-recapture approach (Hastings et al. 2001) combined with repeated counts under varying conditions to create covariate-based corrections to absolute abundance.

While we investigated the effect of movement among sites between years, we did not investigate the effects of movement among sites during the limited duration of an annual survey. Hoover-Miller et al. (2001) point out that some studies have demonstrated movement (- 15%) among neighboring haul-outs within a few days of tagging. However, available data during the summer period from satellite tagging studies in PWS and Kodiak (Lowry et al. 2001; Small, unpublished data) indicate even when seals changed haul-out location they typically moved only a few kilometers. We attempted to minimize the effect of this issue on our results by combining counts for all haul-out sites within 2 km of each other before undertaking our analyses. The principal effect of within-survey movement should be to decrease survey precision.

Two other issues that need to be examined for their effect on area-wide trends are the extirpation of exisring sites and the colonization of new sites; these, and other issues, are reserved for future work. We do not regard the results presented here as comprehensive, but rather as an examination of some of the major issues involved in improving the Gulf of Alaska harbor seal survey.

Survey Design Recommendations

Estimation methods that adjust for the effects of covariates on the fraction of the population hauled out are more robust than methods based on raw counts; thus, a covariate corrected methodology should be employed. If raw counts must be used for detecting trends, using the average of several raw counts will perform better than using the maximum; however, outliers due to a disturbance event should not be included in the average. All potentially pertinent information on covariates should be collected during surveys, with the majority of counts collected under as standard a set of conditions as possible, and timed to coincide with the peak haul- out numbers. However, some effort should also be devoted to counting under contrasting conditions; e.g., allocating some counts to later in the season. The effect of a covariate on the fraction hauled out is much better estimated when observations from contrasting conditions exist.

A robust estimate of trend may be calculated in as few as five years, yet statistical power will be low for annual trends < -5%. A commitment to obtain 10-12 consecutive annual surveys will provide the opportunity to estimate robust site-specific trends and increase power over a broader range of trends. Obtaining estimates of site-specific trends also permits a measure of intersite trend variability, a major influence on the robustness and power of the area-wide trend estimate. Reducing the number of replicate counts within one survey period

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from seven to three or four does not appear to substantially reduce power or accuracy.

The number of sites required for a robust area-wide trend estimate will depend on several factors, especially the variability in trends among sites. If the population boundaries are known, the ability to detect a trend of a specified magnitude is a power calculation based on the number of sites surveyed from the population (Fig. 9). If the population boundaries are unknown, surveying a latget number of sites will increase power, particularly for annual trends < 4%. Annual counts from <20-25 sites will provide minimal power except for dramatic trends ( i e . , >6%/ yr). Additionally, with unknown boundaries a trend route could span two demo- graphically isolated populations with differing trends. The precautionary approach would recommend managers respond in a risk-averse fashion to all haul-outs ex- hibiting a decline, even though some sites may be within a population that is not decreasing.

If a survey route includes sites with substantially different environmental charac- teristics, it is important to determine if the average fraction hauled out differs between site types, especially if movement of seals between haul-outs of different types might be occurring.

The Operating Model Approach

Our “operating model” approach (Linhatt and Zucchini 1986, Cooke 1999), in which we simulated a population along with the collection and analysis of survey data, proved valuable. This simulation approach allowed us to test alternative survey designs and analysis methods where the correct inference was known, and even where key assumptions of the survey and analyses were violated (Thomas 1996). We were thus able to examine questions of power and robustness, and make recommendations for improving current practice. Many concerns about the current survey could be examined for their potential implications. Field investigations may involve daunting logistics over multiple years, and consequently can be very expensive. Using a relatively rapid and inexpensive simulation approach, we were able to winnow competing concerns, identifying key areas of uncertainty and sensitivity that should be a priority for future field investigations.

We believe that this methodology is directly applicable to other marine mammal survey designs with minimal modification. The key steps are to define the survey features of interest to explore, and then to develop a suitable population dynamics model that incorporates the primary features thought to affect the population. For the purpose of trend detection, the simple exponential trend model used in this paper may suffice. Simulation testing of survey design is likely to provide researchers a tool to avoid poor design choices and to increase confidence in the survey results.

ACKNOWLEDGMENTS

We thank Peter Boveng, Kathy Frost, Lauri Jemison, Brendan Kelly, Beth Matthews, John Moran, Peter Olesiuk, Grey Pendleton, Brian Taras, Dave Withrow, and Kate Wynne for their generosity with data and their insights. Special thanks are due to Jay Ver Hoef for generously sharing his preliminary Bayesian analyses of the ADF&G PWS ‘A’ survey data. Comments by two anonymous reviewers improved an earlier version of the manuscript. The Exxon Valdez Oil Spill Trustee Council supported the research described in this paper.

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However, the findings and conclusions presented by the authors are their own and do not necessarily reflect the views or position of the Trustee Council.

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BOVENG, P. L., J. L. BENGSTON, D. E. WITHROW, J. C. CESARONE, M. A. SIMPKINS, K. J. FROST AND J. J. BURNS. 2003. The abundance of harbor seals in the Gulf of Alaska. Marine Mammal Science 19:lll-127.

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Received: 5 March 2002 Accepted: 25 February 2003