CONTENTS Introduction Methods Results Discussion Acknowledgments Literature Cited
Northeast Fisheries Science Center Reference Document 00-07
Abundance of the Gulf of Maine/Bay of Fundy Harbor Porpoise Based on Shipboard and Aerial Surveys during 1999Debra L. Palka
National Marine Fisheries Serv., Woods Hole Lab., 166 Water St., Woods Hole, MA 02543
Web version posted June 19, 2003Citation: Palka DL. 2000. Abundance of the Gulf of Maine/Bay of Fundy Harbor Porpoise Based on Shipboard and Aerial Surveys during 1999. Northeast Fish Sci Cent Ref Doc. 00-07; 29 p.
Information Quality Act Compliance: In accordance with section 515 of Public Law 106-554, the Northeast Fisheries Science Center completed both technical and policy reviews for this report. These predissemination reviews are on file at the NEFSC Editorial Office.
The Northeast Fisheries Science Center (NEFSC) conducted a line transect sighting survey that covered waters from Cape Cod to the Gulf of St. Lawrence during 28 July to 31 August 1999. An airplane and ship surveyed 8,212 km of track lines within a region of 225,400 km2. Over 91% of the survey time was conducted in sighting conditions less than or equal to Beaufort sea state two. In total, 12 cetacean species, 2 seal species, and 2 turtle species were detected. The abundance estimate (and CV) of harbor porpoise was 89,700 (CV=22%). This estimate is greater than previous estimates made in 1991, 1992, and 1995. The 1999 estimate is significantly different from only the smallest estimate, which was made in1991. The main difference between the 1999 and previous surveys was in 1999 an additional region of 12,500 km2 had harbor porpoise present. Within the sub-region surveyed during all years, the 1999 encounter rate was less than that from 1995 and greater than that from 1991 and 1992, the estimates of g(0) and average group size were similar for all years, and the 1999 effective strip half-width, and density estimates were slightly larger than that from previous years. The inter-annual changes in abundance could be due to experimental variability, population growth, small-scale changes in distribution of harbor porpoise and/or their prey, heterogeneities due to, for example, inter-annual differences in the observer skills or sighting conditions, or, most likely, some combination of these. Because the region where harbor porpoise were detected in 1999 was slightly larger than that from previous surveys, the time interval between surveys is fairly long (4 to 9 years), and the possibility of a positive growth rate, the best current abundance estimate for the Gulf of Maine/Bay of Fundy harbor porpoise stock is 89,700 (CV=22%), the 1999 estimate not averaged with other years. The 1999 and previous abundance estimates are minimum estimates because the shipboard surveys were not corrected for effects from responsive movement or dive time.INTRODUCTION
The 1994 Amendments to the Marine Mammal Protection Act (MMPA) mandates periodic assessments of all cetacean stocks in US waters. To fulfill this mandate for the Gulf of Maine/Bay of Fundy harbor porpoise stock, the National Marine Fisheries Service (NMFS) has conducted line transect abundance surveys during the summers of 1991, 1992, 1995, and 1999 and provided annual estimates of harbor porpoise by-catch from US sink gillnet fisheries. As well, incidental takes of by- catch in the Canadian sink gillnet and herring weir fisheries have also been documented. Abundance estimates increased from 37,000 in 1991 to 74,000 in 1995 (Table 1A; Smith et al. 1993, Palka 1995a, Palka 1996a). By-catch in the US Northeast sink gillnet fishery decreased from 2,900 animals in 1990 to 332 in 1998 (Table 1B; Bravington and Bisack 1996; Bisack 1997; Rossman and Merrick 1999). Harbor porpoise by-catch in the US mid-Atlantic coastal gillnet fisheries varied from a low of 103 in 1995 to a high of 572 in 1997 (Rossman and Merrick 1999). By-catch in the Canadian sink gillnet fishery decreased from 424 in 1993 to 10 in 1998 (Trippel et al. 1996, 1999). By-catch in the Canadian herring weir fishery decreased from 33 observed takes in 1993 to 2 in 1998 (Waring et al. 1999). Study area, field procedures and analysis methods used in the 1999 abundance survey were similar to those used during previous surveys (Smith et al. 1993, Palka 1995a, Palka 1996a). This paper presents a description of the field procedures, analysis methods and results from the 1999 survey and compares the abundance estimates from 1991 to 1999.METHODS
The study area (225,400 km2) extending from the eastern Scotian shelf to the southern Gulf of Maine (Figure 1) was surveyed by ship and airplane. A research ship, R/V Abel-J, surveyed the shallow waters (to approximately 100m) of the northern Gulf of Maine, western Scotian Shelf, and lower Bay of Fundy (30,300 km2; Figure 1). An airplane, a NOAA Twin Otter, surveyed the deeper waters of the region surveyed by the ship and the waters from the coast to the 2750 m depth contour on the eastern Scotian Shelf (195,100 km2; Figure 1).
The study area was composed of eight strata defined by harbor porpoise density, location, and survey platform (Figure 1). Strata surveyed by the airplane that had a very low expected harbor porpoise density were the Georges Bank/southern Gulf of Maine (SGOM) and eastern Scotian shelf (ENS) strata. Strata surveyed by the airplane that had an expected low density were the central Gulf of Maine (CGOM), upper Bay of Fundy (UBOF), and southern Scotian shelf (SNS) strata. Strata surveyed by the ship that had an expected intermediate density were the Maine bays (BAYS), and coastal waters of Maine and Nova Scotia (COAST). The stratum with the highest expected density, surveyed by ship, was the lower Bay of Fundy (LBOF) stratum.
The shipboard survey was conducted between 28 July and 31 August 1999 and the aerial survey was conducted between 10 and 29 August 1999. Within a stratum, track lines were approximately uniformly distributed with lines generally running perpendicular to the coastline; thus running through the expected density gradient, as recommended by Buckland et al. (1993) (Figure 1).
Field Methods - Ship
The survey was conducted while the ship traveled at 9-10 knots in Beaufort sea states of three and less. Data were collected by two “independent” teams to estimate g(0), the probability of detecting a group on the track line. Each team consisted of four people, where three were on-duty and the fourth on break. On-duty observers used naked eye to scan for marine mammals and each observer recorded their own sightings. Observers within a team rotated positions every 30 minutes and remained with that team and location for the entire survey. The “upper” team was located in a crow’s nest 14m above the sea surface at the bow of the ship; the “lower” team was in a lower crow’s nest that was 9m above the sea surface. The area in front of the ship from 90° port abeam to 90° starboard abeam was searched, where 0° was defined as straight ahead on the track line.
Sightings data were recorded by each team on a hand-held computerized data entry system, similar to that described in Garrett-Logan and Smith (1997). Sightings data included time, bearing and distance to the initial position of the group, species composition of the group, best, high and low estimate of group size, behavior, sighting cue, and swim direction of the group when initially detected. Species were identified to the lowest taxonomic level feasible. Higher taxonomic groups include unidentified large whale and unidentified porpoise/dolphin. To facilitate determining which groups of animals were detected by both teams, information on the position and swim direction were recorded multiple times for a group when possible; especially at times when the swim direction changed as the group approached the ship.
Effort and environmental data were recorded on two other computers. A computer on the bridge that was connected to a differential GPS and bridge instruments collected information on the ship’s location (position, speed and course) and on environmental conditions (wind speed and direction, depth, surface temperature, and drift set and direction). This information was collected once a minute. In addition, the Chief Scientist recorded, on another computer, effort data (observer’s position) and other environmental conditions (swell height and direction, Beaufort sea state, direction of sun, magnitude of glare, and visibility). This information was recorded when any of the factors changed.
In conjunction to the usual line transect data mentioned above, two types of ancillary data were collected that could be used to reduce bias and increase the precision of the abundance estimate. One type of ancillary data were harbor porpoise vocalizations recorded by a hydrophone trailing behind the ship. Because the hydrophone’s ability to accurately record vocalizations does not change with weather conditions to the extent that the ability of visual observers to detect harbor porpoise deteriorates with increasing Beaufort sea state, it is possible that the joint analysis of the visual and passive acoustic data could lead to a less biased abundance estimate. This study is currently underway.
The second type of ancillary data were harbor porpoise sightings detected using 25x150 power binoculars in waters ahead of the region the visual observers were surveying. It is likely that harbor porpoise detected far from the ship will not be actively avoiding the ship. It is known that if animals avoid the sighting platform before they are detected by visual observers than the estimated abundance will be negatively biased. If the binocular observer detected harbor porpoise before they reacted to the ship, then a more reliable abundance estimate could be produced by analyzing the data collected by the visual and binocular observers in combination. These data will be analyzed in the future.
Field Methods - Airplane
Surveying was conducted when Beaufort sea state conditions were less than or equal to three and visibility was greater than 3.7 km (2 nautical miles). The airplane flew 182m (600 ft) above sea surface at 200 km/hr (110 knots). The airplane stayed on the track line (i.e., was in 'passing mode') except when an unidentified group or individual was within 3.7 km of the track line. On these occasions the plane broke effort and circled the group to correctly identify the species and obtain accurate group size estimates. If another marine mammal group was detected during the time away from the track line, the new group was recorded as 'off effort' and was not used in the abundance estimate.
The observation team consisted of four on-duty people and one person at rest. The on-duty compliment consisted of one observer on each side of the airplane, each viewing through a bubble window, one observer viewing through a window in the belly of the plane, and one person recording data on a lap-top computer. The recorder was dedicated to this job for the entire survey. The remaining four scientists rotated approximately every 30 minutes between the observation windows. All observers scanned using the naked eye and used binoculars, if needed, to confirm a species identification or group size.
Data recorded for each sighting included: time to the nearest second, latitude and longitude (automatically recorded by the plane's GPS which was connected to the data recording computer), species composition, best estimate of group size, best estimate of number of calves, and angle of inclination to the animal group. The angle of inclination, measured when the group passed abeam of the plane, is defined as the angle between the line of sight to the animal group and a vertical line straight down, and measured by either an electronic protractor (inclinometer) or calibrated markings on the window which delineated angles into 10° bins. The inclinometer was always used for harbor porpoise sightings.
Data collected on effort and environmental conditions included: time (to the nearest second) of data being entered and its corresponding position, the location of each scientist, Beaufort sea state, percent of cloud cover, and for each observation position, magnitude of glare (none, slight, moderate or excessive) and overall viewing quality (excellent, good, moderate, fair or poor). As weather conditions changed, or at the beginning of each transect, environmental data were updated with the time and position of the update. Time and position information were automatically recorded every four seconds. Surface water temperature was measured using an infra-red temperature sensor mounted in the belly of the aircraft. The temperature was measured every second and a one-minute average was recording on another computer dedicated to logging this data.
To estimate the probability of detecting a harbor porpoise group on the track line, g(0), two approaches were attempted. First, the Hiby circling procedure (Hiby 1999) was followed when any harbor porpoise sighting was detected. This protocol requires that 20 seconds after a harbor porpoise group was detected the plane leaves the track line (recording the time) and circles back to a spot on the track line prior to the harbor porpoise sighting. During the circling period the observers were off- effort. When the plane returned to the track line (and the time was recorded) observers went back on-effort to re-search the same section of track line where the harbor porpoise was detected. Given the time and position of the original and any re-sightings, the Hiby algorithm determines the probability the sightings are the same group. These probabilities are then used to estimate g(0).
The second approach was similar to that conducted during the 1995 survey (Palka 1996a). That is, both the ship and airplane surveyed the same track lines on the same day (Overlap stratum in Figure 1). The estimate of g(0) from the plane is:
where the calculation for the density estimates are given in the next section.
The standard formula (Buckland et al. 1993) was used to estimate the uncorrected density, Dij, within stratum i for team j:
nij = number of groups detected in stratum i by team j, sij = expected group size in stratum i estimated by team j, ESWj = effective strip half-width for team j = 1/sighting probability density at zero perpendicular distance for team j, Li = length of transect line in stratum i. j = team: plane=single team on the plane, upper=upper team on ship, and lower=lower team on ship.
To account for group-size bias, the regression method (from Buckland et al. 1993) as implemented in the computer program DISTANCE version 2.03 (Laake et al. 1993) was used. Group-size bias results when the probability of detecting a group at a particular distance is dependent on the size of the group. For example, in the case where at far distances, the probability of detecting a large group is significantly higher than the probability of detecting a small group at the same distance, the arithmetic mean of the group size is biased towards larger groups and so the abundance estimate is biased high. In this study, both the arithmetic mean group size and group size as estimated by the regression method were computed. If the regression-corrected mean was significantly different than the arithmetic mean, the corrected mean was used as the expected group size, sij. However, if the difference between the two means was insignificant, then the arithmetic mean was used as the expected group size.
The ESW was estimated from the best fitting detection function of the perpendicular distances; that is, the model with the lowest Aikake Information Criteria (AIC). The choices of models included the uniform model with cosine adjustments, half-normal with hermite adjustments, and the hazard model with cosine adjustments. The computer program DISTANCE was used to fit these detection functions.
The probability of a shipboard team detecting a group on the track line, g(0), was estimated from the shipboard data using the modified direct duplicate (DD) method (Palka 1995a), as was done for previous abundance estimates. The DD method was programmed in Splus. The parameter g(0) for the airplane was estimated using the Hiby procedure (Hiby 1999).
The shipboard density estimate, corrected for g(0), within stratum i, Dc.i.ship, was estimated by:
Dupper = density using only the upper team’s data in Eq. 2 Dlower = density using only the lower team’s data in Eq. 2 Dduplicate = density using only first sighting of harbor porpoise groups that were seen by both the upper and lower team in Eq 2.
Duplicate sightings were determined by using the location, time and swim direction of each team’s sightings in a Visual Basic program that mapped out the position of each sighting relative to the ship at the time of each sighting. For each time of a sighting, the predicted position of previously detected groups were also plotted. The predicted position was estimated by the swim direction, time and location of previous sightings, along with the ship’s speed and estimated swim speed of the group. The swim speed could be adjusted for each sighting. To facilitate determining duplicate sightings, information on the position and swim direction were recorded multiple times for some groups, particularly for those groups where the swim direction changed as the group approached the ship. Only the initial sightings were used in the density estimates, the follow-up sightings were used only to determine duplicate sightings.
The plane density estimate, corrected for g(0), within stratum i, Dc.i.plane, was estimated by:
The total abundance of harbor porpoise in stratum i for j (the airplane or ship), Nij, was estimated as:
Nij = Dcij Ai (5)
where Ai = area of stratum i.
The total abundance from all strata was the sum of the abundance from each stratum.
The coefficient of variation (CV) of density within a stratum was estimated using bootstrap re- sampling techniques (Efron and Tibshirani 1993). The aerial estimates were obtained by using the bootstrap option in DISTANCE and the shipboard estimates were obtained by using the bootstrap function in Splus. For shipboard estimates, the re-sampling unit was a day of surveying within a stratum, with the constraint that the sum of track length within a stratum in a bootstrap replicate was approximately the same length of the tracks within the original stratum. For the plane estimate, the empirical formula for the CV of density within stratum i for team j, CV(Dij), was used where the CV(ESW) was estimated by bootstrapping the observations within a stratum:
The CV of the total abundance, CV(NT), for either platform (ship or airplane) and both platforms was calculated using:
DT = weighted total density from a platform SE(Di) = standard error of Di AT = total area of all strata surveyed by that platform m = maximum number of strata surveyed by that platform.
The plane and ship surveyed 8,212 km of track lines (Figure 1) within 225,400 km2. The R/V Abel-J surveyed 2,563 km of track lines in an area of 30,298 km2 (Table 2) and the NOAA Twin Otter airplane surveyed 5,649 km of track lines in an area of 195,103 km2.
The survey was conducted during good viewing conditions. Nearly all (91%) the track lines were surveyed in sea conditions of Beaufort 2 and less (Table 3). The airplane surveyed 58% of their track lines in Beaufort 1 and less, while the ship surveyed 67% of their track lines in Beaufort 2.
During the shipboard survey there were 10 positively identified species of cetaceans, 2 seal species and 2 turtle species (Table 4). During the aerial survey there were 8 positively identified species of cetaceans, 1 seal species, and 2 turtle species (Table 4). The upper team on the ship detected 599 harbor porpoise groups, the lower team detected 563 groups, and the aerial team detected 31 harbor porpoise groups. Harbor porpoise were detected in the strata where they were seen previously (LBOF, COAST, BAYS, CGOM). In addition, they were found in higher densities then expected in two strata outside the typical harbor porpoise habitat: the upper Bay of Fundy (UBOF) and the southern Nova Scotian shelf (SNS) (Figure 2). Only abundance estimates from harbor porpoise are presented in this document.
The ESW for shipboard harbor porpoise sightings from the upper and lower teams were 375 m (%CV=5.0) and 237 m (%CV=5.6), respectively. The ESW from duplicate sightings was 270 m (%CV=7.1). The best fitting detection function used to estimate the ESW for the upper team was the uniform model with one cosine adjustment ( P2= 2.47 p=0.78); the hazard model with one cosine adjustment best fit the lower team data ( P2= 0.82 p=0.85); and the half-normal model with no adjustments best fit the duplicate sightings data (P2=10.32 P=0.07) (Figure 3a, 3b, and 3c). The truncation perpendicular distance for the shipboard detection curves was 700m. The ESW for the aerial harbor porpoise sightings was 165 m (%CV=8.9). The uniform model with one cosine adjustment best fit the aerial data (P2=5.14 p=0.40), where the truncation perpendicular distance was 274 m, which was the farthest distance of a harbor porpoise sighting (Figure 3d).
The average group sizes, as recorded by the upper and lower teams from the ship, varied more between strata than between teams (Table 5). The average group size was highest in the Coastal stratum (3.16 and 3.18 from the upper and lower teams, respectively) and lowest inside the Bays (1.74 and 1.54 from the upper and lower teams, respectively). The average group size from the aerial survey was 2.69 (%CV=11). Because there were so few sightings within the aerial strata, it was not possible to accurately determine if there were stratum differences in the average group size of aerial sightings. Within all strata, except one, there was no indication of group-size bias in the shipboard or aerial data. Thus, the expected group size in the equation 2 was defined as the arithmetic mean group size. The group size data collected by the lower team while surveying in the lower Bay of Fundy had an indication of group-size bias, where the uncorrected group size was 3.15 (%CV=5.6) and the bias-corrected average group size was 2.73 (%CV=2.5). The bias-corrected average was used in the abundance estimate in this case.
The estimates of g(0) for the upper team on the ship varied from 0.248 (%CV=17) in the Bays stratum to 0.387 (%CV=16) in the Coastal stratum. For the lower team, the estimate of g(0) varied from 0.493 (%CV=28) in the Bays stratum to 0.569 (%CV=13) in the Coastal stratum (Table 5). When both teams were surveying together, it was estimated they missed from 26% (1-0.736) to 38% (1-0.619) of the harbor porpoise groups on the track line, depending on the stratum (Table 5)
The estimate of g(0) for the aerial team using the Hiby circling methodology was not stable because there was an insufficient number of re-sightings. There were 27 harbor porpoise sightings that triggered the circling procedure and 5 groups of harbor porpoise were detected on the second time the track line was searched. Of the five possible re-sightings, two had a high probability of being a re-sighting of the same group seen initially. More surveys using this methodology in the same airplane are needed to accurately estimate g(0).
The other approach to estimate g(0) for the airplane was to compare the g(0)-uncorrected estimated density from the airplane to the g(0)-corrected estimated density from the ship in a region where both platforms surveyed the same track lines on the same day. Only three harbor porpoise groups were seen by the ship’s teams during the day surveying the Overlap stratum. Thus, there were insufficient data to calculate g(0) for the aerial team using this approach. Because both approaches attempted during 1999 to estimate g(0) were unsuccessful, the value of g(0) for the aerial team that was estimated during 1995 was used. It is assumed this value is still valid because it was estimated using the same airplane, some of the same observers, was in the same region and time of year, and for the same target species, harbor porpoise. In conclusion, the estimate of g(0) for aerial harbor porpoise sightings was assumed to be 0.24 (%CV=86), the value estimated from the 1995 survey (Palka 1995a).
The lower Bay of Fundy (LBOF) stratum had the highest estimated density, 4.18 harbor porpoise/km2 (Table 6). The upper Bay of Fundy (UBOF) stratum had the lowest positive density, 0.25 porpoise/km2; this was the first time the UBOF stratum was surveyed. In total, the abundance estimate was 89,739 (%CV=22) harbor porpoise (Table 6).
Comparison between 1999 and previous estimates
The 1999 abundance estimate is higher than previous estimates (Table 1), however it is significantly different from only the lowest abundance estimate (z=2.32 p=0.0102), that estimated in 1991. There is an increasing trend in the point estimates over the years (Figure 4); thus warranting a more detailed investigation to determine possible reasons for the inter-annual differences.
The Coastal, Bays, Central Gulf of Maine, and Lower Bay of Fundy strata constitute the region where it was expected all, or nearly all, of the Gulf of Maine/Bay of Fundy harbor porpoise stock would reside during the survey time period. This “main” region was surveyed in all years: 1991, 1992, 1995 and 1999. One possible reason the1992 point estimate was nearly twice the 1991 point estimate, was the harbor porpoise habitat was actually larger than the “main” region. To address this in 1995 and 1999, aerial surveys were conducted in waters surrounding the “main” region (Figures 2 and 5). During 1995, two harbor porpoise groups were detected just outside the “main”region on Browns Bank (Figure 5) and during 1999, eleven harbor porpoise groups were seen outside the “main” region (Figure 2). Most of the 1999 sightings were in habitats not previously surveyed: the Northern Bay of Fundy and Southern Nova Scotia strata. In 1999, 14% of the estimated total abundance was in these previously un-surveyed strata. If animals always existed in these previously un-surveyed strata, then abundance estimates from the 1991 to 1995 surveys may have missed a portion of the stock; consequently, it would not be possible to determine trends by directly comparing the actual abundance estimates. However, if the “outside” regions are inhabited only periodically, for example, because of changing environmental factors, or just recently, for example, because of an increasing population, then it would be possible to directly compare the actual abundance estimates. To address both of these possibilities, two approaches were explored: (1) only the “main” region surveyed during all years were compared, and (2) trends of estimated abundances were examined.
Components of the abundance estimate from the “main” region were examined to identify patterns (Table 7). The average expected group size and g(0) varied little from year to year. The total area of the region defined as the “main” region varied by less than 6% between years. The areal difference was due to several reasons. First, methods of estimating area have improved over the years as mapping computer programs have become available. Second, due to weather and logistical reasons, regions could not always be surveyed in their entirety every year. Lastly, small-scale harbor porpoise distribution changes between years required changing the geographic area within the high, intermediate, and low density strata. In particular, the density of harbor porpoise in the region south of Grand Manan and east of Maine (Overlap stratum in Figure 1) was assigned to the CGOM stratum (low density stratum) in some years (1991 and 1999) and to the Coastal stratum (intermediate density stratum) in other years (1992 and 1995). Thus, the sum of the Coastal and CGOM areas for the different years are more similar than the areas of each stratum separately.
The difference between the 1995 and 1999 estimated ESW for the airplane team was not statistically different. ESW estimates for a shipboard team varied between years and from the other team on the ship. Differences between teams were expected because teams are at different heights above the water and so sightability also differ. However, within a team between years, the difference between the largest ESW and the smallest ESW for that same team were statistically different. These differences could be due to model mis-specification, observer skill heterogeneities, or sighting condition heterogeneities. The data were tested for model mis-specification, so this is unlikely to be a major cause for the differences. The teams were on the same ship and on the same platforms, so these potentially influential factors have not changed over the years. However, the observers were not the same every year and sighting conditions also varied from year to year (Table 8). Future work should incorporate co-variates into the ESW estimation to reduce potential biases and thus, possibly reduce inter-annual variability.
The component with the largest inter-annual variability was the encounter rate (Table 7). In all the years, the overall large-scale pattern was the same. That is, the encounter rate and corrected density was the highest in the LBOF stratum and the lowest in the CGOM stratum. However, the magnitude of the changes differed between years. The encounter rate of groups in the Bays stratum had the largest variability, from 0.009 to 0.062 groups/km2. This stratum is small (approximately 5% of the main stock region), so it can not contribute a large amount to the inter-annual difference in the total abundance estimate. Palka (1995b) demonstrated that small-scale harbor porpoise distribution and density differences between 1991 and 1992 were correlated with small-scale changes in the surface water temperature and an index of density of herring and silver hake (common harbor porpoise prey). Thus, the inter-annual variability within a stratum could be caused by small-scale inter-annual spatial re-distributions. In the future, water temperature and other environmental factors will be investigated to determine if environmental variation can explain re-distribution and can be used to improve the abundance estimates.
Another possible reason the density estimates increased between surveys is a net population growth. Theoretical potential growth rates for this stock have been estimated at 4% (Woodley and Read 1991), 9.4% (Barlow and Boveng 1991), and 10% (Caswell et al. 1998). Using the four abundance estimates as reported in Table 1 and assuming a constant exponential growth rate for each year and abundance estimates with no error, the average net annual growth rate between 1991 and 1999 was 8.6% (CV=49%; Multiple R2 of regression=0.68, p-value of H0:rate=0 was 0.18) and 4.1% between 1992 and 1999 (CV=12%; Multiple R2 of regression=0.99, p-value of H0:rate=0 was 0.08). In both time periods, the estimated net growth rate (slope of the curve) was not statistically different from zero. These cases, which assume no error in the abundance estimate, are not realistic. Error in the abundance estimates can be incorporated in several ways. One approach is by weighted regression, where each abundance estimate is weighted by its inverse CV2. By doing so, the net growth rate is 7.6% between 1991 to 1999 (CV=51%; Multiple R2 of regression=0.66, p-value of H0:rate=0 was 0.19) and 4.1% between 1992 to1999 (CV=13%; Multiple R2 of regression=0.98, p-value of H0:rate=0 was 0.08). Another approach is to use the 1000 bootstrap estimates from each year to estimate 1000 net growth rates. Using this approach, the annual net growth rate is estimated to be 3.8% between 1991 to 1999 (CV=67%, H0:rate=0 vs HA:rate>0 p=0.16) and 4.7% between 1992 to 1999 (CV=78%, H0:rate=0 vs HA:rate>0 p=0.29). Incorporating error about the abundance estimates increases the CV of the growth rate and down weights the low 1991 abundance estimate that has the largest CV. The net effect of accounting for measurement error is that it is even less likely that the stock’s net growth rate is different than zero.
The above estimated net growth rates include natural and human-induced mortalities. To estimate natural growth rates, the human-induced mortalities must be added back into the above net growth rates. The annual percent of the stock removed due to human interactions is the ratio of by-catch to abundance: 0.053, 0.018, 0.022, and 0.0091 for 1991, 1992, 1995 and 1999, respectively. The average percent removed due to human interactions was 2.5% (CV=77%) during 1991 to 1999 and 1.6% (CV=41%) during 1992 to 1999. Natural growth rates can then be estimated by adding the average percent removed due to human interactions to the net natural and human-induced growth rates. By doing this, the estimated natural growth rate was 6.3% (=3.8+2.5) (CV=51%) between 1991 to 1999 and 6.3% (=4.7+1.6) (CV=59%) between 1992 to 1999. However, due to the high CV’s, the estimated natural growth rates do not differ significantly from zero (for two-sided z-test p=0.05 and p=0.09 for 1991-1999 and 1992-1999, respectively).
With four surveys conducted within nine years, it is difficult to statistically detect a small trend. That is, assuming exponential growth, a one-tailed test for positive growth, CV= 0.20, and "=0.2, the power (1-$) of detecting a 4% growth rate is 0.51. In other words, under these conditions, the minimum rate of change that is detectable with 90% power is a 9.6% growth rate. Thus, to detect a population trend with statistical confidence, future work could include reducing the CV’s of the abundance and by-catch estimates, investigating if the 1991 abundance estimate was more negatively biased than the recent years, conduct more surveys in the future, or incorporate the by-catch estimates and their CV’s into a more detailed population model.
Previous best abundance estimates for this stock were averaged over several years. Because the 1999 survey region covered more harbor porpoise habitat, the time interval between surveys is long (4 to 9 years), and the possibility of a positive growth rate, the best current abundance estimate for the Gulf of Maine/Bay of Fundy harbor porpoise stock is 89,700 (CV=22%), the 1999 estimate, not averaged with other years.
Potential biases in the abundance estimates
The abundance estimates from 1999 and previous years have moderate levels of uncertainty associated with them, as reflected in CVs of 20-29% (Table 1). The largest component of this variability is from the encounter rate (n/L) (Table 9; Palka 1995a). By definition, the CV(n/L) should only include sampling variation. However, practically, the CV(n/L) includes both sampling variation and variation in the spatial distribution of the animals. The encounter rate does have spatial structure; i.e., there is evidence of a density gradient related to depth (Figure 2). Other analytical methods are needed to account for this spatial variability (i.e., the methods developed to estimate the abundance of Norwegian minke whales by Schweder et al. (1999) and Cooke and Leaper (1998)).
Several other possible sources of uncertainty are unaccounted for. These include porpoise avoidance of the ship, observer and/or platform heterogeneities, and effects of environmental conditions on sighting rates and g(0). It has been suggested that harbor porpoise avoid ships (Polacheck and Thorpe 1990). If harbor porpoise avoid the ship before they are detected by the observers on the ship, the abundance estimates will be negatively biased (Buckland et al. 1993). The extent of this bias depends on how many harbor porpoise groups react before being detected. To investigate this, during 1999 harbor porpoise far from the ship were detected by another team of observers who surveyed using 25x150 power binoculars. These data will be used to estimate abundance using the Buckland-Turnock method (Buckland et al. 1993) and the modified Buckland-Turnock method (Palka and Hammond, in review).
Other potential sources of bias are heterogeneities due to differences between observers, platforms and weather conditions. These types of heterogeneities can cause negative or positive biases, depending on the type of heterogeneity. The extent of bias depends on the extent of the differences. Palka (1996b) reported that estimates of g(0), encounter rate and density were influenced by sighting conditions as defined by Beaufort sea state. As Beaufort sea state increased (weather worsened), estimated density decreased. To account for heterogeneities, these factors need to be explicitly modeled using methods similar to Cooke and Leaper (1998) or Hammond et al. (1995).
I am grateful for the hard work and dedication from the observers on both platforms. Observers on the R/V Abel-J were Carol Carson, Virginie Chadenet, Peter Duley, Amy Lamb, Dr. Tim Lewis, Dr. Gordon Waring, Fredrick Wenzel, and Amy Williams. Observers on the plane were Robert DiGiovanni, Kimberly Marks, Cheryl Ryder, David Potter, and Janeen Quintal. I would like to thank the International Friends for Animal Walfare (IFAW), Dr. Jonathon Gordon, Dr. Douglas Gillespie, and Dr. Tim Lewis for providing and running the passive acoustic equipment. I would also like to thank the crew of the NOAA Twin Otter, Lt. Jeff Hagan (Aircraft Commander) and Lt. Mark Moran, and the crew of the R/V Abel-J, in particular Captain Robert Wallace.
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1 Because 1999 by-catch estimates are presently not available, this ratio is the 1998 by- catch estimate over the 1999 abundance estimate.