Estimating Hawaiian monk seal range-wide abundance and associated uncertainty

The type and quantity of survey data, and consequently, applicable methods for estimating abundance, vary throughout the range of the Endangered Hawaiian monk seal Neo mon achus schauinslandi. Here we present a new approach to combine disparate data and methods to estimate the range-wide abundance of this species, along with associated uncertainty. We quantified subpopulation abundance using total enumeration, closed population capture-recapture methods, empirically derived relationships between survey effort and proportion of the population detected, minimum tallies, or standardized land surveys corrected to account for seals in the water. We used a Monte Carlo approximation to generate a distribution of range-wide abundance, by summing randomly drawn values from distributions of site-specific abundance. Data to estimate range-wide abundance were available for 2013, 2014, and 2015; our estimates were 1291, 1309, and 1324 individuals, respectively. Although the point estimates increased over 2 yr, the confidence intervals for all estimates overlapped. We recognize that these estimates are subject to some varying degree of negative bias, which precludes drawing unequivocal conclusions regarding current population trends. However, after a prolonged history of population decline in this species, the lack of evidence for further decline during 2013 to 2015 is encouraging. Additional years of consistent monitoring will enable reliable assessment of the trend in total Hawaiian monk seal abundance.


INTRODUCTION
The Endangered Hawaiian monk seal Neomonachus schauinslandi metapopulation (Littnan et al. 2015) comprises multiple subpopulations distributed throughout the 2600 km wide Hawaiian Archipelago (Fig. 1).Total abundance and trends are important metrics for conservation, but estimating these parameters for the monk seal has been hampered by the logistical, analytical, and funding constraints associated with surveying a sparsely distributed species over such a vast range.From the mid-to late 20th century, standardized counts at the subpopulations from Kure Atoll to French Frigate Shoals (Fig. 1) provided an adequate index of overall trends in abundance (although not actual abundance), because the preponderance of seals resided within that portion of the species' range (Ragen & Lavigne 1999).
Over the past 3 decades, the number of monk seals (as indicated by mean standardized counts) from Kure Atoll to French Frigate Shoals has declined by approximately 50% (Johanos 2015a).During the same period and probably beginning previously, monk seals have been re-colonizing the main Hawaiian Islands (Ni'ihau to Hawaii Island), from which they had likely been extirpated following the arrival Outside the USA © the US Government 2016.Open Access under Creative Commons by Attribution Licence.Use, distribution and reproduction are un restricted.Authors and original publication must be credited.
ABSTRACT: The type and quantity of survey data, and consequently, applicable methods for estimating abundance, vary throughout the range of the Endangered Hawaiian monk seal Neo monachus schauinslandi.Here we present a new approach to combine disparate data and methods to estimate the range-wide abundance of this species, along with associated uncertainty.We quantified subpopulation abundance using total enumeration, closed population capture-recapture methods, empirically derived relationships between survey effort and proportion of the population detected, minimum tallies, or standardized land surveys corrected to account for seals in the water.We used a Monte Carlo approximation to generate a distribution of range-wide abundance, by summing randomly drawn values from distributions of site-specific abundance.Data to estimate range-wide abundance were available for 2013, 2014, and 2015; our estimates were 1291, 1309, and 1324 individuals, respectively.Although the point estimates increased over 2 yr, the confidence intervals for all estimates overlapped.We recognize that these estimates are subject to some varying degree of negative bias, which precludes drawing unequivocal conclusions regarding current population trends.However, after a prolonged history of population decline in this species, the lack of evidence for further decline during 2013 to 2015 is encouraging.Additional years of consistent monitoring will enable reliable assessment of the trend in total Hawaiian monk seal abundance.

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of Polynesians some 800 yr ago (Baker & Johanos 2004, Baker et al. 2011, Wilmshurst et al. 2011).Additionally, monk seals reside on 2 relatively inaccessible islands, Necker and Nihoa (Fig. 1), where standardized counts suggest that abundance has recently been relatively stable and apparently increasing, respectively (Johanos 2015a, A. L. Harting et al. unpubl.).These significant changes in both abundance and distribution of Hawaiian monk seals have rendered the traditional method of characterizing abundance based on only a portion of the range unreliable.Furthermore, the type and quantity of survey data, and consequently, applicable methods for estimating abundance, vary throughout the monk seal's range.Here, we present a new approach to combine disparate data and methods to estimate the range-wide abundance of this species, along with associated uncertainty.

Estimating subpopulation abundance
Abundance of monk seals at individual subpopulations is variously estimated based on the type, quantity, and quality of available data.In general, pups are the most tractable age class to survey.Unlike in many pinnipeds, parturition in Hawaiian monk seals is asynchronous, with a broad peak from March to August (Johanos et al. 1994).However, survival to weaning is typically over 90%, and weaned pups tend to spend most of their time on shore for approximately 2 mo post-weaning (Gilmartin et al. 1993, Hiruki et al. 1993).Thus, a fairly complete count of annual pup production can be obtained from a few well-timed ground surveys, particularly if they are conducted in late summer, when most pups have been born but have not yet begun spending much time at sea (Henderson & Johanos 1988).The exception is that Galapagos shark predation at French Frigate Shoals has reduced survival to weaning to less than 75% in some years (Gobush & Farry 2012).However, duration of field seasons at this site has been consistently sufficient to document the total pups born, including subsequent mortalities.In contrast to tallying pup production, estimating the number of seals older than pups (hereafter referred to as non-pups) is more challenging.Non-pups alternate between foraging at sea and spending time on shore to rest, molt, and, for adult females, to give birth and nurse their young.
Annual field camps are established during late spring to late summer at the 6 subpopulations from Kure Atoll to French Frigate Shoals.Field camp timing varies, but largely overlaps among sites.Camps range from a few weeks to many months in duration, during which staff conduct population research and monitoring, and also undertake numerous conservation actions that yield population benefits (Harting et al. 2014).Historically, each subpopulation has hosted from <100 up to a few hundred seals.Field re searchers conduct regular surveys of island and atoll shorelines where they identify individual seals using plastic flipper tags, applied pelage bleach marks, natural scars, and other marks (Harting et al. 2004).At these sites, pup production is assessed by individually identifying all pups present during the field season.Baker et al. (2006) analyzed discovery curves (accumulation of sightings of new individuals over time during a field season), and determined that all nonpups in a subpopulation could be considered identified if 100 h of survey effort were expended without finding a new individual.Where such total enumeration is not achieved, closed capture-recapture estimates generated with Program CAPTURE are used (Otis et al. 1978, White et al. 1982, Rexstad & Burnham 1991, Baker 2004).However, sometimes no appropriate estimator is obtainable using Program CAPTURE (i.e. the model selection criterion is < 0.75, following Otis et al. 1978) or the estimates are less than the known minimum abundance as described by Baker (2004).For such cases, we developed a new estimation method that uses site-specific empirical relationships between survey effort and the proportion of the population identified to adjust minimum counts.Using discovery curves constructed as described by Baker et al. (2006), we calculated the proportions of the non-pup population identified versus the number of survey effort hours expended for a set of reference years when total enumeration was achieved at a given site (Fig. 2).These observations are the basis for estimating the likely proportion of seals that had been identified in years when field seasons ended before all were detected.For example, a total of 99, 206, and 324 survey effort hours were expended searching for seals at Lisianski Island in 2013 to 2015, respectively, and the criterion for achieving total enumeration was not met in any of those years.Density histograms of the proportion of the population identified in reference years at these same time points can be extracted (inset graphs, Fig. 2).Probability distributions fitted to these histograms (solid curves in Fig. 2) were sampled to pro-vide corrections to minimum counts (details in subsequent section).We fitted beta distributions because the beta function is highly flexible and bounded by 0 and 1.We used the package fitdistrplus in R to fit the beta distributions (Delignette-Muller & Dutang 2015).We prefer capture-recapture estimates derived from Program CAPTURE over estimating the proportion identified using discovery curves because the former is a well-established analytical method, whereas the latter is an empirical approach that necessarily relies on sparse reference data at some subpopulations.However, when a capture-recapture estimate is not obtainable, discovery curve analysis is an acceptable alternative.
Necker and Nihoa Islands are small (<1 km 2 ), isolated, steep-sided basalt volcanic remnants (Evenhuis & Eldredge 2004).They are ecologically and culturally sensitive, and difficult to safely land on with small boats.Consequently, systematic monk seal surveys typically only occur from 0 to 2 times per year at these sites.This level of effort is insufficient for total population enumeration, capture-re capture abundance estimation, or discovery curve analysis.Here we estimated non-pup abundance using the empirical distribution of the ratio of beach counts to total population size at other Northwestern Hawaiian Islands subpopulations to correct standardized counts at Necker and Nihoa Islands for the proportion of seals at sea (A.L.Harting et al. unpubl.).Standardized counts consist of re searchers systematically counting all seals on all shorelines of an island within a several-hour period.Pup production at Necker and Nihoa Islands was estimated as the mean of the annual total pups ob served during the past 5 yr, excluding counts occurring early in the pupping season when most have yet to be born.It is unlikely that all the pups born are detected during 1 or 2 d of survey effort, and the proportion counted varies year to year.The 5 yr mean was used simply to reduce the sensitivity of a single year's count to bias.In years when sufficient effort was expended to give confidence that the pup count is relatively reliable, that single year count would be used instead of the 5 yr mean.
The monk seal subpopulations described thus far are all associated with   et al. 2011).This system tends to effectively identify (again, using tags and natural and applied pelage marks) most of the seals using Kauai, Oahu, Molokai, Maui, and Hawaii Island.Seals at Lanai and Kahoolawe are likely undercounted, although it is believed that these sites host a relatively small portion of the total main Hawaiian Islands population.Thus, from Kauai to Hawaii Island, the total number of individual seals identified in a calendar year is considered the best available estimate of abundance for this region.
In contrast, relatively large numbers of monk seals occur on the islands of Ni'ihau, Lehua, and Ka'ula Rock, which are relatively inaccessible and historically have been rarely surveyed.Since 2013, a small number of surveys of privately owned Ni'ihau Island and nearby Lehua Island have been conducted collaboratively between NMFS, Ni'ihau residents, and the US Navy.These surveys constitute standardized counts analogous to those conducted on Necker and Nihoa Islands, which are corrected for the proportion at sea (A.L. Harting et al. unpubl.).However, Ni'ihau is a much larger island, so that counts are conducted by multiple teams on foot, horseback, in small boats, and using a helicopter to survey all shorelines within a day.There are well-documented differences in terrestrial and marine habitats, piscivorous fish populations, and monk seal foraging behavior between the Northwestern and main Hawaiian Islands (Parrish et al. 2008, Baker et al. 2011, Cahoon 2011, Cahoon et al. 2013).Because these differences could influence the proportion of time seals spend at sea, we chose not to use correction factors derived using Northwestern Hawaiians Islands data (A.L. Harting et al. unpubl.) to correct standardized counts in the main Hawaiian Islands.Consistent with this, a recent telemetry study (Wilson et al. in press) found that main Hawaiian Islands monk seals (N = 23) spent a greater proportion of time ashore (mean = 0.37) than A. L. Harting et al. (unpubl.)estimated for Northwestern Hawaiian Islands seals (mean = 0.29).Therefore, we calculated the total non-pup estimate for Ni'ihau and Lehua Islands as the mean total count at those sites divided by the mean proportion of time on shore in the main Hawaiian Islands (Wilson et al. in press).The total pups observed at Ni'ihau and Lehua Islands during surveys conducted sufficiently late in the year to encompass the majority of the pupping season were added to obtain total estimated abundance for these sites.

Estimating range-wide abundance
We derived total abundance of Hawaiian monk seals from the site-specific estimates obtained using the various methods described above applied to Hawaiian monk seal population data (Johanos et al. 2015a,b).Monk seals move among islands throughout their range, and the likelihood of movement is inversely related to the distance between islands (Johanos et al. 2014).Some seals are seen in more than 1 subpopulation within a single year.To avoid double-counting such individuals, we assigned each seal to a single subpopulation.In this way, discrete subpopulation abundance estimates (regardless of the method by which they were generated) are based only on the individual seals that are assigned to the various sites.
By convention, the main Hawaiian Islands are treated as a single subpopulation because the islands are relatively close to one another and seals readily move among them (Johanos et al. 2014, Lopez et al. 2014).To avoid double-counting and over-amplifying the estimated number of non-pups, we based the calculation of abundance for Ni'ihau and Lehua Islands on the total count of non-pups at those sites less any identified individuals who were seen (and already counted) elsewhere during the same calendar year.

Estimating the distribution and confidence limits of total abundance
To evaluate uncertainty in total range-wide monk seal abundance, we used estimates of error associated with site-specific abundance estimates.Some of those estimates were necessarily treated as invariant, including sites where total enumeration was achieved, the minimum tally for the main Hawaiian Islands other than Ni'ihau and Lehua, and pup counts at all locations.CAPTURE estimates have associated standard deviations and assumed normal error distributions (Otis et al. 1978).For sites where the minimum count was adjusted based on discovery curves, we characterized uncertainty in the unidentified proportion of the population using the fitted beta distributions described above.The estimates for Necker and Nihoa have an empirical distribution reflecting the observed relationship between standardized counts and the total population size (A.L. Harting et al. unpubl.).For Ni'ihau and Lehua, we used the mean correction factor (proportion of time spent on land) and estimated variance from 23 telemetry deployments on seals (Wilson et al. in press).Examination of a quantile-quantile plot of these observations confirmed that their distribution is approximately normal.
We used a Monte Carlo approximation to generate a distribution of range-wide abundance.We experimented with increasing numbers of random trials and determined that the resulting distributions (mean, median, and quantiles) stabilized with 30 000 trials.Thus, 30 000 random draws with replacement from each of the variable site-specific abundance distributions were summed, added to the fixed tally from the sites with invariant estimates (including pups), and stored to obtain a distribution of rangewide abundance.
For CAPTURE estimates, we drew random normal values from the distributions with means and standard deviations equal to those estimated.However, the symmetrical normal distributions often include values that fall below known minimum abundance (Baker 2004).Therefore, when a random draw was lower than the known minimum, that sample was discarded and replaced until 30 000 values greater than or equal to the known minimum were sampled.For the remaining Northwestern Hawaiian Islands sites with discovery curve information, random values were drawn from the fitted beta distributions representing the proportion of non-pups identified at the end of the field season (Fig. 2, and see Fig. S1 in the Supplement at www. int-res.com/ articles/ suppl/ n031 p317 _ supp.pdf).The minimum tally for the site in question was then divided by each of these random proportions to obtain 30 000 estimates of nonpup abundance.For Necker and Nihoa, we simply randomly drew from the distributions of non-pup abundance (A.L. Harting et al. unpubl.).For Ni'ihau and Lehua Islands, we drew random normal values from a distribution with the mean equal to the mean beach count divided by the mean proportion of time ashore.Because the estimate was generated by dividing the mean count by a random variable (proportion of time spent on shore), we used the delta method to estimate the variance of the inverse of the proportion on shore (Seber 1982).Thus, let N ˆ= estimate of non-pup abundance; h _ = mean proportion of time (h) seals spend on land; C = mean non-pup count; var (h) = variance of h

RESULTS AND DISCUSSION
Sufficient data were available to generate rangewide abundance estimates for the Hawaiian monk seal in 2013 to 2015.Due to logistical constraints, counts were conducted on Necker Island only in 2013.Because this island represents only a small fraction of the total, and counts at Necker Island have been relatively stable (Table 1,  At 4 subpopulations (Laysan and Lisianski Islands, Midway and Kure Atolls), there were from 6 to 18 reference years in which total enumeration was achieved, providing a basis for adjusting minimum counts in other years.However, there was only 1 year with total enumeration at Pearl and Hermes Reef, and this was never achieved at French Frigate Shoals.For the former site, we included 4 additional reference years when the total enumeration criterion was nearly, but not quite, achieved.In 3 of these years, only 1 new seal was identified in the final 98 to 108 h of field effort, and in 1 year, no new seals were detected in the final 73 h.At French Frigate Shoals, there were only 2 such years with near total enumeration.Thus, for this site, we used those 2 years combined with the 5 Pearl and Hermes Reef reference years, reasoning that these are both similarly-sized large atolls so that discovery curve patterns would be comparable.Range-wide abundance estimates (median of distributions) and 95% confidence intervals are presented in Fig. 3. Site-specific abundance distributions (Table 1, Figs.S2−S4 in the Supplement) generated using the Monte Carlo approximation process demonstrate the relative size of the various portions of the total population in 2013 to 2015.The minimum tally of non-pups in the main Hawaiian Islands excluding Ni'ihau and Lehua Islands varied little: 123 in 2013, 132 in 2014, and 130 in 2015.The total number of pups counted range-wide was 158, 170, and 198 in 2013, 2014, and 2015, respectively.This new abundance estimation method is a great improvement over the status quo, which characterized abundance trends based only on a portion of the species' range.It also incorporates new information for adjusting counts at Necker, Nihoa, Ni'ihau, and Lehua Islands based on region-specific observations of the proportion of time seals spend on shore.Estimated uncertainty of the 2013 to 2015 estimates is relatively small, with coefficients of variation ranging from 0.033 to 0.040.Still, we acknowledge that these range-wide abundance estimates are somewhat negatively biased, primarily due to incomplete identification of seals in the main Hawaiian Islands.Sightings information about monk seals using Lanai and Kahoolawe Islands is sporadically reported.Counts of seals at remote Ka'ula Rock are rarely obtained.Fortunately, these sites appear to host relatively few seals compared to the remaining, much more thoroughly surveyed, main Hawaiian Islands.In the Northwestern Hawaiian Islands, when field camps are of insufficient duration to achieve total enumeration, closed capture-recapture estimates are used when available, and Baker (2004) showed that these tend to be slightly negatively biased.Estimates based on adjusted minimum counts at Pearl and Hermes Reef and French Frigate Shoals are likely somewhat negatively biased because most of the discovery curve reference data for those sites were from years when the total enumeration criterion was not quite met.Finally, the proportion of the true pup production detected is subject to negative bias depending upon  the duration and timing of field effort, which vary without a consistent temporal trend.A prolonged decline in abundance of Hawaiian monk seals in the Northwestern Hawaiian Islands has been well documented since systematic studies of the species commenced in the late 1950s (Kenyon & Rice 1959).While the individual subpopulations from Kure Atoll to French Frigate Shoals have exhibited asynchronous dynamics at times (some declining, others stable or increasing), their total abundance has dwindled for several decades (Ragen & Lavigne 1999, Carretta et al. 2015).However, the more recent expansion of the seal population in the main Hawaiian Islands and population growth and stability at Nihoa and Necker Islands, respectively, suggest that the trend for the whole species is less bleak (Baker et al. 2011, A. L. Harting et al. unpubl.).The 3 range-wide abundance estimates presented here (Fig. 3) are encouraging -the point estimate for 2014 is higher than for 2013, and 2015 is even higher.These estimates are subject to uncertainty and negative bias as discussed above, and the confidence intervals for all years largely overlap one another.Thus, it is not currently possible to unequivocally conclude whether the current trend is declining, stable, or increasing, but even the lack of evidence for continued decline is a welcome change for this endangered species.Also encouraging is that the estimates for individual sites, even those subpopulations that had been declining over the long term, appear relatively stable if not increasing over the past 3 yr (Fig. S5 in the Supplement).The point estimates for Ni'ihau and Lehua Islands decreased from 2013 to 2015, but these estimates are based on the expansion of just 1 or 2 counts per year and exhibit the greatest relative uncertainty (Figs.S2−S4 in the Supplement).Ideally, continued commitment to conducting surveys that inform these estimates will allow for more conclusive interpretation of both sitespecific and range-wide abundance trends for this species.
A. L. Harting et al. unpubl.),we used the 2013 Necker Island estimate for 2014 and 2015.

Table 1 .
Site-specific and range-wide estimates of Hawaiian monk seal Neomonachus schauinslandi abundance in 2013 to 2015.Methods used to generate abundance estimates are DC: discovery curve analysis, Enum: total enumeration; CR: capture-recapture; CC: counts corrected for the proportion of seals at sea; Min: minimum tally.Median values are presented with (in parentheses) 95% confidence intervals of 30 000 random draws from abundance distributions where estimates of error are available.Note that the median range-wide abundance is not equal to the total of the individual sites' medians, because the median of sums may differ from the sum of medians for non-symmetrical distributions