Estimating population size when individuals are asynchronous: A model illustrated with northern elephant seal breeding colonies

Abstract

Our aim was to develop a method for estimating the number of animals using a single site in an asynchronous species, meaning that not all animals are present at once so that no one count captures the entire population. This is a common problem in seasonal breeders, and in northern elephant seals, we have a model for quantifying asynchrony at the Año Nuevo colony. Here we test the model at several additional colonies having many years of observations and demonstrate how it can account for animals not present on any one day. This leads to correction factors that yield total population from any single count throughout a season. At seven colonies in California for which we had many years of counts of northern elephant seals, we found that female arrival date varied < 2 days between years within sites and by < 5 days between sites. As a result, the correction factor for any one day was consistent, and at each colony, multiplying a female count between 26 and 30 Jan by 1.15 yielded an estimate of total population size that minimized error. This provides a method for estimating the female population size at colonies not yet studied. Our method can produce population estimates with minimal expenditure of time and resources and will be applicable to many seasonal species with asynchronous breeding phenology, particularly colonial birds and other pinnipeds. In elephant seals, it will facilitate monitoring the population over its entire range.

Fig 1. Northern elephant seal breeding colonies.

Locations of the seven colonies analyzed, indicated by red arrows: San Nicolas Island (SNI), Santa Rosa Island (SRI), San Miguel Island (SMI), Año Nuevo island and mainland (ANI & ML), Point Reyes (PR), King Range (KR).

Fig 2. Daily female counts and fitted census curves in sample years.

Black points are observed counts on single days. The black, bell-shaped curve is the fitted census curve, C(t); the blue dotted curve is the estimated cumulative arrival curve, A(t); and the dotted red curve the cumulative departure curve, D(t). A(t) and D(t) reach an asymptote at the total population of females, N_i, using the colony in year i. The examples include years with few counts, demonstrating that the model works well with smaller samples, plus sample years from Point Reyes, King Range, and the Channel Islands; these complement our earlier presentation of the model [4] in which we included similar figures for 18 years at Año Nuevo Mainland, 1978–2006. Abbreviations: ANI, Año Nuevo Island; ANML, Año Nuevo Mainland; PR, Point Reyes; SNI, San Nicolas Island; KR, King Range. Range of the vertical axis varies greatly, but the dates on the horizontal axis are identical, with vertical lines at 1 Jan, 1 Feb, 1 Mar.

Fig 3. Variation in census timing.

A) Mean annual arrival date, ${\widehat{a}}_i$, and B) date of peak female census, both estimated from the census model. Three curves are from colonies with long time series (ANI: Año Nuevo Island; ANML: Año Nuevo Mainland; PR: Point Reyes); the four green points are individual years from the Channel Islands (CI), and the three gray points from King Range (KR). Dashed vertical lines show 95% credible intervals in each year. At the far right, open circles and solid lines show the hyper-means (long-term means) and credible intervals for each site.

Fig 4. Correction factors.

The model’s estimated multiplier for converting any daily count into a total female population, as a function of date (ANI = Año Nuevo Island, ANML = Año Nuevo Mainland, PR = Point Reyes, CI = Channel Islands, KR = King Range). Each panel shows the curve for one of those four sites highlighted in blue, including credible intervals; the red lines are the remaining sites, with King Range added in green in all panels. Dotted horizontal guide lines are at 1.1 and 1.2. The census and hence the correction curve was earlier at Año Nuevo Island and the Channel Islands, later at the other three sites.