Right whale availability in Cape Cod Bay, by month

Table S1 of Ganley et al. (2019): mean dive and surface intervals, percent surface time, and median availability, from 86 focal follows of North Atlantic right whales in Cape Cod Bay during 2016 and 2017. Unlike example_dive_intervals, these are real measurements.

Usage

ganley_availability

Format

A tibble with 4 rows and 8 columns:

month: Month, as an ordered factor from January to April.
percent_surface_time: Percent of time at the surface. See above for why this is not the ratio of the two interval columns.
mean_dive: Mean diving interval, seconds.
mean_surface: Mean surfacing interval, seconds.
availability: Median availability, \(a(x)\).
availability_variance: As labelled in the source; see above.
n_follows: Focal follows behind each row. January's 7 against April's 48 is worth noticing — the month with the lowest availability is also the one measured least well, because the weather that keeps the food deep also keeps observers on the ground.
hours_followed: Total follow time, hours.

The pooled "All sightings" row of Table S1 is kept as the all_sightings attribute rather than a fifth row, so it cannot be summed or plotted alongside the months by accident.

Source

Ganley, L.C., Brault, S. and Mayo, C.A. (2019) What we see is not what there is: estimating North Atlantic right whale Eubalaena glacialis local abundance. Endangered Species Research 38:101-113. doi:10.3354/esr00938 , Table S1. Open access under CC-BY.

Details

Availability runs from 0.27 in January to 0.91 in April, as the copepods the whales feed on move up through the water column. That threefold swing across one season is the case against a constant g(0), in measurements.

Three things not to do with these columns

Do not treat percent_surface_time as \(E(s)/(E(s)+E(d))\): It is not. January is listed at 16% with a mean surface interval of 48 s and a mean dive of 533 s, and \(48/(48+533)\) is 8.3%. The gap appears every month and in both directions — April's intervals give 90% against a listed 55%. The percentage is evidently a mean of per-follow percentages while the interval columns are means of intervals: a mean of ratios against a ratio of means. So it is not the instantaneous availability, and using it as one would be wrong by up to 35 percentage points.
Do not expect availability() to reproduce availability: The reported figure is a median over bootstrap replicates, and \(a(x)\) varies with distance through the time in view. Working backwards from the tabulated means, January's 0.27 implies a window near 122 s and April's 0.91 one near 8 s — they are not evaluated at a common window. The values are measurements to be used, not outputs to be recomputed.
Do not feed availability_variance to g0() without deciding what it is: It is labelled a variance and runs 0.04–0.09. Read literally, January's standard error is \(\sqrt{0.04} = 0.2\) against an estimate of 0.27 — a CV of 74%, which would dominate any correction it entered. Read as a standard error instead, the CV is 15%. Neither matches the very small error bars in the paper's Fig. 4A. It is shipped under the paper's own label and deliberately not converted.

The platform

Cessna 336/337 Skymaster at 185 km/h and 228 or 304 m altitude, surveying January to May. Time in view at the effective trackline was 51.22 s, rising with perpendicular distance — see view_window_aerial(). Their trackline is at 100 m rather than 0 m because the aircraft's flat windows leave a blind spot beneath it, and the surveys were left-truncated there accordingly — the same blind spot sweep_models(left = ) and the gamma key handle at the fitting end.

Two inconsistencies in the source

Recorded so they are not mistaken for transcription errors. February's sample size is 9 in Table S1, summing to the 86 its own total row gives, but 10 in the Fig. 2 caption, summing to the 87 the Methods states. And April's availability is 0.91 here and in Section 3.1, while the abstract gives the seasonal range as 0.27–0.85. Table S1 is followed here, being the tabulated source.

Examples

ganley_availability
#> # A tibble: 4 × 8
#>   month percent_surface_time mean_dive mean_surface availability
#>   <fct>                <dbl>     <dbl>        <dbl>        <dbl>
#> 1 Jan                     16       533           48         0.27
#> 2 Feb                     34       256          226         0.52
#> 3 Mar                     31       219           67         0.52
#> 4 Apr                     55        88          801         0.91
#> # ℹ 3 more variables: availability_variance <dbl>, n_follows <int>,
#> #   hours_followed <dbl>

# The measured seasonal swing, as a g(0) component. A standard error has to
# be decided on first - see above on the variance column - so this uses a
# deliberately explicit placeholder rather than a silent conversion.
avail <- data.frame(
  key = as.character(ganley_availability$month),
  component = "availability",
  value = ganley_availability$availability,
  se = sqrt(ganley_availability$availability_variance)
)
suppressWarnings(g0(avail))
#> <dsfit_g0>
#>   assumed 1:   perception
#>   components:
#>     availability  source not recorded
#> 
#>  key   g0     se    cv
#>  Jan 0.27 0.2000 0.741
#>  Feb 0.52 0.3000 0.577
#>  Mar 0.52 0.2449 0.471
#>  Apr 0.91 0.2236 0.246
#> 
#>   Divide abundance by g0, and propagate cv. This package does not
#>   apply it: correction happens at the abundance step.

attr(ganley_availability, "all_sightings")$availability
#> [1] 0.63