Estimating extinction dates from sighting records

Overview

EDE implements eleven procedures for inference about extinction from sighting records. Some estimate an endpoint directly; others test whether a species could plausibly have persisted to a candidate time. The latter return frequentist p-values, not posterior probabilities that the species is extant.

The column containing these p-values is currently named chance for compatibility with EDE 0.1.0.

Input and observation origin

library(EDE)

years <- c(1900, 1902, 1903, 1905, 1907, 1908, 1910, 1912,
           1915, 1918, 1920, 1923, 1925, 1928, 1930, 1933, 1936)
counts <- c(4, 3, 5, 2, 3, 4, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1)
sd <- sighting_data(data.frame(year = years, sightings = counts))

The earliest supplied time defines the observation origin. Include an initial zero-count row if observation began before the first sighting. Methods differ in their treatment of counts: OLE treats counts as independent events, constant-rate Solow uses occupied times, and Burgman uses full frequencies.

Endpoint estimators

robson1964() uses the final gap for a jackknife point estimate and a one-sided confidence interval. strauss1989() supplies an unbiased endpoint estimate and one-sided interval under uniform occurrence. ole() fits the Weibull extreme-value model to the k most recent sighting events.

robson1964(sd)
#> <Robson & Whitlock (1964)>
#>   estimate: 1939
#>   95% one-sided CI: [1936, 1993]
strauss1989(sd)
#> <Strauss & Sadler (1989)>
#>   estimate: 1938.25
#>   95% one-sided CI: [1936, 1943.41]
ole(sd)
#> <OLE (Roberts & Solow 2003)>
#>   estimate: 1941.97
#>   95% CI: [1937.48, 1956.75]
ole(sd, k = 10)
#> <OLE (Roberts & Solow 2003)>
#>   estimate: 1940.43
#>   95% CI: [1936.35, 1957.28]

Persistence tests

solow1993(sd, test_year = 2000)
#> <Solow (1993)>
#>   estimate: 1944
solow1993b(sd, test_year = 2000)
#> Warning: p-value never falls to alpha before `test_year`; returning NA.
#> <Solow (1993b)>
#>   estimate: NA
solow2005(sd, test_year = 2000)
#> <Solow (2005) Weibull test>
#>   estimate: 1954
mcinerny2006(sd, test_year = 2000)
#> <McInerny, Roberts, Davy & Cribb (2006)>
#>   estimate: 1942
burgman1995(sd, test_year = 2000)
#> <Burgman, Grimson & Ferson (1995)>
#>   estimate: 1944
solow_roberts2003(sd, test_year = 2000)
#> <Solow & Roberts (2003)>
#>   estimate: 1993
jaric2010(sd, test_year = 2000)
#> <Jaric & Ebenhard (2010)>
#>   estimate: 1981

• solow1993() assumes a stationary Poisson process.
• solow1993b() allows an exponentially declining sighting rate.
• solow2005() uses the Weibull extreme-value p-value associated with OLE.
• mcinerny2006() conditions on the previous binary sighting rate.
• burgman1995() tests the longest run of empty discrete periods.
• solow_roberts2003() uses only the two most recent distinct sightings.
• jaric2010() uses the average interval and can adjust it for a trend in consecutive interval lengths.

The full p-value curve is available with data_out = TRUE:

curve <- jaric2010(sd, test_year = 2000, data_out = TRUE)
plot(curve$time, curve$chance, type = "l",
     xlab = "candidate time", ylab = "p-value")
abline(h = 0.05, lty = 2)

Records of variable reliability

jaric_roberts2014() assigns a probability of validity to every occupied time. The current implementation requires binary counts because reliability belongs to individual observations.

uncertain <- sighting_data(data.frame(
  year = c(1900, 1910, 1920, 1930),
  sightings = 1
))

jaric_roberts2014(
  uncertain,
  reliability = c(1.0, 0.9, 0.6, 0.3)
)
#> <Jaric & Roberts (2014)>
#>   estimate: 1930.99
#>   95% upper confidence bound: 2005.22

The result includes the effective number of sightings and the reliability-adjusted endpoint as additional components. Reliabilities should be elicited independently of the extinction analysis.

Choosing a method

• Use OLE when the recent record is sufficiently long and an extreme-value model is defensible.
• Use solow1993() only when a constant sighting rate is plausible.
• Use solow1993b() for an approximately exponential decline.
• Use jaric2010() when the intervals themselves show a gradual trend.
• Use burgman1995() for discrete frequency data and longest-run questions.
• Use jaric_roberts2014() when observations have explicit reliability assessments.

Running several scientifically defensible methods is useful, but p-values from models whose assumptions are violated should not be combined or interpreted as extinction probabilities.

References

Burgman, M. A., Grimson, R. C., & Ferson, S. (1995). Inferring threat from scientific collections. Conservation Biology, 9(4), 923-928.

Jarić, I., & Ebenhard, T. (2010). A method for inferring extinction based on sighting records that change in frequency over time. Wildlife Biology, 16(3), 267-275.

Jarić, I., & Roberts, D. L. (2014). Accounting for observation reliability when inferring extinction based on sighting records. Biodiversity and Conservation, 23(11), 2801-2815.

McInerny, G. J., Roberts, D. L., Davy, A. J., & Cribb, P. J. (2006). Significance of sighting rate in inferring extinction and threat. Conservation Biology, 20(2), 562-567.

Roberts, D. L., & Solow, A. R. (2003). When did the dodo become extinct? Nature, 426, 245.

Robson, D. S., & Whitlock, J. H. (1964). Estimation of a truncation point. Biometrika, 51, 33-39.

Solow, A. R. (1993). Inferring extinction from sighting data. Ecology, 74, 962-964.

Solow, A. R. (1993). Inferring extinction in a declining population. Journal of Mathematical Biology, 32, 79-82.

Solow, A. R. (2005). Inferring extinction from a sighting record. Mathematical Biosciences, 195, 47-55.

Solow, A. R., & Roberts, D. L. (2003). A nonparametric test for extinction based on a sighting record. Ecology, 84, 1329-1332.

Strauss, D., & Sadler, P. M. (1989). Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges. Mathematical Geology, 21, 411-427.