Solow calculation (Prior I)

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Inferring local extinction based on limited occurrence data

To estimate the likelihood of a species’ presence before considering any new evidence, we use a parametric extinction statistic developed by Solow (1993). This approach starts from the simple idea that the timing of past sightings contains information about whether a species might have disappeared. If a species was last observed long ago, and we’ve continued searching without finding it again, our confidence in its persistence declines.

Solow’s method expresses this intuition mathematically by comparing three key times, for a species that has been observed $n$ times during an observation period:

$T_0$ — the beginning of formal record-keeping, or the earliest time we could reasonably have detected the species if it were present
$t_n$ — the time of the most recent confirmed sighting
$T$ — the current time or the endpoint of our study

The formula calculates an odds ratio (called a Bayes factor) that weighs the likelihood that the species is still present versus extinct, based on how long it has gone unobserved. The less time between the last sighting and today $(t_n - T_0)$, relative to the total observation period $(T - T_0)$, and the fewer sightings there have been, the lower the odds that the species persists.

Expand for mathematical details

Solow (1993) provides a framework for determining a reasonable prior distribution for belief about species extinction when observational data are limited. Their Equation 3 presents a Bayes Factor for summarizing evidence in favor of extinction, given by: $B(t) = (n - 1) / [((T - T_0)/(t_n - T_0))^{(n - 1)} - 1]$ where $n$ is the number of observations, $t_i$ represents the $ith$ sighting time, $T$ is the present date and $T_0$ is the start of the period of observation.

In the case $n = 1$ this formula simplifies to $B(t) = 1 / ln((T - T_0)/(t_n - T_0))$.

Assessing extirpation risk Example I