Cacciapaglia and van Woesik. Supplementary document.
Species detectability
To estimate the probability that a species was truly absent from a particular ecoregion (Veron et al.
2009) in which it was not detected, we used all available coral-related published studies as a proxy for
sampling effort. The likelihood of finding a species in an ecoregion was assumed to be greatest on the
first survey, with an increased likelihood of a species being truly absent from a particular ecoregion on
subsequent surveys. These likelihoods were expressed as a geometric distribution, as follows:
𝑃𝑖 = 1 − (1 − 𝑝𝑖 )
𝑛𝑖 +1
( 1) ,
where P is the probability that a species was absent from ecoregion i, p is the probability of detection
within the ecoregion, and n is the sampling effort in ecoregion i. In this context, sampling effort relates
to the number of failures in detecting a species and the probability of detection (p), which is dependent
on the size of the ecoregion, and the number of adjacent ecoregions supporting the species. We also
assumed that as the size of an ecoregion increases, the probability of detection decreases, as follows:
𝑚𝑖𝑛𝑠𝑖𝑧𝑒
𝑆𝑖 = (
𝑠𝑖𝑧𝑒𝑖
4
)
(2),
where for ecoregion i, Si an ecoregion-size ratio, minsize is the size of the smallest ecoregion, and sizei
is the size of the ecoregion of interest, and 4 is a scaling constant. The probability of a false negative
should also theoretically increase as the number of adjacent regions supporting a species increases. The
adjacency relationship was considered as follows:
𝐴𝑑𝑗𝑖 = 0.6𝑎𝑖
(3),
where Adj is the adjacency relationship for ecoregion i, and a is the number of adjacent ecoregions. This
relationship decreases the detection probability by 40% for each adjacent ecoregion containing the
species. Incorporating size (Si) and Adjacency (Adji) into our probability of detection (pi) allowed us to
determine the probability that a particular species of interest was found, given our estimated detection
probability, and the sampling effort. Credible intervals were estimated to determine the likelihood that a
species was truly absent in a given ecoregion by rearranging the geometric cumulative distribution
function as follows:
log(1 − .95)
𝑛𝑖 = (
− 1)
log(1 − 𝑝𝑖 ))
(4)
,
where ni is the sampling effort in ecoregion i required to achieve a 95% probability of observing a
success, with the given detection probability p for ecoregion i. A confidence ceiling was calculated
because the probability of finding a new species tapers off and reaches an asymptote within increased
sampling. The ceiling was accomplished by using the maximum sampling effort of all ecoregions (ni), in
the cumulative distribution function (Pi), from equation 1, to limit Pi. The relationship between observed
failures and the ceiling was expressed as:
𝑃𝑓𝑖 =
𝑃𝑖
𝑚𝑎𝑥𝑃 ∙ 𝑃𝑖
(5),
where Pfi is the probability that the species is truly absent from an ecoregion (i), in which it was not
detected (including a ceiling), P is the probability that the species was absent from an ecoregion in
which it was not detected (not including a ceiling), and maxP is the ceiling.
River Buffering
The 12 largest tropical river outflow areas were masked out in accordance with the size of the drainage
basins, following the function Distance from river mouth= 3992.7268*dbasin.2735)/1000 where dbasin is
the size of the drainage basin in km2 .