Shortly after version 1.0 of this code was published, IUCN clarified that severity should be understood as the population decline “within the scope of the particular threat”. Previously, the definition of severity had been ambiguous, and the Norwegian Red Lists were based on an understanding of severity as the decline of the entire population. Whereas the current IUCN definition requires that threat scores are estimated from the product of scope and severity, the alternative definition required scope to be ignored.
Version 1.1 of this code now includes the possibility to choose between
these two definitions. (This choice is handled by the variable
useScope, see species.md.)
The multiplicative approach had earlier been applied by Garnett et al. (2018, appendix S3) and Mair et al. (2021, supplementary table 2). It should be noted, however, that our code does not use the same threat weights as these earlier studies. The main reasons for this are:
- Garnett et al. and Mair et al. assumed uniform distributions within each scope and severity class. We do the same for scopes (which are fractions of population sizes) but not for severities (which are population declines). Especially in the highest severity class (“very rapid decline” according to IUCN, “rapid decline” according to the Norwegian Red Lists), which spans the interval up to and including 100% decline (i.e. extinction), it seems unrealistic to treat extinction and a 30% decline as equiprobable. We therefore assumed a decreasing distribution for the highest severity interval (and an increasing distribution for the lowest of the Norwegian severity intervals, which is “negligible”; however, this does not make sense for IUCN’s lowest severity interval, which is “no decline”).
- Garnett et al. and Mair et al. used the averages of the products of the limits of each interval, whereas we use the products of the averages of each interval.
The differences are here illustrated with the IUCN classes for scope and severity:
(1) By using averages of products of the limits of each interval, the earlier studies obtained the following values (avoiding their rounding errors, however):
ScopeSev <- list(
c("whole_population", "majority", "minority"),
c("very_rapid", "rapid", "slow", "negligible", "no_decline")
)
average <- function(x, y) (x + y) / 2
table <- average(ScopeIUCN$lower[3:1] %*% t(SeverityIUCN$lower[5:1]),
ScopeIUCN$upper[3:1] %*% t(SeverityIUCN$upper[5:1]))
print(round(matrix(table, 3, 5, dimnames = ScopeSev), 3))
## very_rapid rapid slow negligible no_decline
## whole_population 0.635 0.240 0.109 0.010 0
## majority 0.525 0.185 0.095 0.009 0
## minority 0.250 0.075 0.050 0.005 0
(2) By using products of averages of the limits of each interval instead, one obtains:
table <- average( ScopeIUCN$lower[3:1], ScopeIUCN$upper[3:1]) %*%
t(average(SeverityIUCN$lower[5:1], SeverityIUCN$upper[5:1]))
print(round(matrix(table, 3, 5, dimnames = ScopeSev), 3))
## very_rapid rapid slow negligible no_decline
## whole_population 0.617 0.238 0.104 0.010 0
## majority 0.455 0.175 0.077 0.007 0
## minority 0.162 0.062 0.028 0.002 0
For some combinations of scope and severity, the differences may be negligible. In the lower left corner of the matrix, the differences are clear, however.
Method (2) is statistically more meaningful than method (1). If the true values of scope and severity are uniformly distributed within their respective intervals, their product is not. Method (2) takes this into account, whereas method (1) assumes that the products of the true values of scope and severity are uniformly distributed. The same analogously holds for other distributions: whichever distribution one assumes for scope and severity, their product will necessarily follow a different distribution.
(3) In addition to using products of averages, we use a decreasing distribution for the highest severity class. We therefore obtain:
table <- average( ScopeIUCN$lower[3:1], ScopeIUCN$upper[3:1]) %*%
t(average(SeverityIUCN$lower[5:1], c(0.65, 0.3, 0.2, 0.02, 0)))
# That's a shortcut which reproduces our mean for the highest severity class
print(round(matrix(table, 3, 5, dimnames = ScopeSev), 3))
## very_rapid rapid slow negligible no_decline
## whole_population 0.451 0.238 0.104 0.010 0
## majority 0.332 0.175 0.077 0.007 0
## minority 0.119 0.062 0.028 0.002 0