# Scientific Foundations for an IUCN Red List of Ecosystems

## Figure 1

Probability density functions for the population and ecosystem variables that measure proximity to the thresholds that define species extinction (A, B) and ecosystem collapse (C, D).

The probability density functions represent uncertainty in the measurement of the variables. For species, the population threshold that defines extinction is known with certainty (e.g. zero abundance of a species, defined by the vertical line in A and B). In A, the estimated population is definitely greater than the extinction threshold, so there is no doubt that the species is extant. Alternatively, the probability that the abundance is above the threshold (the area under the curve) might be less than one (B), in which case the species could be extinct or extant. The shaded area is the probability that the species remains extant. For ecosystems, the x-axis could represent spatial distribution, number of species, water quality, etc. In contrast to species, uncertainty about the definition of ecosystem collapse leads to a range of possible values for this threshold (dashed box in C and D). The ecosystem variable is above this upper bound in some cases (C), so there is no doubt that the ecosystem persists. Alternatively, probable values for the ecosystem variable might intersect the uncertain threshold (D), in which case the ecosystem may be collapsed or not. In this case, there is some probability that the ecosystem parameter is above the upper bound of the threshold (shaded dark grey), which places a lower bound on the probability that the ecosystem persists (i.e. that it has not collapsed). There is an additional probability (pale grey) that the ecosystem parameter is above the threshold that depends on the amount of uncertainty in the threshold (i.e. width of the box). The sum of these two probabilities places an upper bound on the probability ecosystem persists. With further deterioration (E), the lower bound on the probability of ecosystem persistence is zero (no dark shading) and the upper bound is the pale shaded area.