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2003, Araújo et al. 2002). In some cases, there may be a direct linear relationshipbetween a risk element and an ecosystem’s response to the threat. Often times, the greaterthe expression of a risk element, the larger that threat may have upon an ecosystem.However, this is not always the case because some ecosystems have differentcharacteristics that govern the way they might respond to a given threat. For example, firein certain ecosystems can be a disaster and immediately destroy or highly degrade anecosystem, such as rainforests in the Amazon. But in grasslands such as in the OrinocoBasin, it is necessary to have fire in certain intensities and frequencies. To little fire is badfor that ecosystem, and too much fire is equally bad. There is a non-linear responserelationship between a grassland and fire that has to be identified and modeled (TNC,2006).Prior to modeling an ERS, experts must identify how risk in each element decays overdistance, or if there is a decay factor at all. PAT provides four decay types for expressingthe function of distance decay. These include a) linear; b) concave; c) convex; and d)constant and are represented in the figure below. The default function is a linear decaytype, where the rate of intensity decay is constant until the maximum distance is reachedand the intensity becomes zero. A concave decay has an initial rapid decrease in intensitywhile a convex has the opposite effect - a gradual intensity decay followed by a steepdecay as maximum distance is reached. A constant decay has no change in intensityvalue until the maximum distance is reached, ending in an abrupt zero. Users shouldconsult with ecological experts who have reviewed each risk element and defined thetypes of decays that are appropriate to apply based on the ecosystem in question.Examples of distance decay functions and the resulting output based on a single point occurrence and a1000m influence distance. Red and orange hues indicate higher intensity values while green and blue huesrepresent lower intensity values.TNC Protected Area Tools (PAT) Version 3.0The Nature Conservancy, August 200913