Original Research Article Extinction debt and the role of static and dynamical fragmentation on biodiversity Elder S. Claudino, M.A.F. Gomes, Paulo R.A. Campos * Departamento de Fı´sica, Universidade Federal de Pernambuco, 52171-900 Recife, PE, Brazil 1. Introduction Empirical evidences demonstrate that recent extinction rates are 100–1000 times higher than background rates (He and Hubbell, 2011; Pimm et al., 1995). Habitat loss and fragmentation are considered as the major mechanisms driving the shrinking of biological diversity in earth (Holt et al., 1995; Wilcove et al., 1998; Balmford and Bond, 2005; Damschen et al., 2006), and hence species extinctions are mostly resulted from the competition for resources and space with humans. The understanding of the effect of habitat fragmentation on ecosystems is crucial in finding alternative solutions to minimize its impact and making-policy recommendations (Mendenhall et al., 2014). In this context, the great majority of research either focused on effects of fragmenta- tion on metapopulations (Hanski and Ovaskainen, 2000; Levins, 1969) or on the dynamic patch-occupancy (Caswell and Cohen, 1991; Hill and Caswell, 1999), and aimed to address the balance between colonization and local extinction. A more thorough study about metapopulation persistence that combines patch dynamics and dynamic landscapes has also been presented (Keymer et al., 2000). An important finding is that in metapopulations, connec- tivity plays an influential role in the way that ecosystems respond to habitat loss and change (Hanski and Ovaskainen, 2000; Hylander and Ehrle ´n, 2013). The species–area relationship (SAR) is a central concept in ecology (Lomolino, 2000). The species–area relationship informs us the rate at which species richness increases along a gradient of ecosystems of increasing size. In this way, the SAR is also used as an indirect manner to assess the impact of habitat loss or habitat change on biodiversity by reversing it, bringing it backwards to smaller areas. Nonetheless, the method usually overestimates the biodiversity loss. The discrepancy between prediction and observation, referred to as extinction debt, may be explained by the fact that local and global extinctions are delayed (Hylander and Ehrle ´n, 2013). Thus extinction debt can also be considered to be an estimator of the number of endangered species in the community. By taking a static view for the community, this quantity is always positive. After a long time has elapsed from the disturbance it is Ecological Complexity 21 (2015) 150–155 A R T I C L E I N F O Article history: Received 4 June 2014 Received in revised form 24 November 2014 Accepted 30 November 2014 Available online Keywords: Landscape ecology Fragmentation Neutral theory Fractal landscapes A B S T R A C T The mass-extinction events caused by human-driven habitat loss are a current concern in conservation science. However, the observed number of extinctions is considerably smaller than predicted. The overestimation of extinction rates comes from the time-delay which depends on the species sensitivity to habitat changes. The standard method of predicting the effect of habitat loss on biodiversity is to use the species–area relationship and progressively following it backwards to smaller areas. The difference between the actual number of species and the one provided by the backwards species–area relationship is dubbed extinction debt. Previous studies in general adopt a static view for the spatial distribution of species. Nonetheless, a precise understanding of the problem urges us to adopt a dynamic framework to this issue since the time between disturbances of the landscape plays an active role in influencing the strength of the extinction debt. In this context, here we address two distinct approaches for this question: a static and a dynamic view of fragmentation. In the former we quantify the extinction debt in a quenched spatial distribution of species, whereas in the latter the community is let to evolve between disturbance events of the landscape. Here we show that the size of the extinction debt depends on the pattern of the fragmentation. It is found that random distributions of destroyed habitats provide larger extinction debts than those obtained for contiguous areas of fragmentation. Furthermore, in the dynamic approach it is observed that dispersal can lead to unexpected outcomes such as lower biodiversity levels than ones inferred from the backwards species–area relationship. ß 2014 Elsevier B.V. All rights reserved. * Corresponding author. Tel.: +55 8199172808. E-mail address: prac@df.ufpe.br (Paulo R.A. Campos). Contents lists available at ScienceDirect Ecological Complexity jo ur n al ho mep ag e: www .elsevier .c om /lo cate/ec o co m http://dx.doi.org/10.1016/j.ecocom.2014.11.011 1476-945X/ß 2014 Elsevier B.V. All rights reserved.