What happens if density increases? Conservation implications of population influx into refuges C. J. E. Metcalf 1 , K. Hampson 2 & D. N. Koons 3 1 Nicholas School of the Environment, Duke University, Durham, NC, USA 2 Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA 3 Department of Wildland Resources and the Ecology Center, Utah State University, Old Main Hill, Logan, UT, USA Keywords catastrophe; crowding; density dependence; extinction; fragmentation. Correspondence C. J. E. Metcalf, Nicholas School of the Environment, Duke University, Durham, NC 27707, USA. Email: cjm29@duke.edu Received 4 March 2007; accepted 16 July 2007 doi:10.1111/j.1469-1795.2007.00138.x Abstract Sudden catastrophic events like fires, hurricanes, tsunamis, landslides and defor- estation increase population densities in habitat fragments, as fleeing animals encroach into these refuges. Such sudden overcrowding will trigger transient fluctuations in population size in the refuges, which may expose refuge populations to an increased risk of extinction. Until recently, detailed information about the operation of density dependence in stage-structured populations, and tools for quantifying the effects of transient dynamics, have not been available, so that exploring the extinction risk of such transient fluctuations has been intractable. Here, we use such recently developed tools to show that extinction triggered by overcrowding can threaten populations in refuges. Apart from situations where density dependence acts on survival, our results indicate that short-lived species may be more at risk than longer-lived species. Because dynamics in local populations may be critical for the preservation of metapopulations and rare species, we argue that this aspect warrants further attention from conservation biologists. Introduction Habitat loss is a ubiquitous threat to the world’s biodiversity (Wilcox & Murphy, 1985; Soule, 1986). It is largely a consequence of human actions such as deforestation (Brooks et al., 2002), but can also be due to natural causes, for example sudden catastrophes like the south-east Asian Tsunami, or wildfires. Following habitat loss, population densities in unaffected habitats may also change, as fleeing animals encroach into these refuges (Hagan, Van Der Haegen & McKinley, 1996). The magnitude of this ‘crowd- ing’ effect depends on accessibility of intact fragments to individuals from the destroyed habitats (Grez et al., 2004) and the dispersal capabilities of affected species (Clobert et al., 2001). Despite empirical and theoretical evidence of crowding due to individuals displaced by habitat loss (Fahrig & Paloheimo, 1988; Bierregaard & Lovejoy, 1989; Collinge & Forman, 1998; Debinski & Holt, 2000; Hannon & Schmiegelow, 2002), and increasing recognition of the importance of density dependence (Bonenfant et al., unpubl.data), the implications of transient influxes on po- pulation dynamics have rarely been explored from a con- servation perspective (but see Ranta, Lundberg & Kaitala, 2006, Chapter 8). Can an influx of individuals be sufficient to put popula- tions at risk? Demographic rates and transitions are gener- ally agreed to be the outcome of endogenous as well as exogenous processes (Turchin, 1999; McLaughlin et al., 2003). The higher density attained may therefore drive a decrease in demographic rates and transitions. Transient oscillations in population size and a decrease in vital rates due to density-dependent effects such as food shortages might reinforce each other, driving the population towards dangerously small sizes, or towards a population age struc- ture that adversely affects population growth. The risk of this occurring will be determined by a population’s dy- namics and structure, and specifically density-dependent processes and their potentially complex interactions with the environment. Although estimating density dependence is fraught with difficulty, failure to consider it may lead to overly optimistic predictions of population health (Sabo, Holmes & Kareiva, 2004). The effect of density on dynamics may be mediated by affecting vital rates such as survival or growth either directly through competition for limiting resources (McCallum Kikkawa & Catterall, 2000), or through disease (Wilcox & Elderd, 2003), or predation, or behavioural responses to density (Hagan et al., 1996). In the simplest models of crowding, established popula- tions will be at risk following an influx of individuals only if the addition of one individual leads to the loss of more than one individual from the population. Density dependence in this case is referred to as ‘over-compensating’. Theoretically, this condition is associated with non-linear relationships (Hassell, 1975) that occur when populations exceed a thresh- old level where resources become limiting (Wilcox & Elderd, Animal Conservation 10 (2007) 478–486 c  2007 The Authors. Journal compilation c  2007 The Zoological Society of London 478 Animal Conservation. Print ISSN 1367-9430