ORIGINAL ARTICLE Zi-Hua Zhao • Da-Han He • Cang Hui From the inverse density–area relationship to the minimum patch size of a host–parasitoid system Received: 25 September 2010 / Accepted: 15 November 2011 / Published online: 7 December 2011 Ó The Ecological Society of Japan 2011 Abstract The minimum amount of suitable habitat (MASH) is an important concept in conservation bio- logical control. Two methods for estimating the MASH have been proposed by McCoy and Mushinsky based on an inverse density–area relationship. Using data of the population densities of aphid host–parasitoid–hyper- parasitoid collected from wheat fields of different habitat sizes, we argued that the inverse density–area relation- ship may be an artifact. Significant correlations between population densities and patch sizes from all three tro- phic levels were found once the population density had been log-transformed. We could not obtain the same results if the population density had not been log-trans- formed. We estimated that the MASH for the aphid M. avena, S. graminum, A. avenae, A. gifuensis, P. aphidis, and Alloxysta sp. were 246, 246, 479, 495, 949, and 835 m 2 according to the methods of McCoy and Mush- insky. The scale-dependence and the systematic spatial variations of the host–parasitoid interaction suggests that we can achieve an optimal effect of biological con- trol by manipulating the habitat patch sizes, although not based on the inverse density–area relationship. Keywords Density–area relationship Æ Extinction threshold Æ Aphids Æ Parasitoid wasps Æ Habitat loss Æ Minimum viable population size Æ Patch size Æ Scaling Introduction Habitat destruction and fragmentation is one of the major drivers of biodiversity loss due mainly to anthropogenic disturbance, e.g., the expansion and intensification of modern agriculture (Tilman et al. 2002; Henle et al. 2004; Zhao et al. 2010). Designing a robust and sensitive estimate of the minimum amount of suit- able habitat, known as the MASH, that can sustain a viable population has become a priority in conservation (e.g., Bart 1995; Akcakaya et al. 1999; Brito and Grelle 2006; McCoy and Mushinsky 1999, 2007; Zhao et al. 2011). The existence of the MASH for species long-term persistence provides us a practical tool, by manipulating the patch size of focal species, to ensure the survival of endangered species and the successful control of the problematic ones (such as pests and invasive species; Brook et al. 2000; Engen and Sather 2000). Indeed, the MASH has been considered a critical indicator for assessing the conservation status of endangered species (Shaffer 1981). Different species had different values of MASH, which reflect their different habitat require- ments and differences in body size, migration, trophic level, and habitat quality. In general, the higher trophic level, the larger MASH. MASH has important impli- cations for integrated pest management, and MASH itself can be used as a pest control tool, especially in agricultural landscape design. As an important aspect of conservation biological control (CBC), the ultimate direction of MASH was the construction and design of agricultural structure in successive spatial–temporal scale, which enhanced activity and predation of natural enemies in agricultural landscape, and suppressed the pest population to the greatest extent. The MASH can generally be estimated by three methods (or defined in three ways): (1) the minimum patch size to ensure a certain probability of presence in a presence–absence survey (Vance et al. 2003); (2) the minimum patch size to ensure a population will persist with a certain probability of long-term survival in the Z.-H. Zhao (&) Æ D.-H. He Institute of Grassland Sciences, Ningxia University, 489 West Helanshan Road, Xixia District, Yinchuan 750021 Ningxia Hui Autonomous Region, People’s Republic of China E-mail: zihuazhao@126.com Tel.: +86-951-2061881 Fax: +86-951-2061874 D.-H. He E-mail: hedahan@163.com C. Hui Department of Botany and Zoology, Centre for Invasion Biology, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa E-mail: chui@sun.ac.za Ecol Res (2012) 27: 303–309 DOI 10.1007/s11284-011-0903-7