Beetles in fragmented woodlands: a formal framework for dynamics of movement in ecological landscapes

Abstract

Summary1. We consider the movement of carabid beetles in a fragmented woodland landscape. Landscape ecology has lacked a formal framework for the analysis of dynamics of this kind, and stochastic spatial simulations have generally been needed to gain insight. 2. We ®rst de®ne an individual-based stochastic model for movement in a heterogeneous landscape. From this a deterministic approximation is derived which describes the build-up in association of the beetles with their environment; the deterministic model makes use of a second-order spatial moment. It is shown that the results of the deterministic approximation match closely those of the underlying stochastic process. On this basis we suggest that the dynamical system provides a formal framework for the dynamics of animal movements in ecological landscapes. 3. The results show that the beetles, starting from an initial random layout, rapidly become associated with the woodlands and, by the time 100 days have elapsed, the association is close to its asymptotic state. The strength of the association depends very much on the spatial auto-covariance function of the environment. 4. A number of extensions are suggested, including landscapes comprising multiple habitats of di erent degrees of suitability, landscapes that change through human activity, birth and death processes of single species, and interactions between species. The method of moments provides a¯exible basis for future work in this area.

Efecto de plantaciones de pino en la artropofauna del suelo de un bosque Altoandino

“…Este podría ser un ejemplo de los efectos negativos de la fragmentación de bosques sobre las comunidades del suelo (Davies & Margules 1998, Ims et al 2004). La reducción de biodiversidad se atribuye básicamente a una limitación en la (Hunter 2002, Murrel & Law 2000, condición que en este estudio parece evidenciarse con el hecho de que transitan en promedio 2.5 veces más artrópodos epigeos en el bosque nativo que en la plantación de pino. Una mayor oferta de nichos dentro del bosque andino, particularmente por la presencia de bromelias, también puede contribuir a la diferencia de biodiversidad encontrada entre sitios (Paoletti et al 1991, Richardson 1999, Ospina-Bautista et al 2004.…”

Spatial Point Processes and Moment Dynamics in the Life Sciences: A Parsimonious Derivation and Some Extensions

“…This contrasts to the master-equation approach, which describes the spatial point process as a sum of Dirac-delta functions Murrell and Law 2000). The derivation includes density-dependent movements and a non-homogeneous space and is related to previous derivations as shown in Table 1.…”

“…The method has been extended to describe the spatial structure that can emerge in the size distribution of plants (Murrell 2009;Adams et al 2013). A similar approach can be applied to the dynamics of animal populations as they become associated with their preferred habitat (Murrell and Law 2000), and to spatial structures that develop between predators and their prey (Murrell 2005; Murrell 2012, 2013). However, the widespread take-up of spatial, agent-based models across the life sciences suggests that spatial-moment dynamics have a potential field of application much broader than ecology.…”

On moment closures for population dynamics in continuous space

“…Another power-2 closure was used for animal movement in a heterogeneous landscape (Murrell and Law, 2000), but is not appropriate in a circumstance when there are births and deaths (i.e., when the first moment can change).…”