## Introduction

Landscape heterogeneity has a profound effect on metapopulation function by influencing both local population dynamics and the dispersal between patches. The metapopulation concept originally referred to homogeneous patchy landscapes in which dispersal was considered only in terms of the colonization of empty patches and was equally likely for all individuals in a population (Levins 1969). Since then metapopulation models have been greatly elaborated to include the wide range of heterogeneity found in natural landscapes (Fahrig 2007) and to incorporate different dispersal strategies (Hanski 2001; Clobert, Ims & Rousset 2004).

Landscape heterogeneity can occur through differences in the characteristics of the habitat both within and surrounding patches. Patches can vary in size (Hanski & Thomas 1994; Griffen & Drake 2008; Nielsen, Wakamiya & Nielsen 2008), quality (Anderson & Danielson 1997; Fahrig 2007; Griffen & Drake 2008; Jaquiery *et al.* 2008; Stasek, Bean & Crist 2008) and connectivity (Gulve 1994; Hanski 1994; Goodwin & Fahrig 2002; Benjamin, Cedric & Pablo 2008; Stasek, Bean & Crist 2008). All of these metrics affect both local and regional population dynamics. Temporal heterogeneity is an equally important aspect of landscape ecology as it describes the change in landscape structure over time because of stochastic and periodically variable environmental conditions. Both temporal and spatial heterogeneity affect the mechanisms of population regulation and hence the carrying capacities and population densities. The existence of a relationship between population density and population growth is well established (Nicholson 1933; Andrewartha & Birch 1954). Understanding the relative importance of density-dependent and density-independent processes (Turchin 1999; Brook & Bradshaw 2006), knowing how to describe the nature of these density-dependent processes and describing how and why they may differ (Murdoch 1994; Sibly *et al.* 2005; Bonenfant *et al.* 2009) are current research priorities in the field of population ecology.

Dispersal has a profound effect on the demographic and genetic structure of local populations within a metapopulation. As such, the importance of an explicit description of dispersal in metapopulation systems is widely recognized. The original metapopulation model (Levins 1969) considered only the colonization of empty patches and therefore ignored a great deal of the complexity of natural systems where all patches can lose and gain individuals through emigration and immigration respectively. Similarly, dispersal theory has developed from being a fixed trait where all individuals have an equal chance of dispersing to one where dispersal is conditional upon the population density in a patch, the age or sex of the individual, interspecific competition, matrix characteristics and patch geometry, and interpatch distances (Clobert, Ims & Rousset 2004). The evolution of dispersal in the presence of spatial and temporal heterogeneity has been the focus of a large body of work. In particular, it is suggested that temporal stochasticity encourages dispersal to a greater extent than spatial heterogeneity alone (Holt 1985; McPeek & Holt 1992). Many studies are based on the theory of ideal free distribution (Fretwell & Lucas 1970) where individuals should disperse to maximize their reproductive fitness (Holt 1985; McPeek & Holt 1992; Holt & Barfield 2001; Morris, Diffendorfer & Lundberg 2004). However, this theory assumes unhindered movement and habitat sampling by dispersing individuals which may make it inadequate to describe dispersal in many natural systems (Leturque & Rousset 2002). Rather, it is probable that dispersal is a function of local population dynamics, interspecific interactions and disturbance, patch size and isolation, and species-specific dispersal behaviour. In heterogeneous landscapes, the most obvious way in which local population dynamics influence immigration and emigration rates is through density-dependent dispersal. When an individual cannot sample and select habitats which maximizes its fitness, only emigration rates may be affected by density-dependent dispersal (Clobert *et al.* 2009). In this case, immigration is a function of the population densities in neighbouring patches within the network. In general, dispersal is positively related to density, with higher dispersal rates out of high-density patches where exploitative and interference competition is strong (Bowler & Benton 2005; Matthysen 2005). There is a reciprocal relationship between dispersal and population dynamics such that population dynamics affect dispersal which in turn influences population dynamics. Dispersal has been demonstrated to affect mean population densities, variation in densities and density dependence in local populations (Coffman, Nichols & Pollock 2001; Lecomte *et al.* 2004).

To test the hypothesis that the mechanisms regulating local population dynamics and dispersal differ depending on the nature of landscape heterogeneity, we use time series collected from metapopulations of the bruchid *Callosobruchus maculatus*. Metapopulation microcosms incorporating spatial, temporal and spatio-temporal heterogeneity, and homogeneity were constructed and replicated using a well-developed system (Bonsall, French & Hassell 2002; Bonsall & Hastings 2004; Bull *et al.* 2006; Hunt & Bonsall 2009). Time series of local population sizes and net dispersal were collected and analysed. These time series were then used to examine the relative importance of explicit descriptions of density-dependent and density-independent population dynamics, and dispersal using mathematical population models. Population models were composed of birth, death, emigration and immigration terms. The relevance of density dependence in all these terms, with the exception of immigration which was a constant based on neighbourhood densities, was examined by using a maximum likelihood approach to fit a range of density-dependent and density-independent models to experimental time series (Bonsall & Hastings 2004; Bonsall & Hassell 2005). Variation in birth, death, emigration and immigration terms comprising the population models were described using different probability distributions (Bonsall & Hastings 2004; Melbourne & Hastings 2008).