Graph models of habitat mosaics

Abstract

Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights. Graphs are models of landscapes -that is, simplifications of a more complicated reality -and so it is appropriate to consider the application of these models in the same way we might evaluate other models used in ecology. This invites a series of very pragmatic questions: What is the underlying conceptual model of the system? How might we formalize and implement (codify) this conceptual model? How will the model be parameterized? Which parameters are most sensitive, most uncertain? What insights might be garnered from a formal analysis of the model? Can the model be extended to applications beyond those used to build it initially, and how might these extensions be validated with independent data? Importantly, can graph models provide predictions about landscapes that are not available from other models we already use?Here we review recent applications of graph theory to habitat mosaics, focusing on applications in landscape

Identifying critical regions in small-world marine metapopulations

“…Thus, it is not the lack of connections that defines nearshore metapopulation networks but the strength of the connections. This is in contrast to most studied networks (e.g., 31,32,37,41,44), which do not show such extreme connectance. Thus, caution should be applied when using network metrics that were originally designed for binary (i.e., networks where pairs of nodes are simply connected or not) and more sparse networks.…”

“…A network perspective is extremely useful for understanding metapopulation structure and dynamics (14,21,29,33,35,(41)(42)(43)(44). However, there are several caveats to its application.…”

Biodiversity, Species Interactions and Ecological Networks in a Fragmented World

“…symmetric), but they can also be unidirectional, for instance, when the connection between lakes is represented by water flow. Spatial networks can thus form a conceptual basis for adding functional interrelations to habitat connectedness and physical structure to ecosystems (Dale and Fortin, 2010;Urban et al, 2009).…”

Railways as Barriers for Wildlife: Current Knowledge

“…In such situations, a region-wide focus that includes future projections is the most suitable approach. For these purposes, graph theory is being increasingly used in conservation biology, as graph models provide simplified representations of ecological networks with flexible data requirements (Urban et al 2009). For instance, Clauzel et al (2013) (see also Chap.…”