NotesLength-based connectivity metrics and their ecological interpretation
Introduction
Habitat change is a key driver of biodiversity loss (Duraiappah et al., 2005) and quantifying how land use change influences habitat connectivity and fragmentation is a challenging problem in landscape ecology. A huge number of landscape metrics exist (Wu, 2013). Many of these are convenient to measure and are capable of identifying patterns in landscapes, but are unable to relate these patterns to underlying processes (Ewers and Didham, 2007, Kupfer, 2012, Moilanen and Hanski, 2001). The relationship between particular metrics and changes in a landscape has been previously addressed (Hargis et al., 1998), but a clear ecological interpretation is not available for every common metric, while the use of metrics without a clear ecological relevance can lead to meaningless results (Li and Wu, 2004, White et al., 2014). The availability of software to facilitate computing landscape metrics, such as the widely used FRAGSTATS package (McGarigal et al., 2012) has greatly empowered ecologists and geographers, but raised the possibility of inappropriate use of quantitative data, and especially of misinterpretation of the ecological significance of measurements.
One metric in particular has been misused in the ecological literature, the ‘radius of gyration’. Keitt et al. (1997) and Riitters et al. (1995) were early users in ecology of what they describe as the radius of gyration, but the equations given differ from one another and neither coincides with the definition of radius of gyration that is in use everywhere except in landscape ecology. The radius of gyration was originally a physics term, used as a measure of the distribution of mass of an object (Synge and Griffith, 1959). Keitt et al. (1997) give two ecological interpretations of the metric, but neither of them corresponds to any definition of the radius of gyration. However, if the radius of gyration is calculated correctly, it can give a meaningful measurement of an animal's dispersal within a habitat patch.
In this note, we discuss six landscape metrics with the units of length, as length metrics are suitable for calculating dispersal range (which is by definition a length). One of these is included in FRAGSTATS as the statistic GYRATE, but all are readily computable from categorical maps. We address the relations between these six distance measures and their ecological significance, and in particular the difference between GYRATE and “radius of gyration” that arises in other disciplines. We also consider a potentially ecologically relevant landscape metric that standard software is unlikely to deliver, based on the time taken for a randomly exploring animal to reach the edge of its allowed habitat, which produces a distance metric quite distinct from the others discussed here.
Section snippets
Six distance scales for discrete data
In this section we consider six landscape metrics that can be easily calculated. We show how they are derived and why they are potentially useful. Finally, we show that only two of these metrics are related, producing an ecological interpretation for the radius of gyration. Meaningful landscape metrics (e.g. to characterize habitat configuration) should be free from any dependence on choices of origin of coordinates or idiosyncrasies in definitions. It is natural, therefore, to compute metrics
Discussion
While many landscape metrics can be computed alongside the six we have considered in Section 2, it is important to ask which are likely to have greatest ecological relevance. There are reasons in the context of organism dispersion for favouring the RMS average Rg over the alternative metric R*, as we now explain.
We consider the case of organisms which move at random and independently within the habitat, but do not cross its boundaries. The dispersal distance for an organism that starts at patch
Conclusion
Naive computation of measures based simply on the geometry of habitat is unlikely to produce landscape metrics of ecological significance. However, if one calculates enough of these metrics it may be possible to observe some empirical correlations between geometric attributes of habitats and field data on the presence of species (Vos et al., 2001). A number of authors have advocated the use of metrics that reveal underlying ecosystem processes, rather than just landscape patterns (Kupfer, 2012,
Acknowledgements
We thank Dr Michael Bode, Dr Luke Kelly and Dr Michael McCarthy for helpful comments. This work was supported by the Australian Research Council (ARC) Centre of Excellence for Environmental Decisions, the National Environment Research Program (NERP) Environmental Decisions Hub and The University of Melbourne.
References (24)
Wildlife and Landscape Ecology – Effects of Pattern and Scale
(1997)- et al.
Introduction to Renormalization Group Methods in Physics
(1992) - et al.
Millennium Ecosystem Assessment, 2005. Ecosystems and Human Well-being: Biodiversity Synthesis, Millennium Ecosystem Assessment
(2005) - et al.
The effect of fragment shape and species sensitivity to habitat edges on animal population size
Conserv. Biol.
(2007) Fractals, Physics of Solids and Liquids
(1988)- et al.
The behavior of landscape metrics commonly used in the study of habitat fragmentation
Landsc. Ecol.
(1998) Random Walks and Random Environments: Volume 1: Random Walks
(1995)Random Walks and Random Environments: Volume 2: Random Environments
(1996)- et al.
Detecting critical scales in fragmented landscapes
Conserv. Ecol.
(1997) Landscape ecology and biogeography: rethinking landscape metrics in a post-FRAGSTATS landscape
Prog. Phys. Geogr.
(2012)
Use and misuse of landscape indices
Landsc. Ecol.
How long is the coast of Britain? Statistical self-similarity and fractional dimension
Science
Cited by (4)
Spatial ecology and conservation modeling: Applications with R
2019, Spatial Ecology and Conservation Modeling: Applications with R