How Has the State-Of-The-Art for Quantification of Landscape Pattern

Landscape Ecol (2019) 34:2065–2072 https://doi.org/10.1007/s10980-018-0709-x (0123456789().,-volV)(0123456789().,-volV) PERSPECTIVE How has the state-of-the-art for quantification of landscape pattern advanced in the twenty-first century? Eric J. Gustafson Received: 25 June 2018 / Accepted: 5 September 2018 / Published online: 14 September 2018 Ó This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018 Abstract Conclusions The patch paradigm is often of limited Context Landscape ecology was founded on the idea usefulness, and other ways to represent the pattern of that there is a reciprocal relationship between spatial landscape properties may reveal deeper insights. The pattern and ecological processes. I provide a retro- field continues to advance as illustrated by papers in spective look at how the state-of-the-art of landscape this special issue. pattern analysis has changed since 1998. Objectives My objective is to show how pattern Keywords Spatial pattern Á Metrics Á Indices Á analysis techniques have evolved and identify some of Landscape ecology Á Scale Á Spatial heterogeneity the key lessons learned. Results The state-of-the-art in 1998 was derived from information theory, fractal geometry, percolation theory, hierarchy theory and graph theory, relying Introduction heavily on the island-patch conceptual model using categorical maps, although point-data analysis meth- Landscape ecology was founded on the premise that ods were actively being explored. We have gradually there is a reciprocal relationship between spatial winnowed down the list of fundamental components pattern and ecological processes such as the spread of spatial pattern, and have clarified the appropriate of disturbance and fluxes of organisms, material and and inappropriate use of landscape metrics for energy (Turner 2005). Its focus on pattern, process, research and application. We have learned to let the change and scale sets landscape ecology apart from objectives choose the metric, guided by the scale and other branches of ecology (Turner 1989). A binary nature of the ecological process of interest. The use of conceptual model of landscape elements (patch vs. alternatives to the binary patch model (such as matrix) inspired by island biogeography dominated gradient analysis) shows great promise to advance early attempts to quantify spatial pattern. The con- landscape ecological knowledge. ceptualization of landscapes as shifting mosaics (Bormann and Likens 1979) was inspired by the change component of landscape ecology, but consis- tent methods to quantify the temporal component E. J. Gustafson (&) lagged behind methods to quantify the spatial Institute for Applied Ecosystem Studies, Northern component. Research Station, USDA Forest Service, 5985 Highway K, Rhinelander, WI, USA e-mail: [email protected] 123 2066 Landscape Ecol (2019) 34:2065–2072 In 1998, I published a widely-cited review of the • Information theory provided a framework for some state-of-the-art of quantifying landscape pattern at that of the earliest attempts to quantify the spatial time (Gustafson 1998). Attempts to quantify land- pattern of landscapes represented as a spatial grid. scape spatial pattern had just begun in the mid-1980s This approach was pioneered by a group at the Oak (Gardner et al. 1987; Krummel et al. 1987; Turner Ridge National Laboratory in Tennessee, resulting 1990), initially borrowing heavily from information in the seminal paper published by O’Neill et al. theory (O’Neill et al. 1988), but quickly developing (1988) in the first volume of the journal Landscape new approaches targeted to the unique challenges of Ecology. Their work adopted Shannon’s (Shannon large spatial grids and vector maps. By 1998 the and Weaver 1949) and Simpson’s (Simpson 1949) landscape metrics field had mushroomed, catalyzed at diversity indices to characterize landscapes, using least partially by the release of FRAGSTATS in 1995 edge counts to create the still popular contagion (McGarigal and Marks 1995), software that automated index, later improved by Li and Reynolds (1993) the computation of a large number of landscape and Riitters et al. (1996). This approach inspired metrics. Although the innovation of methods to other similarly computed metrics to capture other quantify the spatial pattern of landscapes has shifted aspects of pattern, such as the interspersion and somewhat from conceptual methods to technical juxtaposition index of McGarigal and Marks methods (e.g., remote sensing advances, development (1995), patch cohesion (Schumaker 1996) and of R packages) since the 1990s, there have neverthe- the aggregation index of He et al. (2000). less been many significant advances in both our • Percolation theory was cleverly imported from the understanding of the fundamental characteristics of physics literature by Gardner et al. (1987) as a way spatial pattern and methods to quantify those to study landscape connectivity, and it was all the characteristics. rage in the 1990s. Although percolation theory is The purpose of this essay is to provide a perspective rarely directly cited anymore [but see Albanese on the current state-of-the-art of landscape pattern and Haukos (2017)], its main tenet, that the analysis via a retrospective look at how the state-of- probability of randomly occupied cells being the-art has changed over the last 20 years. My connected completely across a spatial grid objective is not to produce a comprehensive review abruptly approaches 1.0 at a predictable fraction of the current state-of-the-art, because that has been of occupancy, is widely known and accepted as done elsewhere (e.g., Kupfer 2012; Lausch et al. 2015; conventional wisdom in landscape ecology. Per- Frazier and Kedron 2017). Instead, my objective is to colation theory also inspired the use of neutral show how we got to where we are and identify some of model landscapes (having a pattern generated by a the key lessons that we landscape ecologists have random process) for comparison with landscapes collectively learned along the way. structured by one or more known or unknown processes, to help understand how ecological Retrospective process creates pattern (O’Neill et al. 1992; With and King 1997). Bob Gardner developed software Thirty years ago, the field of landscape pattern (RULE and its successor, QRULE) to generate quantification was in its infancy. Some of the earliest such neutral models of landscape structure (Gard- conceptual developments remain widely used and ner 1999; Gardner and Urban 2007), which is still highly useful today, while others have disappeared commonly used today for a wide range of almost completely despite considerable promise. landscape studies (e.g., Kashian et al. 2017; Shirk Many of today’s recent advances had not yet been et al. 2018). Statistically robust techniques to conceived (or were effectively hidden within other detect differences in pattern metrics between two disciplines) even 20 years ago. Here is a bullet list, in landscapes (since probability distributions of met- the approximate order of their appearance in the rics cannot be estimated for individual landscapes) literature, of some of the approaches to quantify have been developed using randomization and spatial pattern in use in 1998 and their fate over the last simulation procedures (Fortin et al. 2003; Remmel 20 years. and Fortin 2013). 123 Landscape Ecol (2019) 34:2065–2072 2067 • Fractal geometry was also imported to ecology • The recognition that many statistical methods used from the physical sciences (Burrough 1981; Shel- in ecology are hampered by autocorrelated data berg et al. 1982; Loehle 1983), and it is a powerful prompted the application of alternative approaches and flexible tool to make multi-scale measure- adopted from geosciences to performing statistical ments. Krummel et al. (1987) was the first to use it tests on the autocorrelated data associated with to describe landscape spatial patterns as found in landscape structure (Legendre and Fortin 1989). digital land cover data. Milne (1988) identified five These methods can use point or mapped data to ways to conduct a fractal analysis of landscapes, generate correlograms and semivariograms to but only the perimeter-area method caught on, quantify autocorrelation within a landscape (Bur- perhaps to the detriment of the field. The perime- rough 1995). In the 1990s a great deal of research ter-area measure of fractal dimension was widely focused on refining these techniques and learning used as a metric of patch shape or pattern how to interpret their output to improve the complexity, but because shape complexity is understanding of the link between spatial pattern usually not ecologically important, fractal dimen- and ecological process (e.g., Li and Reynolds sion is rarely reported as a landscape metric these 1995). Although active research in the develop- days. One wonders what may have been learned if ment of these techniques has slowed, they still other fractal measures such as the distribution of form a critical component of the toolbox of mass on a plane [e.g., density of resources or analytical tools (e.g., Moran’s I) used by landscape individuals on a landscape, sensu Milne (1992)] or ecologists. scale-independent fractal measures of diversity • In 1997, graph theory was imported from the were easily computed by metric software in 1998. discipline of operations research and was being • Hierarchy theory was first applied in landscape explored as an alternative lattice structure to ecology as a way to help understand the develop- represent landscapes (Keitt et al. 1997), specifi- ment and organization of landscape pattern cally as a way to study landscape connectivity (O’Neill et al. 1986; Urban et al. 1987). Although (Urban and Keitt 2001). This approach was it has subsequently been applied to a wide range of gradually hailed as a promising way to tackle a landscape ecological phenomena, it remains number of conservation problems at landscape widely used as a framework for scaling and scales, and although it remains in common use understanding the relationship between spatial today, it has not become a standard approach, pattern and ecological process.

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