Cardille-Turner2017_Chapter_UnderstandingLandscapeMetrics

45 © Springer-Verlag New York 2017 S.E. Gergel, M.G. Turner (eds.), Learning Landscape Ecology , DOI 10.1007/978-1-4939-6374-4_4 Chapter 4 Understanding Landscape Metrics Jeffrey A. Cardille and Monica G. Turner OBJECTIVES An extensive set of landscape metrics exists to quantify spatial patterns in heteroge- neous landscapes. Developers and users of these metrics typically seek to objec- tively describe landscapes that humans assess subjectively as, for example, “clumpy,” “dispersed,” “random,” “diverse,” “fragmented,” or “connected.” Because the quan- tification of pattern is fundamental to many of the relationships we seek to under- stand in landscape ecology, a basic familiarity with the most commonly used metrics is extremely important. Several software programs evaluate maps quickly and cheaply, but there are no absolute rules governing the proper use of landscape met- rics. To help foster the appropriate use of landscape metrics, in this lab students will: 1. Become familiar with several commonly used metrics of landscape pattern; 2. Distinguish metrics that describe landscape composition from those that describe spatial configuration; 3. Understand some of the factors that influence the selection and interpretation of landscape metrics; 4. Gain experience with landscape pattern analysis using Fragstats; and 5. Observe the correlation structure among some commonly used landscape metrics. J.A. Cardille ( * ) McGill University, Sainte Anne de Bellevue, QC, Canada e-mail: jeffrey.cardille@mcgill.ca M.G. Turner University of Wisconsin-Madison, Madison, WI, USA

46 This lab explores the calculation and interpretation of metrics commonly used in landscape ecology. Emphasis is placed on the understanding gained from actually calculating select metrics by hand rather than only using a metric-calculation package. In Parts 1 and 2, you will manually calculate several landscape metrics for a small landscape to ensure that you understand their underlying mathematics. Although the landscapes used for the hand calculations are much smaller than those typically input to metric-calculation software packages, the concepts and equations learned are the same as those used for full-sized images. Once you have a basic understanding of several metrics, a section using Fragstats (Part 3), the most widely used analysis pro- gram McGarigal and Marks ( 1993 ) and larger landscape images (Part 4) will help you investigate the behavior of landscape metrics in more realistic settings. In Part 5, you explore the capabilities and limits of using landscape metrics for real-world landscape change at different time periods. Parts 1 and 2 can be completed using only pen and paper (and perhaps a calculator). Parts 3–5 require a computer with the latest version of Fragstats. All files needed to complete the lab are accessible online via links you can find on the website for this book. INTRODUCTION The quantification of landscape pattern has received considerable attention since the early 1980s, in terms of both development and application (Romme and Knight 1982 ; O’Neill et al. 1988 ; Turner et al. 1989 ; Baker and Cai 1992 ; Wickham and Norton 1994 ; Haines-Young and Chopping 1996 ; Gustafson 1998 ; Cardille and Lambois 2010 ). Along with terrestrial landscapes, metrics are also applied in aquatic systems and marine “seascapes” (e.g., Teixido et al. 2007 ; Boström et al. 2011 ). Several of the most commonly used landscape metrics were originally derived from percolation theory, fractal geometry, and information theory (the same branch of mathematics that led to the development of species diversity indices). The increased availability of spatial data, particularly over the past two decades, has also presented myriad opportunities for the development, testing, and application of landscape metrics. To a large degree, metric development has stabilized, caveats about proper use and interpretation are understood (e.g., Li and Wu 2004 ; Corry and Nassauer 2005 ; Turner 2005 ; Cushman et al. 2008 ), and newly developed methods have improved statistical interpretations of metric values (e.g., Fortin et al. 2003 ; Remmel and Csillag 2003 ). Why are methods for describing and quantifying spatial pattern such necessary tools in landscape ecology? Because landscape ecology emphasizes the interac- tions among spatial patterns and ecological processes, one needs to understand and quantify the landscape pattern in order to relate it to a process. Practical appli- cations of pattern quantification include describing how a landscape has changed through time; making future predictions regarding landscape change; determining whether patterns on two or more landscapes differ from one another, and in what ways; evaluating alternative land management strategies in terms of the landscape patterns that may result; and determining whether a particular spatial pattern is J.A. Cardille and M.G. Turner

47 conducive to movement by a particular organism, the spread of disturbance, or the redistribution of nutrients. In all of these cases, the calculation of landscape met- rics is necessary to rigorously describe landscape patterns. However, relating these metrics of pattern to dynamic ecological processes still remains an area in need of further research. In this lab, you will examine and manually calculate several commonly used landscape metrics for a small landscape to ensure that you understand their under- lying mathematics (Parts 1 and 2). Then, once you have a basic understanding of several metrics, two computer-based exercises (Parts 3 and 4) are provided to allow you to calculate metrics using Fragstats and larger landscape images. Finally (Part 5), you explore the capabilities and limits of using landscape metrics for the same real-world landscape at different time periods. During the course of the lab, you will calculate a wide range of metrics of landscape composition and configuration, including Proportion, Dominance, Shannon Evenness, Number of patches, Mean Patch Size, Edge:area ratios, Probability of adjacency, Contagion, Patch Density, Edge Density, Landscape Shape Index, Largest Patch Index, and Patch Richness. Part 1. Metrics of Landscape Composition The simplest landscape metrics focus on the composition of a landscape (e.g., which categories are present and how much of the categories there are), ignoring the spe- cific spatial arrangement of the categories on the landscape. In this section, you will examine three metrics designed to assess the composition of a landscape: (1) the proportion of the landscape occupied by each cover type, (2) Dominance, and (3) Shannon Evenness. Proportion ( p i ) of the landscape occupied by the i th cover type is the most funda- mental metric and is calculated as follows: p i i = Totalnumber of cellsof category Totalnumber of cellsin the lan dscape Proportions of different landscape types have a strong influence on other aspects of pattern, such as patch size or length of edge in the landscape (Gardner et al. 1987 ; Gustafson and Parker 1992 ), and p i values are used in the calculation of many other metrics. Several metrics derived from information theory use the p i values of all cover types to compute one value that describes an entire landscape. First developed by Shannon ( 1948 ), information theoretic metrics were first applied to landscape analyses by Romme ( 1982 ) to describe changes in the area occupied by forests of varying successional stage through time in a watershed in Yellowstone National Park, Wyoming. Romme reasoned that indices used to quantify species diversity in different communities could be modified and applied to describe the diversity of landscapes. Dominance and Shannon Evenness are two 4 Understanding Landscape Metrics

48 such metrics that characterize how evenly the proportions of cover types occur within a landscape. Dominance ( D ) (O’Neill et al. 1988 ) can be calculated as: D S p p S i i i = ( ) + ( )     ( ) ∑ ln *ln ln where S is the number of cover types, p i is the proportion of the i th cover type, and ln is the natural log function. The maximum value of this index, given S cover types, is ln( S ); dividing by the maximum value scales the index to range between 0 and 1. Values of D near 1 indicate a landscape dominated by one or few cover types, while values near 0 indicate that the proportions of each cover type are nearly equal. Shannon Evenness Index ( SHEI ) (Pielou 1975 ) can be calculated as: SHEI p p S i i i = - ( )     ( ) ∑ *ln ln where S is the number of cover types, p i is the proportion of the i th cover type, and ln is the natural log function. Values for SHEI range between 0 and 1; values near 1 indicate that the proportions of each cover type are nearly equal; values near 0 indi- cate a landscape dominated by one or few cover types. A very important detail to note in the formulations of information theoretic met- rics is whether or not a particular metric has been normalized to a standard scale. Some early applications of Dominance and Shannon Evenness were not normalized (e.g., O’Neill et al. 1988 ). The non-normalized forms of these metrics are very sen- sitive to the number of cover types S in the landscapes, and thus comparisons among landscapes that differed in S were problematic. Normalizing a metric ensures that its values fall within a standardized range, such as from 0 to 1 (and not from 0 to 157, for example!). With D and SHEI , the normalization involves dividing the numerator by the maximum possible value of the index (ln S ), as shown above. CALCULATIONS To understand these metrics and calculate them by hand within a reasonable time frame, you will calculate the metrics for two small hypothetical landscapes repre- sented as 10 × 10 grids (Figure 4.1 ). It may be useful to print paper copies of these small landscapes for your hand calculations. J.A. Cardille and M.G. Turner

49 Metrics of Landscape Composition in an Early-Settlement Landscape An invented “early-settlement” landscape is shown on the left in Figure 4.1 . This image is intended to represent an area that was previously fully forested, but has lost some forest to agricultural and urban uses. The landscape is composed of a 10 × 10 grid with each grid cell representing an area of 1 km 2 (1000 m × 1000 m; 10 6 m 2 ). Calculation 1: Calculate the proportions occupied by each of the three land covers in the early-settlement landscape. Record the values in Table 4.1 . Figure 4.1 Hypothetical early-settlement and post-settlement landscape classifications Table 4.1 Metrics of landscape composition in an early-settlement landscape Proportion occupied by: Result Forested Agricultural Urban Dominance Shannon Evenness Index 4 Understanding Landscape Metrics