6 Week 2 Lecture: Landscape Metrics in Landscape Ecology I

6.1 Introduction

Landscape metrics are essential tools in landscape ecology, allowing for the quantitative assessment of spatial patterns. They help us understand the composition, configuration, and connectivity of landscapes, which are useful for describing landscapes and trying to model their influence on diversity or ecological processes. Here, I will briefly introduce some general categories of landscape metrics, but nowadays there are so many they can’t possibly all be covered. You will have time to explore some others yourself in the computer lab exercise.

6.2 Summary of Spatial Scales for Calculating Landscape Metrics

Landscape metrics can be calculated at various spatial scales, each providing different ecological insights:

Patch Level: Metrics calculated for individual patches, such as patch size, edge length, and shape complexity.
Class Level: Metrics aggregated across all patches of the same type (e.g., forest or wetland patches) within a landscape, such as total class area or class connectivity.
Landscape Level: Metrics that consider the entire landscape, encompassing all patch types, such as landscape diversity or fragmentation.
Regional Level (Multiple Landscapes): Metrics calculated across multiple landscapes to assess regional-scale patterns, such as habitat connectivity for wide-ranging species.
Cross-Regional Level (Among Multiple Landscapes): Metrics comparing landscape patterns across regions to analyze broader-scale ecological or management trends.

6.3 Types of Models for Quantifying Landscape Patterns

Understanding and quantifying landscape patterns require models that simplify real-world complexity into manageable frameworks. Below is a summary of key models used to analyze landscape patterns, highlighting their strengths and common applications in landscape ecology.

6.3.1 Summary of Landscape Pattern Models

6.3.1.1 1. Point Pattern Model

Point pattern models analyze the spatial distribution of discrete points in a landscape, such as tree locations, animal sightings, or disease occurrences.

Applications:
- Studying species distribution and clustering.
- Identifying hotspots of ecological activity or disturbance.
Strengths:
- Suitable for fine-scale spatial analyses.
- Can incorporate statistical tools such as Ripley’s K function to detect clustering or dispersion.

6.3.1.2 2. Patch Mosaic Model

Patch mosaic models represent landscapes as a mosaic of discrete patches with distinct boundaries, each classified by land cover or habitat type.

Applications:
- Assessing habitat fragmentation and patch connectivity.
- Quantifying metrics like edge density or patch size.
Strengths:
- Provides intuitive visualizations of landscape structure.
- Ideal for categorical data, such as land-use maps.

6.3.1.3 3. Landscape Gradient Model

Landscape gradient models characterize landscapes as continuous surfaces, capturing gradual transitions in variables like vegetation cover, elevation, or temperature.

Applications:
- Studying ecological processes influenced by gradients (e.g., species distribution along elevation gradients).
- Modeling environmental changes, such as climate-driven shifts in vegetation zones.
Strengths:
- Avoids oversimplification inherent in categorical data.
- Captures fine-scale variability across continuous landscapes.

6.3.1.4 4. Graph Theoretic Model

Graph theoretic models conceptualize landscapes as networks of nodes (e.g., habitat patches) connected by edges (e.g., dispersal pathways).

Applications:
- Identifying critical patches or corridors for species movement.
- Evaluating connectivity in fragmented landscapes.
Strengths:
- Flexible framework for analyzing both structural and functional connectivity.
- Incorporates species-specific movement behaviors and landscape resistance.

6.4 Landscape Metrics: Definitions, Formulas, and Examples by Spatial Scale

We will cover a handful of metrics in our first introductory lecture and then you will have the opportunity to dig further into these different landscape metrics using the ‘landscapemetrics’ R package during the lab exercise.

6.4.1 1. Patch Level Metrics

Patch-level metrics provide detailed insights into the structure and function of individual patches.

6.4.1.1 a. Patch Size (PS)

Formula: $PS = a_i$ Where: - $a_i$ is the area of patch $i$ .

Ecological Relevance: Larger patches may support greater biodiversity and reduce edge effects.

6.4.1.2 b. Patch Shape Index (PSI)

Formula: $PSI = \frac{p_i}{2\sqrt{\pi a_i}}$ Where: - $p_i$ is the perimeter of patch $i$ , - $a_i$ is the area of patch $i$ .

Ecological Relevance: Quantifies patch shape complexity; higher values indicate more irregular shapes, which may increase edge effects.

6.4.1.3 c. Core Area (CA)

Formula: $CA = a_i - (e \cdot b)$ Where: - $e$ is the edge buffer width, - $b$ is the edge perimeter.

Ecological Relevance: Identifies the interior habitat, which is critical for species sensitive to edge effects.

6.4.2 2. Class Level Metrics

Class-level metrics evaluate the composition and configuration of specific patch types.

6.4.2.1 a. Class Area (CA)

Formula: $CA = \sum_{i=1}^{n} a_i$ Where: - $n$ is the total number of patches in the class, - $a_i$ is the area of patch $i$ .

Ecological Relevance: Reflects the dominance of specific habitat types, such as forest or wetlands, in the landscape.

6.4.2.2 b. Edge Density (ED)

Formula: $ED = \frac{e}{A} \times 10,000$ Where: - $e$ is the total edge length, - $A$ is the total landscape area.

Ecological Relevance: Indicates the fragmentation of specific habitat types; higher values suggest more edge effects.

6.4.3 3. Landscape Level Metrics

Landscape-level metrics provide an overview of the entire landscape’s composition and configuration.

6.4.3.1 a. Shannon Diversity Index (SHDI)

Formula: $SHDI = - \sum_{i=1}^{m} (p_i \cdot \ln p_i)$ Where: - $p_i$ is the proportion of the landscape occupied by patch type $i$ , - $m$ is the number of patch types.

Ecological Relevance: Measures landscape diversity; higher values indicate greater heterogeneity. You may recognize this diversity index from general ecology courses where it is applied to species data rather than habitat type data.

6.4.3.2 b. Contagion Index (CONTAG)

Formula: $CONTAG = 100 \cdot \left[ 1 + \sum_{i=1}^{m} \sum_{j=1}^{m} \left( \frac{p_{ij} \cdot \ln p_{ij}}{2 \cdot \ln m} \right) \right]$ Where: - $p_{ij}$ is the proportional adjacency of patch types $i$ and $j$ .

Ecological Relevance: Captures the degree of clumping of patches; higher values indicate more aggregated landscapes. See the lecture powerpoint slide for example raster landscapes with high and low contagion.

6.5 Aquatic Patch and Connectivity Metrics

Aquatic systems, including streams, rivers, and wetlands, are critical components of landscapes. The metrics used to analyze these systems are similar to terrestrial systems but are adapted to account for linear connectivity and the hierarchical nature of hydrological networks. We will explicity model some of these when we cover graph theory.

6.5.1 1. Patch-Level Metrics for Aquatic Systems

6.5.1.1 a. Stream Length (SL)

Formula: $SL = \sum_{i=1}^{n} l_i$ Where: - $l_i$ is the length of stream segment $i$ , - $n$ is the total number of stream segments.

Ecological Relevance: Longer stream lengths in a connected network support greater biodiversity and enhance ecosystem services such as nutrient cycling.

6.5.1.2 b. Stream Order (SO)

Formula: Based on the Strahler method, stream order is determined by: - A headwater stream is assigned Order 1. - When two streams of the same order merge, the downstream order increases by one.

Ecological Relevance: Higher-order streams represent greater connectivity and resource flow integration within the landscape.

6.5.2 2. Class-Level Metrics for Aquatic Systems

6.5.2.1 a. Riparian Buffer Width (RBW)

Formula: $RBW = \frac{\sum_{i=1}^{n} w_i}{n}$ Where: - $w_i$ is the width of the riparian buffer for segment $i$ , - $n$ is the total number of stream segments.

Ecological Relevance: Wider riparian buffers reduce sedimentation, enhance water quality, and support terrestrial-aquatic connectivity.

6.5.3 3. Landscape-Level Metrics for Aquatic Systems

6.5.3.1 a. Drainage Density (DD)

Formula: $DD = \frac{L}{A}$ Where: - $L$ is the total length of stream channels in the landscape, - $A$ is the total landscape area.

Ecological Relevance: High drainage density indicates efficient water transport but can also signify increased risk of erosion and nutrient export.