9 Week 3 Lecture: Landscape Metrics II, Connectivity and Networks

9.1 Introduction

This week we will expand our patch mosaic framework to include connectivity and the consideration of corridors connecting patches. Landscape connectivity is a central concept of landscape ecology, describing the degree to which the landscape facilitates or slows movement of organisms as well as energy and nutrients.

9.2 Connectivity Metrics and Corridors in Patch Mosaic Models

9.2.1 Landscape Connectivity: Definitions and Importance

  • Structural Connectivity: Refers to the physical arrangement of habitat patches in the landscape, but INDEPENDENT of what your organisms are doing like how well they can disperse. Only looks at structure…i.e., geometry, distance, and spatial organization of your landscape.
  • Functional Connectivity: Considers the response of organisms to landscape structures. Here you care about the function of your organisms such as their behavior, dispersal ability and tendencies, and their interaction with the landscape. The same structurally connected network can be functionally quite different depending on your taxa. E.g., fish that can swim upstream versus some stream inverts that have unidirectional dispersal downstream.

9.2.1.1 Key Concepts in Structural Connectivity

  1. Proximity: Measures how close habitat patches are to one another. Proximity affects the likelihood of species dispersal between patches and is often represented using Euclidean distances or other metrics.
    • Example: In a forested landscape, patches of trees that are closer together may be easier for birds to travel between, enhancing connectivity.
  2. Edge and Perimeter: Structural connectivity considers the role of patch edges and their lengths. Linear features such as hedgerows or riparian buffers can act as connections or barriers.
    • Example: A hedgerow between agricultural fields may serve as a movement corridor for small mammals or insects.
  3. Spatial Arrangement of Patches: The layout of patches—whether clustered, evenly distributed, or randomly placed—has significant implications for structural connectivity.
    • A clustered configuration may facilitate movement within localized areas but impede connectivity at larger scales.
    • Conversely, evenly distributed patches can provide broader-scale connectivity.
  4. Corridors: Structural connectivity relies on the presence and quality of physical corridors that directly connect habitat patches. Corridors are often classified into:
    • Natural corridors: Such as streams or ridgelines.
    • Man-made corridors: Such as greenways or wildlife crossings like the one we showed previously for ocelets.
    • These corridors mitigate the effects of fragmentation by providing pathways that organisms can use to traverse non-habitat areas.
  5. Matrix Quality: The surrounding landscape matrix—the non-habitat area between patches—plays a role in structural connectivity. While structural connectivity primarily examines the spatial aspects, the matrix can influence whether physical connectivity is functional.
    • Example: A matrix of grasslands between forest patches may allow for easier movement compared to an urban or industrial area.

9.2.2 Key Concepts in Functional Connectivity

  1. Organism dispersal ability: Functional connectivity is species-specific, as different organisms perceive and interact with the landscape in different ways based on their movement abilities, behaviors, and habitat requirements.
    • Example: A bird may easily fly over a fragmented landscape, while a terrestrial mammal may require continuous corridors or stepping-stone habitats.
  2. Behavioral: Functional connectivity accounts for how organisms perceive and respond to landscape elements, such as avoiding areas with high resistance (e.g., urban environments) or actively seeking corridors that are permeable (e.g., riparian zones).
    • Examples: Amphibians might preferentially move through wetland habitats, even if structurally they are distant from one another. Or, a small mammal may not move through open field and risk predation from birds even though it is not physically limited.
  3. Corridors and Stepping Stones: These landscape elements are critical for functional connectivity as they provide pathways or intermediate habitats that facilitate movement.
    • Corridors: Continuous habitat strips connecting larger patches.
    • Stepping Stones: Small, isolated patches that provide intermediate points for movement across large distances.
  4. Temporal Dynamics: Functional connectivity can change over time due to seasonal behaviors (e.g., birds migrating), life stages (e.g., juvenile dispersal), or human-induced changes like urbanization or climate change.

9.2.2.1 Common Metrics for Functional Connectivity

The following metrics are frequently used to assess functional connectivity:

Metric Definition
Cost-Weighted Distance The cumulative “cost” for an organism to travel across a landscape based on resistance values.
Effective Resistance A measure from circuit theory that quantifies the ease of movement across multiple pathways.
Least-Cost Path The single, optimal pathway for movement between two patches, minimizing resistance.
Connectivity Probability The probability that an organism successfully moves between patches, incorporating movement behavior and resistance.

9.2.2.2 Tools for Analyzing Functional Connectivity

  1. Least-Cost Path Analysis:
    • Uses resistance surfaces to calculate the easiest route between two patches.
    • Example: Identifying migration pathways for large mammals like elk through fragmented landscapes.
  2. Circuit Theory Models:
    • Treat the landscape as a conductive surface and model movement as electrical flow, emphasizing multiple pathways rather than a single optimal route.
    • Example: Modeling gene flow in species with diffusive movement, such as insects.
  3. Individual-Based Models (IBMs):
    • Simulate the movement of individuals through the landscape based on their specific behaviors and habitat preferences.
    • Example: Assessing how wolves navigate human-dominated landscapes using a detailed IBM.

9.3 Landscapes as Networks: A Theoretical Framework

A network-theoretic approach treats landscapes as systems of interconnected nodes (patches) and edges/links (connections), providing a robust framework for examining landscape connectivity and resilience. May be more appropriate when the connectivity pattern itself is your study focus, and when you want to identify how important patches and corridors are to the overall connectivity of your network. This framework can be quite useful if you want to identify patches to prioritize for conservation or where a corridor should be created. It may also be necessary in practice to simplify a landscape for computational purposes if it large and complex. While patch mosaic models emphasize spatial heterogeneity, the network/graph theoretic approach prioritizes relationships among patches with space represented less explicitly.

9.3.1 Components of Network Theory in Landscape Ecology

  1. Nodes:
    • Represent habitat patches or other landscape features.
    • Can include weighted attributes, such as patch quality, environmental characteristics, or area.
    • Mathematically you are collapsing the patch to a point…but that point can have lots of attributes.
  2. Edges:
    • Represent corridors or other connections between nodes.
    • May incorporate resistance or cost to travel trhough
  3. Graph Types:
    • Directed vs. undirected graphs. E.g., a stream has a direction to the edges, although the impact may vary functionally.
    • Weighted vs. unweighted graphs. E.g., different stream reaches may have different flow rates.

9.3.2 Key Metrics in Network Theory

As with our patch mosaic landscape metrics, there are countless ways that people have extracted information out of graph networks. We will spend a bit more time going over and calculating these in this Thursday’s lab since these are less intuitive than many of our patch mosaic metrics. In particular, importance of edges and nodes can be defined in numerous ways in terms of how their presence/absence influences connectivity structure.

Metric Definition “Formula”
Degree (k) Number of edges connected to a node. k = sum of edges for a node
Clustering Coefficient Measures how nodes form clusters. Degree of clustering, like social “cliques”
Betweenness Centrality Importance of a node in connecting other nodes. Sum of shortest paths going through a node
Edge Importance Importance of an edge for maintaining network connectivity. Change in network connectivity when the edge is removed.
Modularity Measures the division of a network into distinct communities or clusters. Computed using modularity algorithms, such as Newman-Girvan modularity. I.e., can you identify subnetworks?