Application of connectivity modeling to identify and predict movement and range redistribution

@FletcherEcology

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Rob Fletcher, Maru Iezzi, and Andrew Marx

Other collaborators: Jorge Sefair, Miguel Acevedo, Divya Vasudev, Robert Holt, Emilio Bruna, Jim Austin, Sarah Duncan, Ellen Robertson, Rodolfo Jaffe, Nick Kortessis, Varun Goswami, Rob Guralnick, Denis Valle

robert.fletcher@ufl.edu

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70% of the world’s remaining forest is within 1 km of an edge

Across the planet, habitats are increasingly isolated

(Haddad et al. 2015)

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Animals are moving less frequently and over shorter distances

(Tucker et al. 2018)

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Movements of mammals in areas with a high human footprint were 1/2 to 1/3 the extent of their movements in areas with a low human footprint

Connectivity as a key limitation

Movement

Habitat / landscape

Connectivity: the degree to which landscapes alter movement (Taylor et al. 1993)

Connectivity as a key limitation and a possible solution

Why is connectivity relevant to range dynamics?

• Dispersal processes are fundamental to colonization and spread

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• We know that landscape structure is crucial to predicting colonization and dispersal (e.g., Watling et al. 2013)

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• Nearly all models incorporate dispersal but the extent to which landscapes are considered vary

Travis et al. (2013)

Models for range dynamics and the role of connectivity

• Macro-ecology increasingly links SDMs to dispersal models

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• We will focus on connectivity in this context

Briscoe et al. (2019)

Agenda for the workshop

Building and tuning different types of SAMC models

Introduction to a generalized framework with the SAMC

Emerging topics

Background and motivation

State of connectivity modeling for ecology and conservation

The state of connectivity modeling

• Connectivity concepts & applications have exploded over the past 20 years

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• The most common techniques view the problem from a network perspective

The rise of connectivity

Raster grid

Patch-based graph

• Connectivity concepts & applications have exploded over the past 20 years

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• The most common techniques view the problem from a network perspective

The rise of connectivity

Raster grid

Patch-based graph

• Site prioritization for connectivity
• Quantifying site isolation
• Identification of stepping stones
• Revealing ‘hubs’
• Determining clusters of patches

• Corridor identification
• Visualizing barriers to movement
• Quantifying effective isolation for input to patch-based graph analysis

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Types of questions and problems addressed:

• Connectivity concepts & applications have exploded over the past 20 years

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• The most common techniques view the problem from a network perspective

The rise of connectivity

Total network

Circuit theory

Patch-based graphs

Least cost

N = 375 articles

Fletcher et al. (2016)

Modeling connectivity with patch-based graphs

• Structural features + dispersal/ movement information

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• ‘Nodes’ or ‘vertices’ are patches

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• ‘Edges’ or ‘arcs’ are connections, determined by dispersal info and /or information on resistance

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• Edges are summarized as an ‘adjacency matrix’

Modeling connectivity with patch-based graphs

• Numerous metrics to describe potential connectivity:
• Patch scale centrality
• Meso-scale (e.g., clusters)
• Entire landscape

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• Can efficiently remove nodes/edges to interpret assumptions and potential habitat loss

y_ij = exp(-αd_ij)

Modeling connectivity with patch-based graphs

Two steps:

• Constructing a spatial graph
• Thresholding to create binary links
• e.g., maximum known movement distance
• Kernels to create probabilistic links
• e.g., negative exponential kernel
• Metrics for connectivity
• Metrics from graph theory
• Metrics from metapopulation theory

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Modeling connectivity with patch-based graphs

Modeling connectivity with patch-based graphs

Protected area connectivity metrics:

• Protected Connected (ProtConn; Saura et al. 2017)
• Protected Area Representativeness and Connectedness (Drielsma et al. 2007)
• Ecosystem Intactness Index (Beyer et al. 2020)

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Ward et al. (2020) Nature Comm

• Most current approaches use the concept of ‘resistance’
• A measure of the relative barrier of a location to movement
• Typically considered the inverse of permeability (or ‘conductance’)

Modeling connectivity with raster grids

• Most current approaches use the concept of ‘resistance’
• A measure of the relative barrier of a location to movement
• Typically considered the inverse of permeability (or ‘conductance’)
• With resistance, algorithms are applied to identify (potential) paths and effective isolation

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Modeling connectivity

• Most current approaches use the concept of ‘resistance’
• A measure of the relative barrier of a location to movement
• Typically considered the inverse of permeability (or ‘conductance’)
• With resistance, algorithms are applied to identify (potential) paths and effective isolation

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Modeling connectivity

Least�cost

Modeling connectivity: least-cost analysis

Resistance

map

Modeling connectivity: least-cost analysis

Resistance

map

Cumulative

cost map

Modeling connectivity: least-cost analysis

Resistance

map

Cumulative

cost map

Least-cost path

Modeling connectivity: least-cost analysis

Resistance

map

Cumulative

cost map

Least-cost path

Least-cost corridor

• Assumptions and things to consider:
• Given start/end locations it is the route with lowest cost
• Implies destination is known and species knows the best route
• To summarize path, the total cost distance is more meaningful than the length of the path
• LCP does not provide information on connectivity more broadly: only identifies a path
• Least-cost paths and corridors can always be made between locations: that does not mean that movement occurs!

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Modeling connectivity: least-cost analysis

• Circuit theory is related to a random-walk process
• Allows accounting for ‘redundancy’ in paths
• Two common metrics
• Resistance distance
• Current density

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Modeling Connectivity: circuit theory

McRae et al. (2008)

• Assumptions and things to consider:
• Given start/end locations it is the route with lowest cost
• Implies destination is known and species knows the best route
• Current flow that ‘lights up’ does not imply higher connectivity—it implies bottlenecks in connectivity
• Current flow can always be made between locations: that does not mean that movement occurs!

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Modeling connectivity: circuit theory

McRae et al. (2008)

R break

Connectivity modeling in R: connectivity_intro.R

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• Part 1: Corridor mapping
• Part 2: Patch-based graphs and site prioritization

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