🌍 Markovian Network Analysis of Land-Use Dynamics : A Quantitative Framework for Landscape Transition & Attractor Identification

📌 Overview

This project introduces a novel approach to analyzing Land-Use/Land-Cover (LULC) dynamics by merging Markov Chains with Network Theory.

Beyond traditional transition matrices, this framework treats the landscape as a complex dynamic system where LULC classes are nodes and transitions are weighted directed edges. By extracting topological properties such as Eigenvector Centrality and PageRank, the model identifies ecological tipping points and anthropogenic attractors.

🎯 Key Objectives

• Stochastic Modeling: Transform multi-temporal raster data into a rigorous transition matrix.
• Flux Analysis: Isolate "active dynamics" by filtering out landscape inertia (self-transitions).
• Topological Diagnostics: Use network algorithms to quantify system resilience and irreversibility.
• Proof of Concept: Demonstrate that a single transition matrix contains massive structural information about an ecosystem's future trajectory.

🧠 Conceptual Methodology

The framework is built on a crucial mathematical distinction between Persistence and Flux:

1. Raw Network: Includes the matrix diagonal (stability). This graph reveals the "rigidity" of the system.
2. Transition Network (Filtered): By removing auto-transition loops (), the actual engine of change is revealed.
3. Network Indicators:

• In-Strength: Measures the "attractiveness" of a class (e.g., Urbanization).
• Out-Strength: Measures the "vulnerability" of a class (e.g., Deforestation).
• PageRank: Identifies the terminal "sinks" towards which the system converges.

🔍 Highlighted Findings (Case Study: 2015-2019)

Applying the model to my study zone revealed critical insights:

• The Urban Attractor: Class 50 (Urban) emerges as the system's global attractor (Max PageRank = 0.24), capturing the vast majority of outgoing flows.
• The Transition Pivot: Class 30 (Herbaceous) acts as the central corridor of change (Eigenvector Centrality = 1.0), bearing the highest pressure from all other classes.
• Forest Isolation: Forest classes (114, 126) show near-zero centrality scores (), confirming a one-way dynamic: once degraded, the return to a forest state is mathematically absent from the current network.

🛠️ Technologies & Tools

• Language: R
• Spatial Analysis: terra (SpatRaster processing)
• Network Science: igraph (Graph theory & topology)
• Data Workflow: Crosstabulation & Stochastic normalization

🚀 Perspectives & Extensions

• Multilayer Graphs: Coupling LULC dynamics with a biophysical layer to model Carbon Metabolism.
• Absorbing Markov Chains: Calculating the "Mean Time to Absorption" before a forest pixel is permanently converted to agriculture.
• Structural Robustness: Simulating "edge removal" to test the impact of conservation policies on the overall network flow.