Predicting modes of spatial change from state-and-transition models

Abstract

State-and-transition models (STMs) can represent many different types of landscape change, from simple gradient-driven transitions to complex, (pseudo-) random patterns. While previous applications of STMs have focused on individual states and transitions, this study addresses broader-scale modes of spatial change based on the entire network of states and transitions. STMs are treated as mathematical graphs, and several metrics from algebraic graph theory are applied—spectral radius, algebraic connectivity, and the S-metric. These indicate, respectively, the amplification of environmental change by state transitions, the relative rate of propagation of state changes through the landscape, and the degree of system structural constraints on the spatial propagation of state transitions. The analysis is illustrated by application to the Gualalupe/San Antonio River delta, Texas, with soil types as representations of system states. Concepts of change in deltaic environments are typically based on successional patterns in response to forcings such as sea level change or river inflows. However, results indicate more complex modes of change associated with amplification of changes in system states, relatively rapid spatial propagation of state transitions, and some structural constraints within the system. The implications are that complex, spatially variable state transitions are likely, constrained by local (within-delta) environmental gradients and initial conditions. As in most applications, the STM used in this study is a representation of observed state transitions. While the usual predictive application of STMs is identification of local state changes associated with, e.g., management strategies, the methods presented here show how STMs can be used at a broader scale to identify landscape scale modes of spatial change.