Integrating temporal variabilily into spatial analyses is one of the abiding challenges in landscape ecology. In this chapter we use landscape trajectory analysis to assess changes in landscape patterns over time. Landscape trajectory analysis is an approach to quantify changes in landscape structure over time. There are three key concepts which underlie the approach-landscape structure, structure space, and location-and there are four useful measurements for analyzing landscape trajectories displacement, velocity, acceleration, and divergence. We illustrate the approach with an analysis of American marten habitat under four timber harvest scenarios. We used the HMLands simulation model to project changes in forest composition and successional stage across a landscape in the Colorado Rockies under scenarios that varied cutting pattern (clumped or aggregated) and rotation length (200 or 300 years). Next, we used a multi-scale habitat capability model to predict American marten habitat at each time step. We then used FRAGSTATS to quantify 31 metrics describing the extent and pattern of marten habitat. We employed multi-temporal principal components analysis to describe the independent suite of major landscape structure components (i.e., the extent and pattern of marten habitat) as well as their trajectories of change under each disturbance scenario. We demonstrate that trajectory analysis in landscape structure space provides a rigorous, intuitive, and highly interpretable description of the interaction between disturbance, ecological process, spatial pattern, and temporal variation. For example, one can quantitatively understand the nature of the impact of each scenario on marten habitat by inspecting the route that each trajectory takes through landscape structure space. Threshold behavior is readily apparent as rapid changes in direction and rate of change in the landscape structure space. In addition, relative to initial conditions, the impact of each modeled disturbance scenario is readily calculated based on the degree of displacement of each scenario from the original extent and pattern of habitat. Furthermore, the relative similarity between scenarios in their impact on marten habitat is obtained by plotting and analyzing the divergence between the trajectories of the various scenarios through time.
Cushman, Samuel A.; McGarigal, Kevin. 2007. Multivariate landscape trajectory analysis: An example using simulation modeling of American marten habitat change under four timber harvest scenarios. In: Bissonette, John A.; Storch, Ilse, eds. Temporal Dimensions of Landscape Ecology Wildlife Responses to Variable Resources. Springer. p. 119-140.