Dean L. Urban

LANDSCAPE CONNECTIVITY: A GRAPH‐THEORETIC PERSPECTIVE

Ecologists are familiar with two data structures commonly used to represent landscapes. Vector-based maps delineate land cover types as polygons, while raster lattices represent the landscape as a grid. Here we adopt a third lattice data structure, the graph. A graph represents a landscape as a set of nodes (e.g., habitat patches) connected to some degree by edges that join pairs of nodes functionally (e.g., via dispersal). Graph theory is well developed in other fields, including geography (transportation networks, routing ap- plications, siting problems) and computer science (circuitry and network optimization). We present an overview of basic elements of graph theory as it might be applied to issues of connectivity in heterogeneous landscapes, focusing especially on applications of metapo- pulation theory in conservation biology. We develop a general set of analyses using a hypothetical landscape mosaic of habitat patches in a nonhabitat matrix. Our results suggest that a simple graph construct, the minimum spanning tree, can serve as a powerful guide to decisions about the relative importance of individual patches to overall landscape con- nectivity. We then apply this approach to an actual conservation scenario involving the

Graph models of habitat mosaics

Graph theory is a body of mathematics dealing with problems of connectivity, flow, and routing in networks ranging from social groups to computer networks. Recently, network applications have erupted in many fields, and graph models are now being applied in landscape ecology and conservation biology, particularly for applications couched in metapopulation theory. In these applications, graph nodes represent habitat patches or local populations and links indicate functional connections among populations (i.e. via dispersal). Graphs are models of more complicated real systems, and so it is appropriate to review these applications from the perspective of modelling in general. Here we review recent applications of network theory to habitat patches in landscape mosaics. We consider (1) the conceptual model underlying these applications; (2) formalization and implementation of the graph model; (3) model parameterization; (4) model testing, insights, and predictions available through graph analyses; and (5) potential implications for conservation biology and related applications. In general, and for a variety of ecological systems, we find the graph model a remarkably robust framework for applications concerned with habitat connectivity. We close with suggestions for further work on the parameterization and validation of graph models, and point to some promising analytic insights.

A Graph‐Theory Framework for Evaluating Landscape Connectivity and Conservation Planning

Connectivity of habitat patches is thought to be important for movement of genes, individuals, populations, and species over multiple temporal and spatial scales. We used graph theory to characterize multiple aspects of landscape connectivity in a habitat network in the North Carolina Piedmont (U.S.A). We compared this landscape with simulated networks with known topology, resistance to disturbance, and rate of movement. We introduced graph measures such as compartmentalization and clustering, which can be used to identify locations on the landscape that may be especially resilient to human development or areas that may be most suitable for conservation. Our analyses indicated that for songbirds the Piedmont habitat network was well connected. Furthermore, the habitat network had commonalities with planar networks, which exhibit slow movement, and scale-free networks, which are resistant to random disturbances. These results suggest that connectivity in the habitat network was high enough to prevent the negative consequences of isolation but not so high as to allow rapid spread of disease. Our graph-theory framework provided insight into regional and emergent global network properties in an intuitive and visual way and allowed us to make inferences about rates and paths of species movements and vulnerability to disturbance. This approach can be applied easily to assessing habitat connectivity in any fragmented or patchy landscape.

Scale and resolution of forest structural pattern

An individual tree-based forest succession model was modified to simulate a forest stand as a grid of contiguous 0.01-ha cells. We simulated a 9 ha stand for 750 years and sampled the stand at 50 yr intervals, outputting structural variables for each grid cell. Principal components analysis was used to depict temporal patterns in forest structure as observed in 0.01 ha samples (individual grid cells). We then resampled the grid using square aggregates of 4 to 100 grid cells as quadrats. Principal component scores recalculated for the aggregates, using the original (0.01 ha scale) scoring matrix, depict the effects of obervational scale on perceived patterns in forest structure. Larger quadrats reduce the apparent variation in forest structure and decrease the apparent rate of structural dynamics. Results support a scale-dependent conceptualization of forest systems by illustrating the qualitative difference in forest dynamics as viewed at the scale of individual gap elements as compared to the larger scale steady state mosaic. The aggregation exercise emphasizes the relationship between these two observational scales and serves as a general framework for understanding scaling relationships in ecological phenomena.

Spatial estimation of air temperature differences for landscape-scale studies in montane environments

Capturing fine-grain environmental patterns at landscape scales cannot be accomplished easily using conventional sampling techniques. Yet increasingly, the landscape is the scale at which ecosystems are managed. Temperature variability is an important control of many ecological processes. Elevation is often used as a proxy for temperature in montane ecosystems, partly because few direct measurements are available. We propose a low-cost and logistically practical approach to collecting spatially explicit temperature data using a network of portable temperature micro-loggers. These data can be used to generate simple, site-specific models for estimating temperature differences across complex terrain. We demonstrate the approach in a predominantly old-growth watershed in the Oregon Western Cascades. Environmental lapse rates are generated for July mean, maximum and minimum temperatures. Temperature estimates are improved substantially over these lapse rate estimates by including measures of relative radiation and relative slope position as additional explanatory variables in the model. The development of temperature estimates that explicitly account for topography has important implications for ecological analysis, which frequently relies upon the simplifying assumptions associated with lapse rates in describing the environmental template.

Spatial applications of gap models

Abstract Recent developments in individual-based forest simulators have made it possible to extend the basic approach to a wider range of forest ecosystems. One recent trend is toward more general representations of abiotic processes, and more attention to the role of tree life-history traits in generating forest response to environmental gradients. Gap models that explicitly attend spatial aspects of the light regime can be extended to simulate forest pattern at scales larger than the forest gap; examples at landscape and geographic scales are presented.

MODELING ECOLOGICAL PROCESSES ACROSS SCALES

The issue of scaling impinges on every aspect of landscape ecology and much of ecology in general. Consequently, the topic has invited a vast commentary. One result of scaling research is so-called scaling laws that describe how observations scale (e.g., as power laws). Importantly, such scaling rules seldom derive from a process-based understanding of why they emerge. Alternatively, the task of scaling is often addressed via simulation models. This is a scaling operation about which we are somewhat less confident, although recent advances in computing power and computational statistics provide for some promising new solutions. Here, I focus on methods for scaling simulations developed at fine grain and small extent, to their implications over much larger extent. The intent in scaling is to simplify the model while retaining those details essential for larger-scale applications. This approach should lead to scaling rules that are well founded in fine-scale ecological process and yet useful for making predictions at the larger scales of management and environmental policy.

Avian response to landscape pattern: The role of species' life histories

We suggest that the life histories of species within communities may differ among geographic locations and that communities from distinct biomes may respond uniquely to a given trajectory of landscape change. This paper presents initial tests relevant to these hypotheses. First, the representation of various life-history guilds in avifaunas from the Eastern Deciduous (EDF) and Pacific Northwest (PNW) forests were compared. Three guilds contained more species in the EDF community (large patch and/or habitat interior guild, small patch and/or edge guild, and fragmentation-sensitive guild). The guild of predators requiring large forest tracts was better represented in the PNW. Next, the relative sensitivity of each community to habitat change was ranked based on the life-history traits of their species. The EDF avifauna had a significantly higher index of sensitivity to both forest fragmentation and to landscape change in general. Among the birds with high scores for sensitivity to landscape change were several species that have received little conservation attention thus far including some associated with open-canopy habitats. Lastly, the validity of using life histories to predict community response to landscape change was supported by the fact that the sensitivity scores for PNW species correlated significantly with independent data on species population trends. While more rigorous analyses are suggested, we conclude that knowledge of life histories is useful for predicting community response to landscape change and that conservation strategies should be uniquely tailored to local communities.

Connectivity of forest fuels and surface fire regimes

The connectivity of a landscape can influence the dynamics of disturbances such as fire. In fire-adapted ecosystems, fire suppression may increase the connectivity of fuels and could result in qualitatively different fire patterns and behavior. We used a spatially explicit forest simulation model developed for the Sierra Nevada to investigate how the frequency of surface fires influences the connectivity of burnable area within a forest stand, and how this connectivity varies along an elevation gradient. Connectivity of burnable area was a function of fuel loads, fuel moisture, and fuel bed bulk density. Our analysis isolated the effects of fuel moisture and fuel bed bulk density to emphasize the influence of fuel loads on connectivity. Connectivity was inversely related to fire frequency and generally increased with elevation. However, certain conditions of fuel moisture and fuel bed bulk density obscured these relationships. Nonlinear patterns in connectivity across the elevation gradient occurred as a result of gradients in fuel loads and fuel bed bulk density that are simulated by the model. Changes in connectivity with elevation could affect how readily fires can spread from low elevation sites to higher elevations.

Forest gradient response in Sierran landscapes: the physical template

Vegetation pattern on landscapes is the manifestation of physical gradients, biotic response to these gradients, and disturbances. Here we focus on the physical template as it governs the distribution of mixed-conifer forests in Californias Sierra Nevada. We extended a forest simulation model to examine montane environmental gradients, emphasizing factors affecting the water balance in these summer-dry landscapes. The model simulates the soil moisture regime in terms of the interaction of water supply and demand: supply depends on precipitation and water storage, while evapotranspirational demand varies with solar radiation and temperature. The forest cover itself can affect the water balance via canopy interception and evapotranspiration. We simulated Sierran forests as slope facets, defined as gridded stands of homogeneous topographic exposure, and verified simulated gradient response against sample quadrats distributed across Sequoia National Park. We then performed a modified sensitivity analysis of abiotic factors governing the physical gradient. Importantly, the models sensitivity to temperature, precipitation, and soil depth varies considerably over the physical template, particularly relative to elevation. The physical drivers of the water balance have characteristic spatial scales that differ by orders of magnitude. Across large spatial extents, temperature and precipitation as defined by elevation primarily govern the location of the mixed conifer zone. If the analysis is constrained to elevations within the mixed-conifer zone, local topography comes into play as it influences drainage. Soil depth varies considerably at all measured scales, and is especially dominant at fine (within-stand) scales. Physical site variables can influence soil moisture deficit either by affecting water supply or water demand; these effects have qualitatively different implications for forest response. These results have clear implications about purely inferential approaches to gradient analysis, and bear strongly on our ability to use correlative approaches in assessing the potential responses of montane forests to anthropogenic climatic change.