Jeremy W. Lichstein

SPATIAL AUTOCORRELATION AND AUTOREGRESSIVE MODELS IN ECOLOGY

Recognition and analysis of spatial autocorrelation has defined a new par- adigm in ecology. Attention to spatial pattern can lead to insights that would have been otherwise overlooked, while ignoring space may lead to false conclusions about ecological relationships. We used Gaussian spatial autoregressive models, fit with widely available software, to examine breeding habitat relationships for three common Neotropical migrant songbirds in the southern Appalachian Mountains of North Carolina and Tennessee, USA. In preliminary models that ignored space, the abundance of all three species was cor- related with both local- and landscape-scale habitat variables. These models were then modified to account for broadscale spatial trend (via trend surface analysis) and fine-scale autocorrelation (via an autoregressive spatial covariance matrix). Residuals from ordinary least squares regression models were autocorrelated, indicating that the assumption of independent errors was violated. In contrast, residuals from autoregressive models showed little spatial pattern, suggesting that these models were appropriate. The magnitude of habitat effects tended to decrease, and the relative importance of different habitat variables shifted when we incorporated broadscale and then fine-scale space into the analysis. The degree to which habitat effects changed when space was added to the models was roughly correlated with the amount of spatial structure in the habitat variables. Spatial pattern in the residuals from ordinary least squares models may result from failure to include or adequately measure autocorrelated habitat variables. In addition, con- tagious processes, such as conspecific attraction, may generate spatial patterns in species abundance that cannot be explained by habitat models. For our study species, spatial patterns in the ordinary least squares residuals suggest that a scale of 500-1000 m would be ap- propriate for investigating possible contagious processes.

Multiple regression on distance matrices: a multivariate spatial analysis tool

I explore the use of multiple regression on distance matrices (MRM), an extension of partial Mantel analysis, in spatial analysis of ecological data. MRM involves a multiple regression of a response matrix on any number of explanatory matrices, where each matrix contains distances or similarities (in terms of ecological, spatial, or other attributes) between all pair-wise combinations of n objects (sample units); tests of statistical significance are performed by permutation. The method is flexible in terms of the types of data that may be analyzed (counts, presence–absence, continuous, categorical) and the shapes of response curves. MRM offers several advantages over traditional partial Mantel analysis: (1) separating environmental distances into distinct distance matrices allows inferences to be made at the level of individual variables; (2) nonparametric or nonlinear multiple regression methods may be employed; and (3) spatial autocorrelation may be quantified and tested at different spatial scales using a series of lag matrices, each representing a geographic distance class. The MRM lag matrices model may be parameterized to yield very similar inferences regarding spatial autocorrelation as the Mantel correlogram. Unlike the correlogram, however, the lag matrices model may also include environmental distance matrices, so that spatial patterns in species abundance distances (community similarity) may be quantified while controlling for the environmental similarity between sites. Examples of spatial analyses with MRM are presented.

Tree mortality from drought, insects, and their interactions in a changing climate

Climate change is expected to drive increased tree mortality through drought, heat stress, and insect attacks, with manifold impacts on forest ecosystems. Yet, climate-induced tree mortality and biotic disturbance agents are largely absent from process-based ecosystem models. Using data sets from the western USA and associated studies, we present a framework for determining the relative contribution of drought stress, insect attack, and their interactions, which is critical for modeling mortality in future climates. We outline a simple approach that identifies the mechanisms associated with two guilds of insects - bark beetles and defoliators - which are responsible for substantial tree mortality. We then discuss cross-biome patterns of insect-driven tree mortality and draw upon available evidence contrasting the prevalence of insect outbreaks in temperate and tropical regions. We conclude with an overview of tools and promising avenues to address major challenges. Ultimately, a multitrophic approach that captures tree physiology, insect populations, and tree-insect interactions will better inform projections of forest ecosystem responses to climate change.

Global Leaf Trait Relationships: Mass, Area, and the Leaf Economics Spectrum

Getting It Wright? In 2004, a paper by Wright et al. comparing six leaf traits of over 2000 plant species showed that between-species variation among the traits was confined primarily to a single multidimensional axis, but only if traits were normalized by leaf mass. This “leaf economic spectrum” has been influential in guiding understanding of the roles of plants in global carbon cycling. Osnas et al. (p. 741, published online 28 March) now show that the principal finding of Wright et al. is primarily a mathematical consequence of the way that the data were normalized. Analysis of the same data suggests that traits are primarily proportional to leaf area, not leaf mass. Using a method to analyze relationships among traits without normalization-induced correlations revealed a multidimensional correlation between leaf traits. These relationships imply weaker effects of leaf nitrogen on rates of photosynthesis and respiration, with important implications for current models of global change. Leaf traits are distributed in proportion to area; relationships between leaf traits are independent of leaf mass and area. The leaf economics spectrum (LES) describes multivariate correlations that constrain leaf traits of plant species primarily to a single axis of variation if data are normalized by leaf mass. We show that these traits are approximately distributed proportional to leaf area instead of mass, as expected for a light- and carbon dioxide–collecting organ. Much of the structure in the mass-normalized LES results from normalizing area-proportional traits by mass. Mass normalization induces strong correlations among area-proportional traits because of large variation among species in leaf mass per area (LMA). The high LMA variance likely reflects its functional relationship with leaf life span. A LES that is independent of mass- or area-normalization and LMA reveals physiological relationships that are inconsistent with those in global vegetation models designed to address climate change.

LANDSCAPE EFFECTS ON BREEDING SONGBIRD ABUNDANCE IN MANAGED FORESTS

We examined the relationship between songbird relative abundance and local and landscape-scale habitat variables in two predominately mid- to late-successional man- aged National Forests in the southern Appalachian Mountains, USA. We used partial- regression analysis to remove correlations between habitat variables measured at different spatial scales (local habitat and square landscape regions with sides of 0.5, 1, and 2 km) and between landscape composition (proportion of different land cover types) and pattern (spatial arrangement of land cover) variables. To account for spatial autocorrelation, we used autoregressive models that incorporated information on bird abundance in the spatial neighborhood surrounding each sample point. Most species, especially Neotropical mi- grants, were significantly correlated with at least one landscape variable. These correlations included both composition and pattern variables at 0.5-2 km scales. However, landscape effects explained only a small amount of the variation in bird abundance that could not be explained by local habitat. Our results are consistent with other studies of songbird abun- dance in large managed forests that have found weak or moderate landscape effects. These studies suggest that songbird abundance in forested landscapes will primarily reflect the quantity of different habitats in the landscape rather than the spatial arrangement of those habitats. Although some studies have suggested consolidating clearcuts in large managed forests to reduce edge and landscape heterogeneity, much of the current evidence does not support this management recommendation. An important future challenge in avian con- servation is to better understand how the importance of landscape effects varies in relation to (1) the amount of suitable habitat in the landscape, and (2) land use patterns at broader spatial scales.

Predicting and understanding forest dynamics using a simple tractable model

The perfect-plasticity approximation (PPA) is an analytically tractable model of forest dynamics, defined in terms of parameters for individual trees, including allometry, growth, and mortality. We estimated these parameters for the eight most common species on each of four soil types in the US Lake states (Michigan, Wisconsin, and Minnesota) by using short-term (≤15-year) inventory data from individual trees. We implemented 100-year PPA simulations given these parameters and compared these predictions to chronosequences of stand development. Predictions for the timing and magnitude of basal area dynamics and ecological succession on each soil were accurate, and predictions for the diameter distribution of 100-year-old stands were correct in form and slope. For a given species, the PPA provides analytical metrics for early-successional performance (H20, height of a 20-year-old open-grown tree) and late-successional performance (Ẑ*, equilibrium canopy height in monoculture). These metrics predicted which species were early or late successional on each soil type. Decomposing Ẑ* showed that (i) succession is driven both by superior understory performance and superior canopy performance of late-successional species, and (ii) performance differences primarily reflect differences in mortality rather than growth. The predicted late-successional dominants matched chronosequences on xeromesic (Quercus rubra) and mesic (codominance by Acer rubrum and Acer saccharum) soil. On hydromesic and hydric soils, the literature reports that the current dominant species in old stands (Thuja occidentalis) is now failing to regenerate. Consistent with this, the PPA predicted that, on these soils, stands are now succeeding to dominance by other late-successional species (e.g., Fraxinus nigra, A. rubrum).

Crown Plasticity and Competition for Canopy Space: A New Spatially Implicit Model Parameterized for 250 North American Tree Species

Background Canopy structure, which can be defined as the sum of the sizes, shapes and relative placements of the tree crowns in a forest stand, is central to all aspects of forest ecology. But there is no accepted method for deriving canopy structure from the sizes, species and biomechanical properties of the individual trees in a stand. Any such method must capture the fact that trees are highly plastic in their growth, forming tessellating crown shapes that fill all or most of the canopy space. Methodology/Principal Findings We introduce a new, simple and rapidly-implemented model–the Ideal Tree Distribution, ITD–with tree form (height allometry and crown shape), growth plasticity, and space-filling, at its core. The ITD predicts the canopy status (in or out of canopy), crown depth, and total and exposed crown area of the trees in a stand, given their species, sizes and potential crown shapes. We use maximum likelihood methods, in conjunction with data from over 100,000 trees taken from forests across the coterminous US, to estimate ITD model parameters for 250 North American tree species. With only two free parameters per species–one aggregate parameter to describe crown shape, and one parameter to set the so-called depth bias–the model captures between-species patterns in average canopy status, crown radius, and crown depth, and within-species means of these metrics vs stem diameter. The model also predicts much of the variation in these metrics for a tree of a given species and size, resulting solely from deterministic responses to variation in stand structure. Conclusions/Significance This new model, with parameters for US tree species, opens up new possibilities for understanding and modeling forest dynamics at local and regional scales, and may provide a new way to interpret remote sensing data of forest canopies, including LIDAR and aerial photography.

Linking dispersal, immigration and scale in the neutral theory of biodiversity

In the classic spatially implicit formulation of Hubbells neutral theory of biodiversity a local community receives immigrants from a metacommunity operating on a relatively slow timescale, and dispersal into the local community is governed by an immigration parameter m. A current problem with neutral theory is that m lacks a clear biological interpretation. Here, we derive analytical expressions that relate the immigration parameter m to the geometry of the plot defining the local community and the parameters of a dispersal kernel. Our results facilitate more rigorous and extensive tests of the neutral theory: we conduct a test of neutral theory by comparing estimates of m derived from fits to empirical species abundance distributions to those derived from dispersal kernels and find acceptable correspondence; and we generate a new prediction of neutral theory by investigating how the shapes of species abundance distributions change theoretically as the spatial scale of observation changes. We also discuss how our main analytical results can be used to assess the error in the mean-field approximations associated with spatially implicit formulations of neutral theory.

Thermal acclimation of leaf respiration of tropical trees and lianas: response to experimental canopy warming, and consequences for tropical forest carbon balance

Climate warming is expected to increase respiration rates of tropical forest trees and lianas, which may negatively affect the carbon balance of tropical forests. Thermal acclimation could mitigate the expected respiration increase, but the thermal acclimation potential of tropical forests remains largely unknown. In a tropical forest in Panama, we experimentally increased nighttime temperatures of upper canopy leaves of three tree and two liana species by on average 3 °C for 1 week, and quantified temperature responses of leaf dark respiration. Respiration at 25 °C (R25 ) decreased with increasing leaf temperature, but acclimation did not result in perfect homeostasis of respiration across temperatures. In contrast, Q10 of treatment and control leaves exhibited similarly high values (range 2.5-3.0) without evidence of acclimation. The decrease in R25 was not caused by respiratory substrate depletion, as warming did not reduce leaf carbohydrate concentration. To evaluate the wider implications of our experimental results, we simulated the carbon cycle of tropical latitudes (24°S-24°N) from 2000 to 2100 using a dynamic global vegetation model (LM3VN) modified to account for acclimation. Acclimation reduced the degree to which respiration increases with climate warming in the model relative to a no-acclimation scenario, leading to 21% greater increase in net primary productivity and 18% greater increase in biomass carbon storage over the 21st century. We conclude that leaf respiration of tropical forest plants can acclimate to nighttime warming, thereby reducing the magnitude of the positive feedback between climate change and the carbon cycle.

Intraspecific Variation and Species Coexistence

We use a two‐species model of plant competition to explore the effect of intraspecific variation on community dynamics. The competitive ability (“performance”) of each individual is assigned by an independent random draw from a species‐specific probability distribution. If the density of individuals competing for open space is high (e.g., because fecundity is high), species with high maximum (or large variance in) performance are favored, while if density is low, species with high typical (e.g., mean) performance are favored. If there is an interspecific mean‐variance performance trade‐off, stable coexistence can occur across a limited range of intermediate densities, but the stabilizing effect of this trade‐off appears to be weak. In the absence of this trade‐off, one species is superior. In this case, intraspecific variation can blur interspecific differences (i.e., shift the dynamics toward what would be expected in the neutral case), but the strength of this effect diminishes as competitor density increases. If density is sufficiently high, the inferior species is driven to extinction just as rapidly as in the case where there is no overlap in performance between species. Intraspecific variation can facilitate coexistence, but this may be relatively unimportant in maintaining diversity in most real communities.