Donald R. Schoolmaster

Guidelines for a graph‐theoretic implementation of structural equation modeling

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for an updated definition of the SEM process that subsumes the historical matrix approach under a graph-theory implementation. The implementation is also designed to permit complex specifications and to be compatible with various estimation methods. Finally, they are meant to foster the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.

Mapping the niche space of soil microorganisms using taxonomy and traits

The biodiversity of microbial communities has important implications for the stability and functioning of ecosystem processes. Yet, very little is known about the environmental factors that define the microbial niche and how this influences the composition and activity of microbial communities. In this study, we derived niche parameters from physiological response curves that quantified microbial respiration for a diverse collection of soil bacteria and fungi along a soil moisture gradient. On average, soil microorganisms had relatively dry optima (0.3 MPa) and were capable of respiring under low water potentials (-2.0 MPa). Within their limits of activity, microorganisms exhibited a wide range of responses, suggesting that some taxa may be able to coexist by partitioning the moisture niche axis. For example, we identified dry-adapted generalists that tolerated a broad range of water potentials, along with wet-adapted specialists with metabolism restricted to less-negative water potentials. These contrasting ecological strategies had a phylogenetic signal at a coarse taxonomic level (phylum), suggesting that the moisture niche of soil microorganisms is highly conserved. In addition, variation in microbial responses along the moisture gradient was linked to the distribution of several functional traits. In particular, strains that were capable of producing biofilms had drier moisture optima and wider niche breadths. However, biofilm production appeared to come at a cost that was reflected in a prolonged lag time prior to exponential growth, suggesting that there is a trade-off associated with traits that allow microorganisms to contend with moisture stress. Together, we have identified functional groups of microorganisms that will help predict the structure and functioning of microbial communities under contrasting soil moisture regimes.

Mechanisms contributing to stability in ecosystem function depend on the environmental context.

Stability in ecosystem function is an important but poorly understood phenomenon. Anthropogenic perturbations alter communities, but how they change stability and the strength of stabilizing mechanisms is not clear. We examined temporal stability (invariability) in aboveground productivity in replicated 18-year time series of experimentally perturbed grassland plant communities. We found that disturbed annual-dominated communities were more stable than undisturbed perennial communities, coincident with increases in the stabilizing effect of mean-variance scaling. We also found that nitrogen-fertilized communities maintained stability despite losses in species richness, probably because of increased compensatory dynamics and increased dominance by particularly stable dominant species. Among our communities, slight variation in diversity was not the strongest mechanism driving differences in stability. Instead, our study suggests that decreases in individual species variabilities and increases in the relative abundance of stable dominant species may help maintain stability in the functioning of ecosystems confronted with eutrophication, disturbance, and other global changes.

Responses of Cambarid Crayfish to Predator Odor

The responses of individuals of four sympatric species of cambarid crayfish to the introduction of the odor of a common predator, the snapping turtle Chelydra serpentina, were recorded in the laboratory. Adult Orconectes virilis spent significantly more time in a lowered posture and reduced the frequency of nonlocomotory movements following introduction of snapping turtle odor but showed no change in behavior upon introduction of the odor of painted turtle (Chrysemys picta). Recently released young O. virilis did not respond to snapping turtle odor initially but did so after turtle odor and conspecific alarm odor had been paired. Individuals of O. propinquus did not respond to snapping turtle odor. Initial tests with O. rusticus did not yield any response to snapping turtle odor but after experience with paired turtle and alarm odor, individuals showed a decrease in nonlocomotory movements when just snapping turtle odor was introduced. Individuals of Cambarus robustus spent less time in the lowered posture, less time in their burrow, and more frequently executed nonlocomotory movements, in response to snapping turtle odor. The differences in responses to the odor of a common predator are correlated with ecological differences among the crayfish species.

Plants Mediate the Sensitivity of Soil Respiration to Rainfall Variability

Soil respiration from grasslands plays a critical role in determining carbon dioxide (CO2) feedbacks between soils and the atmosphere. In these often mesic systems, soil moisture and temperature tend to co-regulate soil respiration. Increasing variance of rainfall patterns may alter aboveground–belowground interactions and have important implications for the sensitivity of soil respiration to fluctuations in moisture and temperature. We conducted a set of field experiments to evaluate the independent and interactive effects of rainfall variability and plant–soil processes on respiration dynamics. Plant removal had strong effects on grassland soils, which included altered CO2 flux owing to absence of root respiration; increased soil moisture and temperature; and reduced availability of dissolved organic carbon (DOC) for heterotrophic respiration by microorganisms. These plant-mediated effects interacted with our rainfall variability treatments to determine the sensitivity of soil respiration to both moisture and temperature. Using time-series multiple regression, we found that plants dampened the sensitivity of respiration to moisture under high variability rainfall treatments, which may reflect the relative stability of root contributions to total soil respiration. In contrast, plants increased the sensitivity of respiration to temperature under low variability rainfall treatment suggesting that the environmental controls on soil CO2 dynamics in mesic habitats may be context dependent. Our results provide insight into the aboveground–belowground mechanisms controlling respiration in grasslands under variable rainfall regimes, which may be important for predicting CO2 dynamics under current and future climate scenarios.

Invasibility in a spatiotemporally fluctuating environment is determined by the periodicity of fluctuations and resident turnover rates.

The ability of a species to invade a community is influenced by the traits of the invader, the resident community and the environment. However, qualitative generalizations are possible. Using a model of perennial plants in a spatiotemporally fluctuating environment, we find that fluctuating environments may be more or less invasible than static environments. Invasibility is strongly dependent on the interaction of the difference in turnover rates of resident and invader populations and the rate of temporal change of the environment. If resident population turnover is faster than the invaders, then invasibility is an initially positive, decreasing function of the period temporal variation, such that invasibility is increased by rapid temporal fluctuations but slightly reduced in slowly fluctuating environments. If resident turnover is slower than the invaders, then invasibility is an initially negative, increasing function of temporal period, such that invasibility is reduced in rapidly changing environment facilitated by slow temporal fluctuations. These results are explained by the relative abilities of resident and invader populations to successfully respond to environmental variation at different temporal scales.

Causal mechanisms of soil organic matter decomposition: Deconstructing salinity and flooding impacts in coastal wetlands

Coastal wetlands significantly contribute to global carbon storage potential. Sea-level rise and other climate-change-induced disturbances threaten coastal wetland sustainability and carbon storage capacity. It is critical that we understand the mechanisms controlling wetland carbon loss so that we can predict and manage these resources in anticipation of climate change. However, our current understanding of the mechanisms that control soil organic matter decomposition, in particular the impacts of elevated salinity, are limited, and literature reports are contradictory. In an attempt to improve our understanding of these complex processes, we measured root and rhizome decomposition and developed a causal model to identify and quantify the mechanisms that influence soil organic matter decomposition in coastal wetlands that are impacted by sea-level rise. We identified three causal pathways: (1) a direct pathway representing the effects of flooding on soil moisture, (2) a direct pathway representing the effects of salinity on decomposer microbial communities and soil biogeochemistry, and (3) an indirect pathway representing the effects of salinity on litter quality through changes in plant community composition over time. We used this model to test the effects of alternate scenarios on the response of tidal freshwater forested wetlands and oligohaline marshes to short- and long-term climate-induced disturbances of flooding and salinity. In tidal freshwater forested wetlands, the model predicted less decomposition in response to drought, hurricane salinity pulsing, and long-term sea-level rise. In contrast, in the oligohaline marsh, the model predicted no change in response to drought and sea-level rise, and increased decomposition following a hurricane salinity pulse. Our results show that it is critical to consider the temporal scale of disturbance and the magnitude of exposure when assessing the effects of salinity intrusion on carbon mineralization in coastal wetlands. Here, we identify three causal mechanisms that can reconcile disparities between long-term and short-term salinity impacts on organic matter decomposition.

Barrier Displacement on a Neutral Landscape: Toward a Theory of Continental Biogeography

&NA; Macroevolutionary theory posits three processes leading to lineage diversification and the formation of regional biotas: dispersal (species geographic range expansion), speciation (species lineage splitting), and extinction (species lineage termination). The Theory of Island Biogeography (TIB) predicts species richness values using just two of these processes; dispersal and extinction. Yet most species on Earth live on continents or continental shelves, and the dynamics of evolutionary diversification at regional and continental scales are qualitatively different from those that govern the formation of species richness on biogeographic islands. Certain geomorphological processes operating perennially on continental platforms displace barriers to gene flow and organismal dispersal, and affect all three terms of macroevolutionary diversification. For example, uplift of a dissected landscape and river capture both merge and separate portions of adjacent areas, allowing dispersal and larger geographic ranges, vicariant speciation and smaller geographic ranges, and extinction when range sizes are subdivided below a minimum persistence threshold. The TIB also does not predict many biogeographic and phylogenetic patterns widely observed in continentally distributed taxa, including: (i) power function‐like species‐area relationships; (ii) log‐normal distribution of species geographic range sizes, in which most species have restricted ranges (are endemic) and few species have broad ranges (are cosmopolitan); (iii) mid‐domain effects with more species toward the geographic center, and more early‐branching, species‐poor clades toward the geographic periphery; (iv) exponential rates of net diversification with log‐linear accumulation of lineages through geological time; and (v) power function‐like relationships between species‐richness and clade diversity, in which most clades are species‐poor and few clades are species‐rich. Current theory does not provide a robust mechanistic framework to connect these seemingly disparate patterns. Here we present SEAMLESS (Spatially Explicit Area Model of Landscape Evolution by SimulationS) that generates clade diversification by moving geographic barriers on a continuous, neutral landscape. SEAMLESS is a neutral Landscape Evolution Model (LEM) that treats species and barriers as functionally equivalent with respect to model parameters. SEAMLESS differs from other model‐based biogeographic methods (e.g., Lagrange, GeoSSE, BayArea, and BioGeoBEARS) by modeling properties of dispersal barriers rather than areas, and by modeling the evolution of species lineages on a continuous landscape, rather than the evolution of geographic ranges along branches of a phylogeny. SEAMLESS shows how dispersal is required to maintain species richness and avoid clade‐wide extinction, demonstrates that ancestral range size does not predict species richness, and provides a unified explanation for the suite of commonly observed biogeographic and phylogenetic patterns listed above. SEAMLESS explains how a simple barrier‐displacement mechanism affects lineage diversification under neutral conditions, and is advanced here toward the formulation of a general theory of continental biogeography.

Do the rich get richer? Varying effects of tree species identity and diversity on the richness of understory taxa

Understory herbs and soil invertebrates play key roles in soil formation and nutrient cycling in forests. Studies suggest that diversity in the canopy and in the understory are positively associated, but these studies often confound the effects of tree species diversity with those of tree species identity and abiotic conditions. We combined extensive field sampling with structural equation modeling to evaluate the simultaneous effects of tree diversity on the species diversity of understory herbs, beetles, and earthworms. The diversity of earthworms and saproxylic beetles was directly and positively associated with tree diversity, presumably because species of both these taxa specialize on certain species of trees. Tree identity also strongly affected diversity in the understory, especially for herbs, likely as a result of interspecific differences in canopy light transmittance or litter decomposition rates. Our results suggest that changes in forest management will disproportionately affect certain understory taxa. For instance, changes in canopy diversity will affect the diversity of earthworms and saproxylic beetles more than changes in tree species composition, whereas the converse would be expected for understory herbs and detritivorous beetles. We conclude that the effects of tree diversity on understory taxa can vary from positive to negative and may affect biogeochemical cycling in temperate forests. Thus, maintaining high diversity in temperate forests can promote the diversity of multiple taxa in the understory.

Resource competition and coexistence in heterogeneous metacommunities: many-species coexistence is unlikely to be facilitated by spatial variation in resources.

There is little debate about the potential of environmental heterogeneity to facilitate species diversity. However, attempts to show the relationship between spatial heterogeneity and diversity empirically have given mixed results. One reason for this may be the failure to consider how species respond to the factor in the environment that varies. Most models of the heterogeneity-diversity relationship assume heterogeneity in non-resource environmental factors. These models show the potential for spatial heterogeneity to promote many-species coexistence via mainly the spatial storage effect. Here, I present a model of species competition under spatial heterogeneity and resource factors. This model allows for the stable coexistence of only two species. Partitioning the model to quantify the contributions of variation-dependent coexistence mechanisms shows contributions from only one mechanism, growth-density covariance. More notably, it shows the lack of potential for any contribution from the spatial storage effect, the only mechanism that can facilitate stable many-species coexistence. This happens because the spatial storage effect measures the contribution of different species to specializing on different parts of the gradient of the heterogeneous factor. Under simple models of resource competition, in which all species grow best at high resource levels, such specialization is impossible. This analysis suggests that, in the absence of additional mechanisms, spatial heterogeneity in a single resource is unlikely to facilitate many-species coexistence and, more generally, that when evaluating the relationship between heterogeneity and diversity, a distinction should be made between resource and non-resource factors.