Brian J. Enquist

A general model for the structure and allometry of plant vascular systems

Vascular plants vary in size by about twelve orders of magnitude, and a single individual sequoia spans nearly this entire range as it grows from a seedling to a mature tree. Size influences nearly all of the structural, functional and ecological characteristics of organisms,. Here we present an integrated model for the hydrodynamics, biomechanics and branching geometry of plants, based on the application of a general theory of resource distribution through hierarchical branching networks to the case of vascular plants. The model successfully predicts a fractal-like architecture and many known scaling laws, both between and within individual plants, including allometric exponents which are simple multiples of 1/4. We show that conducting tubes must taper and, consequently, that the resistance and fluid flow per tube are independent of the total path length and plant size. This resolves the problem of resistance increasing with length, thereby allowing plants to evolve vertical architectures and explaining why the maximum height of trees is about 100 m. It also explains why the energy use of plants in ecosystems is size independent.

A general model for ontogenetic growth.

Several equations have been proposed to describe ontogenetic growth trajectories for organisms justified primarily on the goodness of fit rather than on any biological mechanism. Here, we derive a general quantitative model based on fundamental principles for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass. We thus predict the parameters governing growth curves from basic cellular properties and derive a single parameterless universal curve that describes the growth of many diverse species. The model provides the basis for deriving allometric relationships for growth rates and the timing of life history events.

Allometric Scaling of Plant Energetics and Population Density

Scaling relationships that describe variation in population density with body size in ecological communities, such as the thinning law in plant ecology, can be explained in terms of how individuals use resources as a function of their size. Data for rates of xylem transport as a function of stem diameter show that rates of resource use in individual plants scale as approximately the 3/4 power of body mass, which is the same as metabolic rates of animals. Here we use this relationship to develop a mechanistic model for relationships between density and mass in resource-limited plants. It predicts that average plant size should scale as the −4/3 power of maximum population density, in agreement with empirical evidence and comparable relationships in animals,,, but significantly less than the −3/2 power predicted by geometric models. Our model implies that fundamental constraints on metabolic rate are reflected in the scaling of population density and other ecological and evolutionary phenomena, including the finding that resource allocation among species in ecosystems is independent of body size,,.

Allometric scaling of production and life-history variation in vascular plants

A prominent feature of comparative life histories is the well documented negative correlation between growth rate and life span. Patterns of resource allocation during growth and reproduction reflect life-history differences between species. This is particularly striking in tropical forests, where tree species can differ greatly in their rates of growth and ages of maturity but still attain similar canopy sizes. Here we provide a theoretical framework for relating life-history variables to rates of production, dM/dt, where M is above-ground mass and t is time. As metabolic rate limits production as an individual grows, dM/dt ∝ M3/4. Incorporating interspecific variation in resource allocation to wood density, we derive a universal growth law that quantitatively fits data for a large sample of tropical tree species with diverse life histories. Combined with evolutionary life-history theory, the growth law also predicts several qualitative features of tree demography and reproduction. This framework also provides a general quantitative answer to why relative growth rate (1/M)(dM/df) decreases with increasing plant size (∝M-1/4) and how it varies with differing allocation strategies.

Microbes on mountainsides: Contrasting elevational patterns of bacterial and plant diversity

The study of elevational diversity gradients dates back to the foundation of biogeography. Although elevational patterns of plant and animal diversity have been studied for centuries, such patterns have not been reported for microorganisms and remain poorly understood. Here, in an effort to assess the generality of elevational diversity patterns, we examined soil bacterial and plant diversity along an elevation gradient. To gain insight into the forces that structure these patterns, we adopted a multifaceted approach to incorporate information about the structure, diversity, and spatial turnover of montane communities in a phylogenetic context. We found that observed patterns of plant and bacterial diversity were fundamentally different. While bacterial taxon richness and phylogenetic diversity decreased monotonically from the lowest to highest elevations, plants followed a unimodal pattern, with a peak in richness and phylogenetic diversity at mid-elevations. At all elevations bacterial communities had a tendency to be phylogenetically clustered, containing closely related taxa. In contrast, plant communities did not exhibit a uniform phylogenetic structure across the gradient: they became more overdispersed with increasing elevation, containing distantly related taxa. Finally, a metric of phylogenetic beta-diversity showed that bacterial lineages were not randomly distributed, but rather exhibited significant spatial structure across the gradient, whereas plant lineages did not exhibit a significant phylogenetic signal. Quantifying the influence of sample scale in intertaxonomic comparisons remains a challenge. Nevertheless, our findings suggest that the forces structuring microorganism and macroorganism communities along elevational gradients differ.

Invariant scaling relations across tree-dominated communities

Organizing principles are needed to link organismal, community and ecosystem attributes across spatial and temporal scales. Here we extend allometric theory—how attributes of organisms change with variation in their size—and test its predictions against worldwide data sets for forest communities by quantifying the relationships among tree size–frequency distributions, standing biomass, species number and number of individuals per unit area. As predicted, except for the highest latitudes, the number of individuals scales as the -2 power of basal stem diameter or as the -3/4 power of above-ground biomass. Also as predicted, this scaling relationship varies little with species diversity, total standing biomass, latitude and geographic sampling area. A simulation model in which individuals allocate biomass to leaf, stem and reproduction, and compete for space and light obtains features identical to those of a community. In tandem with allometric theory, our results indicate that many macroecological features of communities may emerge from a few allometric principles operating at the level of the individual.

Invariant scaling relationships for interspecific plant biomass production rates and body size

The allometric relationships for plant annualized biomass production (“growth”) rates, different measures of body size (dry weight and length), and photosynthetic biomass (or pigment concentration) per plant (or cell) are reported for multicellular and unicellular plants representing three algal phyla; aquatic ferns; aquatic and terrestrial herbaceous dicots; and arborescent monocots, dicots, and conifers. Annualized rates of growth G scale as the 3/4-power of body mass M over 20 orders of magnitude of M (i.e., G ∝ M3/4); plant body length L (i.e., cell length or plant height) scales, on average, as the 1/4-power of M over 22 orders of magnitude of M (i.e., L ∝ M1/4); and photosynthetic biomass Mp scales as the 3/4-power of nonphotosynthetic biomass Mn (i.e., Mp ∝ Mn3/4). Because these scaling relationships are indifferent to phylogenetic affiliation and habitat, they have far-reaching ecological and evolutionary implications (e.g., net primary productivity is predicted to be largely insensitive to community species composition or geological age).

Ecological and evolutionary determinants of a key plant functional trait: wood density and its community-wide variation across latitude and elevation

Wood density is an important trait in trees indicative of their life history and mechanical and physiological strategies. The following examines the evolutionary ecology of wood density using a large database for seed plants. In particular, we focused on the geographic and phylogenetic variation in wood density for both gymnosperms and angiosperms. A phylogenetic supertree was constructed for over 4600 taxa, allowing for comprehensive analyses of divergences across the seed plant phylogeny. Community-wide means and variances for wood densities were quantified for 171 standardized forest communities. Wood density was generally highly conserved across the entire seed plant phylogeny, yet large divergences were found within the rosid clade. Geographic and community variation in wood density, however, was significantly lower in temperate and high elevation communities, dominated by gymnosperms, than in tropical lowland communities, dominated by angiosperms, suggesting an increase in trait and, to some extent, clade filtering with latitude and elevation. Together, our results support the notion that both biotic and abiotic forces have been important in the evolution of wood density as well as in controlling the observed trait mean and variance across geographic gradients.

Scaling metabolism from organisms to ecosystems

Understanding energy and material fluxes through ecosystems is central to many questions in global change biology and ecology. Ecosystem respiration is a critical component of the carbon cycle and might be important in regulating biosphere response to global climate change. Here we derive a general model of ecosystem respiration based on the kinetics of metabolic reactions and the scaling of resource use by individual organisms. The model predicts that fluxes of CO2 and energy are invariant of ecosystem biomass, but are strongly influenced by temperature, variation in cellular metabolism and rates of supply of limiting resources (water and/or nutrients). Variation in ecosystem respiration within sites, as calculated from a network of CO2 flux towers, provides robust support for the models predictions. However, data indicate that variation in annual flux between sites is not strongly dependent on average site temperature or latitude. This presents an interesting paradox with regard to the expected temperature dependence. Nevertheless, our model provides a basis for quantitatively understanding energy and material flux between the atmosphere and biosphere.

The iPlant Collaborative: Cyberinfrastructure for Plant Biology

The iPlant Collaborative (iPlant) is a United States National Science Foundation (NSF) funded project that aims to create an innovative, comprehensive, and foundational cyberinfrastructure in support of plant biology research (PSCIC, 2006). iPlant is developing cyberinfrastructure that uniquely enables scientists throughout the diverse fields that comprise plant biology to address Grand Challenges in new ways, to stimulate and facilitate cross-disciplinary research, to promote biology and computer science research interactions, and to train the next generation of scientists on the use of cyberinfrastructure in research and education. Meeting humanitys projected demands for agricultural and forest products and the expectation that natural ecosystems be managed sustainably will require synergies from the application of information technologies. The iPlant cyberinfrastructure design is based on an unprecedented period of research community input, and leverages developments in high-performance computing, data storage, and cyberinfrastructure for the physical sciences. iPlant is an open-source project with application programming interfaces that allow the community to extend the infrastructure to meet its needs. iPlant is sponsoring community-driven workshops addressing specific scientific questions via analysis tool integration and hypothesis testing. These workshops teach researchers how to add bioinformatics tools and/or datasets into the iPlant cyberinfrastructure enabling plant scientists to perform complex analyses on large datasets without the need to master the command-line or high-performance computational services.