Allometric Convergence in Savanna Trees and Implications for the Use of Plant Scaling Models in Variable Ecosystems

Theoretical models of allometric scaling provide frameworks for understanding and predicting how and why the morphology and function of organisms vary with scale. It remains unclear, however, if the predictions of ‘universal’ scaling models for vascular plants hold across diverse species in variable environments. Phenomena such as competition and disturbance may drive allometric scaling relationships away from theoretical predictions based on an optimized tree. Here, we use a hierarchical Bayesian approach to calculate tree-specific, species-specific, and ‘global’ (i.e. interspecific) scaling exponents for several allometric relationships using tree- and branch-level data harvested from three savanna sites across a rainfall gradient in Mali, West Africa. We use these exponents to provide a rigorous test of three plant scaling models (Metabolic Scaling Theory (MST), Geometric Similarity, and Stress Similarity) in savanna systems. For the allometric relationships we evaluated (diameter vs. length, aboveground mass, stem mass, and leaf mass) the empirically calculated exponents broadly overlapped among species from diverse environments, except for the scaling exponents for length, which increased with tree cover and density. When we compare empirical scaling exponents to the theoretical predictions from the three models we find MST predictions are most consistent with our observed allometries. In those situations where observations are inconsistent with MST we find that departure from theory corresponds with expected tradeoffs related to disturbance and competitive interactions. We hypothesize savanna trees have greater length-scaling exponents than predicted by MST due to an evolutionary tradeoff between fire escape and optimization of mechanical stability and internal resource transport. Future research on the drivers of systematic allometric variation could reconcile the differences between observed scaling relationships in variable ecosystems and those predicted by ideal models such as MST.     

Uncovering the design principles of circadian clocks: mathematical analysis of flexibility and evolutionary goals

In this paper, we present the mathematical details underlying both an approach to the flexibility of regulatory networks and an analytical characterization of evolutionary goals of circadian clock networks. A fundamental problem in cellular regulation is to understand the relation between the form of regulatory networks and their function. Circadian clocks present a particularly interesting instance of this. Recent work has shown that they have complex structures involving multiple interconnected feedback loops with both positive and negative feedback. We address the question of why they have such a complex structure and argue that it is to provide the flexibility necessary to simultaneously attain multiple key properties of circadian clocks such as robust entrainment and temperature compensation. To do this we address two fundamental problems: (A) to understand the relationships between the key evolutionary aims of the clock and (B) to ascertain how flexible the clock's structure is. To address the first problem we use infinitesimal response curves (IRCs), a tool that we believe will be of general utility in the analysis of regulatory networks. To understand the second problem we introduce the flexibility dimension d, show how to calculate it and then use it to analyse a range of models. We believe our results will generalize to a broad range of regulatory networks.     

A Scaling Rule for Landscape Patches and How It Applies to Conserving Soil Resources in Savannas

Scaling issues are complex, yet understanding issues such as scale dependencies in ecological patterns and processes is usually critical if we are to make sense of ecological data and if we want to predict how land management options, for example, are constrained by scale. In this article, we develop the beginnings of a way to approach the complexity of scaling issues. Our approach is rooted in scaling functions, which integrate the scale dependency of patterns and processes in landscapes with the ways that organisms scale their responses to these patterns and processes. We propose that such functions may have sufficient generality that we can develop scaling rules—statements that link scale with consequences for certain phenomena in certain systems. As an example, we propose that in savanna ecosystems, there is a consistent relationship between the size of vegetation patches in the landscape and the degree to which critical resources, such as soil nutrients or water, become concentrated in these patches. In this case, the features of the scaling functions that underlie this rule have to do with physical processes, such as surface water flow and material redistribution, and the ways that patches of plants physically “capture” such runoff and convert it into plant biomass, thereby concentrating resources and increasing patch size. To be operationally useful, such scaling rules must be expressed in ways that can generate predictions. We developed a scaling equation that can be used to evaluate the potential impacts of different disturbances on vegetation patches and on how soils and their nutrients are conserved within Australian savanna landscapes. We illustrate that for a 10-km² paddock, given an equivalent area of impact, the thinning of large tree islands potentially can cause a far greater loss of soil nitrogen (21 metric tons) than grazing out small grass clumps (2 metric tons). Although our example is hypothetical, we believe that addressing scaling problems by first conceptualizing scaling functions, then proposing scaling rules, and then deriving scaling equations is a useful approach. Scaling equations can be used in simulation models, or (as we have done) in simple hypothetical scenarios, to collapse the complexity of scaling issues into a manageable framework. Received 8 December 1998; accepted 17 August 1999.     

De Novo Evolution of Complex, Global and Hierarchical Gene Regulatory Mechanisms

Gene regulatory networks exhibit complex, hierarchical features such as global regulation and network motifs. There is much debate about whether the evolutionary origins of such features are the results of adaptation, or the by-products of non-adaptive processes of DNA replication. The lack of availability of gene regulatory networks of ancestor species on evolutionary timescales makes this a particularly difficult problem to resolve. Digital organisms, however, can be used to provide a complete evolutionary record of lineages. We use a biologically realistic evolutionary model that includes gene expression, regulation, metabolism and biosynthesis, to investigate the evolution of complex function in gene regulatory networks. We discover that: (i) network architecture and complexity evolve in response to environmental complexity, (ii) global gene regulation is selected for in complex environments, (iii) complex, inter-connected, hierarchical structures evolve in stages, with energy regulation preceding stress responses, and stress responses preceding growth rate adaptations and (iv) robustness of evolved models to mutations depends on hierarchical level: energy regulation and stress responses tend not to be robust to mutations, whereas growth rate adaptations are more robust and non-lethal when mutated. These results highlight the adaptive and incremental evolution of complex biological networks, and the value and potential of studying realistic in silico evolutionary systems as a way of understanding living systems.     

Evolutionary Tradeoffs between Economy and Effectiveness in Biological Homeostasis Systems

Biological regulatory systems face a fundamental tradeoff: they must be effective but at the same time also economical. For example, regulatory systems that are designed to repair damage must be effective in reducing damage, but economical in not making too many repair proteins because making excessive proteins carries a fitness cost to the cell, called protein burden. In order to see how biological systems compromise between the two tasks of effectiveness and economy, we applied an approach from economics and engineering called Pareto optimality. This approach allows calculating the best-compromise systems that optimally combine the two tasks. We used a simple and general model for regulation, known as integral feedback, and showed that best-compromise systems have particular combinations of biochemical parameters that control the response rate and basal level. We find that the optimal systems fall on a curve in parameter space. Due to this feature, even if one is able to measure only a small fraction of the system''s parameters, one can infer the rest. We applied this approach to estimate parameters in three biological systems: response to heat shock and response to DNA damage in bacteria, and calcium homeostasis in mammals.     

“Hypothesis for the Modern RNA World”: A <Emphasis Type="Italic">pervasive</Emphasis> Non-coding RNA-Based Genetic Regulation is a Prerequisite for the Emergence of Multicellular Complexity

The transitions to multicellularity mark the most pivotal and distinctive events in life’s history on Earth. Although several transitions to “simple” multicellularity (SM) have been recorded in both bacterial and eukaryotic clades, transitions to complex multicellularity (CM) have only happened a few times in eukaryotes. A large number of cell types (associated with large body size), increased energy consumption per gene expressed, and an increment of non-protein-coding DNA positively correlate with CM. These three factors can indeed be understood as the causes and consequences of the regulation of gene expression. Here, we discuss how a vast expansion of non-protein-coding RNA (ncRNAs) regulators rather than large numbers of novel protein regulators can easily contribute to the emergence of CM. We also propose that the evolutionary advantage of RNA-based gene regulation derives from the robustness of the RNA structure that makes it easy to combine genetic drift with functional exploration. We describe a model which aims to explain how the evolutionary dynamic of ncRNAs becomes dominated by the accessibility of advantageous mutations to innovate regulation in complex multicellular organisms. The information and models discussed here outline the hypothesis that pervasive ncRNA-based regulatory systems, only capable of being expanded and explored in higher eukaryotes, are prerequisite to complex multicellularity. Thereby, regulatory RNA molecules in Eukarya have allowed intensification of morphological complexity by stabilizing critical phenotypes and controlling developmental precision. Although the origin of RNA on early Earth is still controversial, it is becoming clear that once RNA emerged into a protocellular system, its relevance within the evolution of biological systems has been greater than we previously thought.     

Glycan Evolution in Response to Collaboration,Conflict, and Constraint

Glycans, oligo- and polysaccharides secreted or attached to proteins and lipids, cover the surfaces of all cells and have a regulatory capacity and structural diversity beyond any other class of biological molecule. Glycans may have evolved these properties because they mediate cellular interactions and often face pressure to evolve new functions rapidly. We approach this idea two ways. First, we discuss evolutionary innovation. Glycan synthesis, regulation, and mode of chemical interaction influence the spectrum of new forms presented to evolution. Second, we describe the evolutionary conflicts that arise when alleles and individuals interact. Glycan regulation and diversity are integral to these biological negotiations. Glycans are tasked with such an amazing diversity of functions that no study of cellular interaction can begin without considering them. We propose that glycans predominate the cell surface because their physical and chemical properties allow the rapid innovation required of molecules on the frontlines of evolutionary conflict.     

Comparative studies of gene expression and the evolution of gene regulation

The hypothesis that differences in gene regulation have an important role in speciation and adaptation is more than 40 years old. With the advent of new sequencing technologies, we are able to characterize and study gene expression levels and associated regulatory mechanisms in a large number of individuals and species at an unprecedented resolution and scale. We have thus gained new insights into the evolutionary pressures that shape gene expression levels and have developed an appreciation for the relative importance of evolutionary changes in different regulatory genetic and epigenetic mechanisms. The current challenge is to link gene regulatory changes to adaptive evolution of complex phenotypes. Here we mainly focus on comparative studies in primates and how they are complemented by studies in model organisms.     

The effect of stress on genome regulation and structure

BACKGROUND: Stresses exert evolutionary pressures on all organisms, which have developed sophisticated responses to cope and survive. These responses involve cellular physiology, gene regulation and genome remodelling. SCOPE: In this review, the effects of stress on genomes and the connected responses are considered. Recent developments in our understanding of epigenetic genome regulation, including the role of RNA interference (RNAi), suggest a function for this in stress initiation and response. We review our knowledge of how different stresses, tissue culture, pathogen attack, abiotic stress, and hybridization, affect genomes. Using allopolyploid hybridization as an example, we examine mechanisms that may mediate genomic responses, focusing on RNAi-mediated perturbations. CONCLUSIONS: A common response to stresses may be the relaxation of epigenetic regulation, leading to activation of suppressed sequences and secondary effects as regulatory systems attempt to re-establish genomic order.     

Allometric scaling and morphological variation in sinking rate of phytoplankton

Since the first decades of the last century, several hypotheses have been proposed on the role of phytoplankton morphology in maintaining a favorable position in the water column. Here, by an extensive review of literature on sinking rate and cell volume, we firstly attempted to explore the dependency of sinking rate on morphological traits using the allometric scaling approach. We found that sinking rate tends to increase with increasing cell volume showing the allometric scaling exponent of 0.43, which is significantly different than the Stokes’ law exponent of 0.66. The violation of the 2/3 power rule clearly indicates that cell shape changes as size increases. Both size and shape affect how phytoplankton sinking drives nutrient acquisition and losses to sinking. Interestingly, from an evolutionary perspective, simple and complex cylindrical shapes can get much larger than spherical and spheroidal shapes and sink at similar rates, but simple and complex cylindrical shapes cannot get small enough to sink slower than small spherical and spheroidal shapes. Cell shape complexity is a morphological attribute resulting from the combination of two or more simple geometric shapes. While the effect of size on sinking rate is well documented, this study deepens the knowledge on how cell shape or geometry affect sinking rates that still needs further consideration.     

Adaptive evolution in ecological communities

Understanding how natural selection drives evolution is a key challenge in evolutionary biology. Most studies of adaptation focus on how a single environmental factor, such as increased temperature, affects evolution within a single species. The biological relevance of these experiments is limited because nature is infinitely more complex. Most species are embedded within communities containing many species that interact with one another and the physical environment. To understand the evolutionary significance of such ecological complexity, experiments must test the evolutionary impact of interactions among multiple species during adaptation. Here we highlight an experiment that manipulates species composition and tracks evolutionary responses within each species, while testing for the mechanisms by which species interact and adapt to their environment. We also discuss limitations of previous studies of adaptive evolution and emphasize how an experimental evolution approach can circumvent such shortcomings. Understanding how community composition acts as a selective force will improve our ability to predict how species adapt to natural and human-induced environmental change.     

Geometry of gene expression dynamics

MOTIVATION: A gene expression trajectory moves through a high dimensional space where each axis represents the mRNA abundance of a different gene. Genome wide gene expression has a dynamic structure, especially in studies of development and temporal response. Both visualization and analyses of such data require an explicit attention to the temporal structure. RESULTS: Using three cell cycle trajectories from Saccharomyces cerevisiae to illustrate, we present several techniques which reveal the geometry of the data. We import phase-delay time plots from chaotic systems theory as a dynamic data visualization device and show how these plots capture important aspects of the trajectories. We construct an objective function to find an optimal two-dimensional projection of the cell cycle, demonstrate that the system returns to this plane after three different initial perturbations, and explore the conditions under which this geometric approach outperforms standard approaches such as singular value decomposition and Fourier analysis. Finally, we show how a geometric analysis can isolate distinct parts of the trajectories, in this case the initial perturbation versus the cell cycle. CONTACT: junhyong.kim@yale.edu