The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

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Statistical mechanics of complex networks

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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The Structure and Function of Complex Networks

Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

The Theory of Island Biogeography

Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.

So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

Erratum to: Biodiversity and climate determine the functioning of Neotropical forests (Global Ecology and Biogeography, (2017), 26, 12, (1423-1434), 10.1111/geb.12668)

Assessing the impacts of anthropogenic degradation and climate change on global carbon cycling is hindered by a lack of clear, flexible and easy-to-use productivity models along with scarce trait and productivity data for parameterizing and testing those models. We provide a simple solution: a mechanistic framework (RS-CFM) that combines remotely-sensed foliar-trait and canopy-structural data with trait-based metabolic theory to efficiently map productivity at large spatial scales. We test this framework by quantifying net primary productivity (NPP) at high-resolution (0.01-ha) in hyper-diverse Peruvian tropical forests (30040 hectares) along a 3322-m elevation gradient. Our analysis captures hotspots and elevational shifts in productivity more accurately and in greater detail than alternative empirical- and process-based models that use plant functional types. This result exposes how high-resolution, location-specific variation in traits and light competition drive variability in productivity, opening up possibilities to fully harness remote sensing data and reliably scale up from traits to map global productivity in a more direct, efficient and cost-effective manner. 

Improving landscape‐scale productivity estimates by integrating trait‐based models and remotely‐sensed foliar‐trait and canopy‐structural data

GEMTraits: A database and R package for accessing and analyzing plant functional traits from the Global Ecosystems Monitoring Network

D’Emic and Myhrvold raise a number of statistical and methodological issues with our recent analysis of dinosaur growth and energetics. However, their critiques and suggested improvements lack biological and statistical justification.

https://science.sciencemag.org/content/sci/348/6238/982.4.full.pdf

Response to comments on "evidence for mesothermy in dinosaurs"

A prominent signal of the Anthropocene is the extinction and population reduction of the megabiota – the largest animals and plants on the planet. However, we lack a predictive framework for the sensitivity of megabiota during times of rapid global change and how they impact the functioning of ecosystems and the biosphere. Here, we extend metabolic scaling theory and use global simulation models to demonstrate that the megabiota (i) are more prone to extinction due to human land use, hunting, and climate change; (ii) their loss has a negative impact on ecosystem metabolism and functioning; and (iii) their continued reduction will significantly decrease biosphere functioning. Analyses of several forest and animal datasets and large-scale simulation models largely support these predictions. Global simulations show that continued loss of large animals could lead to a 44%, 18% and 92% reduction in terrestrial heterotrophic biomass, metabolism, and fertility respectively. Landscapes with megabiota buffer ecosystem functioning, diversity, and likely human health. As a result, policies that emphasize the promotion of large trees and animals will have disproportionate impact on biodiversity, ecosystem processes, and climate mitigation.

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Brian J. Enquist

Papers

Erratum to: Biodiversity and climate determine the functioning of Neotropical forests (Global Ecology and Biogeography, (2017), 26, 12, (1423-1434), 10.1111/geb.12668)

Improving landscape‐scale productivity estimates by integrating trait‐based models and remotely‐sensed foliar‐trait and canopy‐structural data

GEMTraits: A database and R package for accessing and analyzing plant functional traits from the Global Ecosystems Monitoring Network

Response to comments on "evidence for mesothermy in dinosaurs"

On the importance of the megabiota to the functioning of the biosphere