Are biological networks different from other large complex networks? Both large biological and non-biological networks exhibit power-law graphs (number of nodes with degree k, N(k) ~ k-b) yet the exponents, b, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein-protein interaction networks), and is fundamentally different from the mechanisms thought to dominate the growth of most non-biological networks (such as the internet [1-4]). The preferential choice models non-biological networks like web graphs can only produce power-law graphs with exponents greater than 2 [1-4,8]. We use combinatorial probabilistic methods to examine the evolution of graphs by duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph.

Duplication Models for Biological Networks

Human–nature relations encompass many of the age-old questions about our existence, place, and time. This chapter explores some of these notions and offers insight into the question “why protect nature?”, the Gaia theory, and linkages from a historical and economical viewpoint between the Global North and the Global South. Arguments in regard to moral and utilitarian viewpoints explore nature conservation with respect to ecocentrism versus anthropocentrism. Gaian ideology is defined and used as a premise to tie sustainability and human responsibility to human–nature and human–human relations. Example research interplays between the Global North and the Global South as two subsystems of human settlement. We utilize Africa as an example of the Global South subsystem and the global economy as an indicator for differentiation. In addition, the objectives, i.e., a recap, of the book and synopsis of the individual chapters are presented.

Human-Nature Relations: The Unwanted Filibuster

We review recent work aimed at modeling species extinction over geological time. We discuss a number of models which, rather than dealing with the direct causes of particular extinction events, attempt to predict overall statistical trends, such as the relative frequencies of large and small extinctions, or the distribution of the lifetimes of species, genera or higher taxa. We also describe the available fossil and other data, and compare the trends visible in these data with the predictions of the models.

Models of Extinction: A Review

Historical and emerging practices in ecological topology

/pdf/revosim-organism-level-simulation-of-macro-and-1cjvcnj63n.pdf

REvoSim: Organism-level simulation of macro and microevolution

http://www2.imperial.ac.uk/~hjjens/ECOCOM_3_253_06.pdf

The Tangled Nature model with inheritance and constraint: Evolutionary ecology restricted by a conserved resource

We present a review of the Tangled Nature model. The model is developed to focus on the effect of evolution and multiple interactions on ecological and evolutionary observables. The model is individual based and ecological structures, such as species, are emergent quantities. The dynamics consists of a simplistic mutation-prone multiplication in which the probability of producing an offspring is determined by the occupancy in genotype space. The macroscopic long time dynamics is intermittent and exhibits a slow decrease in the macroscopic extinction rate. Ecological quantities such as the species abundance distribution and the species-area relationship compare qualitatively well with observations, as does the relation between interaction and diversity. The effect of correlations between parents and mutants has been studied, as has the effect of a conserved resource.

The Tangled Nature Model of Evolutionary Ecology: An Overview

Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential attachment is counterbalanced by preferential detachment. The mean field evolution is considered and the 1/k law is verified under certain approximations. An ansatz for the degree distribution is proposed on the basis of symmetry considerations and is shown to coincide well with the simulation data. Distributional forms other than power law are also shown to arise when the condition of perfect duplication is relaxed.

A steady state network model with a 1/k scale-free degree distribution

Correlation, selection and the evolution of species networks

We study a version of the Tangled Nature model of evolutionary ecology redefined in a phenotype space where mutants have properties correlated to their parents. The model has individual-based dynamics whilst incorporating species scale competitive constraints and a system scale resource constraint. Multiple species arise that coexist in a species interaction network with evolving global properties. Both the mean interaction strength and the network connectance increase relative to the null system as mutualism becomes more extensive. From a study of the dependence of average degree on the resource level we extract the diversity-connectance relationship which conforms to the hyperbolic form seen in field data. This is adjudged to arise as a consequence of the evolutionary pressure to achieve positive interactions. The network degree distributions conform more strongly to exponential than to the null binomial distributions in all cases. This effect is believed to be caused by correlations in the reproductive process. We also study how resource availability influences the phenotypical lifetime distribution which is approximately of power law form. We observe that the mean lifetime is inversely related to the resource level.

The Tangled nature model with inheritance and constraint: Evolutionary ecology restricted by a conserved resource

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