Yule (1924) observed that distributions of number of species per genus were typically long-tailed, and proposed a stochastic model to fit this data. Modern taxonomists often prefer to represent relationships between species via phylogenetic trees; the counterpart to Yule's observation is that actual reconstructed trees look surprisingly unbalanced. The imbalance can readily be seen via a scatter diagram of the sizes of clades involved in the splits of published large phylogenetic trees. Attempting stochastic modeling leads to two puzzles. First, two somewhat opposite possible biological descriptions of what dominates the macroevolutionary process (adaptive radiation; "neutral" evolution) lead to exactly the same mathematical model (Markov or Yule or coalescent). Second, neither this nor any other simple stochastic model predicts the observed pattern of imbalance. This essay represents a probabilist's musings on these puzzles, complementing the more detailed survey of biol...

Evolutionary programming typically uses tournament selection to choose parents for reproduction. Tournaments naturally emphasize survival. However, a natural opposite of survival is extinction, and a study of the fossil record shows extinction plays a key role in the evolutionary process. This paper presents a new evolutionary algorithm that emphasizes extinction to conduct search operations over a tness landscape. 1Introduction It is now well known that evolutionary programming (EP) can be an e ective search technique. Although there are several versions of EP, they are all biologically inspired and generally follow the format depicted in Figure 1. initialize

Abstract- Under a species-level abstraction of classical evolutionary programming, the standard tournament selection model is not appropriate. When viewed in this manner, it is more appropriate to consider two modes of life histories: background evolution and extinction. The utility of this approach as an optimization procedure is evaluated on a series of test functions relative to the performance of classical evolutionary programming and fast evolutionary programming. The results indicate that on some smooth, convex landscapes and over noisy, highly multimodal landscapes, extinction evolutionary programming can outperform classical and fast evolutionary programming. On other landscapes, however, extinction evolutionary programming performs considerably worse than classical and fast evolutionary programming. Potential reasons for this variability in performance are indicated. 1

this paper, it is worth mentioning that, for orders of mollusks, echinoderms, mammals, and insects (with cumulative number of genera being used as a proxy for cumulative number of tries for mollusks and echinoderms, and cumulative number of families as such a proxy for mammals and insects), the rugged fitness landscapes model also does not hold, at least as far as the assumption of a single landscape is concerned (Eble 1995a). Deformation of landscapes with environmental change is a relevant issue here. It has been said that the ad hoc invocation of landscape deformation through time would render Kauffman's arguments essentially untestable (Levinton 1995). However, Kauffman (1993) implicitly assumes that deformation, even in the face of pronounced environmental perturbation, would be minor and not affect the general structure of the landscape at the higher taxonomic levels considered here. That the generation of morphological innovations in long-jump adaptation would be achieved by early ontogeny mutants lends support to claims for a relative stability of landscapes at higher levels, since the developmentally constrained set of possible changes at deeper levels of the hierarchy would be quite Gunther J. Eble 35 independent of environmental changes. Here is the irony of the rugged fitness landscapes model: by relying on ahistorical principles to explain history, historical effects must a priori be assumed to be largely ineffective; if history could change the nature of those ahistorical principles, then there would be nothing left to test. Landscapes in the present context would change only if fundamentally different genetic and morphogenetic controls were repeatedly appearing through time. This may well be the case in view of the present results, suggesting that histo...

Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model where the diversity of species, i.e. the dimension of the equation, is a time-dependent variable. The system shows very different behavior from the original replicator equation and leads to mass extinction when the system initially has high diversity. The present theory can serve as a mathematical foundation for the paleontologic theory for mass extinction. This extinction dynamics is a prototype of dynamical systems where the variable dimension is inevitable. PACS numbers: 87.10.+e, 05.40.+j, 64.60.Lx Typeset using REVT E X 1 INTRODUCTION Mathematical biological models of evolution [1--6] have been a recent object of study in relation to complex systems [7] in which the techniques of statistical physics play a powerful role. In particular, the problem of the extinction of species in ecosystem [8] has been discussed within the framework of physic...

We give a mathematician’s view of evolutionary biology literature concerning stochastic models for phylogenetic trees. We spotlight a model for the tree on n extant species that would be observed if macroevolution were purely random. The model can be extended in two ways – to time series of observed taxa in a fossil record, and to different levels of the taxonomic hierarchy – and provides a logically consistent (“coherent”) framework for simultaneous study thereof. We illustrate with a variety of theoretical calculations and simulations, and propose a variety of real-data projects suggested by our analysis. xxx This is a draft summarizing current state of an ongoing research project, not intended for publication in this form. 1 1

Introducing the e#ect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system initially has a large number of species (diversity). The extinction dynamics shows several significant features such as a power law in basin size distribution, induction time, etc. The present theory can be a mathematical foundation of the species-area e#ect in the paleontologic theory for mass extinction. PACS numbers: 87.10.+e, 05.40.+j, 64.60.Lx Typeset using REVT E X Mechanisms of mass extinction of species in ecosystems have been studied by a number of researchers [1,2]. Their conclusions can be divided into two categories, one emphasizing exogenous shocks [3--6] and the other, endogenous causes [7--9]. Building on both views, we construct a general mathematical biological model of ecosystems. This model reflects the former view, e.g., the situation w...

Abstract. It is argued that astrobiology in general, and the search for extraterrestrial intelligence in particular, are of foremost importance for the transhumanist endeavor. It is sketched how one can show incompleteness, at best, of the arguments usually cited in support of the uniqueness of human intelligence in the Galactic context. In addition to the arguments conventionally cited in support of SETI, and which can be easily cast in the form in which their significance for the future of humanity is manifest, a specific class of phase-transition models of development of complex life and intelligence, suggests another powerful motivation: a very practical issue of strategic information in the great strife for creating values out of the Galactic material resources. 1.

Abstract: The scale of the human enterprise has increased to the point where Homo sapiens has become a global force. Global change is the result, an altering the Earth’s surface and atmosphere to a degree unknown since the great extinction episode at the KT boundary, and an unprecedented disruption because it is caused by a single species. The major impacts (I) driving this change are the three multiplicative factors of the I=PAT identity: population size (P), affluence (A-- which equals per capita consumption), and the use of environmentally inappropriate technologies (T) and socio-economic-political arrangements to service consumption. The most serious impacts are the extinctions of populations and species of nonhuman organisms, the working parts of humanity’s life-support systems. The failure of societies to come to grips with population, consumption, and power issues is itself tightly tied to the distribution of power. Ecologists must deal with these fundamental issues while they direct more of their scientific and policy research towards finding stop-gap measures to slow the decay of biodiversity. It is difficult for most people to realize just how massively and rapidly humanity has transformed its earthly home in the process of becoming the dominant animal on Earth. In 16,000 years (an

We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die, keeping the population constant. An offspring has the same genome as its (randomly chosen) parent, except for a small amount of (also random) mutations. Chance may thus generate a newborn with a genome that is better than that of its parent, and the newborn will have a smaller death probability. When this happens, this individual is a would-be founder of a new lineage. A new lineage is considered created if its alive descendence grows above a certain previously defined threshold. The time evolution of populations evolving under these rules is followed by computer simulations and the probability densities of lineage duration and size, among others, are computed. These densities show a scale-free behaviour, in accordance with some conjectures in paleoevolution, and suggesting a simple mechanism as explanation for the ubiquity of these power-laws.