variety of graphs ensue, including com- for the dynamics of the nutrient re- Press, Cambridge, Massachusetts, USA, plete graphs given by the Moran source, R, is coupled to the Eigen- 1980. process of any individual being re- Schuster Equation: [3] R. A. Fisher, The Genetical Theory of Nat- placed by any other with equal proba- n ural Selection. Oxford University Press, Ox- bility, to cyclic graphs, and to a wide x, = ~ xJ/R)qs,- 4,x, ford, UK, 1930. variety of other graphs of great aesthetic j=O [4] J. B. S. Haldane, A mathematical theory of and mathematical beauty. However, natural and artificial selection, Part I. Trans. perhaps because of the newness of this \i=0 Cambridge Philosophical Soc. 23 (1924), approach to evolutionary theory, the where /R and eR are inputs and out- 19-41. biological implications are not as de- puts, respectively, of the nutrient R [5] S. Wright, Evolution in Mendelian popula- tailed as with the chapters that build from and to the external environment. tions. Genetics 16 (1931), 97-159. on dynamical systems and game theo- The function g describes the total re- [6] J. Hofbauer and K. Sigmund, Evolutionary ries. Perhaps this chapter will stimulate lease of nutrient R from dead individ- Games and Population Dynamics. Cam- research into the application of this po- uals of xi based on mi, the mortality bridge University Press, Cambridge, UK, tentially powerful technique to partic- rate of &; ci, the concentration of nu- 1998. ular ecological and evolutionary situa- trient in the dead individuals or dead [7] J. A. Schweitzer, et al, Genetically based tions. shed parts of &; k~, the release rate of trait in a dominant tree affects ecosystem One frontier in evolutionary theory, the nutrient during decomposition; and processes. Ecol. Lett. 7 (2004), 127-134. which has barely begun to be explored, the ellipsis denotes other factors, such is its interface with ecosystems ecology. as climate, that also affect decay rate. Department of Biology Ecosystems ecologists study the biolog- This coupled system is a framework for University of Minnesota Duluth ical and physical processes that control examining how mutations qj, affect the Duluth, MN 55812 the flux of nutrients in forests, lakes, cycling of R and conversely how the USA prairies, oceans, and other ecosystems. cycling of R affects the trajectory of x e-mail: [email protected] The growth of populations is often lim- in sequence space by means of the fit- ited by the availabilities of nutrients. ness function fj(R). The entire system However, individuals also affect their is constrained by the mass balance im- availabilities through such traits as up- posed by IR and eR. One can therefore take rates and the release of nutrients also investigate how increased nutrient during the decay of leaf litter and car- The Trouble with inputs, such as the increased phos- casses when they are returned to the phorus loading of a lake that causes al- soil. It would seem logical to suppose Physics: The Rise gal blooms, affects the evolutionary dy- that the ways in which individuals af- namics of x. Depending on the forms fect resource availability, through their of String Theory, of fj(R) and g( . ) there could be uptake and through the decay of dead some interesting bifurcations in this sys- material, could be powerful selective tem. the Fall of a forces. But evolutionary biologists have Nowak's book is a readable, hand- ignored ecosystem processes because somely illustrated, and thought-provok- Science, and What the resources themselves do not evolve ing guide to modern evolutionary the- (and are therefore assumed to remain ory. Some beautiful mathematics is used Comes Next fixed), whereas ecosystem ecologists to illuminate difficult evolutionary ideas, by Lee Smolin have ignored individual variation in or- and evolutionary biology is used to mo- ganismal traits that could affect nutrient tivate the synthesis of dynamical sys- BOSTON, MASSACHUSETTS, HOUGHTON MIFFLIN, cycling, preferring to concentrate on the 2006, 456 pp, HARDCOVER US $26.00.1SBN-10: tems theory, game theory, and graph larger differences between species. But 0618551050,1SBN-13:978-O-8218-3933-1. theory. The book is suitable for gradu- the approach outlined by Nowak could 2007, PAPERBACK, US $15.95.1SBN-13EAN: ate classes in evolution, ecology, or bio- 9780618918683,1SBN-10:O65891868X be used to unify evolutionary and mathematics. In my view, it would be ecosystems theory. For example, the best used in a seminar class where stu- REVIEWED BY JOHN HARNAD chemistry of leaf litter, which often de- dents are encouraged to develop one termines decay rates and the rate of re- or more of these techniques further to lease of nutrients, is partly under ge- ,~uperstring Theory has been the shed some light on their thesis prob- netic control [7]. Different sequences, ~subject of intense study by a sub- lems. &, may therefore have different decay "f~stantial segment of the theoretical rates and influence soil nutrient avail- physics community for over two decades. ability differently. Assume also that the REFERENCES The theory's goal is extremely ambitious, fitness, fi, depends on nutrient avail- [1] G. H. Hardy, Mendelian proportions in a to say the least: nothing less than a uni- ability, perhaps by means of a mixed population. Science 28 (1908), fied quantum framework for all the fun- Michaelis-Menten or other suitable 49-50. damental interactions of matter, a "the- function. We can now propose a dy- [2] E. Mayr and W. B. Provine, editors, The ory of everything" [1, 2]. Its mathematical namical system in which an equation Evolutionary Synthesis. Harvard University intricacies, however, are barely under- THE MATHEMATICALINTELLIGENCER standable even to a majority of physi- tiques, Smolin adds some that are more Nobel prizes to eight theoretical physi- cists, and it has yet to prove itself a specific to the String Theory commu- cists, and six more to experimentalists valid physical theory. Nevertheless, in nity. This is an exceptional one, both who discovered or confirmed many of The Trouble with Physics, Lee Smolin in the incomparable ambitiousness of its observable consequences. The theory tries to give an overview, including the its scientific agenda and, according to seems at least to have no intrinsic de- background, history, motivation, and the author, its particular susceptibility to fects other than those shared by any rel- content, as well as a detailed critique, the "group thought" phenomenon. ativistic quantum field theoretic model. at a level accessible to a general read- Apart from this, many would agree that These include, of course, one un- ership. String Theory suffers from a central de- usual feature that physicists have To help understand why a physicist fect that sets it apart from nearly all learned to live with for decades; might want to address an audience that other scientific pursuits: it is unable as namely, the fact that perturbation the- cannot be expected to comprehend yet to provide anything that may be ory, based on successive approxima- such a subject's hermetic details, it subjected to the test of experimental tions, leads at first to infinite quantities should be mentioned that only about a verification, beyond what is already ad- that must be eliminated through a third of the book is concerned with equately provided by more conven- scheme of infinite renormalization be- String Theory per se. The remainder tional frameworks, such as the "Stan- fore arriving at anything that may be consists of an earnest plea for two dard Model." From the viewpoint of the compared with experiment. However, things. The first is greater attention to Scientific Method this is anathema, this is generally not seen as an essen- alternative approaches to the funda- putting the subject into a difficult posi- tial defect but rather a necessary feature mental questions of theoretical physics, tion to defend. Is it really physics, or of the perturbative approach, and the in particular the line of research con- just mathematical conjecture that is too final results do agree with experiment cerning quantum gravity that comprises incomplete to stand up as a physical to a high accuracy -- at least in the the author's own main interests; the sec- theory? All depends on promises of weak and electromagnetic case. The ond is a critique of the assumptions and things to come. fact that perturbation theory is not re- social pressures of the research com- The Standard Model has been very ally applicable to the Strong interactions munity in which he works, with sug- successful in accounting for observable is partially mitigated by the fact that cal- gestions for improvements. Nearly as phenomena involving the electromag- culations valid to all orders, using the much of this book is devoted to the so- netic and Weak nuclear forces as parts <'renormalization group" approach, ciology of science -- more specifically, of a unified theory of electroweak in- demonstrate the existence of "Asymp- the String Theory community -- as to teractions. It also includes a consistent totic Freedom"; that is, the Strong in- science itself. framework, Quantum Chromodynam- teractions become arbitrarily weak at In view of the exceptionally high ics (QCD), for the Strong nuclear sufficiently short distances. level of mathematical preparation that forces, which hold the atomic nucleus No known quantum field theoretical a genuine understanding of the subject together, although these are not yet framework exists, however, that in- would require, only a selective, non- fully understood at a sufficiently de- cludes gravitation and is consistent with technical description of the ingredients tailed level to be able to account for General Relativity. The incompatibility can be presented in such a work. To the huge quantity of strong interaction lies in the fact that when trying to treat make this at all meaningful is a very dif- data accu-mulated over decades in gravitation as a quantum field, infinities ficult task.