567so that only a single channel is conducting(12, 13), the researchers can detect smallchanges in the electrostatic environment.Hence, when an antiparallel spin-qubit pairtunnels into the right dot, the quantum wirecan detect its presence there. The remarkable recent experimentalrealizations involving the control, manipu-lation, and detection of spins in quantumdots (14–18) are breathtaking; they defi-nitely pave the way to an actual implemen-tation of the spin-parity meter of Loss andEngel. A successful realization of spin-based quantum computing depends on adetailed experimental investigation of thedecoherence of the spin qubits (that is, theloss of their quantum mechanical integritydue to interactions with the environment).With a spin-parity meter in hand (togetherwith spin-qubit rotations, perhaps viapulsed magnetic fields) and with decoher-ence under control, spin-based quantumcomputation may be closer at hand.References and Notes1. H.A. Engel, D. Loss,Science309, 586 (2005).2. C. W. J. Beenakker et al.,Phys. Rev. Lett.93, 020501(2004).3. M.A. Nielsen, I. L. Chuang,Quantum Computation andQuantum Information(Cambridge Univ. Press, NewYork, 2000).4. E. Knill et al.,Nature409, 46 (2001).5. D. Loss, D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).6. D.D.Awschalom,D.Loss,N. Samarth,Eds.,SemiconductorSpintronics and Quantum Computation(Springer, Berlin,2002).7. J. M. Kikkawa, D.D.Awschalom,Nature397, 139 (1999).8. R. Fiederling et al.,Nature402, 787 (1999).9. Y. Ohno et al.,Nature402, 790 (1999).10. For quantum spin filtering with spin-dependent “mag-netic” barriers, see J. C. Egues,Phys. Rev. Lett.80, 4578(1998).11. B. M. Terhal, D. P. DiVincenzo,Phys. Rev. A65, 032325(2002).12. M. Field et al.,Phys. Rev. Lett. 70, 1311 (1993).13. J. M. Elzerman et al.,Phys. Rev. B67, R161308 (2003).14. J. A. Folk, R. M.Potok, C. M. Marcus,V. Umansky,Science299, 679 (2003).15. T. Hayashi et al.,Phys. Rev. Lett. 91, 226804 (2003).16. J. M. Elzerman et al.,Nature430, 431 (2004).17. M. Kroutvar et al.,Nature432, 81 (2004).18. For a review of spin-based quantum computing and adetailed account of recent experimental accomplish-ments on charge and spin control in dots, see V.Cerletti, W. A. Coish, O. Gywat, D. Loss,Nanotechnology16, R27 (2005).10.1126/science.1115256We have all heard about the hypo-thetical pair of houseflies thatcould cover the Earth with theiroffspring in a matter of months if all oftheir descendants survived to reproduce.This hasn’t happened yet because as popu-lations grow, their numbers become lim-ited by a lack of resources or by increasesin predators and parasites. But how quicklydo such limiting factors come into play andhow do they affect dynamics of differentspecies? Ecologists have been obsessedwith these questions and cracking theunderlying mechanisms that explain thembecause the answers go to the heart ofunderstanding ecology. On page 607 of thisissue, Sibly et al. (1) undertake the mostambitious analyses yet of this problem byexamining growth rates of 1780 popula-tions of birds, mammals, bony fishes, andinsects. They uncover some interesting pat-terns, which could contribute fundamen-tally to our understanding of populationdynamics. The data analyzed by Sibly et al. (1)were derived from the Global PopulationDynamics Database (2), which containsnearly 5000 time series of population esti-mates for a wide variety of plant and animalspecies. This is an important repository fordata that often remain concealed in obscurejournals and reports but, if carefullyscreened, can support powerful statisticalanalyses to search for broad patterns. Afterexcluding data that covered short time peri-ods or were unsuitable in other ways, theauthors were left with 1780 time series for674 species. It may seem straightforward to simplyplot population growth rates against popu-lation size and then assess the relationshipby asking whether the shape of the curve isconcave, linear, or convex (see the figure).But a large amount of statistical gymnas-tics is required to fit an appropriate mathe-matical model to measure the shape.Consider the logistic model, which isarguably the best-known model in ecology,used in hundreds of modeling and statisti-cal studies. This model has only twoparameters: r, the maximal rate of popula-tion increase from low density, and K, thecarrying capacity of the given environment(also called equilibrium). This modelmakes the restrictive assumption that therelationship between population growthrate and density is linear. But it doesn’thave to be, and indeed, that is what theauthors were trying to find out. So theyused a modified logistic model that con-tains an extra parameter, θ, which allowsthe shape of the relationship to be convex(θ > 1), linear (θ = 1), or concave (θ < 1).Different values of θ may reflect funda-mental differences in the nature of densitydependence among populations. The linearlogistic model (θ = 1) assumes that theabsolute negative effect of each additionalindividual on population growth is thesame. This implies scramble competition,whereby each individual requires a fixedamount of resource to survive and repro-duce (3). A convex (θ > 1) relationshipimplies that a population can grow almostunchecked until it approaches equilibrium,ECOLOGYPopulation Dynamics:Growing to ExtremesJohn D. Reynolds and Robert P. FreckletonDifferent shapes for the relationshipbetween population growth rate anddensity. The shapes of the curves reflectthe way a population changes with time,as described in the text. The growthrate–density relationship can be modeledby the θ-logistic equation pgr= r1[1 −(N/K)θ]:r1is the rate of population growthat density 1 [r1= r0/(1 – K−θ), where r0isthe maximal rate of population growthfrom low density];Kis the carrying capac-ity of the environment, or equilibrium; θcontrols the shape of the relationship anddepends on the ways that members of apopulation interact at different densities.Sibly et al. (1) find that mammals, birds,fish, and insects do not generally growexponentially to carrying capacity, as had been widely thought. Instead, population growth deceler-ates well before carrying capacity is achieved, as illustrated by the concave curve.J. D. Reynolds is in the Centre for Ecology, Evolutionand Conservation, School of Biological Sciences,University of East Anglia, Norwich NR4 7TJ, UK.E-mail: [email protected] R. P. Freckleton is in theDepartment of Zoology, University of Oxford,South Parks Road, Oxford OX1