A general model of the public goods dilemma

An individually costly act that benefits all group members is a public good. Natural selection favors individual contribution to public goods only when some benefit to the individual offsets the cost of contribution. Problems of sex ratio, parasite virulence, microbial metabolism, punishment of noncooperators, and nearly all aspects of sociality have been analyzed as public goods shaped by kin and group selection. Here, I develop two general aspects of the public goods problem that have received relatively little attention. First, variation in individual resources favors selfish individuals to vary their allocation to public goods. Those individuals better endowed contribute their excess resources to public benefit, whereas those individuals with fewer resources contribute less to the public good. Thus, purely selfish behavior causes individuals to stratify into upper classes that contribute greatly to public benefit and social cohesion and to lower classes that contribute little to the public good. Second, if group success absolutely requires production of the public good, then the pressure favoring production is relatively high. By contrast, if group success depends weakly on the public good, then the pressure favoring production is relatively weak. Stated in this way, it is obvious that the role of baseline success is important. However, discussions of public goods problems sometimes fail to emphasize this point sufficiently. The models here suggest simple tests for the roles of resource variation and baseline success. Given the widespread importance of public goods, better models and tests would greatly deepen our understanding of many processes in biology and sociality

Real Rational Curves in Grassmannians

Fulton asked how many solutions to a problem of enumerative geometry can be real, when that problem is one of counting geometric figures of some kind having specified position with respect to some general fixed figures. For the problem of plane conics tangent to five general conics, the (surprising) answer is that all 3264 may be real. Similarly, given any problem of enumerating p-planes incident on some general fixed subspaces, there are real fixed subspaces such that each of the (finitely many) incident p-planes are real. We show that the problem of enumerating parameterized rational curves in a Grassmannian satisfying simple (codimension 1) conditions may have all of its solutions be real.Comment: 9 pages, 1 eps figure, uses epsf.sty. Below the LaTeX source is a MAPLE V.5 file which computes an example in the paper, and its outpu

Some real and unreal enumerative geometry for flag manifolds

We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this method to show that two new classes of enumerative geometric problems on flag manifolds may have all their solutions be real and modify this method to show that another class may have no real solutions, which is a new phenomenon. This method originated in a numerical homotopy continuation algorithm adapted to the special Schubert calculus on Grassmannians and in principle gives optimal numerical homotopy algorithms for finding explicit solutions to these other enumerative problems.Comment: 19 pages, LaTeX-2e; Updated and final version. To appear in the issue of Michigan Mathematical Journal dedicated to Bill Fulto

SUSY Before the Next Lepton Collider

After a brief review of the Minimal Supersymmetric Standard Model (MSSM) and specifically the Minimal Supergravity Model (SUGRA), the prospects for discovering and studying SUSY at the CERN Large Hadron Collider are reviewed. The possible role for a future Lepton Collider --- whether $\mu^+\mu^-$ or $e^+e^-$ --- is also discussed.Comment: LaTeX with included aipproc.sty, 17 pages, 12 figures. To appear in Workshop on Physics at the First Muon Collide

Preventing extinction and outbreaks in chaotic populations

Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small or large population abundances that might cause extinction and recurrent outbreaks, respectively. We present a simple method that can guide management efforts to prevent crashes, peaks, or any other undesirable state. At the same time, the irregularity of the dynamics can be preserved when chaos is desirable for the population. The control scheme is easy to implement because it relies on time series information only. The method is illustrated by two examples: control of crashes in the Ricker map and control of outbreaks in a stage-structured model of the flour beetle Tribolium. It turns out to be effective even with few available data and in the presence of noise, as is typical for ecological settings.Comment: 10 pages, 6 figure

The hadron-quark transition with a lattice of nonlocal confining solitons

We use a lattice of nonlocal confining solitons to describe nuclear matter in the Wigner-Seitz approximation. The average density is varied by changing the size of the Wigner-Seitz cell. At sufficiently large density quark energy bands develop. The intersection of the filled valence band with the next empty band at a few times standard nuclear density signals a transition from a color insulator to a color conductor and is identified with the critical density for quark deconfinement.Comment: 12 pages Latex with one PS figur