Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

Co-Evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes

Co-evolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this co-adaptive model, besides the classical error catastrophe for high virus mutation rates, a second ``adaptation-'' catastrophe occurs, when virus mutation rates are too small to escape immune attack. Maximizing both regimes of viral error catastrophes is a possible strategy for an optimal immune response, reducing the range of allowed viral mutation rates to a minimum. From this requirement one obtains constraints on B-cell mutation rates and receptor lengths, yielding an estimate of somatic hypermutation rates in the germinal center in accordance with observation.Comment: 4 pages RevTeX including 2 figure

Characteristics of tropospheric ozone depletion events in the Arctic spring: analysis of the ARCTAS, ARCPAC, and ARCIONS measurements and satellite BrO observations

Arctic ozone depletion events (ODEs) are caused by halogen catalyzed ozone loss. In situ chemistry, advection of ozone-poor air mass, and vertical mixing in the lower troposphere are important factors affecting ODEs. To better characterize the ODEs, we analyze the combined set of surface, ozonesonde, and aircraft in situ measurements of ozone and bromine compounds during the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS), the Aerosol, Radiation, and Cloud Processes affecting Arctic Climate (ARCPAC), and the Arctic Intensive Ozonesonde Network Study (ARCIONS) experiments (April 2008). Tropospheric BrO columns retrieved from satellite measurements and back trajectory calculations are also used to investigate the characteristics of observed ODEs. In situ observations from these field experiments are inadequate to validate tropospheric BrO columns derived from satellite measurements. In view of this difficulty, we construct an ensemble of tropospheric column BrO estimates from two satellite (OMI and GOME-2) measurements and with three independent methods of calculating stratospheric BrO columns. Furthermore, we select analysis methods that do not depend on the absolute magnitude of column BrO, such as time-lagged correlation analysis of ozone and tropospheric column BrO, to understand characteristics of ODEs. Time-lagged correlation analysis between in situ (surface and ozonesonde) measurements of ozone and satellite derived tropospheric BrO columns indicates that the ODEs are due to either local halogen-driven ozone loss or short-range (∼1 day) transport from nearby regions with ozone depletion. The effect of in situ ozone loss is also evident in the diurnal variation difference between low (10th and 25th percentiles) and higher percentiles of surface ozone concentrations at Alert, Canada. Aircraft observations indicate low-ozone air mass transported from adjacent high-BrO regions. Correlation analyses of ozone with potential temperature and time-lagged tropospheric BrO column show that the vertical extent of local ozone loss is surprisingly deep (1–2 km) at Resolute and Churchill, Canada. The unstable boundary layer during ODEs at Churchill could potentially provide a source of free-tropospheric BrO through convective transport and explain the significant negative correlation between free-tropospheric ozone and tropospheric BrO column at this site

Characteristics of tropospheric ozone depletion events in the Arctic spring: analysis of the ARCTAS, ARCPAC, and ARCIONS measurements and satellite BrO observations

Arctic ozone depletion events (ODEs) are caused by halogen catalyzed ozone loss. In situ chemistry, advection of ozone-poor air mass, and vertical mixing in the lower troposphere are important factors affecting ODEs. To better characterize the ODEs, we analyze the combined set of surface, ozonesonde, and aircraft in situ measurements of ozone and bromine compounds during the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS), the Aerosol, Radiation, and Cloud Processes affecting Arctic Climate (ARCPAC), and the Arctic Intensive Ozonesonde Network Study (ARCIONS) experiments (April 2008). Tropospheric BrO columns retrieved from satellite measurements and back trajectory calculations are also used to investigate the characteristics of observed ODEs. In situ observations from these field experiments are inadequate to validate tropospheric BrO columns derived from satellite measurements. In view of this difficulty, we construct an ensemble of tropospheric column BrO estimates from two satellite (OMI and GOME-2) measurements and with three independent methods of calculating stratospheric BrO columns. Furthermore, we select analysis methods that do not depend on the absolute magnitude of column BrO, such as time-lagged correlation analysis of ozone and tropospheric column BrO, to understand characteristics of ODEs. Time-lagged correlation analysis between in situ (surface and ozonesonde) measurements of ozone and satellite derived tropospheric BrO columns indicates that the ODEs are due to either local halogen-driven ozone loss or short-range (∼1 day) transport from nearby regions with ozone depletion. The effect of in situ ozone loss is also evident in the diurnal variation difference between low (10th and 25th percentiles) and higher percentiles of surface ozone concentrations at Alert, Canada. Aircraft observations indicate low-ozone air mass transported from adjacent high-BrO regions. Correlation analyses of ozone with potential temperature and time-lagged tropospheric BrO column show that the vertical extent of local ozone loss is surprisingly deep (1–2 km) at Resolute and Churchill, Canada. The unstable boundary layer during ODEs at Churchill could potentially provide a source of free-tropospheric BrO through convective transport and explain the significant negative correlation between free-tropospheric ozone and tropospheric BrO column at this site

Forward pi^0 Production and Associated Transverse Energy Flow in Deep-Inelastic Scattering at HERA

Deep-inelastic positron-proton interactions at low values of Bjorken-x down to x \approx 4.10^-5 which give rise to high transverse momentum pi^0 mesons are studied with the H1 experiment at HERA. The inclusive cross section for pi^0 mesons produced at small angles with respect to the proton remnant (the forward region) is presented as a function of the transverse momentum and energy of the pi^0 and of the four-momentum transfer Q^2 and Bjorken-x. Measurements are also presented of the transverse energy flow in events containing a forward pi^0 meson. Hadronic final state calculations based on QCD models implementing different parton evolution schemes are confronted with the data.Comment: 27 pages, 8 figures and 3 table

Differential (2+1) Jet Event Rates and Determination of alpha_s in Deep Inelastic Scattering at HERA

Events with a (2+1) jet topology in deep-inelastic scattering at HERA are studied in the kinematic range 200 < Q^2< 10,000 GeV^2. The rate of (2+1) jet events has been determined with the modified JADE jet algorithm as a function of the jet resolution parameter and is compared with the predictions of Monte Carlo models. In addition, the event rate is corrected for both hadronization and detector effects and is compared with next-to-leading order QCD calculations. A value of the strong coupling constant of alpha_s(M_Z^2)= 0.118+- 0.002 (stat.)^(+0.007)_(-0.008) (syst.)^(+0.007)_(-0.006) (theory) is extracted. The systematic error includes uncertainties in the calorimeter energy calibration, in the description of the data by current Monte Carlo models, and in the knowledge of the parton densities. The theoretical error is dominated by the renormalization scale ambiguity.Comment: 25 pages, 6 figures, 3 tables, submitted to Eur. Phys.

Multi-Jet Event Rates in Deep Inelastic Scattering and Determination of the Strong Coupling Constant

Jet event rates in deep inelastic ep scattering at HERA are investigated applying the modified JADE jet algorithm. The analysis uses data taken with the H1 detector in 1994 and 1995. The data are corrected for detector and hadronization effects and then compared with perturbative QCD predictions using next-to-leading order calculations. The strong coupling constant alpha_S(M_Z^2) is determined evaluating the jet event rates. Values of alpha_S(Q^2) are extracted in four different bins of the negative squared momentum transfer~\qq in the range from 40 GeV2 to 4000 GeV2. A combined fit of the renormalization group equation to these several alpha_S(Q^2) values results in alpha_S(M_Z^2) = 0.117+-0.003(stat)+0.009-0.013(syst)+0.006(jet algorithm).Comment: 17 pages, 4 figures, 3 tables, this version to appear in Eur. Phys. J.; it replaces first posted hep-ex/9807019 which had incorrect figure 4

Multiplicity Structure of the Hadronic Final State in Diffractive Deep-Inelastic Scattering at HERA

The multiplicity structure of the hadronic system X produced in deep-inelastic processes at HERA of the type ep -> eXY, where Y is a hadronic system with mass M_Y< 1.6 GeV and where the squared momentum transfer at the pY vertex, t, is limited to |t|<1 GeV^2, is studied as a function of the invariant mass M_X of the system X. Results are presented on multiplicity distributions and multiplicity moments, rapidity spectra and forward-backward correlations in the centre-of-mass system of X. The data are compared to results in e+e- annihilation, fixed-target lepton-nucleon collisions, hadro-produced diffractive final states and to non-diffractive hadron-hadron collisions. The comparison suggests a production mechanism of virtual photon dissociation which involves a mixture of partonic states and a significant gluon content. The data are well described by a model, based on a QCD-Regge analysis of the diffractive structure function, which assumes a large hard gluonic component of the colourless exchange at low Q^2. A model with soft colour interactions is also successful.Comment: 22 pages, 4 figures, submitted to Eur. Phys. J., error in first submission - omitted bibliograph