Frederic A. Hopf

Classical theory of a free-electron laser☆

Abstract We present a completely classical analysis of the small-signal regime of a free-electron laser. It is explicitly shown that the amplification is due to stimulated scattering produced by a bunching of the electron distribution.

Origin of sex

The competitive advantage of sex consists in being able to use redundancy to recover lost genetic information while minimizing the cost of redundancy. We show that the major selective forces acting early in evolution lead to RNA protocells in which each protocell contains one genome, since this maximizes the growth rate. However, damages to the RNA which block replication and failure of segregation make it advantageous to fuse periodically with another protocell to restore reproductive ability. This early, simple form of genetic recovery is similar to that occurring in extant segmented single stranded RNA viruses. As duplex DNA became the predominant form of the genetic material, the mechanism of genetic recovery evolved into the more complex process of recombinational repair, found today in a range of species. We thus conclude that sexual reproduction arose early in the evolution of life and has had a continuous evolutionary history. We cite reasons to reject arguments for gaps in the evolutionary sequence of sexual reproduction based on the presumed absence of sex in the cyanobacteria. Concerning the maintenance of the sexual cycle among current organisms, we take care to distinguish between the recombinational and outbreeding aspects of the sexual cycle. We argue that recombination, whether it be in outbreeding organisms, self-fertilizing organisms or automictic parthenogens, is maintained by the advantages of recombinational repair. We also discuss the role of DNA repair in maintaining the outbreeding aspects of the sexual cycle.

The Molecular Basis of the Evolution of Sex

Traditionally, sexual reproduction has been explained as an adaptation for producing genetic variation through allelic recombination. Serious difficulties with this explanation have led many workers to conclude that the benefit of sex is a major unsolved problem in evolutionary biology. A recent informational approach to this problem has led to the view that the two fundamental aspects of sex, recombination and outcrossing, are adaptive responses to the two major sources of noise in transmitting genetic information, DNA damage and replication errors. We refer to this view as the repair hypothesis, to distinguish it from the traditional variation hypothesis. On the repair hypothesis, recombination is a process for repairing damaged DNA. In dealing with damage, recombination produces a form of informational noise, allelic recombination, as a by-product. Recombinational repair is the only repair process known which can overcome double-strand damages in DNA, and such damages are common in nature. Recombinational repair is prevalent from the simplest to the most complex organisms. It is effective against many different types of DNA-damaging agents, and, in particular, is highly efficient in overcoming double-strand damages. Current understanding of the mechanisms of recombination during meiosis suggests that meiosis is designed for repairing DNA. These considerations form the basis for the first part of the repair hypothesis, that recombination is an adaptation for dealing with DNA damage. The evolution of sex can be viewed as a continuum on the repair hypothesis. Sex is presumed to have arisen in primitive RNA-containing protocells whose sexual process was similar to that of recombinational repair in extent segmented, single-stranded RNA viruses, which are among the simplest known organisms. Although this early form of repair occurred by nonenzymatic reassortment of replicas of undamaged RNA segments, it evolved into enzyme-mediated breakage and exchange between long DNA molecules. As some lines of descent became more complex, their genome information increased, leading to increased vulnerability to mutation. The diploid stage of the sexual cycle, which was at first transient, became the predominant stage in some lines of descent because it allowed complementation, the masking of deleterious recessive mutations. Out-crossing, the second fundamental aspect of sex, is also maintained by the advantage of masking mutations. However, outcrossing can be abandoned in favor of parthenogenesis or selfing under conditions in which the costs of mating are very high.(ABSTRACT TRUNCATED AT 400 WORDS)

The role of the Allee effect in species packing

Abstract The species-packing model of May and MacArthur is modified to include a commonly-expected influence of sexual reproduction, namely a systematic diminishing of the rate of increase in a population when it becomes rare (called the “Allee effect”). This effect causes discreteness, i.e., a finiteness to the density of species found along a resource axis. The species separate in a manner that relates to their intrinsic capacities to utilize the resources. Also discussed is the issue of species diversity gradients, and how the question of species discreteness might apply to it. The model with the Allee effect is in reasonable accord with island diversity patterns, but is minimally applicable to longitudinal gradients. Environmental stochasticity is modelled with noise terms governed by widely varying timescales. However, the resulting stochastic extinction is found neither to generate discrete distributions by itself, nor to have substantive effects on the discrete distributions generated by the Allee effect.

Second-harmonic interferometers

Experiments on interferometers based on the second-harmonic generation of light from phase-matched crystals are described. This technique has potential applications for transmission tests of semiconductors and for contouring the surface of a three-dimensional object with fringes corresponding to wavelengths much larger than that of visible light.

Interferometry using conjugate-wave generation

Interferometers based on conjugate-wave generation using three- and four-wave mixing are described theoretically. They are shown to be self-referencing and sensitive to small changes in the phase front.

Sex and the emergence of species

We argue that the existence of species as distinct and relatively homogeneous groupings of individuals is a consequence of the nonlinear dynamics inherent in sexual reproduction. This approach provides an answer to two interrelated problems which Darwin posed and tried to solve. Why are there missing links (i.e. gaps) between species in habitat space, and why are there missing links between species in time as evidenced in the fossil record? A crucial difference between outcrossing sexual organisms (i.e. organisms in which mating is between different individuals) and obligate selfers or parthenogens lies in the dynamic of the underlying replication process. Replication is a linear function of density for obligate selfers or parthenogens but nonlinear for outcrossing sexuals. The non-linearity stems from the simple fact that with outcrossing, two individuals must come together to mate. We argue that this fact leads to density dependent fitness (per capita rate of increase) with an intrinsic disadvantage of low population density. This cost of rarity results in a distribution of distinct species. By establishing the causal connections in evolution between outcrossing sex and the very existence of species as distinct collections of organisms, our account lends theoretical support to a unitary concept of species with interbreeding as the fundamental defining property.

The Evolutionary Role of Recombinational Repair and Sex

We have argued that sexual reproduction arose very early in the evolution of life as a way of overcoming informational damage or loss through recombinational repair. As organisms became more complex and genome information content expanded, diploidy, at first transient, became the predominant way of coping with increased vulnerability to mutation. This allowed further genome expansion. Once such expansion had occurred, however, diploidy became essentially irreversible, since reversion to haploidy would lead to expression of accumulated deleterious recessive alleles. This expression of recessive alleles also imposes a stiff penalty on organisms that experiment with close inbreeding forms of recombinational repair. A consequence of sex is that fitness (defined as per capita rate of increase) is density dependent. At low population density, fitness declines due to increased costs of finding a mate. This fundamental constraint on population increase can inhibit evolutionary success of the best adapted species if it is small in numbers. Sexual reproduction also tends to eliminate new coadapted genotypes within a species by breaking up their coadapted gene complexes; this also contributes to the cohesion of species. In general, we think the existence of species and their characteristic cohesion and stability over time are direct consequences of sex; and sex in turn is a consequence of the need to overcome gene damage through recombinational repair while at the same time masking the deleterious effects of mutation.

Anomalous switching in dispersive optical bistability

Abstract The response of a dispersive bistable optical device to an instantaneous change in the driving field is studied theoretically. The device is shown to respond in ways that are significantly different from absorptive bistability. Threshold for switching between stable states do not occur at the same values as in the quasi-steady-state. Instead, anomalous thresholds are predicted. It is suggested that this anomalous switching behaviour may place limitations on the possible device applications. It also implies that dispersive bistable devices may be switched merely by an appropriate change of the phase of the driving field.

Quality of phase conjugation in silicon

Abstract The quality of phase conjugates generated by real-time holography in silicon is assessed interferometrically. The conjugate phase is found to be degraded by about a half wave distortion due to self-defocussing. We infer that the nonlinearly- induced gratings decay at a rate much faster than the value suggested previously.