One-third rules with equality: Second-order evolutionary stability conditions in finite populations

The one-third law of evolutionary dynamics [Nowak et al. 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650] describes a robustness criterion for evolution in a finite population: If at an A-frequency of 1/3, the fitness of an A player is greater (smaller) than the fitness of a B player, then a single A mutant that appears in a population of otherwise all B has a fixation probability greater (smaller) than the neutral threshold 1/N, the inverse population size. We examine the case where at an A-frequency of 1/3, the fitness of an A player is exactly equal to the fitness of a B player. We find that in this case the relative magnitude of the cross payoffs matters: If the payoff of A against B is larger (smaller) than the payoff of B against A, then a single A mutant has a fixation probability larger (smaller) than 1/N. If the cross payoffs coincide, we are in the special case of a partnership game, where the deviation cost from an inefficient equilibrium is exactly balanced by the potential gain of switching to the payoff dominant equilibrium. We show that in this case the fixation probability of A is lower than 1/N. Finally, we illustrate our findings by a language game with differentiated costs of signals.     

Fixation procedures for flow cytometric analysis of environmental bacteria

Analysis of environmental bacteria on the single cell level often requires fixation to store the cells and to keep them in a state as near life-like as possible. Fixation procedures should furthermore counteract the increase of autofluorescence, cell clogging, and distortion of surface characteristics. Additionally, they should meet the specific fixation demands of both aerobically and anaerobically grown bacteria. A fixation method was developed based on metal solutions in combination with sodium azide. The fixation efficiencies of aluminium, barium, bismuth, cobalt, molybdenum, nickel, and tungsten salts were evaluated by flow cytometric measurement of the DNA contents as a bacterial population/community stability marker. Statistical equivalence testing was involved to permit highly reliable flow cytometric pattern evaluation. Investigations were carried out with pure cultures representing environmentally important metabolic and respiratory pathways as controls and with activated sludge as an example for highly diverse bacterial communities. A mixture of 5 mM barium chloride and nickel chloride, each and 10% sodium azide was found to be a suitable fixative for all tested bacteria. The described method provided good sample stability for at least 9 days.     

Antinoceptive effect of triterpenoid α,β-amyrin in rats on orofacial pain induced by formalin and capsaicin

The effects of α,β-amyrin, a pentacyclic triterpene isolated from Protium heptaphylum was investigated on rat model of orofacial pain induced by formalin or capsaicin. Rats were pretreated with α,β-amyrin (10, 30, and 100 mg/kg, i.p.), morphine (5 mg/kg, s.c.) or vehicle (3% Tween 80), before formalin (20 μl, 1.5%) or capsaicin (20 μl, 1.5 μg) injection into the right vibrissa. In vehicle-treated controls, formalin induced a biphasic nociceptive face-rubbing behavioral response with an early first phase (0–5 min) and a late second phase (10–20 min) appearance, whereas capsaicin produced an immediate face-rubbing (grooming) behavior that was maximal at 10–20 min. Treatment with α,β-amyrin or morphine significantly inhibited the face-rubbing response in both test models. While morphine produced significant antinociception in both phases of formalin test, α,β-amyrin inhibited only the second phase response, more prominently at 30 mg/kg, in a naloxone-sensitive manner. In contrast, α,β-amyrin produced much greater antinociceptive effect at 100 mg/kg in the capsaicin test, which was also naloxone-sensitive. These results provide first time evidence to show that α,β-amyrin attenuates orofacial pain atleast, in part, through a peripheral opioid mechanism but warrants further detailed study for its utility in painful orofacial pathologies.     

Kinetic studies of glutaraldehyde binding in liver

To study the kinetics of glutaraldehyde fixation, fresh rabbit liver cubes were immersed in 3% buffered ³H-glutaraldehyde for various periods of time. Following weighing and a brief rinse in water, the tissues were solubilized, and the radioactivity was measured in a scintillation counter. Binding of the isotope was half-maximal after approximately 4 h and a plateau was reached after approximately 20 h. We also investigated the reversibility of glutaraldehyde fixation. Fixed liver cubes were weighed and immersed in water for various periods of time, and after solubilization, the radioactivity was determined. After rinsing for 48 h, approximately 95% of the radioactivity was lost from the tissue specimens, indicating that fixation with glutaraldehyde is largely reversible. Light and electron microscopy of specimens rinsed for 1 and 48 h showed essentially similar morphology. Rinsing for 48 h restored some of the immunoreactivity that was absent after rinsing for only 1 h.     

Stress-shielding induced bone remodeling in cementless shoulder resurfacing arthroplasty: a finite element analysis and in vivo results

Cementless surface replacement arthroplasty (CSRA) of the shoulder was designed to preserve the individual anatomy and humeral bone stock. A matter of concern in resurfacing implants remains the stress shielding and bone remodeling processes. The bone remodeling processes of two different CSRA fixation designs, conical-crown (Epoca RH) and central-stem (Copeland), were studied by three-dimensional (3-D) finite element analysis (FEA) as well as evaluation of contact radiographs from human CSRA retrievals. FEA included one native humerus model with a normal and one with a reduced bone stock quality. Compressive strains were evaluated before and after virtual CSRA implantation and the results were then compared to the bone remodeling and stress-shielding pattern of eight human CSRA retrievals (Epoca RH n=4 and Copeland n=4). FEA revealed for both bone stock models increased compressive strains at the stem and outer implant rim for both CSRA designs indicating an increased bone formation at those locations. Unloading of the bone was seen for both designs under the central implant shell (conical-crown 50–85%, central-stem 31–93%) indicating high bone resorption. Those effects appeared more pronounced for the reduced than for the normal bone stock model. The assumptions of the FEA were confirmed in the CSRA retrieval analysis which showed bone apposition at the outer implant rim and stems with highly reduced bone stock below the central implant shell. Overall, clear signs of stress shielding were observed for both CSRAs designs in the in vitro FEA and human retrieval analysis. Especially in the central part of both implant designs the bone stock was highly resorbed. The impact of these bone remodeling processes on the clinical outcome as well as long-term stability requires further evaluation.     

Fixation probabilities of additive alleles in diploid populations

The calculation of the survival probability of a selectively advantageous allele is a central part of the quantitative theory of genetic evolution. However, several areas of investigation in population genetics theory, including the generalized neutrality theory, the concept of Muller's ratchet, and the risk of extinction of sexually reproducing populations due to the accumulation of deleterious mutations, rely on the calculation of the survival probability of selectively disadvantageous mutant genes. The calculation of these probabilities in the standard Wright-Fisher model of genetic evolution appears to be intractable, and yet is a key element in the above investigations. In this paper we find bounds for the fixation probability of deleterious and advantageous additive mutants, as well as finding close approximations for these probabilities. In addition, we derive analytical estimates for the relative error of our approximations and compare our results with those from numerical computation. Our results justify the diffusion approximation for the fixation probability of a single mutant.     

Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill-Robertson effect and to the joint evolution of helping and punishment

Natural populations are of finite size and organisms carry multilocus genotypes. There are, nevertheless, few results on multilocus models when both random genetic drift and natural selection affect the evolutionary dynamics. In this paper we describe a formalism to calculate systematic perturbation expansions of moments of allelic states around neutrality in populations of constant size. This allows us to evaluate multilocus fixation probabilities (long-term limits of the moments) under arbitrary strength of selection and gene action. We show that such fixation probabilities can be expressed in terms of selection coefficients weighted by mean first passages times of ancestral gene lineages within a single ancestor. These passage times extend the coalescence times that weight selection coefficients in one-locus perturbation formulas for fixation probabilities. We then apply these results to investigate the Hill-Robertson effect and the coevolution of helping and punishment. Finally, we discuss limitations and strengths of the perturbation approach. In particular, it provides accurate approximations for fixation probabilities for weak selection regimes only (Ns?1), but it provides generally good prediction for the direction of selection under frequency-dependent selection.     

Role of selection in fixation of gene duplications

New genes commonly appear through complete or partial duplications of pre-existing genes. Duplications of long DNA segments are constantly produced by rare mutations, may become fixed in a population by selection or random drift, and are subject to divergent evolution of the paralogous sequences after fixation, although gene conversion can impede this process. New data shed some light on each of these processes. Mutations which involve duplications can occur through at least two different mechanisms, backward strand slippage during DNA replication and unequal crossing-over. The background rate of duplication of a complete gene in humans is 10(-9)-10(-10) per generation, although many genes located within hot-spots of large-scale mutation are duplicated much more often. Many gene duplications affect fitness strongly, and are responsible, through gene dosage effects, for a number of genetic diseases. However, high levels of intrapopulation polymorphism caused by presence or absence of long, gene-containing DNA segments imply that some duplications are not under strong selection. The polymorphism to fixation ratios appear to be approximately the same for gene duplications and for presumably selectively neutral nucleotide substitutions, which, according to the McDonald-Kreitman test, is consistent with selective neutrality of duplications. However, this pattern can also be due to negative selection against most of segregating duplications and positive selection for at least some duplications which become fixed. Patterns in post-fixation evolution of duplicated genes do not easily reveal the causes of fixations. Many gene duplications which became fixed recently in a variety of organisms were positively selected because the increased expression of the corresponding genes was beneficial. The effects of gene dosage provide a unified framework for studying all phases of the life history of a gene duplication. Application of well-known methods of evolutionary genetics to accumulating data on new, polymorphic, and fixed duplication will enhance our understanding of the role of natural selection in the evolution by gene duplication.     

Examination of the interaction between peripheral diclofenac and gabapentin on the 5% formalin test in rats

It has been shown that the association of diclofenac with other analgesic agents can increase its antinociceptive activity, allowing the use of lower doses and thus limiting side effects. Therefore, the aim of the present study was to examine the possible pharmacological interaction between diclofenac and gabapentin at the peripheral level in the rat using the 5% formalin test and isobolographic analysis. Diclofenac, gabapentin or a fixed-dose ratio diclofenac-gabapentin combination were administrated locally in the formalin-injured paw and the antinociceptive effect was evaluated using the 5% formalin test. All treatments produced a dose-dependent antinociceptive effect. ED30 values were estimated for the individual drugs and an isobologram was constructed. The derived theoretical ED30 for the diclofenac-gabapentin combination was 597.5+/-87.5 microg/paw, being significantly higher than the actually observed experimental value, 170.9+/-26.07 microg/paw. These results correspond to a synergistic interaction between diclofenac and gabapentin at the peripheral level, potency being about three times higher with regard to that expected from the addition of the effects of the individual drugs. Data suggest that low doses of the diclofenac-gabapentin combination can interact synergistically at the peripheral level and therefore this drug association may represent a therapeutic advantage for the clinical treatment of inflammatory pain.