Single dose thermoresponsive dexamethasone prodrug completely mitigates joint pain for 15 weeks in a murine model of osteoarthritis

In this study, we aimed to assess the analgesic efficacy of a thermoresponsive polymeric dexamethasone (Dex) prodrug (ProGel-Dex) in a mouse model of osteoarthritis (OA). At 12 weeks post model establishment, the OA mice received a single intra-articular (IA) injection of ProGel-Dex, dose-equivalent Dex, or Saline. Comparing to Saline and Dex controls, ProGel-Dex provided complete and sustained pain relief for >15 weeks according to incapacitance tests. In vivo optical imaging confirmed the continuous presence of ProGel-Dex in joints for 15 weeks post-injection. According to micro-CT analysis, ProGel-Dex treated mice had significantly lower subchondral bone thickness and medial meniscus bone volume than Dex and Saline controls. Except for a transient delay of body weight increase and slightly lower endpoint liver and spleen weights, no other adverse effect was observed after ProGel-Dex treatment. These findings support ProGel-Dex's potential as a potent and safe analgesic candidate for management of OA pain.

Adaptive immune responses in patients requiring revision after total knee arthroplasty

Dissatisfaction occurs in nearly 20% of patients after total knee arthroplasty (TKA); however, there remains only limited understanding of the biologic mechanisms that may contribute to suboptimal postoperative outcomes requiring revision surgery. Expansion of effector T and B cells, could promote an abnormal healing response via local or peripheral immune system mechanisms and contribute to inferior outcomes necessitating revision TKA. In this pilot study, we hypothesized that patients suffering from complications of arthrofibrosis or instability may exhibit differences in adaptive immune function. Patients (n = 31) undergoing revision TKA for an indication of arthrofibrosis or instability were prospectively enrolled. Whole blood and synovial fluid (SF) from the operative knee were collected at time of surgery. Peripheral blood mononuclear cells were isolated and analyzed by flow cytometry. Serum and SF were assessed for immunoglobulin levels by Luminex and antiphospholipid antibodies by enzyme-linked immunoassay. No significant differences were observed in peripheral blood T/B cell populations or serum immunoglobulins levels between groups. SF analysis demonstrated significant differences between the two groups, with higher levels of immunoglobulin G1 (IgG1) (p = 0.0184), IgG3 (p = 0.0084) and antiphosphatidyl serine IgG (p = 0.034) in arthrofibrosis relative to instability patients. Increased levels of both IgG subclasses and antiphospholipid antibodies in the SF suggest that intra-articular T-B cell interactions, potentially triggered by exposure to apoptotic components generated during post-op healing, could be functioning as a source of immune complexes that fuel fibrous tissue growth in arthrofibrotic patients.

Sensitive detection of Cre-mediated recombination using droplet digital PCR reveals Tg(BGLAP-Cre) and Tg(DMP1-Cre) are active in multiple non-skeletal tissues

In humans, somatic activating mutations in PIK3CA are associated with skeletal overgrowth. In order to determine if activated PI3K signaling in bone cells causes overgrowth, we used Tg(BGLAP-Cre) and Tg(DMP1-Cre) mouse strains to somatically activate a disease-causing conditional Pik3ca allele (Pik3ca^H1047R) in osteoblasts and osteocytes. We observed Tg(BGLAP-Cre);Pik3ca^H1047R/+ offspring were born at the expected Mendelian frequency. However, these mice developed cutaneous lymphatic malformations and died before 7 weeks of age. In contrast, Tg(DMP1-Cre);Pik3ca^H1047R/+ offspring survived and had no cutaneous lymphatic malformations. Assuming that Cre-activity outside of the skeletal system accounted for the difference in phenotype between Tg(BGLAP-Cre);Pik3ca^H1047R/+ and Tg(DMP1-Cre);Pik3ca^H1047R/+ mice, we developed sensitive and specific droplet digital PCR (ddPCR) assays to search for and quantify rates of Tg(BGLAP-Cre)- and Tg(DMP1-Cre)-mediated recombination in non-skeletal tissues. We observed Tg(BGLAP-Cre)-mediated recombination in several tissues including skin, muscle, artery, and brain; two CNS locations, hippocampus and cerebellum, exhibited Cre-mediated recombination in >5% of cells. Tg(DMP1-Cre)-mediated recombination was also observed in muscle, artery, and brain. Although we cannot preclude that differences in phenotype between mice with Tg(BGLAP-Cre)- and Tg(DMP1-Cre)-mediated PIK3CA activation are due to Cre-recombination being induced at different stages of osteoblast differentiation, differences in recombination at non-skeletal sites are the more likely explanation. Since unanticipated sites of recombination can affect the interpretation of data from experiments involving conditional alleles, we recommend ddPCR as a good first step for assessing efficiency, leakiness, and off-targeting in experiments that employ Cre-mediated or Flp-mediated recombination.

Mouse Models of Osteoarthritis: Surgical Model of Post-traumatic Osteoarthritis Induced by Destabilization of the Medial Meniscus

The surgical model of destabilization of the medial meniscus (DMM) has become a gold standard for studying the onset and progression of post-traumatic osteoarthritis (OA). The DMM model mimics clinical meniscal injury, a known predisposing factor for the development of human OA, and permits the study of structural and biological changes over the course of the disease. In addition, when applied to genetically modified or engineered mouse models, this surgical procedure permits dissection of the relative contribution of a given gene to OA initiation and/or progression. This chapter describes the requirements for the surgical induction of OA in mouse models, and provides guidelines and tools for the subsequent histological, immunohistochemical, and molecular analyses. Methods for the assessment of the contributions of selected genes in genetically modified strains are also provided.

Role of iRhoms 1 and 2 in Endochondral Ossification

Growth of the axial and appendicular skeleton depends on endochondral ossification, which is controlled by tightly regulated cell–cell interactions in the developing growth plates. Previous studies have uncovered an important role of a disintegrin and metalloprotease 17 (ADAM17) in the normal development of the mineralized zone of hypertrophic chondrocytes during endochondral ossification. ADAM17 regulates EGF-receptor signaling by cleaving EGFR-ligands such as TGFα from their membrane-anchored precursor. The activity of ADAM17 is controlled by two regulatory binding partners, the inactive Rhomboids 1 and 2 (iRhom1, 2), raising questions about their role in endochondral ossification. To address this question, we generated mice lacking iRhom2 (iR2−/−) with floxed alleles of iRhom1 that were specifically deleted in chondrocytes by Col2a1-Cre (iR1∆Ch). The resulting iR2−/−iR1∆Ch mice had retarded bone growth compared to iR2−/− mice, caused by a significantly expanded zone of hypertrophic mineralizing chondrocytes in the growth plate. Primary iR2−/−iR1∆Ch chondrocytes had strongly reduced shedding of TGFα and other ADAM17-dependent EGFR-ligands. The enlarged zone of mineralized hypertrophic chondrocytes in iR2−/−iR1∆Ch mice closely resembled the abnormal growth plate in A17∆Ch mice and was similar to growth plates in Tgfα−/− mice or mice with EGFR mutations. These data support a model in which iRhom1 and 2 regulate bone growth by controlling the ADAM17/TGFα/EGFR signaling axis during endochondral ossification.

Demonstration of a 120° hybrid based simplified coherent receiver on SOI for high speed PON applications

We demonstrate the first simplified coherent receiver using a 120° hybrid on silicon-on-insulator (SOI) for high speed PON applications. This coherent receiver integrates an inverse taper edge coupler for the received signal, a vertical grating coupler for the local oscillator input, a polarization splitter and rotator (PSR), a 120° hybrid based on a 3×3 multimode interference (MMI) coupler, and three germanium photodetectors. We achieved 25 Gbit/s two-level pulse amplitude modulation (PAM-2) transmission over 30 km standard single mode fiber (SMF) in the C-band without any digital signal processing (DSP) (e.g., pre-emphasis, pulse shaping, equalization, nonlinearity compensation) and dispersion compensation (e.g., optical or digital) either at the transmitter or at the receiver. The requirements for frequency and phase locking of the local oscillator (LO) were avoided due to the use of intensity modulated signals. Receiver sensitivities of -23.70 dBm, -20.30 dBm, and -15.10 dBm are achieved at a bit error rate (BER) below the hard-decision forward error correction (HD-FEC) threshold (i.e., 3.8 × 10^-3) in back-to-back (B2B), after 21 km and 30 km, respectively. We also demonstrate 25 Gbit/s PAM-4 transmission achieving receiver sensitivities of -15.30 dBm, -13.90 dBm, and -9.50 dBm below the HD-FEC threshold in B2B, after 10.5 km and 21 km, respectively.

The long-term clinical benefit and effectiveness of switching to once-daily quetiapine extended release in patients with schizophrenia

OBJECTIVE

To evaluate the long-term clinical benefit and effectiveness of switching to once-daily quetiapine extended release (XR) from an oral antipsychotic in patients with schizophrenia. Reasons for switching included insufficient efficacy, tolerability, and/or non-acceptability. The primary endpoint was the percentage of patients achieving an improvement in Clinical Global Impression - Clinical Benefit (CGI-CB) scale scores.

RESEARCH DESIGN AND METHODS

A 24-week, international, multicentre, open-label, prospective study ( www.clinicaltrials.gov : NCT00640601). After a 7-14 day enrolment period (depending whether prior antipsychotic mono- or combination therapy), all patients received quetiapine XR 300 mg once daily (day 1), 600 mg/day (day 2), 600-800 mg/day (day 3) and 400-800 mg/day thereafter, with down-titration and discontinuation of prior antipsychotic by day 4.

RESULTS

A total of 62% of patients completed the study and 56.9% (LOCF, ITT) achieved a significant improvement in CGI-CB (95% CI [0.51, 0.63]; p = 0.02). Switches due to insufficient efficacy showed a significant improvement (60%, 95% CI [0.51, 0.68]; p = 0.02), compared to 54.4% ([0.44, 0.64]; p = 0.38) and 52.4% ([0.36, 0.68]; p = 0.76) of switches due to insufficient tolerability and non-acceptability respectively (both p = ns). Patients previously on olanzapine and quetiapine IR showed a significant improvement in CGI-CB (62.6% [p = 0.02] and 61.2% [p = 0.04], respectively). Somnolence (18.0%) and dizziness (14.6%) were the main adverse events. Anticholinergic use decreased from 7.1 to 2.7%. Overall mean weight gain was 0.4 kg; 12.9% of patients experienced a weight gain of ≥7% and 15% experienced a clinically relevant shift in triglycerides from baseline.

CONCLUSIONS

A majority of patients switched from other antipsychotics to quetiapine XR experienced clinical benefit. This was supported by all other efficacy outcomes regardless of the reason for switching. Safety data confirmed quetiapine XR was safe and well tolerated. The open-label design and lack of a placebo group represent limitations.

Quetiapine as an adjunctive pharmacotherapy for the treatment of non-remitting generalized anxiety disorder: a flexible-dose, open-label pilot trial

BACKGROUND

Generalized anxiety disorder (GAD) is a chronic disorder associated with significant morbidity and disability. Traditional therapies are associated with poor levels of remission, and often result in troublesome side effects.

METHODS

This was a 12-week, open-label, flexible-dose study to assess the efficacy and tolerability of quetiapine as an adjunctive treatment to traditional medication. 40 outpatients with GAD who had not achieved remission following at least 8 weeks of an adequate dose of traditional therapy were enrolled. The primary endpoint was the mean change from pre-treatment to week 12 in the Hamilton Anxiety Rating Scale (HAM-A) total scores. Secondary endpoints included: the proportion of patients achieving remission (HAM-A total score of < or =10 at week 12), Clinical Global Impressions-Severity of Illness (CGI-S), Clinical Global Impressions-Global Improvement (CGI-I), Pittsburgh Sleep Quality Index (PSQI) and Penn State Worry Questionnaire (PSWQ).

RESULTS

Adjunctive quetiapine (mean dose 386mg/day at week 12) significantly reduced the HAM-A total scores from pre-treatment (29.8+/-9.0) to week 12 (9.0+/-10.2) (-20.6; p<0.001). The HAM-A remission rate was 72.1% at week 12. Adjunctive quetiapine resulted in a significant reduction in all efficacy measures by study end. Quetiapine was well tolerated: the most common adverse event (AE) was sedation, with no incidence of serious AEs and no clinically significant changes in vital signs, weight (mean gain 0.5kg at week 12) or laboratory assessments.

CONCLUSION

The results of this small pilot trial suggest that quetiapine adjunctive to traditional therapy may be a useful treatment in patients with GAD or treatment-resistant GAD, and warrant further investigation.

Ouabain stimulates unidirectional and net potassium efflux in resting mammalian skeletal muscle

The present study compared ouabain-sensitive unidirectional K+ flux into (JinK) and out of (JoutK) perfused rat hindlimb skeletal muscle in situ and mouse flexor digitorum brevis (FDB) in vitro. In situ, 5 mM ouabain inhibited 54 +/- 4% of the total JinK in 28 +/- 1 min, and increased the net and unidirectional efflux of K+ within 4 min. In contrast, 1.8 mM ouabain inhibited 40 +/- 8% of the total JinK in 38 +/- 2 min, but did not significantly affect JoutK. In vitro, 1.8 and 0.2 mM ouabain decreased JinK to a greater extent (83 +/- 5%) than in situ, but did not significantly affect 42K loss rate compared with controls. The increase in unidirectional K+ efflux (JoutK) with 5 mM ouabain in situ was attributed to increased K+ efflux through cation channels, since addition of barium (1 mM) to ouabain-perfused muscles returned JoutK to baseline values within 12 min. Perfusion with 5 mM ouabain plus 2 mM tetracaine for 30 min decreased JinK 46 +/- 9% (0.30 +/- 0.03 to 0.16 +/- 0.02 micromol x min(-1) x g(-1)), however tetracaine was unable to abolish the ouabain-induced increase in unidirectional K+ efflux. In both rat hindlimb and mouse FDB, tetracaine had no effect on JoutK. Perfusion of hindlimb muscle with 0.1 mM tetrodotoxin (TTX, a Na+ channel blocker) decreased JinK by 15 +/- 1%, but had no effect on JoutK; subsequent addition of ouabain (5 mM) decreased JinK a further 32 +/- 2%. The ouabain-induced increase in unidirectional K+ efflux did not occur when TTX was perfused prior to and during perfusion with 5 mM ouabain. We conclude that 5 mM ouabain increases the unidirectional efflux of K+ from skeletal muscle through a barium and TTX-sensitive pathway, suggestive of voltage sensitive Na+ channels, in addition to inhibiting Na+/K+-ATPase activity.

Equilibrium structure and stability in a frequency-dependent, two-population diploid model

We investigate the equilibrium structure for an evolutionary genetic model in discrete time involving two monoecious populations subject to intraspecific and interspecific random pairwise interactions. A characterization for local stability of an equilibrium is found, related to the proximity of this equilibrium with evolutionarily stable strategies (ESS). This extends to a multi-population framework a principle initially proposed for single populations, which states that the mean population strategy at a locally stable equilibrium is as close as possible to an ESS.

Optimal sex ratios in structured populations

In this paper, we develop a general method to determine evolutionary equilibrium sex ratios and to check evolutionary stability, continuous stability and invadability in exact genetic models with or without dominance. This method is then applied to three kinds of models for structured populations: the first one concerns Hamilton's LMC model, except that only a fraction beta of female offspring mate with male offspring born in the same colonies, while a fraction 1-beta mate with male offspring chosen at random within the whole population; in the second model, it is assumed that partial dispersal of inseminated females occurs after mating; in the third model, partial dispersal of male and female offspring occurs before mating. In the first model, the effect of population regulation is studied while, in the other models, two kinds of dispersal are considered: proportional and uniform.

Fundamental theorem of natural selection and frequency-dependent selection: analysis of the matrix game diploid model

Following Ewens' interpretation about Fisher's fundamental theorem of natural selection, the matrix game model for diploid populations undergoing non-overlapping, discrete generations is investigated. The total genetic variance is decomposed and it is shown that the partial change in the mean fitness, which is equal to the additive genetic variance over the mean fitness, can be thought of as a change due only to the partial changes in the phenotypic frequencies.

Variability in centred house-of-cards mutation models

Convergence of variability in phenotypic models with balance between selection and mutation is analysed. The mutation assumed occurs with weak probability and brings down the evolutionary process built up by selection around the mean in the population. Gaussian approximations are used.

Stability analysis of the partial selfing selection model

We undertake a detailed study of the one-locus two-allele partial selfing selection model. We show that a polymorphic equilibrium can exist only in the cases of overdominance and underdominance and only for a certain range of selfing rates. Furthermore, when it exists, we show that the polymorphic equilibrium is unique. The local stability of the polymorphic equilibrium is investigated and exact analytical conditions are presented. We also carry out an analysis of local stability of the fixation states and then conclude that only overdominance can maintain polymorphism in the population. When the linear local analysis is inconclusive, a quadratic analysis is performed. For some sets of selective values, we demonstrate global convergence. Finally, we compare and discuss results under the partial selfing model and the random mating model.

Evolutionarily stable strategy in a sex- and frequency-dependent selection model

In this paper, a sex-dependent matrix game haploid model is investigated. For this model, since the phenotypes of female and male individuals are determined by alleles located at a single locus and are sex dependent, any given genotype corresponds to a strategy pair. Thus, a strategy pair is an ESS if and only if the allele corresponding to this strategy pair cannot be invaded by any mutant allele. We show that an ESS equilibrium must be locally asymptotically stable if it exists.

Stochastic effects in LMC models

LMC (local mate competition) was first introduced by W. D. Hamilton to explain extraordinary female-biased sex ratios observed in a variety of insects and mites. In the original model, the population is subdivided into an infinite number of colonies founded by a fixed number of inseminated females producing the same very large number of offspring. The male offspring compete within the colonies to inseminate the female offspring and then these disperse at random to found new colonies. An unbeatable sex ratio strategy is found to be female-biased. In this paper, the effects of having colonies of random size and foundresses producing a random finite number of offspring are considered. The exact evolutionarily stable strategy (ESS) sex ratio is deduced and comparisons with previous approximate or numerical results are made. As the mean or the variance of brood size increases, the ESS sex ratio becomes more female-biased. An increase in the variance of colony size increases the ESS proportion of males when the mean brood size and colony size are both small, but decreases this proportion when the mean brood size or the mean colony size is large.

Fisher's fundamental theorem of natural selection revisited

W. J. Ewens, following G. R. Price, has stressed that Fisher's fundamental theorem of natural selection about the increase in mean fitness is of general validity without any restrictive assumptions on the mating system, the fitness parameters, or the numbers of loci and alleles involved, but that it concerns only a partial change in mean fitness. This partial change is obtained by replacing the actual genotypic fitnesses by the corresponding additive genetic values and by keeping these values fixed in the change of the mean with respect to changes in genotype frequencies. We propose an alternate interpretation for this partial change which uses partial changes in genotype frequencies directly consequent on changes in gene frequencies, the fitness parameters being kept constant. We argue that this interpretation agrees more closely with Fisher's own explanations. Moreover, this approach leads to a decomposition for the total change in mean fitness which explains, unifies, and extends previous decompositions. We consider a wide range of models, from discrete-time selection models with nonoverlapping generations to continuous-time models with overlapping generations and age effects on viability and fecundity, which is the original framework for Fisher's fundamental theorem.

On the non-existence of an optimal migration rate

We show that an optimal migration rate may not exist in a population distributed over an infinite number of individual living sites if empty sites occur. This is the case when the mean number of offspring per individual mu is finite. We make the assumption of uniform migration to other sites whose rate is determined by the parent's genotype or the offspring's genotype at a single locus in a diploid hermaphrodite population undergoing random mating. In both cases, for mu small enough, any population at fixation would go to extinction. Moreover, in the latter case, for intermediate values of mu, the only fixation state that could resist the invasion of any mutant would lead the population to extinction. These are the two conditions for the non-existence of an optimal migration rate. They become less stringent as the cost for migration expressed by a coefficient of selection 1-beta becomes larger, that is closer to 1. The results are obtained assuming that the allele at fixation is either nondominant or dominant. Although the optimal migration rate is the same in both cases when it exists, the optimality properties may differ.

Person-based information from Canadian hospital discharge data

Statistics summarizing Canadians' use of hospital services are usually based on simple discharge totals, without any attempt to distinguish which discharges may have belonged to the same person. This leads to a distorted view of the prevalence of illness and the resources required to serve each patient. Statistics based on the number of people going to hospital shed new light on the demand for resources by various groups, now and in the future.

The fundamental theorem of natural selection in Ewens' sense (case of many loci)

We correct an equation characterizing the additive allelic effects on fitness determined at many loci without the assumption of random mating given in Ewens (1989, 1992) and we show that the additive genetic variance in fitness divided by the mean fitness is equal to a partial change in the mean fitness from one generation to the next as stated in Ewens (1989).

The Fundamental Theorem of Natural Selection in Ewens' sense (case of fertility selection)

We show that the Fundamental Theorem of Natural Selection in Ewens' sense is valid in the case of fertility selection: the additive genetic variance in fertility divided by the mean fertility is exactly equal to the partial change in the mean fertility from the current generation to the next. This partial change is the increase in the mean additive value caused by frequency changes from on generation to the next. This partial change is the increase in the mean additive value caused by frequency changes from one generation to the next but keeping unchanged the additive values. The only hypothesis on mating is that it does not affect the allelic frequencies in the sense that these are the same before and after mating in the parental generation, which occurs for a wide range of mating patterns going from random mating to several regular systems of inbreeding and cases of assortative mating. The fertility of couples is determined by the genes at an arbitrary number of loci, and the additive (average) allelic allelic effects are defined by a linear system of equations, which is used to extend Ewens' optimality principle to the case of fertility selection.

Relatedness and inclusive fitness with inbreeding

Relatedness arising in kin selection theory is measured by a variable taking as values two pedigree indices in populations with inbreeding when selection is weak. This variable reduces to a single pedigree index when inbreeding is caused by partial selfing or partial sib-mating. General inclusive fitness formulations of kin selection models based on such a variable of relatedness are proposed.

The role of recombination and selection in the modifier theory of sex-ratio distortion

The equilibrium configurations for a two-locus multialle model of sex-linked meiotic drive are studied with regard to the recombination fraction:limit cycles can occur in the case of small recombination while stable equilibrium points associated with linkage equilibrium can exist for an intermediate range of recombination values depending on the equilibrium sex ratio, linkage disequilibrium at nearby equilibrium points taking turn with loser linkage. The evolutionary dynamics in two-locus sex-ratio distortion systems is enlightened: while equilibria with a sex ratio closer to 1/2 are more likely to be stable with respect to perturbations on the frequencies of sex-ratio distorters that are represented at equilibrium, such equilibria are also more vulnerable to the invasion of mutant distorters when there is some degree of linkage with the sex-determining locus. For X-linked multimodifier systems of sex-ratio distortion, differential fertilities and viabilities are incorporated and a maximum principle is suggested.

Evolutionary principles for general frequency-dependent two-phenotype models in sexual populations

The evolutionary dynamics in general two-sex two-phenotype frequency-dependent selection models are studied with respect to underlying multi-allele one-locus genetic systems. Two classes of equilibria come into play: genotypic equilibria, with equilibrium allelic frequencies independent of the phenotype, and phenotypic equilibria, which are characterized by equal mean phenotypic fitnesses. The exact conditions for genotypic equilibria to exist and be stable and for phenotypic equilibria to exist and be evolutionarily attractive are examined. Using adequate definitions of mean fitnesses in general contexts of frequency-dependent selection in dioecious populations, we show that two phenotypes, when they can coexist in the population, tend to balance their fitnesses as far as is allowed by the genetic system as more alleles responsible for phenotype determination are introduced into the population.

On the optimal sex-ratio: a stability analysis based on a characterization for one-locus multiallele viability models

Theoretical one-locus multiallele sex-determination models are found to admit even sex ratio equilibrium surfaces besides the equilibria for corresponding one-locus multiallele viability models. Both types of equilibria can be defined in terms of a single spectral radius function, the former corresponding to level surfaces and the latter to critical points. The stable equilibria in the corresponding viability models are associated with the local maxima, and the equilibrium structures for the sex-determination models can be fully described. Several optimality properties of the even-sex-ratio equilibrium surfaces can be deduced.

Evolutionary dynamics in frequency-dependent two-phenotype models

General frequency-dependent selection models based on two phenotypic classes are analyzed with underlying one-locus multiallele phenotypic determination systems in diploid populations. It is proved that the mean phenotypic fitnesses tend to equality over discrete generations and genetic mutations if a phenotypic polymorphism is to be maintained. The exact conditions are examined. The present results are valid for a wide class of models whenever random groupings or assortative patterns based on phenotype and affecting fitness, linearly or not, are independent of sex, mating preferences, or kinship. They can also be applied to two-sex haploid models.

On the optimal sex ratio

The equilibrium structures for various multiallele sex-determining genetic models of panmictic populations with sex expression depending on the genotypes of either the zygote or a parent are described. Even-sex-ratio equilibrium surfaces can exist apart from equilibrium points having coincident male and female allelic frequency sets. The latter (symmetric) equilibrium states entail biased sex ratios. A stable symmetric equilibrium and an even-sex-ratio equilibrium segregating the same alleles cannot coexist. The tendency to evolve toward an even-sex ratio is embodied by the following optimality property: starting from an equilibrium having a biased sex ratio, mutant sex-determining alleles can accumulate only in the case in which in the augmented system all attainable equilibrium states have a sex ratio closer to one to one.