Operational effectiveness of tafenoquine and primaquine for the prevention of Plasmodium vivax recurrence in Brazil: a retrospective observational study.

BACKGROUND: Prevention of Plasmodium vivax malaria recurrence is essential for malaria elimination in Brazil. We evaluated the real-world effectiveness of an updated treatment algorithm for P vivax radical cure in the Brazilian Amazon. METHODS: In this non-interventional observational study, we used retrospective data from the implementation of a P vivax treatment algorithm at 43 health facilities in Manaus and Porto Velho, Brazil. The treatment algorithm consisted of chloroquine (25 mg/kg over 3 days) and point-of-care quantitative glucose-6-phosphate dehydrogenase (G6PD) testing followed by single-dose tafenoquine 300 mg (G6PD normal, aged ≥16 years, not pregnant and not breastfeeding), 7-day primaquine 0·5 mg/kg per day (G6PD intermediate or normal, aged ≥6 months, not pregnant, and not breastfeeding or breastfeeding for >1 month), or primaquine 0·75 mg/kg per week for 8 weeks (G6PD deficient, aged ≥6 months, not pregnant, and not breastfeeding or breastfeeding for >1 month). P vivax recurrences were identified from probabilistic linkage of routine patient records from the Brazilian malaria epidemiological surveillance system. Recurrence-free effectiveness at day 90 and day 180 was estimated using Kaplan-Meier analysis and hazard ratios (HRs) by multivariate analysis. This clinical trial is registered with ClinicalTrials.gov, NCT05096702, and is completed. FINDINGS: Records from Sept 9, 2021, to Aug 31, 2022, included 5554 patients with P vivax malaria. In all treated patients of any age and any G6PD status, recurrence-free effectiveness at day 180 was 75·8% (95% CI 74·0-77·6) with tafenoquine, 73·4% (71·9-75·0) with 7-day primaquine, and 82·1% (77·7-86·8) with weekly primaquine. In patients aged at least 16 years who were G6PD normal, recurrence-free effectiveness until day 90 was 88·6% (95% CI 87·2-89·9) in those who were treated with tafenoquine (n=2134) and 83·5% (79·8-87·4) in those treated with 7-day primaquine (n=370); after adjustment for confounding factors, the HR for recurrence following tafenoquine versus 7-day primaquine was 0·65 (95% CI 0·49-0·86; p=0·0031), with similar outcomes between the two treatments at day 180 (log-rank p=0·82). Over 180 days, median time to recurrence in patients aged at least 16 years who were G6PD normal was 92 days (IQR 76-120) in those treated with tafenoquine and 68 days (52-94) in those treated with 7-day primaquine. INTERPRETATION: In this real-world setting, single-dose tafenoquine was more effective at preventing P vivax recurrence in patients aged at least 16 years who were G6PD normal compared with 7-day primaquine at day 90, while overall efficacy at 180 days was similar. The public health benefits of the P vivax radical cure treatment algorithm incorporating G6PD quantitative testing and tafenoquine support its implementation in Brazil and potentially across South America. FUNDING: Brazilian Ministry of Health, Municipal and State Health Secretariats; Fiocruz; Medicines for Malaria Venture; Bill & Melinda Gates Foundation; Newcrest Mining; and the UK Government. TRANSLATION: For the Portuguese translation of the abstract see Supplementary Materials section.

Operational feasibility of Plasmodium vivax radical cure with tafenoquine or primaquine following point-of-care, quantitative glucose-6-phosphate dehydrogenase testing in the Brazilian Amazon: a real-life retrospective analysis.

BACKGROUND: To achieve malaria elimination, Brazil must implement Plasmodium vivax radical cure. We aimed to investigate the operational feasibility of point-of-care, quantitative, glucose-6-phosphate dehydrogenase (G6PD) testing followed by chloroquine plus tafenoquine or primaquine. METHODS: This non-interventional, observational study was done at 43 health facilities in Manaus (Amazonas State) and Porto Velho (Rondônia State), Brazil, implementing a new P vivax treatment algorithm incorporating point-of-care quantitative G6PD testing to identify G6PD status and single-dose tafenoquine (G6PD normal, aged ≥16 years, and not pregnant or breastfeeding) or primaquine (intermediate or normal G6PD, aged ≥6 months, not pregnant, or breastfeeding >1 month). Following training of health-care providers, we collated routine patient records from the malaria epidemiological surveillance system (SIVEP-Malaria) retrospectively for all consenting patients aged at least 6 months with parasitologically confirmed P vivax malaria mono-infection or P vivax plus P falciparum mixed infection, presenting between Sept 9, 2021, and Aug 31, 2022. The primary endpoint was the proportion of patients aged at least 16 years with P vivax mono-infection treated or not treated appropriately with tafenoquine in accordance with their G6PD status. The trial is registered with ClinicalTrials.gov, NCT05096702, and is completed. FINDINGS: Of 6075 patients enrolled, 6026 (99·2%) had P vivax mono-infection, 2685 (44·6%) of whom were administered tafenoquine. G6PD status was identified in 2685 (100%) of 2685 patients treated with tafenoquine. The proportion of patients aged at least 16 years with P vivax mono-infection who were treated or not treated appropriately with tafenoquine in accordance with their G6PD status was 99·7% (95% CI 99·4-99·8; 4664/4680). INTERPRETATION: Quantitative G6PD testing before tafenoquine administration was operationally feasible, with high adherence to the treatment algorithm, supporting deployment throughout the Brazilian health system. FUNDING: Brazilian Ministry of Health, Municipal and State Health Secretariats; Fiocruz; Medicines for Malaria Venture; Bill & Melinda Gates Foundation; Newcrest Mining; and the UK Government. TRANSLATION: For the Portuguese translation of the abstract see Supplementary Materials section.

Essential Oil Composition and DNA Barcode and Identification of Aniba species (Lauraceae) Growing in the Amazon Region.

Lauraceae species are widely represented in the Amazon, presenting a significant essential oil yield, large chemical variability, various biological applications, and high economic potential. Its taxonomic classification is difficult due to the accentuated morphological uniformity, even among taxa from a different genus. For this reason, the present work aimed to find chemical and molecular markers to discriminate Aniba species collected in the Pará State (Brazil). The chemical composition of the essential oils from Aniba canelilla, A. parviflora, A. rosaeodora, and A. terminalis were grouped by multivariate statistical analysis. The major compounds were rich in benzenoids and terpenoids such as 1-nitro-2-phenylethane (88.34-70.85%), linalool (15.2-75.3%), α-phellandrene (36.0-51.8%), and ß-phellandrene (11.6-25.6%). DNA barcodes were developed using the internal transcribed spacer (ITS) nuclear region, and the matK, psbA-trnH, rbcL, and ycf1 plastid regions. The markers psbA-trnH and ITS showed the best discrimination for the species, and the phylogenic analysis in the three- (rbcL + matK + trnH - psbA and rbcL + matK + ITS) and four-locus (rbcL + matK + trnH - psbA + ITS) combination formed clades with groups strongly supported by the Bayesian inference (BI) (PP:1.00) and maximum likelihood (ML) (BS ≥ 97%). Therefore, based on statistical multivariate and phylogenetic analysis, the results showed a significant correlation between volatile chemical classes and genetic characteristics of Aniba species.

Esquemas de gênero de adolescentes do sexo feminino / Gender schemas of female adolescents

Este estudo objetivou identificar os esquemas de gênero entre adolescentes do sexo feminino. Participaram 93 adolescentes do sexo feminino (idade média 16 anos), estudantes de uma escola de Ensino Médio Integrado à Educação Profissional no estado de Minas Gerais. Os dados foram coletados por meio da aplicação do Inventário Feminino dos Esquemas de Gênero do Autoconceito que avalia fatores do esquema de gênero feminino (Sensualidade, Inferioridade e Ajustamento social) e masculino (Arrojamento, Egocentrismo e Negligência) em mulheres. Os dados foram analisados estatisticamente por Análises de Variância (ANOVA). Os resultados indicaram uma predominância do perfil de esquema de gênero isoesquemático (93,6%), demonstrando uma simetria entre os esquemas masculino e feminino. Os perfis de esquemas de gêneros se diferenciaram significativamente em relação ao Egocentrismo, Negligência, Ajuste Social e Sensualidade. São resultados importantes, pois a maioria dos estudos em esquema de gênero foca a população adulta.

This study aimed to identify the gender schemas among students adolescents women. A total of 93 female adolescents students (mean age 16 years) from a secondary school integrated to vocational education of the state of Minas Gerais participated in the study. Data were collected through the collective application of the Female Inventory of Gender Schemes of Self-Conception that evaluates factors of the female gender schema (factors: Sensuality, Inferiority and Social Adjustment) and male (factors: Burden, Egocentrism and Neglect) in women. The data were analyzed statistically by Analysis of Variance (ANOVA). The results indicated a predominance of the isoschematic gender scheme profile (93.6%), demonstrating a symmetry between the male and female schemes. The gender schema profiles differed significantly from Egocentrism, Neglect, Social Adjustment, and Sensuality. It is important result, since most studies in a gender scheme focus on the adult population.

Effects of the application of the amniotic membrane in the healing process of skin wounds in rats.

PURPOSE: To evaluate the efficacy of the application of the human amniotic membrane (HAM) on the inflammatory process, fibroblast proliferation, formation of collagenand reduction of skin wound areas in rats. METHODS: Thirty six rats were submitted to a surgical injury induction and divided into two groups (n = 18): group C (control) and T (treated with the HAM). The macroscopic evolution in the wound area and the histological characteristics of the skin samples were evaluated. RESULTS: The regression of the wound area was greater in group T. The histological analysis revealed a significant reduction (p < 0.05) in the inflammatory infiltrate in group T at all experimental periods compared with that in the control group. Furthermore, the group T presented a significant increase in the proliferation of fibroblasts at 14 and 21 days compared with group C (p < 0.05). Regarding the deposition of mature collagen fibers, there was an increase in the replacement of type III collagen by type I collagen in group T (p < 0.05). CONCLUSION: Treatment with the HAM reduced the healing time as well as the inflammatory responses, increased the proliferation of fibroblasts, and induced a higher concentration of mature collagen fibers.

Effects of the application of the amniotic membrane in the healing process of skin wounds in rats

Abstract Purpose: To evaluate the efficacy of the application of the human amniotic membrane (HAM) on the inflammatory process, fibroblast proliferation, formation of collagenand reduction of skin wound areas in rats. Methods: Thirty six rats were submitted to a surgical injury induction and divided into two groups (n = 18): group C (control) and T (treated with the HAM). The macroscopic evolution in the wound area and the histological characteristics of the skin samples were evaluated. Results: The regression of the wound area was greater in group T. The histological analysis revealed a significant reduction (p < 0.05) in the inflammatory infiltrate in group T at all experimental periods compared with that in the control group. Furthermore, the group T presented a significant increase in the proliferation of fibroblasts at 14 and 21 days compared with group C (p < 0.05). Regarding the deposition of mature collagen fibers, there was an increase in the replacement of type III collagen by type I collagen in group T (p < 0.05). Conclusion: Treatment with the HAM reduced the healing time as well as the inflammatory responses, increased the proliferation of fibroblasts, and induced a higher concentration of mature collagen fibers.

Automated pulse discrimination of two freely-swimming weakly electric fish and analysis of their electrical behavior during dominance contest.

Electric fishes modulate their electric organ discharges with a remarkable variability. Some patterns can be easily identified, such as pulse rate changes, offs and chirps, which are often associated with important behavioral contexts, including aggression, hiding and mating. However, these behaviors are only observed when at least two fish are freely interacting. Although their electrical pulses can be easily recorded by non-invasive techniques, discriminating the emitter of each pulse is challenging when physically similar fish are allowed to freely move and interact. Here we optimized a custom-made software recently designed to identify the emitter of pulses by using automated chirp detection, adaptive threshold for pulse detection and slightly changing how the recorded signals are integrated. With these optimizations, we performed a quantitative analysis of the statistical changes throughout the dominance contest with respect to Inter Pulse Intervals, Chirps and Offs dyads of freely moving Gymnotus carapo. In all dyads, chirps were signatures of subsequent submission, even when they occurred early in the contest. Although offs were observed in both dominant and submissive fish, they were substantially more frequent in submissive individuals, in agreement with the idea from previous studies that offs are electric cues of submission. In general, after the dominance is established the submissive fish significantly changes its average pulse rate, while the pulse rate of the dominant remained unchanged. Additionally, no chirps or offs were observed when two fish were manually kept in direct physical contact, suggesting that these electric behaviors are not automatic responses to physical contact.

Sex ratio of equine offspring is affected by the ages of the mare and stallion.

The aim of this study was to determine the influence of parental age on the sex ratio of offspring in horses. Two trials were performed. In the first trial, the data from a randomly obtained population with a 1:1 sex ratio of 59,950 Mangalarga Marchador horses born in Brazil from 1990 to 2011 were analyzed. The sex ratios of the offspring were compared among groups according to the mare and the stallion ages (from 3 to 25 years). In the first step of the analysis, the mares and stallions were grouped according to age in 5-year intervals. In the second step, the groups were based on the parental age gap at conception. In the third step, the group of the mares and stallions with similar ages from the second step was subdivided, and the different parental age subgroups that were divided into 5-year intervals were compared. In the fourth step, the sex ratio of the offspring was determined according to the ages of the mares and the stallions at conception. The second trial was based on the data from 253 horses of several breeds that were born after natural gestation into a herd from 1989 to 2010, and the offspring of groups that were younger or older than 15 years were compared. The data from both trials were analyzed using a chi-square test (P ≤ 0.01 for the first trial; and P ≤ 0.05 for the second trial) for the comparisons of the sex ratios. In the first trial, the Spearman test (P ≤ 0.01) was used to verify the correlations between the parental age and the offspring sex ratio. In the first trial, the offspring sex ratio decreased as the mare or stallion age increased, and the decrease was more marked for the mares than for the stallions. In the second trial, the mares older than 15 years had more fillies than the younger mares, but the stallion age had no effect on the sex of the offspring. The first trial, with a large number of horses, revealed the pattern of the distribution of the sex ratios of offspring according to the parental age in horses, whereas the second trial, with a more restricted number of horses, confirmed the influence of the age of the mare on the offspring sex ratio. We concluded that the parental age affected the offspring sex ratio in horses and that this effect was stronger for the mares than for the stallions.

Optimal channel efficiency in a sensory network.

Spontaneous neural activity has been increasingly recognized as a subject of key relevance in neuroscience. It exhibits nontrivial spatiotemporal structure reflecting the organization of the underlying neural network and has proved to be closely intertwined with stimulus-induced activity patterns. As an additional contribution in this regard, we report computational studies that strongly suggest that a stimulus-free feature rules the behavior of an important psychophysical measure of the sensibility of a sensory system to a stimulus, the so-called dynamic range. Indeed in this paper we show that the entropy of the distribution of avalanche lifetimes (information efficiency, since it can be interpreted as the efficiency of the network seen as a communication channel) always accompanies the dynamic range in the benchmark model for sensory systems. Specifically, by simulating the Kinouchi-Copelli (KC) model on two broad families of model networks, we generically observed that both quantities always increase or decrease together as functions of the average branching ratio (the control parameter of the KC model) and that the information efficiency typically exhibits critical optimization jointly with the dynamic range (i.e., both quantities are optimized at the same value of that control parameter, that turns out to be the critical point of a nonequilibrium phase transition). In contrast with the practice of taking power laws to identify critical points in most studies describing measured neuronal avalanches, we rely on data collapses as more robust signatures of criticality to claim that critical optimization may happen even when the distribution of avalanche lifetimes is not a power law, as suggested by a recent experiment. Finally, we note that the entropy of the size distribution of avalanches (information capacity) does not always follow the dynamic range and the information efficiency when they are critically optimized, despite being more widely used than the latter to describe the computational capabilities of a neural network. This strongly suggests that dynamical rules allowing a proper temporal matching of the states of the interacting neurons is the key for achieving good performance in information processing, rather than increasing the number of available units.

Recovery of iron oxides from acid mine drainage and their application as adsorbent or catalyst.

Iron oxide particles recovered from acid mine drainage represent a potential low-cost feedstock to replace reagent-grade chemicals in the production of goethite, ferrihydrite or magnetite with relatively high purity. Also, the properties of iron oxides recovered from acid mine drainage mean that they can be exploited as catalysts and/or adsorbents to remove azo dyes from aqueous solutions. The main aim of this study was to recover iron oxides with relatively high purity from acid mine drainage to act as a catalyst in the oxidation of dye through a Fenton-like mechanism or as an adsorbent to remove dyes from an aqueous solution. Iron oxides (goethite) were recovered from acid mine drainage through a sequential precipitation method. Thermal treatment at temperatures higher than 300 °C produces hematite through a decrease in the BET area and an increase in the point of zero charge. In the absence of hydrogen peroxide, the solids adsorbed the textile dye Procion Red H-E7B according to the Langmuir model, and the maximum amount adsorbed decreased as the temperature of the thermal treatment increased. The decomposition kinetics of hydrogen peroxide is dependent on the H(2)O(2) concentration and iron oxides dosage, but the second-order rate constant normalized to the BET surface area is similar to that for different iron oxides tested in this and others studies. These results indicate that acid mine drainage could be used as a source material for the production of iron oxide catalysts/adsorbents, with comparable quality to those produced using analytical-grade reagents.

Saúde e segurança no ambiente rural: uma análise das condições de trabalho em um setor de ordenha / Health and safety at rural environment: an analysis of work conditions in a milking sector

A saúde e a segurança no trabalho são fatores preponderantes em todos os setores produtivos, assim como no agronegócio e, especificamente, na cadeia produtiva do leite. Neste artigo, apresentam-se os resultados de uma análise das condições do ambiente de trabalho de um setor de ordenha de leite localizado na região Sudoeste do Estado da Bahia. Buscou-se identificar os riscos ocupacionais (físicos, químicos, biológicos, ergonômicos e de acidentes), bem como aspectos relativos à higiene do alimento. A pesquisa consistiu de um estudo de caso, com características qualitativas e exploratórias, tendo por finalidade descrever a situação encontrada no setor, confrontando-a com as legislações vigentes. Foram diagnosticados, predominantemente, riscos ergonômicos e de acidentes, além de irregularidades nas condições higiênico-sanitárias, que podem constituir riscos biológicos. Não foram constatados riscos químicos ou físicos no setor. Os resultados apontam para a necessidade de melhoria no setor, que vão desde mudanças estruturais, questões organizacionais, como o oferecimento de treinamentos sobre procedimentos operacionais e em saúde e segurança no trabalho.

The health and safety at work are important and might be considered as essential and relevant for all productive sectors, including agribusiness, specifically in the milk chain production. This paper presents the results of an environment work conditions analysis in a milking sector at southwest region of Bahia State. The study aimed to identify the occupational risks (physical, chemical, biological, ergonomic and accidents), as well as aspects related to food hygiene. The research consisted in a case study with qualitative and exploratory characteristics, aiming to observe and report the real conditions identified in the work environment and comparing with the current legislation. It was diagnosed predominantly ergonomic and accident risks, as well as irregular sanitary conditions that can result in biological risks. It was not found chemical or physical risks in the sector. Facing the results, it was proposed some recommendations involving issues related to organizational conditions, by offering training on operational procedures and health and safety at work.

Estudo comparativo entre três técnicas de desglaciamento de filé de pescada / Comparative study of three techniques desglaciamento fillet of fish

O glaciamento consiste na aplicação de uma camada de gelo no produto congelado, com a finalidade de proteger o produto, principalmente o pescado, contra a desidratação e a oxidação durante a conservação pelo frio industrial. O processo inverso é o desglaciamento a retirada desta camada de gelo, ou “glacê” , sem promover o descongelamento do mesmo. Pode ser efetuado através de várias técnicas, que visam calcular o peso líquido do produto. O objetivo desta pesquisa foi verificar a correlação entre as metodologias para desglaciamento aplicadas no Brasil (Portaria INMETRO n.005, de 12 de janeiro de 2006), Portugal (Decreto-Lei n. 37/2004 de 26 de Fevereiro de 2004) e Estados Unidos (CODEX STAN 165-1989 (REV. 1 – 1995).

Facial features of patients with sickle cell anemia.

OBJECTIVE: To characterize the craniofacial features of patients with sickle cell anemia (SCA). MATERIALS AND METHODS: Fifty patients with SCA in the north of Minas Gerais, Brazil, were evaluated using standardized photographs (front and profile) for a subjective facial analysis and digital radiographs for a computerized cephalometric analysis. To obtain linear and angular measurements, cephalometric points were marked on the digital images by a single examiner, using the program Radiocef 6.0, and facial analyses were performed by four different orthodontists. RESULTS: Of the population studied, 28 patients were female with a mean age of 27.7 years. Most of the patients (64%) had their faces classified as esthetically acceptable, although results showed a predominance of convex profiles (72%). The mean of the SNA angle was 84.56°, diagnosing proper positioning of the maxilla from the base of the skull. The prevalence of pattern II was 32%, and 31% showed maxillary protrusion; the effective length of the maxilla was reduced in 64%. Retrusion of the mandible was observed in 30%, and 76% had reduced mandibular length. Four measurements (mandibular length, maxillary length, anterior face height, and maxillomandibular difference) showed statistically significant differences between genders, where these measurements were higher for males than for females. CONCLUSION: Most patients did not show compensatory maxillary expansion, which was determined by the prevalence of decreased maxillary length (64%) and by the absence of maxillary protrusion in 69% of the SCA patients evaluated.

Analytical results on Muller's ratchet effect in growing populations.

Fontanari introduced [Phys. Rev. Lett. 91, 218101 (2003)] a model for studying Muller's ratchet phenomenon in growing asexual populations. They studied two situations, either including a death probability for each newborn or not, but were able to find analytical (recursive) expressions only in the no-decay case. In this Brief Report a branching process formalism is used to find recurrence equations that generalize the analytical results of the original paper besides confirming the interesting effects their simulations revealed.

Supporting adherence to highly active antiretroviral therapy and protected sex among people living with HIV/AIDS: the role of patient-provider communication in Rio de Janeiro, Brazil.

This exploratory study examined patient-provider communication dynamics regarding adherence to highly active antiretroviral therapy (HAART) and protective sexual behavior among people living with HIV/AIDS (PLWHA). We conducted 20 direct observations of routine consultations between PLWHA and care providers in two large public health clinics providing free HIV medications and clinical care to PLWHA in the greater Rio de Janeiro area of Brazil. Immediately after these observations, 20 semistructured in-depth interviews were conducted with observation participants regarding their communication with providers, overall clinic experience, and questions and concerns about adherence to HAART and safe sex. Findings from observations showed that patient-provider communication focused almost exclusively on biomedical aspects of HIV-related treatment such as symptom management. In most observations, adherence to HAART was addressed. However, questions posed by providers regarding adherence were generally close-ended and leading, discouraging an open exchange regarding potential difficulties related to adherence. HIV/sexually transmitted infection (STI)- related protective behaviors were seldom addressed except when the patient displayed STI symptoms or was thought to be pregnant. In qualitative interviews, patients generally reported satisfaction with their providers, but also reported a variety of concerns and challenges related to adherence to HAART and protective sexual behavior that were not expressed in patient-provider interactions. We conclude that one way in which adherence to HAART and protective sexual behavior among PLWHA could be facilitated is by improving patient- provider communication on these topics, including increasing the frequency of openended, nonjudgmental dialogue initiated by care providers.

The dynamical way to mutation-selection balance of an infinite population evolving on a truncated fitness landscape.

This paper presents the exact analytical solution, valid for all generations and initial conditions, for the frequency distribution of haploids with infinite-sites genome carrying a given number of mutations in a population evolving deterministically on a truncated fitness landscape. This landscape is a generalization of the single sharp peak one, widely used in quasispecies theory, although here there are no reverse mutations.

A educação pelo fora: pedagogia e filosofia da diferença

A educação encontra seu princípio formador num processo de ‘condução para fora’. Quais exatamente as condições de realização desse princípio atualmente? Ela encontraria uma inspiração possível na Filosofia da diferença contemporânea, que teve no fora um dos seus temas maiores.(AU)

Effect of selection on the topology of genealogical trees.

Selection is one of the factors that most influence the shape of genealogical trees. Here we report results of simulations of the infinite-sites version of Moran's model of population genetics aiming at quantifying how the presence of selection affects the branching pattern (topology) of binary genealogical trees. In particular, we consider a scenario of purifying or negative selection in which all mutations are deleterious and each new mutation reduces the fitness of the individual by the same fraction. Analysis of five statistical measures of tree balance or symmetry borrowed from taxonomy indicates that the genealogical trees of samples of populations in which selection is actuating are in the average more asymmetric than neutral trees and that this effect is enhanced by increasing the sample size. However, a quantitative evaluation of the power of these balance measures to detect a tree topology significantly distinct from the neutral one indicates that they are not useful as tests of neutrality of mutations.

Analytical solution of the evolution dynamics on a multiplicative-fitness landscape.

In an infinite population the frequency distribution of individuals carrying a given number of mutations obeys a set of recursion equations, the equilibrium solution of which describes the mutation-selection balance. Although this solution is well-known in the case of a multiplicative-fitness landscape, where it is assumed that all mutations are deleterious and that each new mutation reduces the fitness of the individual by the same fraction, we are not aware of the existence of an analytical solution for the full dynamics. Using the generating function approach, we present here an explicit analytical solution for the frequency distribution recursion equations valid for all generations and initial conditions.