Aerobic bacterial profile and antibiotic resistance in patients with diabetic foot infections

ABSTRACTINTRODUCTION: This study aimed to determine the frequencies of bacterial isolates cultured from diabetic foot infections and assess their resistance and susceptibility to commonly used antibiotics.METHODS: This prospective study included 41 patients with diabetic foot lesions. Bacteria were isolated from foot lesions, and their antibiotic susceptibility pattern was determined using the Kirby-Bauer disk diffusion method and/or broth method [minimum inhibitory concentration (MIC)].RESULTS: The most common location of ulceration was the toe (54%), followed by the plantar surface (27%) and dorsal portion (19%). A total of 89 bacterial isolates were obtained from 30 patients. The infections were predominantly due to Gram-positive bacteria and polymicrobial bacteremia. The most commonly isolated Gram-positive bacteria were Staphylococcus aureus, followed by Staphylococcus saprophyticus, Staphylococcus epidermidis, Streptococcus agalactiae, and Streptococcus pneumoniae. The most commonly isolated Gram-negative bacteria were Proteus spp. and Enterobacterspp., followed by Escherichia coli, Pseudomonasspp., and Citrobacterspp. Nine cases of methicillin-resistant Staphylococcus aureus (MRSA) had cefoxitin resistance, and among these MRSA isolates, 3 were resistant to vancomycin with the MIC technique. The antibiotic imipenem was the most effective against both Gram-positive and Gram-negative bacteria, and gentamicin was effective against Gram-negative bacteria.CONCLUSIONS: The present study confirmed the high prevalence of multidrug-resistant pathogens in diabetic foot ulcers. It is necessary to evaluate the different microorganisms infecting the wound and to know the antibiotic susceptibility patterns of the isolates from the infected wound. This knowledge is crucial for planning treatment with the appropriate antibiotics, reducing resistance patterns, and minimizing healthcare costs.

Phenotypic and genotypic profile of pyrethroid resistance in populations of the mosquito Aedes aegypti from Goiânia, Central West Brazil

ABSTRACTINTRODUCTION:The mosquito Aedes aegypti has evolved resistance to pyrethroid insecticides. The present study evaluated Ae. aegypti from Goiânia for the resistant phenotype and for mutations associated with resistance.METHODS:Insecticide dose-response bioassays were conducted on mosquitoes descended from field-collected eggs, and polymerase chain reaction (PCR) was used to genotype 90 individuals at sites implicated in pyrethroid resistance.RESULTS:All mosquito populations displayed high levels of resistance to deltamethrin, as well as high frequencies of the 1016Ile kdr and 1534Cys kdrmutations.CONCLUSIONS:Aedes aegypti populations in the Goiânia area are highly resistant to deltamethrin, presumably due to high frequencies of kdr(knockdown-resistance) mutations.

Frequency of histopathological changes in Howler monkeys ( Alouatta sp.) naturally infected with yellow fever virus in Brazil

Abstract: INTRODUCTION: Due to the importance that Howler monkeys have on the yellow fever (YF) epidemiological sylvatic cycle in Brazil, more accurate morphological diagnostic criteria needs to be established, especially considering the differences that may exist between the genera of Brazilian non-human primates (NHPs) involved in yellow fever virus (YFV) epizootics. METHODS: Records of YF epizootics in NHPs in Brazil between 2007 and 2009 were obtained from the Brazilian Ministry of Health database to select YF positive (n=98) Howler monkeys (Alouatta sp.) for this study. The changes described in the histopathological reports were categorized by organ and their frequencies calculated. RESULTS: The most frequent lesions observed in the animals with YF were hepatocyte apoptosis (Councilman body formation), midzonal hepatocyte necrosis, steatosis, liver hemorrhage, inflammatory mononuclear cell infiltration of the liver, renal acute tubular necrosis and interstitial nephritis. Midzonal hepatocyte necrosis, steatosis and hemorrhage presented positive correlations with apoptosis of hepatocytes, suggesting strong YFV pathogenic effect association; they were also the main histopathological changes in the Alouatta sp. A pronounced negative correlation between apoptosis of hepatocytes and hepatic mononuclear cell infiltration pointed to significant histopathological differences between YFV infection in Howler monkeys and humans. CONCLUSIONS: The results warn that NHPs may exhibit different response patterns following YFV infection and require a more careful diagnosis. Presumptive diagnosis based on primate histopathological lesions may contribute to public health service control.

Secular trends in Klebsiella pneumoniae isolated in a tertiary-care hospital: increasing prevalence and accelerated decline in antimicrobial susceptibility

Abstract: INTRODUCTION Klebsiella pneumoniae has become an increasingly important etiologic agent of nosocomial infections in recent years. This is mainly due to the expression of virulence factors and development of resistance to several antimicrobial drugs. METHODS This retrospective study examines data obtained from the microbiology laboratory of a Brazilian tertiary-care hospital. To assess temporal trends in prevalence and antimicrobial susceptibility, K. pneumoniae isolates were analyzed from 2000 to 2013. The relative frequencies of K. pneumoniae isolation were calculated among all Gram-negative bacilli isolated in each period analyzed. Susceptibility tests were performed using automated systems. RESULTS: From 2000-2006, K. pneumonia isolates comprised 10.7% of isolated Gram-negative bacilli (455/4260). From 2007-2013, this percentage was 18.1% (965/5331). Strictly considering isolates from bloodstream infections, the relative annual prevalence of K. pneumoniae increased from 14-17% to 27-32% during the same periods. A progressive decrease in K. pneumoniae susceptibility to all antimicrobial agents assessed was detected. Partial resistance was also observed to antimicrobial drugs that have been used more recently, such as colistin and tigecycline. CONCLUSIONS Our study indicates that K. pneumoniae has become a major pathogen among hospitalized patients and confirms its recent trend of increasing antimicrobial resistance.

Antiphospholipid antibodies in 57 children and adolescents with systemic lupus erythematosus

OBJECTIVE: To investigate the frequencies and behavior of antiphospholipid antibodies in 57 children and adolescents with systemic lupus erythematosus. METHODS: Anticardiolipin antibodies were investigated by ELISA and lupus anticoagulant antibodies by the international tests recommended. The antiphospholipid antibodies analyses were performed in frozen samples (mean of 5.3 samples per patient obtained during a mean follow-up period of 3 years and 7 months) and on blood samples collected between January 1997 and November 1998 (mean of 2.5 samples per patient during a 2-year follow-up period). RESULTS: The frequencies of antiphospholipid antibodies (anticardiolipin and lupus anticoagulant) were similar in the samples collected prospectively and in the frozen samples (retrospective study): 63.2% and 75.4% respectively. Positivity for these antibodies fluctuated during the follow-up period and was not associated with any clinical or laboratory parameters of lupus erythematosus, including autoantibodies and also including disease activity and/or severity scores. CONCLUSIONS: The frequencies of antiphospholipid antibodies in children and adolescents with lupus erythematosus were similar to those observed in adults. The positivity fluctuated during the follow-up and was not correlated with clinical and/or laboratory disease parameters.

Use of nonradioactive labeling to detect large gene rearrangements in 21-hydroxylase deficiency

PURPOSE: To establish the Southern blotting technique using hybridization with a nonradioactive probe to detect large rearrangements of CYP21A2 in a Brazilian cohort with congenital adrenal hyperplasia due to 21-hydroxylase deficiency (CAH-21OH). METHOD: We studied 42 patients, 2 of them related, comprising 80 non-related alleles. DNA samples were obtained from peripheral blood, digested by restriction enzyme Taq I, submitted to Southern blotting and hybridized with biotin-labeled probes. RESULTS: This method was shown to be reliable with results similar to the radioactive-labeling method. We found CYP21A2 deletion (2.5%), large gene conversion (8.8%), CYP21AP deletion (3.8%), and CYP21A1P duplication (6.3%). These frequencies were similar to those found in our previous study in which a large number of cases were studied. Good hybridization patterns were achieved with a smaller amount of DNA (5 mug), and fragment signs were observed after 5 minutes to 1 hour of exposure. CONCLUSIONS: We established a non-radioactive (biotin) Southern blot/hybridization methodology for CYP21A2 large rearrangements with good results. Despite being more arduous, this technique is faster, requires a smaller amount of DNA, and most importantly, avoids problems with the use of radioactivity.

Geographic pattern of genetic diversity in natural populations of Rosewood (Aniba rosaeodora), in the Central Amazonia

Rosewood (Aniba rosaeodora Ducke, Lauraceae) is an Amazonian evergreen tree and a source of the purest linalool, the main component of its essential oil, which is very valuable in the international perfumery market. After decades of over-exploitation it is currently considered as threatened. We evaluated the genetic diversity and its distribution in four populations in Central Amazonia. Thirty-five reliable RAPD markers were generated, of which 32 were polymorphic (91.4%). Variation was higher within the populations (76.5%; p < 0.0001) and geographic distribution contributed to population differentiation (23.4%; p < 0.0001). The Amazon River had a small influence on gene flow (3.3%; p < 0.0001), but we identified evidence of gene flow across the river. There were significant differences in marker frequencies (p < 0.05), in agreement with the low gene flow (Nm = 2.02). The correlation between genetic distance and gene flow was - 0.95 (p = 0.06) and between geographic distance and gene flow was -0.78 (p = 0.12). There was a geographic cline of variability across an East-West axis, influenced as well by the Amazon River, suggesting the river could be a barrier to gene flow. Although threatened, these Rosewood populations retain high diversity, with the highest levels in the Manaus population, which has been protected for over 42 years in a Reserve.

Cardiovascular assessment of patients with Ullrich-Turner's Syndrome on Doppler echocardiography and magnetic resonance imaging

OBJECTIVE: To assess the cardiovascular features of Ullrich-Turner's syndrome using echocardiography and magnetic resonance imaging, and to correlate them with the phenotype and karyotype of the patients. The diagnostic concordance between the 2 methods was also assessed. METHODS: Fifteen patients with the syndrome were assessed by echocardiography and magnetic resonance imaging (cardiac chambers, valves, and aorta). Their ages ranged from 10 to 28 (mean of 16.7) years. The karyotype was analyzed in 11 or 25 metaphases of peripheral blood lymphocytes, or both. RESULTS: The most common phenotypic changes were short stature and spontaneous absence of puberal development (100%); 1 patient had a cardiac murmur. The karyotypes detected were as follows: 45,X (n=7), mosaics (n=5), and deletions (n=3). No echocardiographic changes were observed. In regard to magnetic resonance imaging, coarctation and dilation of the aorta were found in 1 patient, and isolated dilation of the aorta was found in 4 patients. CONCLUSION: The frequencies of coarctation and dilation of the aorta detected on magnetic resonance imaging were similar to those reported in the literature (5.5% to 20%, and 6.3% to 29%, respectively). This confirmed the adjuvant role of magnetic resonance imaging to Doppler echocardiography for diagnosing cardiovascular alterations in patients with Ullrich-Turner's syndrome.

Analysis of the Prevalence of Ventricular Late Potentials in the Late Phase of Myocardial Infarction Based on the Site of Infarction

OBJECTIVE: The initial site of myocardial infarction (MI) may influence the prevalence of ventricular late potentials (VLP), high-frequency signals, due to the time course of ventricular activation. The prevalence of VLP in a period of more than 2 years after acute MI was assessed focusing on the initially injured wall . METHODS: The prevalence of VLP in a late phase after MI (median of 924 days) in anterior/antero-septal and inferior/infero-dorsal wall lesion was analyzed using signal-averaged electrocardiogram in time domain. The diagnostic performance of the filters employed for analysis on was tested at high-pass cut-off frequencies of 25 Hz, 40 Hz and 80 Hz. RESULTS: The duration of the ventricular activation and its terminal portion were larger in inferior than anterior infarction, at high-pass cut-off frequencies of 40 Hz and 80 Hz. In patients with ventricular tachycardia, these differences were more remarked. The prevalence of ventricular late potentials was three times greater in inferior than anterior infarction. CONCLUSION: Late after myocardial infarction, the prevalence and the duration of ventricular late potentials are greater in lesions of inferior/infero-dorsal than anterior/antero-septal wall confirming their temporal process, reflecting their high-frequency content.

Analysis of the Association Between Apolipoprotein E Polymorphism and Cardiovascular Risk Factors in an Elderly Population with Longevity

OBJECTIVE: To establish the allelic and genotypic frequencies related to apolipoprotein E (ApoE) polymorphism and association of the genotypes with risk factors and cardiovascular morbidity in an elderly population with longevity. METHODS: We analyzed 70 elderly patients aged 80 years or more who were part of the Projeto Veranópolis. We used the gene amplification technique through the polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) and cleavage with the restriction enzyme Hha I to identify the ApoE genotypes. The most frequent genotypes were compared considering biological variables and cardiovascular risks and morbidity. RESULTS: The frequencies of the E2, E3, and E4 alleles were 0.05, 0.84, and 0.11, respectively, and of the genotypes were as follows: E3E3 (0.70), E3E4 (0.22), E2E3 (0.06), and E2E2 (0.02). Individuals with the E3E4 had a mean age greater than those with the E3E3. No association was observed between the genotypes and the variables analyzed, except for obesity, which was associated with the E3E3 genotype. Individuals with the E3E4 genotype had high levels of LDL-cholesterol and fibrinogen as compared with those with the E3E3 genotype. CONCLUSION: The results suggest that the E4E4 genotype may be associated with early mortality. A balance between the protective or neutral factors and the cardiovascular risk factors may occur among the individuals with different genotypes, attenuating the negative effects of the E4 allele.

Medical care and deaths due to coronary artery disease in Brazil, 1980-1999

OBJECTIVE: To estimate the frequency of medical care preceding deaths due to coronary artery diseases (CAD) in different Brazilian regions and capitals and to describe trends in medical care from 1980 to 1999. METHODS: Information on medical care preceding deaths due to coronary artery diseases/acute myocardial infarction in adults > 20 years from 1980 to 1999 was collected in the DATASUS, the databank of the Brazilian Health Ministry. Sex, states, and capitals selected for 1999 were analyzed in the study. Medical care was stratified as follows: with, without, and ignored medical care. The descriptive analysis comprised frequencies, ratios of frequency, test for proportions, and increments or reductions in frequencies. RESULTS: Acute myocardial infarction (AMI) represented 75 to 85% of the CAD in the period; the frequency of deaths with medical care ranged from 48.9 to 63%, and that of ignored medical care ranged from 27.2 to 41.5%. The frequency of other CAD with medical care ranged from 56 to 76%. The frequency of deaths preceded by medical care decreased by 17.8%, and that with ignored medical care increased by 36.5% (RF=2). The values for the other CAD were -20.2% and +64.6% (RF=44.4). Deaths preceded by medical care were more frequent in females at all ages and in all Brazilian regions. CONCLUSION: The results show a high frequency of sudden death and suggest errors in diagnosis or codification and overestimation of the statistics about mortality. Validation of the death certificate diagnosis and frequent surveillance are required.

Post-Acute Coronary Syndrome Alcohol Abuse: Prospective Evaluation in the ERICO Study

Background:Some studies have indicated alcohol abuse as one of the contributors to the development of cardiovascular disease, particularly coronary heart disease. However, this relationship is controversial.Objective:To investigate the relationship between post-acute coronary syndrome (ACS) alcohol abuse in the Acute Coronary Syndrome Registry Strategy (ERICO Study).Methods:146 participants from the ERICO Study answered structured questionnaires and underwent laboratory evaluations at baseline, 30 days and 180 days after ACS. The Alcohol Use Disorders Identification Test (AUDIT) was applied to assess harmful alcohol consumption in the 12 months preceding ACS (30 day-interview) and six months after that.Results:The frequencies of alcohol abuse were 24.7% and 21.1% in the 12 months preceding ACS and six months after that, respectively. The most significant cardiovascular risk factors associated with high-risk for alcohol abuse 30 days after the acute event were: male sex (88.9%), current smoking (52.8%) and hypertension (58.3%). Six months after the acute event, the most significant results were replicated in our logistic regression, for the association between alcohol abuse among younger individuals [35-44 year-old multivariate OR: 38.30 (95% CI: 1.44-1012.56) and 45-54 year-old multivariate OR: 10.10 (95% CI: 1.06-96.46)] and for smokers [current smokers multivariate OR: 51.09 (95% CI: 3.49-748.01) and past smokers multivariate OR: 40.29 (95% CI: 2.37-685.93)].Conclusion:Individuals younger than 54 years and smokers showed a significant relation with harmful alcohol consumption, regardless of the ACS subtype.

Variations in the Prevalence of Risk Factors for Coronary Artery Disease in Rio Grande do Sul-Brazil: A Comparative Analysis between 2002 and 2014

Abstract Background: Due to the importance of coronary artery disease (CAD), continuous investigation of the risk factors (RFs) is needed. Objective: To evaluate the prevalence of RFs for CAD in cities in Rio Grande do Sul State, and compare it with that reported in a similar study conducted in the same cities in 2002. Methods: Cross-sectional study on 1,056 healthy adults, investigating the prevalence and absolute and relative frequencies of the following RFs for CAD: obesity, systemic arterial hypertension (SAH), dyslipidemias, smoking, sedentary lifestyle, diabetes mellitus, and family history, as well as age and sex. Data was collected in 19 cities, host of the Offices of the Regional Coordinators of Health, as in the 2002 study. Results: Twenty-six percent of the sample consisted of older adults and 57% were women. The prevalence of sedentary lifestyle was 44%, history family 50%, smoking 23%, overweight/obesity 68%, dyslipidemia (high cholesterol levels) 43%, SAH 40%, and diabetes 11%. When compared to the 2002 study, the prevalence of active smoking and sedentary behavior decreased, whereas the prevalence of hypertension, dyslipidemia and obesity increased. Obesity is the most prevalent RF in women, and SAH the most prevalent in men. Conclusions: The prevalence of RFs for CAD in Rio Grande do Sul State remains high. Hypertension, obesity and dyslipidemia are still prevalent and require major prevention programs. Smoking and physical inactivity have decreased in the state, suggesting the efficacy of related campaigns.

Análise estatística da distribuição de Poisson

The general properties of POISSON distributions and their relations to the binomial distribuitions are discussed. Two methods of statistical analysis are dealt with in detail: X2-test. In order to carry out the X2-test, the mean frequency and the theoretical frequencies for all classes are calculated. Than the observed and the calculated frequencies are compared, using the well nown formula: f(obs) - f(esp) 2; i(esp). When the expected frequencies are small, one must not forget that the value of X2 may only be calculated, if the expected frequencies are biger than 5. If smaller values should occur, the frequencies of neighboroughing classes must ge pooled. As a second test reintroduced by BRIEGER, consists in comparing the observed and expected error standard of the series. The observed error is calculated by the general formula: δ + Σ f . VK n-1 where n represents the number of cases. The theoretical error of a POISSON series with mean frequency m is always ± Vm. These two values may be compared either by dividing the observed by the theoretical error and using BRIEGER's tables for # or by dividing the respective variances and using SNEDECOR's tables for F. The degree of freedom for the observed error is one less the number of cases studied, and that of the theoretical error is always infinite. In carrying out these tests, one important point must never be overlloked. The values for the first class, even if no concrete cases of the type were observed, must always be zero, an dthe value of the subsequent classes must be 1, 2, 3, etc.. This is easily seen in some of the classical experiments. For instance in BORKEWITZ example of accidents in Prussian armee corps, the classes are: no, one, two, etc., accidents. When counting the frequency of bacteria, these values are: no, one, two, etc., bacteria or cultures of bacteria. Ins studies of plant diseases equally the frequencies are : no, one, two, etc., plants deseased. Howewer more complicated cases may occur. For instance, when analising the degree of polyembriony, frequently the case of "no polyembryony" corresponds to the occurrence of one embryo per each seed. Thus the classes are not: no, one, etc., embryo per seed, but they are: no additional embryo, one additional embryo, etc., per seed with at least one embryo. Another interestin case was found by BRIEGER in genetic studies on the number os rows in maize. Here the minimum number is of course not: no rows, but: no additional beyond eight rows. The next class is not: nine rows, but: 10 rows, since the row number varies always in pairs of rows. Thus the value of successive classes are: no additional pair of rows beyond 8, one additional pair (or 10 rows), two additional pairs (or 12 rows) etc.. The application of the methods is finally shown on the hand of three examples : the number of seeds per fruit in the oranges M Natal" and "Coco" and in "Calamondin". As shown in the text and the tables, the agreement with a POISSON series is very satisfactory in the first two cases. In the third case BRIEGER's error test indicated a significant reduction of variability, and the X2 test showed that there were two many fruits with 4 or 5 seeds and too few with more or with less seeds. Howewer the fact that no fruit was found without seed, may be taken to indicate that in Calamondin fruits are not fully parthenocarpic and may develop only with one seed at the least. Thus a new analysis was carried out, on another class basis. As value for the first class the following value was accepted: no additional seed beyond the indispensable minimum number of one seed, and for the later classes the values were: one, two, etc., additional seeds. Using this new basis for all calculations, a complete agreement of the observed and expected frequencies, of the correspondig POISSON series was obtained, thus proving that our hypothesis of the impossibility of obtaining fruits without any seed was correct for Calamondin while the other two oranges were completely parthenocarpic and fruits without seeds did occur.

A determinação dos números de indivíduos mínimos necessários na experimentação genética

The main object of the present paper consists in giving formulas and methods which enable us to determine the minimum number of repetitions or of individuals necessary to garantee some extent the success of an experiment. The theoretical basis of all processes consists essentially in the following. Knowing the frequency of the desired p and of the non desired ovents q we may calculate the frequency of all possi- ble combinations, to be expected in n repetitions, by expanding the binomium (p-+q)n. Determining which of these combinations we want to avoid we calculate their total frequency, selecting the value of the exponent n of the binomium in such a way that this total frequency is equal or smaller than the accepted limit of precision n/pª{ 1/n1 (q/p)n + 1/(n-1)| (q/p)n-1 + 1/ 2!(n-2)| (q/p)n-2 + 1/3(n-3) (q/p)n-3... < Plim - -(1b) There does not exist an absolute limit of precision since its value depends not only upon psychological factors in our judgement, but is at the same sime a function of the number of repetitions For this reasen y have proposed (1,56) two relative values, one equal to 1-5n as the lowest value of probability and the other equal to 1-10n as the highest value of improbability, leaving between them what may be called the "region of doubt However these formulas cannot be applied in our case since this number n is just the unknown quantity. Thus we have to use, instead of the more exact values of these two formulas, the conventional limits of P.lim equal to 0,05 (Precision 5%), equal to 0,01 (Precision 1%, and to 0,001 (Precision P, 1%). The binominal formula as explained above (cf. formula 1, pg. 85), however is of rather limited applicability owing to the excessive calculus necessary, and we have thus to procure approximations as substitutes. We may use, without loss of precision, the following approximations: a) The normal or Gaussean distribution when the expected frequency p has any value between 0,1 and 0,9, and when n is at least superior to ten. b) The Poisson distribution when the expected frequecy p is smaller than 0,1. Tables V to VII show for some special cases that these approximations are very satisfactory. The praticai solution of the following problems, stated in the introduction can now be given: A) What is the minimum number of repititions necessary in order to avoid that any one of a treatments, varieties etc. may be accidentally always the best, on the best and second best, or the first, second, and third best or finally one of the n beat treatments, varieties etc. Using the first term of the binomium, we have the following equation for n: n = log Riim / log (m:) = log Riim / log.m - log a --------------(5) B) What is the minimun number of individuals necessary in 01der that a ceratin type, expected with the frequency p, may appaer at least in one, two, three or a=m+1 individuals. 1) For p between 0,1 and 0,9 and using the Gaussean approximation we have: on - ó. p (1-p) n - a -1.m b= δ. 1-p /p e c = m/p } -------------------(7) n = b + b² + 4 c/ 2 n´ = 1/p n cor = n + n' ---------- (8) We have to use the correction n' when p has a value between 0,25 and 0,75. The greek letters delta represents in the present esse the unilateral limits of the Gaussean distribution for the three conventional limits of precision : 1,64; 2,33; and 3,09 respectively. h we are only interested in having at least one individual, and m becomes equal to zero, the formula reduces to : c= m/p o para a = 1 a = { b + b²}² = b² = δ2 1- p /p }-----------------(9) n = 1/p n (cor) = n + n´ 2) If p is smaller than 0,1 we may use table 1 in order to find the mean m of a Poisson distribution and determine. n = m: p C) Which is the minimun number of individuals necessary for distinguishing two frequencies p1 and p2? 1) When pl and p2 are values between 0,1 and 0,9 we have: n = { δ p1 ( 1-pi) + p2) / p2 (1 - p2) n= 1/p1-p2 }------------ (13) n (cor) We have again to use the unilateral limits of the Gaussean distribution. The correction n' should be used if at least one of the valors pl or p2 has a value between 0,25 and 0,75. A more complicated formula may be used in cases where whe want to increase the precision : n (p1 - p2) δ { p1 (1- p2 ) / n= m δ = δ p1 ( 1 - p1) + p2 ( 1 - p2) c= m / p1 - p2 n = { b2 + 4 4 c }2 }--------- (14) n = 1/ p1 - p2 2) When both pl and p2 are smaller than 0,1 we determine the quocient (pl-r-p2) and procure the corresponding number m2 of a Poisson distribution in table 2. The value n is found by the equation : n = mg /p2 ------------- (15) D) What is the minimun number necessary for distinguishing three or more frequencies, p2 p1 p3. If the frequecies pl p2 p3 are values between 0,1 e 0,9 we have to solve the individual equations and sue the higest value of n thus determined : n 1.2 = {δ p1 (1 - p1) / p1 - p2 }² = Fiim n 1.2 = { δ p1 ( 1 - p1) + p1 ( 1 - p1) }² } -- (16) Delta represents now the bilateral limits of the : Gaussean distrioution : 1,96-2,58-3,29. 2) No table was prepared for the relatively rare cases of a comparison of threes or more frequencies below 0,1 and in such cases extremely high numbers would be required. E) A process is given which serves to solve two problemr of informatory nature : a) if a special type appears in n individuals with a frequency p(obs), what may be the corresponding ideal value of p(esp), or; b) if we study samples of n in diviuals and expect a certain type with a frequency p(esp) what may be the extreme limits of p(obs) in individual farmlies ? I.) If we are dealing with values between 0,1 and 0,9 we may use table 3. To solve the first question we select the respective horizontal line for p(obs) and determine which column corresponds to our value of n and find the respective value of p(esp) by interpolating between columns. In order to solve the second problem we start with the respective column for p(esp) and find the horizontal line for the given value of n either diretly or by approximation and by interpolation. 2) For frequencies smaller than 0,1 we have to use table 4 and transform the fractions p(esp) and p(obs) in numbers of Poisson series by multiplication with n. Tn order to solve the first broblem, we verify in which line the lower Poisson limit is equal to m(obs) and transform the corresponding value of m into frequecy p(esp) by dividing through n. The observed frequency may thus be a chance deviate of any value between 0,0... and the values given by dividing the value of m in the table by n. In the second case we transform first the expectation p(esp) into a value of m and procure in the horizontal line, corresponding to m(esp) the extreme values om m which than must be transformed, by dividing through n into values of p(obs). F) Partial and progressive tests may be recomended in all cases where there is lack of material or where the loss of time is less importent than the cost of large scale experiments since in many cases the minimun number necessary to garantee the results within the limits of precision is rather large. One should not forget that the minimun number really represents at the same time a maximun number, necessary only if one takes into consideration essentially the disfavorable variations, but smaller numbers may frequently already satisfactory results. For instance, by definition, we know that a frequecy of p means that we expect one individual in every total o(f1-p). If there were no chance variations, this number (1- p) will be suficient. and if there were favorable variations a smaller number still may yield one individual of the desired type. r.nus trusting to luck, one may start the experiment with numbers, smaller than the minimun calculated according to the formulas given above, and increase the total untill the desired result is obtained and this may well b ebefore the "minimum number" is reached. Some concrete examples of this partial or progressive procedure are given from our genetical experiments with maize.