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.

Determinação do sexo do pinto pela forma do ovo

Este trabalho foi feito afim de determinar uma hipotética correlação existente entre a forma do ôvo e o sexo do pinto. Dois métodos foram utilizados. No primeiro considerou-se apenas a "ponta" do ôvo, dividindo-se um lote de 1100 ovos em dois grupos, um considerado ponteagudo e outro arredondado. Os resultados totais mostraram a nenhuma influência da forma da ponta na determinação do sexo, isto é, a falta de correlação era completa. No segundo método, determinou-se a média da relação entre a largura e o comprimento do ôvo, e adotou-se essa medida como linha divisória de dois grupos : um de ovos grossos com 223 ovos e outro de ovos finos, com 183 ovos. A relação sexual foi respectivamente de 38.60 e 37.07 o que mostra a falta de correlação. Os dez ovos mais compridos e os dez mais redondos, incubados separadamente, confirmaram os resultados anteriores. A determinação do sexo dos pintos foi feita pelo método de JAAP, aperfeiçoado nesta Seção. O Autor conclui, que na população estudada, da raça Rhode I. Red, não existe absolutamente a menor correlação entre a forma do ôvo e o sexo do pinto que êle possa determinar. Acredita que essas conclusões possam se aplicar a todas as variedades industriais, mas acha possível, que em raças muito antigas não provenientes de cruzamentos, talvez nalguma raça de briga, tal correlação possa existir.

Determinação do sexo em pintos da raça Rhode Island Red

Examinando 201 pintos de um dia da raça Rhode Island Red, de rebanho selecionado pela postura e considerando diversos caracteres, principalmente os relacionados com a côr da penugem, conseguimos acertar em 197, numa proporção de 98,01%, não relatada da bibliografia que conhecemos. Julgamos como mais importantes, os seguintes caracteres : mancha clara na asa notada em 100% dos machos e 6,30% das fêmeas; o anel claro na perna ocorreu em 91,80% dos machos e 3,70% das fêmeas. Estas duas particularidades, sòmente, permitem separação de sexo superior a 96%. O sinal junto ao ângulo posterior do olho foi observado em 95,10% das fêmeas e 36,70% dos machos; ponta da asa escura não ocorreu em um macho sequer, mas em 53.20% das fêmeas; ponta da asa clara foi notada em todos os machos e em 46,80% das fêmeas. Os demais caracteres mencionados no quadro, constituem elementos auxiliares de menor valor mas devem ser examinados para se esclarecerem dúvidas. Os erros decorreram de se dar mais importância à pinta escura na cabeça que ao anel claro na perna e à mancha no bordo da asa. O presente trabalho contribui para o esclarecimento do assunto principalmente por considerar o anel claro da perna e o sinal escuro próximo ao ângulo posterior do olho, caracteres valiosos e ainda não apontados anteriormente. Ainda mais, a observação metódica e conjunta de um grande número de atributos relacionados com o dimorfismo sexual constitui um subsídio ao esclarecimento de tão interessante questão.

Determinação fotométrica do ácido ascórbico

The photometric determination of ascorbic acid with the "E. E. L. portable colorimeter" can be carried" out rapid and conveniently using either 3% HPO3 or 0,4% (COOH) 2 as protective agent. The standards would contain from 2 to 20 micrograms of ascorbic acid per ml of metaphosphoric or oxalic acid solutions. We mix 10 ml of these solutions with 3 ml of the adequate citrate buffer solutions, and we pipet 5 ml of the resulting mixture to a matched test tube containing 5 ml of sodium - 2,6 - dichlorobenzenoneindophenol (80 mg per liter); then we shake well and after 15 seconds the extintion is read using green filter. The readings are subtracted from the blank one. Designating the differences by x and the concentrations of ascorbic acid/ml in the standards by y, we get, with the acid of the method of least squares, the following regression equations: for the metaphosphoric acid Y = 0,543x + 0,629 for the oxalic acid Y = 0,516x + 0,422, which permit, by interpolating, the determination of the ascorbic acid content in plant materials.

Fatôres que afetam a determinação da vitamina C na goiaba (Psidium guajava L.)

In the present paper the authors deal with the content of ascorbic acid in guavas (Psidium guajava L.) and the methods of sampling used. Ascorbic acid was determined directly in the photoeletric colorimeter (EEL), after extraction with a 4 per cent solution of oxalic acid. Guavas from various parts of State of S.Paulo were used and the general mean found was around 100 mgm of ascorbic acid per 100 gm fresh weight of the material used for extraction. It was found that there is great variation in the ascorbic acid content according to the condition of the fruit: Ascorbic acid Condition content in Mean mgm/100 gm Green and hard 93,36 - 119,54 102,43 Small green 57,34 - 92,30 83,40 Firm ripe 71,28 - 115,98 90,32 Overripe 63,22 - 85,98 77,36 Of the diferent parts of the fruit, the skin has the highest content; the pulp between the skin and the parts containing the seeds, the "inner pulp" contains little and finallw the central parts, formed by the pulp between seeds, the "inter pulp" a engligible amount. The proportion of ascorbic acid found in the skin, inner pulp and inter pulp may be as high as 1.6: 1: 0. Furthermore, the section near the peduncule and the sepals are richer than equatorial crossections. It was proved that the amount and intensity of sun-light is at least one important factant factor determining differences in the ascorbic acid content of the fruit, which is higer in the parts which have received more light. A sharp decrease was found in the vitamin C content of ripe fruite stored in a home refrigerator. The periods of the preservation were 12-24-48-96 hours and the decrease of the ascorbic acid content m per cent was 23.4 - 42.0 - 66.8 - 76.4 of the initial content of 144.28 mgm/100 gm. The following five different methods of sampling in the determination of the amount of vitamin C were tested, with extraction in a Waring blendor: 1) whole fruit; 2,) sample taken form fruits cut into many small pieces; 3) half of a fruit divided by a crossection at equal distance from both ends; 4) half of fruit divided lenghtwise; 5) a transversal slice of about 1 cm. It was found that the two first methods geve the most reliable results.

O brix na determinação da riqueza em açúcares do mamão como auxiliar no melhoramento do mamoeiro (Carica papaya L.)

There is in the literature a noteworthy lack of sampling methods to be employed in the selection of papaya fruits for genetical improvement purposes. In the present experiment methods applied to melon and watermelon were extended to papaya with good results. The authors tried to correlate the solids content-as determined by a hand refractometer-with total sugars in the fruit. The correlation does exist being significant and positive. A regression equation was worked out; it permits to calculate the total sugar content provided the Brix value determined by the hand refractometer is known. The equation is as follows: a = 0.57 s where a = total amount of sugar as glucose, and s = total solids.

Sorbímetro (Um aparêlho para a determinação das relações solo/água)

Os autores descrevem um aparelho destinado à medida contínua da água absorvida pela TFSA em condições de laboratório. O sorbímetro, cujo funcionamento obedece ao princípio dos vasos comunicantes, consta de um tubo em U cujos ramos verticais se ligam respectivamente à uma coluna de terra e à uma bureta de 100 ml. A bureta restabelece no tubo, a água absorvida pela terra. As leituras de bureta substituem as pesagens do método gravimétrico. O aparelho é recomendado para medidas a intervalos de tempo para os quais, o método usual é ineficiente.

Sôbre a determinação do nitrogênio, do fósforo e do potássio no mesmo extrato

The determination of total nitrogen, phosphorus, and potassium in plant material can be carried out in a common extract prepared with sulphuric acid and 30 per cent hydrogen peroxide. Nitrogen is estimated by direct nesslerization of a suitable aliquot (1-5 ml of the 50 ml extract made out of 250 mg of dried material); in order to avoid excessive acidity, 10 ml of Nessler's reagent should be employed. An aliquot of 1-5 ml suffices for the colorimetric determination of phosphorus by the molybdenum method; to reduce the phosphomolybdate complex 2 ml of a 2% SnC12 soln are necessary. Potassium is determined by the cobaltinitrite method after elimination of ammonium salts with the aid of aqua-regia.

Determinação da média aritmética e desvio padrão de quocientes de séries independentes e dependentes

The authors prove some approximate formulas for the computation of the mean and the standard error of quotients of two variates, correlated or uncorrelated, with not too high coefficient of variation. The formulas obtained are subsequently applied to some date on mensuration of horses of the Brazilian breed Mangalarga, by the eclectic system of LESBRE. The relsults obtained directly by the actual computation of the quotients as well as by means of the formulas with the aid of statistics of the numerators and the denominators are given in table 3, showing excellent agreement.

O método potenciométrico na determinação do H+ trocável em solos

For the determination of exchangeable hydrogen ion in soils, the authors of the presente work made the extraction with normal calcium acetate solution that may have an initial pH between 7 and 8 without altering the amount of hydrogen ion extracted. The extraction was made by shaking 5,0 grams of air dry soil with 100 ml of normal calcium acetate solution, the pH of wich was ascertained to 7,0, 7,5 and 8,0 with acetic acid, in 250 mil conical flasks for 30 minutes in a Wagner shaker (30-40 rpm). The contents of the flasks were then, filtered. A 50 ml aliquot of each of the leachate was titrated with a 0,020 N NaOH solution and the volumes consumed sodium hydroxide were ploted against pH. The titration curves thus obtained showed to be straight lines between pH 8 and 9 and parallel to the curve obtained by the titration of the blank. Two ways of locating the end point of the titration showed to be possible: the use of a pHmeter or titrimeter or the use of phenolphtalein as indicator. When using a pH meter or a titrimeter, the end point may rest in any point between pH 8 and 9, and the volume of sodium hydroxide consumed is found by comparison with a similar curve obtained by the titration of the blank. When using phenolphtalein the calcium acetate solution must have a pH below 8.

Determinação e comparação dos valôres Mi, A, Y e S, em dois tipos de solo do est. de S. Paulo

No presente trabalho, determinou-se e comparou-se os valores Mi de BARBIER et al., 1954, SCHEFFER e ULRICH, 1958, A de FRIED e DEAN, 1952 Y de LARSEN, 1952, e S de SOKOLOV, 1958, em dois tipos de solo do Estado de São Paulo: terra roxa legítima e um solo arenoso do campo da Secção Técnica de Química Agrícola da Escola Superior de Agricultura "Luiz de Queiroz". Aplicou-se 23,58 mg de fósforo, por vaso, na forma de superfosfato simples, contendo fósforo radioativo com uma atividade de 120.736 ipm; na forma de solução, aplicou-se também 200 mg de NH4N0(3) e 100 mg de KC1. Misturou-se bem para que houvesse homogenização a mais perfeita possível. Depois plantou-se 25 sementes de trigo, variedade 1146BH, deixando-se apenas 16 plantas após o desbaste. Procedeu-se àcolheita 55 dias após o plantio. Tanto a parte aérea como as raízes foram sêcas em estufa a 70-80°C. Sôbre o material triturado, digerido e diluído, retirou-se partes alíquotas para a determinação do P81 e do P32. Os valores obtidos para os dois tipos de solos foram os seguintes: mg de P por 1,5 kg de solo Valores Terra roxa legítima Solo arenoso Mi 177,96 92,62 A 177,55 92,71 Y 178,97 92,98 S 173,42 64,75 A análise estatística não revelou diferença significativa entre os valores Mi, A e Y, mas sim dêstes para o valor S. Quanto a este último valor, pode-se dizer que quanto mais rico em fósforo fôr o solo e quanto menor fôr o teor dêste elemento na semente, quanto mais êle deverá se aproximar dos valores Mi, A e Y.

Determinação polarografica do zinco em plantas, após a sua separação em resina trocadora de íons

O presente trabalho relata os dados obtidos na determinaçao do zinco em plantas segundo uma nova técnica. Esta nova técnica consistiu em se aliar a separação do zinco de outros interferentes, através do emprego de uma coluna de resina trocadora de anions, ao método polarografico da dosagem do citado elemento. A amostra de planta (1, 000g) foi incinerada em copo de Pyrex a 450-5009C durante 90 minutos e o zinco foi extraido da cinza com solução de HC1 2N. A separação do zinco de outros elementos interferentes foi feita pela passagem da solução através da resina trocadora de anions, Amberlite, IRA-401. Após a eluiçao do zinco da coluna, a solução obtida foi levada ao polarografo registrador. (Sargent, modelo XXI) para a determinação, Trabalhando-se com um conjunto de 10 (dez) a 12 (doze) colunas de resina, pode-se executar 10 (dez) a 12 (doze) determinações num periodo de 6 (seis) horas.

Determinação do zinco em vegetais pelo método do zincon

Este trabalho teve por objetivo o estudo do método de separação do zinco dos outros elementos por meio de resina trocadora de ânions (III, Merck), e a sua determinação colorimétrica por meio do Zincon, em vegetais. Estudou-se particularmente: 1 - estabilidade do complexo; 2 - formação do complexo em diversos pH; 3 - a influencia da concentração de ácido clorídrico na adsorção do zinco pela resina; 4 - efeito do volume de KC1 e NaNO3 na eluição do zinco ; 5 - influência de outros íons; 6 - exatidão e precisão do método; 7 - estudo comparativo de três métodos de preparo do extrato de vegetais.