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.

A influência dos pigmentos amarelo -laranja de vários alimentos na coloração da gema de ôvo de galinha

The effect of different feeds in comparison with that of maize grains on the egg yolk color was observed. It was found that deep orange and yellow orange maize give satisfactory coloration to the yolk, respectively orange and yellow. The most intense color was observed when green feed was used in combination with deep orange maize. Green feeds as chicory, alfafa, cabbage, welsh onion and banana leaves and alfafa or chicory meal proved to be good in giving orange color to the yolk. Yellow yolk was obtained when Guinea grass or carica fruit were used in the ration. Carrot and beet without leaves did not give satisfactory color to the egg yolk. The observations with other feeds are being continued.

O problema técnico-econômico da adubação

The authors discuss from the economic point of view the use of a few functions intended to represent the yield y corresponding to a level xof the nutrient. They point out that under conditions of scarce capital what is actually most important is not to obtain the highest profit per hectare but the highest return per cruzeiro spent, so that we should maximize the function z = _R - C_ = _R_ - 1 , C C where R is the gross income and C the cost of production (fixed plus variable, both per hectare). Being C = M + rx, with r the unit price of the nutrient and Af the fixed cost of the crop, wo are led to the equation (M + rx)R' - rR = 0. With R = k + sx + tx², this gives a solution Xo = - Mt - √ M²t² - r t(Ms - Kr)- _____________________ rt on the other hand, with R = PyA [1 - 10-c(x + b)], x0 will be the root of equation (M + rx)cL 10 + r 10c(x + b) = 0 (12). Another solution, pointed out by PESEK and HEADY, is to maximize the function z = sx + tx² _________ m + rx where the numerator is the additional income due to the nutrient, and m is the fixed cost of fertilization. This leads to a solution x+ = - mt - √m²t² - mrst (13) _________________ rt However, we must have x+< _r_-_s_ I if we want to satisfy t _dy_ > r. dx This condition is satisfied only if we have m < _(s__-__r)² (14), - 4 t a restriction apparently not perceived by PESEK and HEADY. A similar reasoning using Mitscherlich's law leads to equation (mcL 10 + r) + cr(L 10)x - r 10cx = 0 (15), with a similar restriction. As an example, data of VIEGAS referring to fertilization of corn (maize) gave the equation y - 1534 + 22.99 x - 0. 1069 x², with x in kg/ha of the cereal. With the prices of Cr$ 5.00 per kilo of maize, Cr$ 26.00 per kilo of P2O3,. and M = Cr$ 5,000.00, we obtain x0 = 61 kg/ha of P(2)0(5). A similar reasoning using Mitscherlich's law leads to x0 = 53 kg/ha. Now, if we take in account only the fixed cost of fertilization m = Cr$ 600.00 per hectare, we obtain from (13) x+ = 51 kg/ha of P2O5, while (14) gives x+ - 41 kg/ha. Note that if m = Cr$ 5,000.00, we obtain by formula (13) x+ = 88 kg/ha of P2O5, a solution which is not valid, since condition (14) is not satisfied.

Milho: a Interação Y1 Y3 Y7 na coloração amarela do endosperma

This paper deals with the genetic interaction of Yl Y3 Y7 in producing yellow endosperm in maize. The new data presented are in accordance with preliminary notes on the same subject. The recessive yl, y3 and y7produce respectively green plants, albescent plants and white seedlings.

Observações preliminares sôbre a longevidade dos "Seedlings" de feijoeiro - Phaseolus vulgaris : em função das reservas cotiledonares

According previous studies about longevity in maize by ACCORSI e ADÂMOLI DE BARROS, (1961) the authors presents in this paper the results of work on longevity of seedlings of beans. Seeds were separated in three groups according their weight, as followings: small 80-120 mg; medium 130-140 mg and big 150-200 mg. The sowing of the seeds was made in pure sand and the seedlings were distributed in distil. water and in complete solution of Arnon and Hoagland. Each treatment was made in two replications with eight seedlings by treatment. At present time the following conclusions can be related: 1.°) - Eight days after germination, the cotiledones of all the seedlings started to fell down, fourteen days after, all cotiledones had fell down. 2.°) - Fifteen days after germination, the seedlings in nutritive solution showed better development than those in distil. water. Table I e II gives results. 3.°) - All seedlings in distil. water showed symptoms of N, Ca, Fe deficiencies. 4.°) - Twenty nine days after germination the seedlings in distil. water manifested exhaust trace, by falling of the leaves and death of some plants although the aplicai buds keep green. 5.°) - After thirty-one days the plants in nutritives solution was in better condition than those in distil. water, although some alteration aboved mentioned was observed. The causes of this alteration are being studied. 6.°) - In many plants in complet solution the seminal leaves showed clorosis initial and some with necrosis, although apical buds keeps in ativity. 7.°) - Symptoms of clorosis and necrosis in diferents stages were observed in all leaflet; these symptoms were more strong in the groups of little seed and medium seeds.

Cotton Rats (Sigmodon hispidus) and Black Rats (Rattus rattus) as Possible Reservoirs of Leishmania spp. in Lara State, Venezuela

A total of 519 wild animals belonging to eleven species were collected during a two year study in a cutaneous leishmaniasis endemic area in Venezuela (La Matica, Lara State). The animals were captured in home-made Tomahawk-like traps baited with maize, bananas or other available local fruits, and parasites were isolated from 27 specimens. Two different species were found naturally infected with flagellates, i.e., cotton rats (Sigmodon hispidus) and black rats (Rattus rattus). Characterization of the parasites using PCR, kDNA restriction pattern and hybridization with species-specific probes revealed the presence of Leishmania (L.) mexicana in three of the black rats and Leishmania (V.) braziliensis in two others. The latter species was also identified in the single positive specimen of S. hispidus. The results suggested both species of animals as possible reservoirs of Leishmania sp.

Genetic diversity of environmental Aspergillus flavus strains in the state of São Paulo, Brazil by random amplified polymorphic DNA

Aspergillus flavus is a very important toxigenic fungus that produces aflatoxins, a group of extremely toxic substances to man and animals. Toxigenic fungi can grow in feed crops, such as maize, peanuts, and soybeans, being thus of high concern for public health. There are toxigenic and non-toxigenic A. flavus variants, but the necessary conditions for expressing the toxigenic potential are not fully understood. Therefore, we have studied total-DNA polymorphism from toxigenic and non toxigenic A. flavus strains isolated from maize crops and soil at two geographic locations, 300 km apart, in the Southeast region of Brazil. Total DNA from each A. flavus isolate was extracted and subjected to polymerase chain reaction amplification with five randomic primers through the RAPD (random amplified polymorphic DNA) technique. Phenetic and cladistic analyses of the data, based on bootstrap analyses, led us to conclude that RAPD was not suitable to discriminate toxigenic from non toxigenic strains. But the present results support the use of RAPD for strain characterization, especially for preliminary evaluation over extensive collections.

Mauritinus seferi Bondar, 1960: bionomy, description of immature stages and redescription of adult (Coleoptera, Curculionidae)

Mature larvae of Mauritinus seferi Bondar, 1960 were collected in the mesocarp of murity palm (Mauritia flexuosa Linnaeus), in the State of Pará, Brazil. Larvae were reared to pupa and adults in the laboratory. Mature larva and pupa are described and adult redescribed. Adult and immature are illustrated for the first time. Observations about bionomy are included and discussed.

Caracterização morfológica de espécies de Hemerobius Linnaeus, 1758 (Neuroptera, Hemerobiidae) associadas a cultivos de café (Coffea arabica L.), milho (Zea mays L.) e erva-mate (Ilex paraguariensis St. Hill.)

The predators were collected in mate crop in Cascavel and São Mateus do Sul, Paraná, Brazil and some other additional specimens in coffee and maize crops in Ribeirão Preto, São Paulo, Brazil. Illustrations obtained by SEM are given by the first time to the principal structures. Three species of Hemerobius were identified: H. bolivari Banks, 1910; H. domingensis Banks, 1941 and H. gaitoi Monserrat, 1996. H. domingensis is recorded for the first time to Brazil.

A new species of Cervellus Szépligeti (Hymenoptera, Braconidae, Braconinae) with biological notes

A new Cervellus species is described from Brazil. The male to this genus is described for the first time as well its cocoon is illustrated. The specimens parasitize the papaya borer weevil Pseudopiazurus obesus (Boheman, 1838) (Coleoptera, Curculionidae) associated with Carica papaya Linnaeus, 1753 (Caricaceae) at Rio Grande do Norte and Bahia Brazilian States.

The effect of sub-lethal doses of Azadirachta indica (Meliaceae) oil on the midgut of Spodoptera frugiperda (Lepidoptera, Noctuidae)

The fall armyworm, Spodoptera frugiperda, is one of the major field pests for maize production. It is mainly controlled by means of synthetic, and more recently by resistant cultivar of maize expressing Bt toxins. The neem tree, Azadirachta indica, is a plant that can potentially control insects with the advantage of being food and environmental safe. The aim of this study was to assess the effect of neem oil on the development and survival of S. frugiperda caterpillars by assessing histological alterations caused on their midgut. Newly hatched caterpillars were submitted to three neem oil concentrations: 0.006; 0.05; 0.4%, which were added to their artificial diet. Ten 3rd instar caterpillars, taken from each treatment, were submitted to histological analysis. The alimentary canals from the specimens were fixed in Baker for 12 hours, desiccated and diaphanized in alcohol/xylol (1:1) and xylol. After placing the samples in paraffin, they were sliced in 8 µm sections and stained with hematoxylin-eosin stain. The neem oil added to the diet of S. frugiperda caused total mortality at dose of 0.4% whilst still in the first instars, prolonged the larval and pupal stages, and reduced the pupal weight. Histo-physiological alterations such as degeneration of the epithelial lining of the midgut and in the peritrophic matrix were found at all concentrations of neem oil.

Toxic effects of essential plant oils in adult Sitophilus oryzae (Linnaeus) (Coleoptera, Curculionidae)

Toxic effects of essential plant oils in adult Sitophilus oryzae (Linnaeus) (Coleoptera, Curculionidae). Stored grains are subject to losses in quality nutritional value and in sanitation from the time they are stored to the time they are consumed. Botanical insecticides may offer an alternative solution for pest control. The objective was to test the insecticidal properties of the essential oils of Cymbopogon citratus (leaf), Zingiber officinale (root) and Mentha sp. (leaf). The efficacy of these oils was tested to control the rice weevil, S. oryzae, using hydrodistillation. Chemical analysis of the essential oils was carried out by gas chromatography. Major components of C. citratus were geranial (48%) and neral (31%), of Z. officinale were α-zingibereno (13%), geranial (16%), neral (10%) and α-farneseno (5%) and of Mentha sp. was menthol (92%). Bioassays were carried out by fumigation and topical application. In topical application assays, the essential oil of C. citratus had greater toxicity (LC50 0.027 µL mL-1) and shorter exposure time than the oils of the other two plants. After 24 h and 48 h, 70% and 100% mortality of S. oryzae occurred, respectively. In fumigation assays, essential oil of Z. officinale had a lower LC50 (1.18 µL cm-2) and 70% mortality after 24 h exposure. Therefore, we recommend the use of essential oils of C. citratus and Z. officinale to control the rice weevil S. oryzae.

Functionality of the plastron in adults of Neochetina eichhorniae Warner (Coleoptera, Curculionidae): aspects of the integument coating and submersion laboratory experiments

The plastron theory was tested in adults of Neochetina eichhorniae Warner, 1970, through the analysis of the structure that coats these insects' integument and also through submersion laboratorial experiments. The tegument processes were recognized in three types: agglutinated scales with large perforations, plumose scales of varied sizes and shapes, and hairs. The experiments were carried out on 264 adult individuals which were kept submerged at different time intervals (n = 11) and in two types of treatment, natural non-aerated water and previously boiled water, with four repetitions for each treatment. The tests showed a maximum mortality after 24 hours of immersion in the previously boiled water treatment. The survival of the adults was negative and significantly correlated with the types of treatment employed and within the different time intervals. The values of oxygen dissolved in water (mg/l) differed significantly within the types of treatment employed. They were positively correlated with the survival of the adults in the two types of treatment, although more markedly in the treatment with previously boiled water. The mortality of adults after 24 hours of submersion in the treatment with previously boiled water may be associated with the physical-chemical conditions of the non-tested water in this study, such as low surface tension and concentration of solutes. These results suggest plastron functionality in the adults of this species.

Genetic structure of populations of Pissodes castaneus (De Geer) (Coleoptera, Curculionidae) using amplified fragment length polymorphism

Genetic structure of populations of Pissodes castaneus (De Geer) (Coleoptera, Curculionidae) using amplified fragment length polymorphism. The objective of this study was to determine the genetic structure of populations of Pissodes castaneus from different areas and on different species of Pinus using the PCR-AFLP technique. Twenty samples were analyzed, representing 19 populations from Brazil and one from Florence, Italy, which is the region of origin of P. castaneus. The four combinations of primers generated a total of 367 fragments of DNA, and 100% of polymorphic loci, indicating high degree of molecular polymorphism. The dendrogram did not reveal trends for grouping the populations in relation to origin. The low genetic similarity (0.11 between the most distant groups) and genetic distances of 0.13 and 0.44 for 10 out of the 20 samples may indicate several founding events or multiple introductions of heterogeneous strains into Brazil. The allelic fixation index (Fst) was 0.3851, considered high, and the number of migrants (Nm) was 0.3991, indicating low gene flow among populations. The highest genetic distances were between the population from Irani, SC and Cambará do Sul, RS and Bituruna, PR, indicating an independent founding event or a particular allelic fixation in the former location. The high genetic diversity among populations points out that the populations are genetically heterogeneous with a diverse gene pool in the surveyed areas, what makes them to respond differently to control measures.

A new species of Homalocerus Schoenherr from the Atlantic coast of the State of São Paulo, Brazil (Coleoptera, Belidae, Belinae), with notes on color pattern and on the sclerites of the internal sac

A new species of Homalocerus Schoenherr from the Atlantic coast of the State of São Paulo, Brazil (Coleoptera, Belidae, Belinae), with notes on color pattern and on the sclerites of the internal sac. Homalocerus bimaculatus sp. nov. (type locality: Brazil, São Paulo) is described and illustrated, and comments on the sclerites of the internal sac of aedeagus and on color pattern are provided. The new species is compared to other similar species of the genus, being distinguished by having three clusters of carmine pubescence on pronotum and two lateral whitish oval spots located slightly before the middle of each elytron. Six species of Homalocerus, including the new one, are known from the State of São Paulo. The previously published identification key for species of Homalocerus is updated to include H. bimaculatus.