As distribuições do acaso

1) Chamamos um desvio relativo simples o quociente de um desvio, isto é, de uma diferença entre uma variável e sua média ou outro valor ideal, e o seu erro standard. D= v-v/ δ ou D = v-v2/δ Num desvio composto nós reunimos vários desvios de acordo com a equação: D = + Σ (v - 2)²: o o = o1/ o o Todo desvio relativo é caracterizado por dois graus de liberdade (número de variáveis livres) que indicam de quantas observações foi calculado o numerador (grau de liberdade nf1 ou simplesmente n2) e o denominador (grau de liberdade nf2 ou simplesmente n2). 2) Explicamos em detalhe que a chamada distribuição normal ou de OAUSS é apenas um caso especial que nós encontramos quando o erro standard do dividendo do desvio relativo é calculado de um número bem grande de observações ou determinado por uma fórmula teórica. Para provar este ponto foi demonstrado que a distribuição de GAUSS pode ser derivada da distribuição binomial quando o expoente desta torna-se igual a infinito (Fig.1). 3) Assim torna-se evidente que um estudo detalhado da variação do erro standard é necessário. Mostramos rapidamente que, depois de tentativas preliminares de LEXIS e HELMERT, a solução foi achada pelos estatísticos da escola londrina: KARL PEARSON, o autor anônimo conhecido pelo nome de STUDENT e finalmente R. A. FISHER. 4) Devemos hoje distinguir quatro tipos diferentes de dis- tribuições de acaso dos desvios relativos, em dependência de combinação dos graus de liberdade n1 e n2. Distribuição de: fisher 1 < nf1 < infinito 1 < nf2 < infinito ( formula 9-1) Pearson 1 < nf1 < infinito nf 2= infinito ( formula 3-2) Student nf2 = 1 1 < nf2= infinito ( formula 3-3) Gauss nf1 = 1 nf2= infinito ( formula 3-4) As formas das curvas (Fig. 2) e as fórmulas matemáticas dos quatro tipos de distribuição são amplamente discutidas, bem como os valores das suas constantes e de ordenadas especiais. 5) As distribuições de GAUSS e de STUDENT (Figs. 2 e 5) que correspondem a variação de desvios simples são sempre simétricas e atingem o seu máximo para a abcissa D = O, sendo o valor da ordenada correspondente igual ao valor da constante da distribuição, k1 e k2 respectivamente. 6) As distribuições de PEARSON e FISHER (Fig. 2) correspondentes à variação de desvios compostos, são descontínuas para o valor D = O, existindo sempre duas curvas isoladas, uma à direita e outra à esquerda do valor zero da abcissa. As curvas são assimétricas (Figs. 6 a 9), tornando-se mais e mais simétricas para os valores elevados dos graus de liberdade. 7) A natureza dos limites de probabilidade é discutida. Explicámos porque usam-se em geral os limites bilaterais para as distribuições de STUDENT e GAUSS e os limites unilaterais superiores para as distribuições de PEARSON e FISHER (Figs. 3 e 4). Para o cálculo dos limites deve-se então lembrar que o desvio simples, D = (v - v) : o tem o sinal positivo ou negativo, de modo que é em geral necessário determinar os limites bilaterais em ambos os lados da curva (GAUSS e STUDENT). Os desvios relativos compostos da forma D = O1 : o2 não têm sinal determinado, devendo desprezar-se os sinais. Em geral consideramos apenas o caso o1 ser maior do que o2 e os limites se determinam apenas na extremidade da curva que corresponde a valores maiores do que 1. (Limites unilaterais superiores das distribuições de PEARSON e FISHER). Quando a natureza dos dados indica a possibilidade de aparecerem tanto valores de o(maiores como menores do que o2,devemos usar os limites bilaterais, correspondendo os limites unilaterais de 5%, 1% e 0,1% de probabilidade, correspondendo a limites bilaterais de 10%, 2% e 0,2%. 8) As relações matemáticas das fórmulas das quatro distribuições são amplamente discutidas, como também a sua transformação de uma para outra quando fazemos as necessárias alterações nos graus de liberdade. Estas transformações provam matematicamente que todas as quatro distribuições de acaso formam um conjunto. Foi demonstrado matematicamente que a fórmula das distribuições de FISHER representa o caso geral de variação de acaso de um desvio relativo, se nós extendermos a sua definição desde nfl = 1 até infinito e desde nf2 = 1 até infinito. 9) Existe apenas uma distribuição de GAUSS; podemos calcular uma curva para cada combinação imaginável de graus de liberdade para as outras três distribuições. Porém, é matematicamente evidente que nos aproximamos a distribuições limitantes quando os valores dos graus de liberdade se aproximam ao valor infinito. Partindo de fórmulas com área unidade e usando o erro standard como unidade da abcissa, chegamos às seguintes transformações: a) A distribuição de STUDENT (Fig. 5) passa a distribuição de GAUSS quando o grau de liberdade n2 se aproxima ao valor infinito. Como aproximação ao infinito, suficiente na prática, podemos aceitar valores maiores do que n2 = 30. b) A distribuição de PEARSON (Fig. 6) passa para uma de GAUSS com média zero e erro standard unidade quando nl é igual a 1. Quando de outro lado, nl torna-se muito grande, a distribuição de PEARSON podia ser substituída por uma distribuição modificada de GAUSS, com média igual ale unidade da abcissa igual a 1 : V2 n 1 . Para fins práticos, valores de nl maiores do que 30 são em geral uma aproximação suficiente ao infinito. c) Os limites da distribuição de FISHER são um pouco mais difíceis para definir. I) Em primeiro lugar foram estudadas as distribuições com n1 = n2 = n e verificamos (Figs. 7 e 8) que aproximamo-nos a uma distribuição, transformada de GAUSS com média 1 e erro standard l : Vn, quando o valor cresce até o infinito. Como aproximação satisfatória podemos considerar nl = n2 = 100, ou já nl =r n2 - 50 (Fig. 8) II) Quando n1 e n2 diferem (Fig. 9) podemos distinguir dois casos: Se n1 é pequeno e n2 maior do que 100 podemos substituir a distribuição de FISHER pela distribuição correspondente de PEARSON. (Fig. 9, parte superior). Se porém n1é maior do que 50 e n2 maior do que 100, ou vice-versa, atingimos uma distribuição modificada de GAUSS com média 1 e erro standard 1: 2n1 n3 n1 + n2 10) As definições matemáticas e os limites de probabilidade para as diferentes distribuições de acaso são dadas em geral na literatura em formas bem diversas, usando-se diferentes sistemas de abcissas. Com referência às distribuições de FISHER, foi usado por este autor, inicialmente, o logarítmo natural do desvio relativo, como abcissa. SNEDECOR (1937) emprega o quadrado dos desvios relativos e BRIEGER (1937) o desvio relativo próprio. As distribuições de PEARSON são empregadas para o X2 teste de PEARSON e FISHER, usando como abcissa os valores de x² = D². n1 Foi exposto o meu ponto de vista, que estas desigualdades trazem desvantagens na aplicação dos testes, pois atribui-se um peso diferente aos números analisados em cada teste, que são somas de desvios quadrados no X2 teste, somas des desvios quadrados divididos pelo grau de liberdade ou varianças no F-teste de SNEDECOR, desvios simples no t-teste de STUDENT, etc.. Uma tábua dos limites de probabilidade de desvios relativos foi publicada por mim (BRIEGER 1937) e uma tábua mais extensa será publicada em breve, contendo os limites unilaterais e bilaterais, tanto para as distribuições de STUDENT como de FISHER. 11) Num capítulo final são discutidas várias complicações que podem surgir na análise. Entre elas quero apenas citar alguns problemas. a) Quando comparamos o desvio de um valor e sua média, deveríamos corretamente empregar também os erros de ambos estes valores: D = u- u o2 +²5 Mas não podemos aqui imediatamente aplicar os limites de qualquer das distribuições do acaso discutidas acima. Em geral a variação de v, medida por o , segue uma distribuição de STUDENT e a variação da média V segue uma distribuição de GAUSS. O problema a ser solucionado é, como reunir os limites destas distribuições num só teste. A solução prática do caso é de considerar a média como uma constante, e aplicar diretamente os limites de probabilidade das dstribuições de STUDENT com o grau de liberdade do erro o. Mas este é apenas uma solução prática. O problema mesmo é, em parte, solucionado pelo teste de BEHRENDS. b) Um outro problema se apresenta no curso dos métodos chamados "analysis of variance" ou decomposição do erro. Supomos que nós queremos comparar uma média parcial va com a média geral v . Mas podemos calcular o erro desta média parcial, por dois processos, ou partindo do erro individual aa ou do erro "dentro" oD que é, como explicado acima, uma média balançada de todos os m erros individuais. O emprego deste último garante um teste mais satisfatório e severo, pois êle é baseado sempre num grau de liberdade bastante elevado. Teremos que aplicar dois testes em seguida: Em primeiro lugar devemos decidir se o erro ou difere do êrro dentro: D = δa/δ0 n1 = np/n2 m. n p Se este teste for significante, uma substituição de oa pelo oD não será admissível. Mas mesmo quando o resultado for insignificante, ainda não temos certeza sobre a identidade dos dois erros, pois pode ser que a diferença entre eles é pequena e os graus de liberdade não são suficientes para permitir o reconhecimento desta diferença como significante. Podemos então substituirmos oa por oD de modo que n2 = m : np: D = V a - v / δa Np n = 1 n2 = np passa para D = v = - v/ δ Np n = 1 n2 = m.n p as como podemos incluir neste último teste uma apreciação das nossas dúvidas sobre o teste anterior oa: oD ? A melhor solução prática me parece fazer uso da determinação de oD, que é provavelmente mais exata do que oa, mas usar os graus de liberdade do teste simples: np = 1 / n2 = np para deixar margem para as nossas dúvidas sobre a igualdade de oa a oD. Estes dois exemplos devem ser suficientes para demonstrar que apesar dos grandes progressos que nós podíamos registrar na teoria da variação do acaso, ainda existem problemas importantes a serem solucionados.

Pesquisas sôbre a análise estatística de experiências de adubação com o auxílio da lei de Mitscherlich

Statistical analyses of an experiment on wheat were carried out with the aid of Mitscherlich's law. The experiment was made in Ponta Grossa, Paraná, by the Ministry of Agriculture of Brasil. Lime, in the form of Ca(OH)2, was applied at the levels of 0, 2, 4, 6 and 8 metric tons per hectare. A 5 x 5 Latin square was used. Lime was applied in 1940 and wheat was cultivated in the same plots for several years. The following fertilizers were annually used for all plots: NaNO3 100 kilograms per hectare, Superphosphate 350 kilograms per hectare, K2S04 80 kilograms per hectare. The statistical analysis of the data collected in 1941, 1942, 1943, 1947 and 1948, carried out in accordance with the methods previously introduced by Pimentel Gomes and Malavolta (1949 a, 1949 b) and Pimentel Gomes (1950), proved: I. That Mitscherlich's law could be correctly applied to the data. II. That there was a statistically significant effect of lime on wheat yield. III. That the optimum amount of lime to be applied to the soil lies between 5 and 15 hundred kilograms of Ca(OH)2 per hectare. IV. That there is a migration of calcium from some plots to others, in such a way that the data obtained in 1947 and 1948 are not representative of the amounts of lime applied in 1940. V. That the analysis of variance can be used, as the Bartlett test shows that the variances at the distinct levele of lime application are not statistically different. It must be noted that, with improved variety and fertilization, the yield was rised to about 2500 kilograms per hectare in 1947, and 1600 in 1948, being only of about 100 kilograms per hectare in 1940.

Riqueza em óleo nas sementes, amêndoas e cascas das bagas de mamona

This paper is a joined publication of the Depts. of Genetics and of Technology, of the E. S. A. "Luiz de Queiroz", Universidade de São Paulo, and deals with the variation of the percentage oil content in the whole seeds, the embryos and the seed-coat of 28 varieties of castor-beans (Ricinus communis, L.). Primarily, the authors, as a justification of this paper, make reference to the applications which castor-oil has in industry, medicine, etc. In accordance with the weight of 100 seeds, the varieties of castor-beans were classified into 3 classes : small seeds (100 seeds less than 30 g), medium seeds (100 seeds between 30 g and 60) and large seeds (100 seeds more than 60 g). The percentage of oil in the seed, embryo and seed-coat, the dimensions of the seeds and the weight of 100 seeds are given for every variety in table 1. In order to obtain an estimate of the variability for the methods of determination of the oil percentage, in the 3 differents parts of the seeds and also in the 3 groups of seeds, the coefficient of variability was calculate (table 2). It is showed that the variation in the seed and embryo is low and that in the seed-coat is very high. The analysis of variance, with regard to the difference among the 3 types of seeds (small, medium and large), among the 3 parts of the seed (whole seed, embryo and seed-coat) and residual error, is given in table 3. Only, the oil content of whole seeds among types of seeds was significant at the 5% level. The t test among the correspondent means is not significant for the difference between medium and large seeds is significant between both these types (medium and large) and small seeds. The fiducial limits in relation to the mean of the oil percentage in the 3 differents types of seed, show that there is one variety (n. 1013-2), which has a percentage of oil, in the medium type of seed, significantly at the 5% level (table 4), higher than the general mean. Since the distribution of the percentage of oil in the seedcoat is discontinuous, 5 groups were established (table 5). All the differences between groups are significant (table 6). For practical purposes, when we have to remove the seed coat, one should eliminate those varieties which loose at least 3% of oil by this procedure. There is a significant linear correlation at 5% level between the percentage of oil in the seed and in the embryo, of the smali and medium type of seeds (table 7), and also, when taking the 3 types together (lower part of table 7), one finds that the same is true. Also, the correlation between the percentages of oil in the embryo and in the seed-coat of the 3 types together is significant at 5% level. According to the results obtained in relation to the percentage in 28 varieties studied, it can be recommended, for breeding purposes, to work only with those varieties which belong to the medium and the large types of seeds.

Estudos sôbre o quiabeiro II: efeitos da autofecundação e do cruzamento

The present work deals with the study of the effects of selfing and crossing in pures lines of okra inbred for five generations and the methods of breeding in this plant. This work is party of a large program of this Dept. to study heterosis in plants naturally self pollinated. The technic of selfing consists of tying with a string the floral bud before anthesis. To make controlled crosses, it is necessary to emasculate the flowers removing the anthers with small forceps, and to cover the flowers with a bag and wait for 1 or 2 days until the blooming. Also, the male parents are covered with paper bags prior to flowering. Finally, the pollen is brushed lightly over the stigma of the emasculated flowers and the females unit rebagged. The authors have tried without sucess the technic of soda fountain straw used for cotton. The treatments were: I) Fl of the cross pure-line x foreign variety (not improved by breeding). II) Fl of the cross pure-line x parental variety and III) pure-line 5 generations inbred. In order to compare the production of these three treatments, a randomized blocks with 4 replications was designed; since we had 6 families in each treatment, the total number was: 4 replications x 3 treatments x 6 families: = 72. Each familiy was planted in lines of 10 plants. Owing to the design devised, the present experiment corresponds to a split-plot. The analysis of variance of the number and the weight of the pods is given in tables 2 and 4, and shows the following: 1) The production expressed in both numbers and weights of the cross, - pure lines x foreign variety - was statistically smaller than the others treatments, i, e., the cross of pure-lines x parental variety and the pure-lines; 2) The production of the treatments pure-lines x parental variety and selfed purelines was the same. It was proved that the selfing do not produce harmful effects in okra, it was benefical, since after 5 inbred generations the production was the same when compared with Fl of the parental variety. Also, the methods of pure-lines are indicated to improve varieties of okra.

Estudo comparativo entre métodos de contrôle quantitativo da produção leiteira

This paper deals with the estimation of milk production by means of weekly, biweekly, bimonthly observations and also by method known as 6-5-8, where one observation is taken at the 6th week of lactation, another at 5th month and a third one at the 8th month. The data studied were obtained from 72 lactations of the Holstein Friesian breed of the "Escola Superior de Agricultura "Luiz de Queiroz" (Piracicaba), S. Paulo, Brazil), being 6 calvings on each month of year and also 12 first calvings, 12 second calvings, and so on, up to the sixth. The authors criticize the use of "maximum error" to be found in papers dealing with this subject, and also the use of mean deviation. The former is completely supersed and unadvisable and latter, although equivalent, to a certain extent, to the usual standard deviation, has only 87,6% of its efficiency, according to KENDALL (9, pp. 130-131, 10, pp. 6-7). The data obtained were compared with the actual production, obtained by daily control and the deviations observed were studied. Their means and standard deviations are given on the table IV. Inspite of BOX's recent results (11) showing that with equal numbers in all classes a certain inequality of varinces is not important, the autors separated the methods, before carrying out the analysis of variance, thus avoiding to put together methods with too different standard deviations. We compared the three first methods, to begin with (Table VI). Then we carried out the analysis with the four first methods. (Table VII). Finally we compared the two last methods. (Table VIII). These analysis of variance compare the arithmetic means of the deviations by the methods studied, and this is equivalent to compare their biases. So we conclude tht season of calving and order of calving do not effect the biases, and the methods themselves do not differ from this view point, with the exception of method 6-5-8. Another method of attack, maybe preferrable, would be to compare the estimates of the biases with their expected mean under the null hypothesis (zero) by the t-test. We have: 1) Weekley control: t = x - 0/c(x) = 8,59 - 0/ = 1,56 2) Biweekly control: t = 11,20 - 0/6,21= 1,80 3) Monthly control: t = 7,17 - 0/9,48 = 0,76 4) Bimonthly control: t = - 4,66 - 0/17,56 = -0,26 5) Method 6-5-8 t = 144,89 - 0/22,41 = 6,46*** We denote above by three asterisks, significance the 0,1% level of probability. In this way we should conclude that the weekly, biweekly, monthly and bimonthly methods of control may be assumed to be unbiased. The 6-5-8 method is proved to be positively biased, and here the bias equals 5,9% of the mean milk production. The precision of the methods studied may be judged by their standard deviations, or by intervals covering, with a certain probability (95% for example), the deviation x corresponding to an estimate obtained by cne of the methods studied. Since the difference x - x, where x is the mean of the 72 deviations obtained for each method, has a t distribution with mean zero and estimate of standard deviation. s(x - x) = √1+ 1/72 . s = 1.007. s , and the limit of t for the 5% probability, level with 71 degrees of freedom is 1.99, then the interval to be considered is given by x ± 1.99 x 1.007 s = x ± 2.00. s The intervals thus calculated are given on the table IX.

Influência lunar sobre plantas hortícolas

The aim of this paper is the study of moon effects on ten different crops divided in four groups: 1) salad and cole crops (lettuce, endive, cabbage, cauliflower); 2) root crops (beet, carrot, radish, turnip); 3) bulb crops (onion); 4) solanaceous fruits (eggplant). The design of the experiment was randomized blocks, with four replications, the different treatments being the four phases of the moon. The analyses of variance are given in the work of Simão (1953) and the analises of the mean in tables 1 to 2. The main conclusions are: 1) No difference in production were found related to different moon phases, even it the crops supposed to be sensible to moon effects. 2) In a few cases, where some increase in production was observed, such increase could be atributed by other apents 3) The agents supposed to interfere with increase in production were temperature and photoperiodism, rather than moon phases. 4) The most sensible crops to low temperature, during the night, were: lettuce, endive, cauliflower, cabbage, carrots, turnips and radish. 5) The most sensible crops to both low temperature and photoperiodism were: onion and beet. 6) The moon phases supposed to have opposed effects, namely full-moon and half-moon, gave mixed results sometimes both giving the best yield simultaneously and sometimes giving the poorest crops. 7) As a final conclusion, no moon effects could be detectable in the present experiment.

A farinha de Rami como sucedâneo da farinha de fêno da alfafa, na alimentação de pintos

The ramie leaf meal was used in a feeding trial, in comparison with alfalfa hay meal in the range of 5% of the ration. Each lot consisted of two pens of 45 White American chicks was raised in batteries for 6 weeks. From results of the analisis of variance the AA. concluded for the superiority of the ramie leaf meal (586,4 g) over the alfalfa hay meal (540,1 g) in the conditions of the experiment.

Comparação da soja germinada, com a soja em grão e com o farelo de soja na alimentação de suínos em crescimento

Three groups of 6 pigs, three months old, were fed the same basal ration of corn and mineral mixture ad libitum. The control group received soybeans oil meal (solvent proc.), the second group raw soybeans and the third one, sprouted soybeans. The feed intake, daily gain and conversion were practically the same in the three groups as the analisis of variance revealed. Conclusion is it does not pay to sprout soybeans for pigs.

O tamanho dos vasos e fibras do xilema-secundário nos anéis de crescimento da Tecoma chrysothrica, Mart.

This paper deals with the macroscopic and microscopic observation of the growth ringe in two disks from the crossing section of wood stem of Tecoma chrysothrica and also deals with statistical analysis of the size of fiber and vessel member in different grow rings of secondary xilem. By statistical analyses of variance the authors verified the following: first, the fiber reaches its utmost length at the 11 th and 12 th grow rings; second, the vessel member reaches its utmost width in the same region as the fiber length. This point out there is certain correlation between the width of vesses member with the fiber length at the same growth rings. There was no statistical signification in the variation of the vessel length and the fiber width.

A amostragem da cana-de-açúcar para determinações tecnológicas

The authors carried out 3 experiments on the sampling of sugar cane for technological determinations, one with each of the varieties Co 419, CB 40-69 and CB 41-58, in Piracicaba, State of São Paulo, Brasil. The main intent of the project was to compare 2 methods of sampling, namely: 1) Method A, where the sample is a hill (CATANI et al, 1959) or, more generally, 20 stalks all together in a randomly selected point of the furrow; 2) Method B, where 20 stalks are taken, from 20 points evenly spread but on the whole plot. Coefficients of variation for 20 stalk samples Variety Characteristic 20 stalks per hill 1 stalk per hill Brix 4.8% 1.9% Pol 6.4% 2.5% CB 40-69 Coefficient of purity 2.1% 0.83% Available sucrose 7.3% 2.7% Weight 6.6% 6.9% Brix 5.3% 1.8% Pol 7.6% 2.6% Co 419 Coefficient of purity 2.9% 1.0% Available sucrose 8.6% 3.0% Weight 21.2% 6.5% Brix 2.8% 1.4% Pol 4.1% 1.9% CB 41-58 Coefficient of purity 1.8% 0.8% Available sucrose 5.0% 2.2% Weight 10.9% 6.2% For the 3 varieties studied and for the data on Brix, pol, coefficient of purity, available sucrose and weight, analyses of variance were carried out. Further computations led to the following coefficients of variation. For available sucrose, which is probably the most important characteristic studied, the average coefficient of variation for the 3 varieties was 2.7%, for the case of method B, that is, 20 stalk samples, one stalk per hill. Assuming this coefficient of variation, in a trial with 5 treatments and 6 replications, in randomised blocks, the least significant difference among treatment means, at the 5% level, would be 4.7% of available sucrose by Tukey's test, and 3.3% by the t test. For the case of method A the average coefficient of variation is 7.0% and, in similar conditions, the least significant difference would be 15.1% by Tukey's test, and 12.1% by the t test. Since differences of available sucrose among treatments in experiments with fertilizers seldom are higher than 3 or 4% of the mean (PIMENTEL GOMES & CARDOSO, 1958), method B with a 20 stalk sample per plot gives more or less the minimum amount of cane to be sampled for technological determinations. In experiments with varieties, however, where differences may be assumed to be higher, a sample of 10 to 20 stalks one per hill, can be enough.

Estacas de amoreira tratadas com hormônios vegetais em dois sistemas de plantio e referentes coberturas do estufim

Four experiments on root formation on cuttings of mulberry trees of the variety Catania 1 were carried out. In each case the hormones Dieradix "M D", Dieradix "D", indol 3-yl-acetic acid, and I-naphthyl acetic acid were used, besides the control, without hormone. In all cases "normal" and "upside-down" planting were tried. The percentage x of cuttings with roots, after 54 days, were computed and transformed by the formula y = arc sin √P/100 for use in statistical analysis. The combined analysis of variance of the 4 trials led to the following results: "Upside-down" planting showed significantly higher percentage of rooting; Indol 3-yl-acetic acid was significantly better than control or other hormones. The percentages of rooted cuttings were as follows: Normal planting Upside-dow planting Indol 3-yl acetic acid 43.5% 90.9% I-naphthyl acetic acid 1.9% 69.3% Control 4.7% 22.2% Dieradix «M D» 2.4% 63.8% Dieradix «D» 1.3% 36.0%

Padrão reprodutivo de Elachistocleis bicolor (Anura, Microhylidae) na Serra da Bodoquena, Mato Grosso do Sul, Brasil

The reproductive pattern of Elachistocleis bicolor (Guérin Méneville, 1838) was studied at Serra da Bodoquena, from October 2000 to September 2001. Reproduction occurred in the wet season (October to April) and was correlated to high continuous pluviometric precipitation. The species presents sexual size dimorphism, with females larger than males. The number of mature eggs per ovary was 620 ± 251 (n=39) and mature eggs measured 1.15 ± 0.30 mm (n=40). Elachistocleis bicolor presented significant relations between snout-vent length and number of mature eggs (n=39; r²=0.25; p=0.001), individual weight and number of mature eggs (n=41, r²=0.30; p=0.002), snout-vent length and ovarian weight (n=35; r²=0.47; p<0.01), and individual weight and ovarian weight (n=36; r²=0.55; p<0.01). Weight and volume are better to study size-fecundity relationships than snout-vent length. The females invested 22.7 ± 6.3 % (n=35) of their weights in reproduction and the variance associated to this variable was high, related to the reproductive mode of the species.

Skull morphometrics of adult male Antartic fur seal, Arctocephalus gazella, and South American fur seal A. australis

The skull morphometrics of adult male Antarctic fur seal, Arctocephalus gazella (Peters, 1875) and South American fur seal, A. australis (Zimmermann, 1783) were investigated using a collection of 45 and 38 skulls, respectively. Eighteen measurements were taken for each specimen. Comparative univariate and multivariate statistical analyses included standard statistics, one-way analysis of variance, principal component analysis and discriminant analysis. Individual variation was relatively high for some variables, as expressed by the coefficient of variation. Skulls of A. gazella were larger than those of A. australis for all but two variables: squamosal jugal suture and rostral length. Both species differed significantly as shown by both univariate and multivariate analyses. The discriminant function correctly classified all specimens. The standardized canonical coefficients showed that the variables which most contribute to the differentiation between species were, in decreasing order, the rostral length, palatal length, palatal width at postcanine 5 and braincase width. The present study corroborates that A. gazella and A. australis are phenotipically distinct species.

Oligochaetes (Annelida, Clitellata) in a neotropical stream: a mesohabitat approach

This paper analyses the relationship among mesohabitat and aquatic oligochaete species in the Galharada Stream (Campos do Jordão State Park, state of São Paulo, Brazil). Between August 2005 and May 2006 a total of 192 samples were obtained in areas of four different mesohabitats: riffle leaf litter (RL), pool leaf litter (PL), pool sediment (PS) and interstitial sediment from rocky beds in riffle areas (IS). In the mesohabitats sampled, 2007 specimens were identified, belonging to two families (Naididae and Enchytraeidae). Among the oligochaetes identified Naididae was represented by six genera (Allonais, Chaetogaster, Nais, Pristina, Aulodrilus and Limnodrilus). Principal components analysis (PCA) revealed the first two axes explained 85.1% of the total variance of the data. Limnodrilus hoffmeisteri Claparede, 1862 and Aulodrilus limnobius Bretscher, 1899 were associated with the pool areas (PL and PS). Most species of genera Pristina and Nais demonstrated apparent affinity with the riffle mesohabitats. The Indicator Species Analysis (IndVal) revealed that Nais communis Piguet, 1906, Pristina leidyi Smith, 1896 and Pristina (Pristinella) jenkinae (Stephenson, 1931) are indicative of RL mesohabitat, while family Enchytraeidae was considered indicative of PL mesohabitat.

Temporal and spatial variation of rocky shores intertidal benthic communities in Southeast Brazil

The relationships between environmental factors and temporal and spatial variations of benthic communities of three rocky shores of the state of Espírito Santo, Southeast Brazil, were studied. Sampling was conducted every three months, from August 2006 to May 2007, using intersection points. Chthamalus bisinuatus (Pilsbry, 1916) (Crustacea) and Brachidontes spp. (Mollusca) were the most abundant taxa, occupying the upper level of the intertidal zone of the rocky shore. The species richness was higher at the lower levels. The invasive species Isognomon bicolor (C. B. Adams, 1845) (Mollusca) occurred at low densities in the studied areas. The clustering analysis dendrogram indicated a separation of communities based on exposed and sheltered areas. According to the variance analyses, the communities were significantly different among the studied areas and seasons. The extent of wave exposure and shore slope influenced the species variability. The Setibão site showed the highest diversity and richness, most likely due to greater wave exposure. The communities showed greater variation in the lower levels where environmental conditions were less severe, relative to the other levels.