O Florescimento da cana de açúcar

1 - Análise do Brix Em três das variedades analisadas - F 29-7, Co. 285 e Tuc. 519, - a diferença entre o Brix do caldo das canas florescidas e das canas não florescidas foi estatisticamente insignificante. Apenas em uma variedade - Co. 312 - tivemos um resultado duvidoso. Em F 29-7 nota-se que o erro nas' canas florescidas é maior que nas não florescidas, o que parece indicar uma tendência a maior instabilidade do Brix com o florescimento. A diferença entre os dois erros é, poréxn, de significação duvidosa, embora o valor de P exceda bastante o limite de 5% de probabilidade, sem atingir o de 1%. 2 - Análise dos redutores Houve uma diferença sem significação em F 29-7 e Co. 285. Em Co. 312, porém, o resultado foi duvidoso e em Tuc. 519 foi significante, e em ambas estas variedades as canas não florescidas eram as mais ricas em redutores, o que merece ser salientado. Nota-se que o erro nas canas não florescidas é maior do que nas florescidas, o que indica uma estabilização de percentagem de redutores com o florescimento em F 29-7. A diferença entre os erros é, porém, de significação duvidosa, de sorte que só futuras pesquisas poderão esclarecer essa dúvida. 3 - Análise da pol Neste caso a diferença foi insignificante em F 29-7 e Co. 312 e duvidosa nas outras duas variedades. E nos casos de diferença duvidosa a pol foi maior no caldo das canas florescidas, o que é digno de destaque. O erro foi insignificantemente maior nas canas florescidas do que nas não florescidas. 4 - Análise das cinzas A diferença entre as médias foi insignificante em F 29-7 e Co. 312; foi duvidosa em Tuc. 519 e significante em Co. 285. Nos dois últimos casos a quantidade de cinzas foi maior no caldo das canas não florescidas do que no das florescidas. Nota-se, pelo erro, uma maior variação nas canas não florescidas, mas o teste F dá um resultado duvidoso, que exige novas pesquisas. 5 - Análise da acidez sulfúrica A diferença entre as médias foi insignificante em F 29-7 e Tuc. 519, tendo sido significante nas duas variedades restantes. Nestes dois últimos casos foi o caldo das canas florescidas favorecido com uma acidez menor do que o das não florescidas. O teste F foi absolutamente sem significação, o que significa que a variação é a mesma nas canas florescidas e não florescidas em F 29-7. 6 - Análise de litros de cadlo por quilo de cana A diferença entre as médias foi significante em F 29-7, Co. 285 e Co. 312, sempre com menor quantidade de caldo nas canas n florescidas. Em Tuc. 519 o resultado foi duvidoso, mas como se aproxima bastante do limite de 1% e concorda com os resultados obtidos nas outras variedades e ainda com a observação de medula seca nos gomos terminais das canas florescidas, como já foi dito atrás, esse resultado pode ser tomado como significante. O erro maior nas canas n florescidas e o teste F significante indicam que com o florescimento se estabiliza a relação litros de caldo por quilo de cana. 7 - Análise da fibra Neste caso os resultados foram análogos aos obtidos no caso da relação litros de caldo por quilo' de cana, como era de se esperar. De fato, em F 29-7, Co. 285 e Co. 312 as diferenças foram significantes. Em Tuc. 519 o resultado foi duvidoso, mas as mesmas considerações apresentadas no caso anterior nos levam a considerá-lo significante. Em todas as variedades analisadas as canas florescidas foram sempre mais ricas em fibra. O teste F foi insignificante, c que indica que não há diferença notável entre os erros. 8 - Análise do pêso Esta análise, que só foi feita em F 29-7, nos leva a concluir que o pequeno excesso de peso apresentado pelas canas florescidas n tem a menor significação. Como as nossas observações indicam para as canas florescidas maior comprimento e maior grossura, esse resultado evidencia um murchamente, o que é, aliás, confirmado pela diminuição da relação litros de caldo por quilo dé caria e pelo aumento da quantidade de fibra. Sobre o teste F já salientámos que êle neste caso nos indica que o peso das canas se estabiliza com o florescimento.

Estudos citológicos em Hemíoteros da família Coreidae

A more or less detailed study of the spermatogenesis in six species of Hemiptera belonging to the Coreid Family is made in the present paper. The species studied and their respective chromosome numbers were: 1) Diactor bilineatus (Fabr.) : spermatogonia with 20 + X, primary spermatocytes with 10 + X, X dividing equationaliv in the first division and passing undivided to one pole in the second. 2) Lcptoglossus gonagra (Fabr.) : spermatogonia with 20 + X, primary spermatocytes with 10 + X, X dividing equationally in the first division and passing undivided to one pole in the second. 3) Phthia picta (Drury) : spermatogonia with 20 + X, primary spermatocytes with 10 + X, X dividing equationally in the first division and passing undivided to one pole in the second. 4) Anisocelis foliacea Fabr. : spermatogonia with 26 + X fthe highest mumber hitherto known in the Family), primary .spermatocytes with 13 + X, X dividing equationally in the first division an passing undivided to one pole in the second. 5) Pachylis pharaonis (Herbtst) : spermatogonia with 16 + X, primary spermatocytes with 8 + X. Behaviour of the heteroehromosome not referred. 6) Pachylis laticornis (Fabr.) : spermatogonia with 14 + X, primary spermatocytes with 7 + X, X passing undivided to one pole in the first division and therefore secondary spermatocytes with 7 + X and 7 chromosomes. General results and conclusions a) Pairing modus of the chromosomes (Telosynapsis or Farasynapsis ?) - In several species of the Coreld bugs the history of the chromosomes from the diffuse stage till diakinesis cannot be follewed in detail due specially to the fact that lhe bivalents, as soon as they begin to be individually distinct they appear as irregular and extremely lax chromatic areas, which through an obscure process give rise to the diakinesis and then to the metaphase chomosomes. Fortunately I was able to analyse the genesis of the cross-shaped chromosomes, becoming thus convinced that even in the less favorable cases like that of Phthia, in which the crosses develop from four small condensation areas of the diffuse chromosomes, nothing in the process permit to interpret the final results as being due to a previous telosynaptic pairing. In the case of long bivalents formed by two parallel strands intimately united at both endsegments and more or less widely open in the middle (Leptoglossus, Pachylis), I could see that the lateral arms of the crosses originate from condensation centers created by a torsion or bending in the unpaired parts of the chromosomes In the relatively short bivalents the lateral branches of the cross are formed in the middle but in the long ones, whose median opening is sometimes considerable, two asymetrical branches or even two independent crosses may develop in the same pair. These observations put away the idea of an end-to-end pairing of the chromosomes, since if it had occured the lateral arms of the crosses would always be symetrical and median and never more than two. The direct observation of a side- toside pairing of the chromosomal threads at synizesis, is in foil agreement with the complete lack of evidence in favour of telosynapsis. b) Anaphasic bridges and interzonal connections - The chromosomes as they separate from each other in anaphase they remain connected by means of two lateral strands corresponding to the unpaired segmenas observed in the bivalents at the stages preceding metaphase. In the early anaphase the chromosomes again reproduce the form they had in late diafcinesis. The connecting threads which may be thick and intensely coloured are generally curved and sometimes unequal in lenght, one being much longer than the other and forming a loop outwardly. This fact points to a continuous flow of chromosomal substance independently from both chromosomes of the pair rather than to a mechanical stretching of a sticky substance. At the end of anaphase almost all the material which formed the bridges is reduced to two small cones from whose vertices a very fine and pale fibril takes its origin. The interzonal fibres, therefore, may be considered as the remnant of the anaphasic bridges. Abnormal behaviour of the anaphase chromosomes showed to be useful in aiding the interpretation of normal aspects. It has been suggested by Schrader (1944) "that the interzonal is nothing more than a sticky coating of the chromosome which is stretched like mucilage between the daughter chromosomes as they move further and further apart". The paired chromosomes being enclosed in a commom sheath, as they separate they give origin to a tube which becomes more and more stretched. Later the walls of the tube collapse forming in this manner an interzonal element. My observations, however, do not confirm Schrader's tubular theory of interzonal connections. In the aspects seen at anaphase of the primary spermatocytes and described in this paper as chromosomal bridges nothing suggests a tubular structure. There is no doubt that the chromosomes are here connected by two independent strands in the first division of the spermatocytes and by a single one in the second. The manner in which the chromosomes separate supports the idea of transverse divion, leaving little place for another interpretation. c) Ptafanoeomc and chromatoid bodies - The colourabtlity of the plasmosome in Diactor and Anisocelis showed to be highly variable. In the latter species, one may find in the same cyst nuclei provided with two intensely coloured bodies, the larger of which being the plasmosome, sided by those in which only the heterochromosome took the colour. In the former one the plasmosome strongly coloured seen in the primary metaphase may easily be taken for a supernumerary chromosome. At anaphase this body stays motionless in the equator of the cell while the chromosomes are moving toward the poles. There, when intensely coloured ,it may be confused with the heterochromosome of the secondary spermatocytes, which frequently occupies identical position in the corresponding phase, thus causing missinterpretation. In its place the plasmosome may divide into two equal parts or pass undivided to one cell in whose cytoplasm it breaks down giving rise to a few corpuscles of unequal sizes. In Pachylis pharaonis, as soon as the nuclear membrane breate down, the plasmosome migrates to a place in the periphery of the cell (primary spermatocyte), forming there a large chromatoid body. This body is never found in the cytoplasm prior to the dissolution of the nuclear membrane. It is certain that chromatoid bodies of different origin do exist. Here, however, we are dealing, undoubtedly, with true plasmosomes. d) Movement of the heterochromosome - The heterochromosome in the metaphase of the secondary spermatocytes may occupy the most different places. At the time the autosomes prient themselves in the equatorial plane it may be found some distance apart in this plane or in any other plane and even in the subpolar and polar regions. It remains in its place during anaphase. Therefore, it may appear at the same level with the components of one of the anaphase plates (synchronism), between both plates (succession) or between one plate and tbe pole (precession), what depends upon the moment the cell was fixed. This does not mean that the heterochromosome sometimes moves as quickly as the autosomes, sometimes more rapidly and sometimes less. It implies, on the contrary, that, being anywhere in the cell, the heterochromosome m he attained and passed by the autosomes. In spite of being almost motionless the heterochromosome finishes by being enclosed in one of the resulting nuclei. Consequently, it does move rapidly toward the group formed by the autosomes a little before anaphase is ended. This may be understood assuming that the heterochromosome, which do not divide, having almost inactive kinetochore cannot orient itself, giving from wherever it stays, only a weak response to the polar influences. When in the equator it probably do not perform any movement in virtue of receiving equal solicitation from both poles. When in any other plane, despite the greater influence of the nearer pole, the influence of the opposite pole would permit only so a slow movement that the autosomes would soon reach it and then leave it behind. It is only when the cell begins to divide that the heterochromosome, passing to one of the daughter cells scapes the influence of the other and thence goes quickly to join the autosomes, being enclosed with them in the nucleus formed there. The exceptions observed by BORING (1907) together with ; the facts described here must represent the normal behavior of the heterocromosome of the Hemiptera, the greater frequency of succession being the consequence of the more frequent localization of the heterochromosome in the equatorial plane or in its near and of the anaphase rapidity. Due to its position in metaphase the heterochromosome in early anaphase may be found in precession. In late anaphase, oh the contrary ,it appears almost always in succession. This is attributed to the fact of the heterochromosome being ordinairily localized outside the spindle area it leaves the way free to the anaphasic plate moving toward the pole. Moreover, the heterochromosome being a round element approximately of the size of the autosomes, which are equally round or a little longer in the direction of the movement, it can be passed by the autosomes even when it stands in the area of the spindle, specially if it is not too far from the equatorial plane. e) The kinetochore - This question has been fully discussed in another paper (PIZA 1943a). The facts treated here point to the conclusion that the chromosomes of the Coreidae, like those of Tityus bahiensis, are provided with a kinetochore at each end, as was already admitted by the present writer with regard to the heterochromosome of Protenor. Indeed, taking ipr granted the facts presented in this paper, other cannot be the interpretation. However, the reasons by which the chromosomes of the species studied here do not orient themselves at metaphase of the first division in the same way as the heterochromosome of Protenor, that is, with the major axis parallelly to the equatorial plane, are claiming for explanation. But, admiting that the proximity of the kinetochores at the ends of chromosomes which do not separate until the second division making them respond to the poles as if they were a single kinetochore ,the explanation follows. (See PIZA 1943a). The median opening of the diplonemas when they are going to the diffuse stage as well as the reappearance of the bivalents always united at the end-segments and open in the middle is in full agreement with the existence of two terminal kinetochores. The same can be said with regard to the bivalents which join their extremities to form a ring.

Comportamento do Heterocromossômio em alguns Ortópteros do Brasil

In the present paper the behavior of the heterochromoso-mes in the course of the meiotic divisions of the spermatocytes in 15 species of Orthoptera belonging to 6 different families was studied. The species treated and their respective chromosome numbers were: Phaneropteridae: Anaulacomera sp. - 1 - 2n = 30 + X, n +15+ X and 15. Anaulacomera sp. - 2 - 2n - 30 + X, n = 15+ X and 15. Stilpnochlora marginella - 2n = 30 + X, n = 15= X and 15. Scudderia sp. - 2n = 30 + X, n = 15+ X and 15. Posldippus citrifolius - 2n = 24 + X, n = 12+X and 12. Acrididae: Osmilia violacea - 2n = 22+X, n = 11 + X and 11. Tropinotus discoideus - 2n = 22+ X, n = 11 + X and 11. Leptysma dorsalis - 2n = 22 + X, n = 11-J-X and 11. Orphulella punctata - 2n = 22-f X, n = 11 + X and 11. Conocephalidae: Conocephalus sp. - 2n = 32 + X, n = 16 + X and 16. Proscopiidae: Cephalocoema zilkari - 2n = 16 + X, n = 8+ X and 8. Tetanorhynchus mendesi - 2n = 16 + X, n = 8+X and 8. Gryliidae: Gryllus assimilis - 2n = 28 + X, n = 14+X and 14. Gryllodes sp. - 2n = 20 + X, n = 10- + and 10. Phalangopsitidae: Endecous cavernicola - 2n = 18 +X, n = 94-X and 9. It was pointed out by the present writer that in the Orthoptera similarly to what he observed in the Hemiptera the heterochromosome in the heterocinetic division shows in the same individual indifferently precession, synchronism or succession. This lack of specificity is therefore pointed here as constituting the rule and not the exception as formerly beleaved by the students of this problem, since it occurs in all the species referred to in the present paper and probably also m those hitherto investigated. The variability in the behavior of the heterochromosome which can have any position with regard to the autosomes even in the same follicle is attributed to the fact that being rather a stationary body it retains in anaphase the place it had in metaphase. When this place is in the equator of the cell the heterochromosome will be left behind as soon as anaphase begins (succession). When, on the contrary, laying out of this plane as generally happens (precession) it will sooner be reached (synchronism) or passed by the autosomes (succession). Due to the less kinetic activity of the heterochromosome it does not orient itself at metaphase remaining where it stands with the kinetochore looking indifferently to any direction. At the end of anaphase and sometimes earlier the heterochromosome begins to show mitotic activities revealed by the division of its body. Then, responding to the influence of the nearer pole it moves to it being enclosed with the autosomes in the nucleus formed there. The position of the heterochromosome in the cell is explained in the following manner: It is well known that the heterochromosome of the Orthoptera is always at the periphery of the nucleus, just beneath the nuclear membrane. This position may be any in regard of the axis of the dividing cell, so that if one of the poles of the spindle comes to coincide with it, the heterochromosome will appear at this pole in the metaphasic figures. If, on the other hand, the angle formed by the axis of the spindle with the ray reaching the heterochromosome increases the latter will appear in planes farther and farther apart from the nearer pole until it finishes by being in the equatorial plane. In this way it is not difficult to understand precession, synchronism or succession. In the species in which the heterochromosome is very large as it generally happens in the Phaneropteridae, the positions corresponding to precession are much more frequent. This is due to the fact that the probabilities for the heterochromosome taking an intermediary position between the equator and the poles at the time the spindle is set up are much greater than otherwise. Moreover, standing always outside the spindle area it searches for a place exactly where this area is larger, that is, in the vicinity of the poles. If it comes to enter the spindle area, what has very little probability, it would be, in virtue of its size, propelled toward the pole by the nearing anaphasic plate. The cases of succession are justly those in which the heterochromosome taking a position parallelly to the spindle axis it can adjust its large body also in the equator or in its proximity. In the species provided with small heterochromosome (Gryllidae, Conocephalidae, Acrididae) succession is found much more frequently because here as in the Hemiptera (PIZA 1945) the heterochromosome can equally take equatorial or subequatorial positions, and, furthermore, when in the spindle area it does offer no sereous obstacle to the passage of the autosomes. The position of the heterochromosome at the periphery of the nucleus at different stages may be as I suppose, at least in part a question of density. The less colourability and the surface irregularities characteristic of this element may well correspond to a less degree of condensation which may influence passive movements. In one of the species studied here (Anaulacomera sp.- 1) included in the Phaneropteridae it was observed that the plasmosome is left motionless in the spindle as the autosomes move toward the poles. It passes to one of the secondary spermatocytes being not included in its nucleus. In the second division it again passes to one of the cells being cast off when the spermatid is being transformed into spermatozoon. Thus it is regularly found among the tails of the spermatozoa in different stages of development. In the opinion of the present writer, at least in some cases, corpuscles described as Golgi body's remanents are nothing more than discarded plasmosomes.

Estudos genéticos sôbre o milho tunicata

The study of pod corn seems still of much importance from different points of view. The phylogenetical importance of the tunicate factor as a wild type relic gene has been recently discussed in much detail by MANGELSDORF and REEVES (1939), and by BRIEGER (1943, 1944a e b). Selection experiments have shown that the pleiotropic effect of the Tu factor can be modified very extensively (BRIEGER 1944a) and some of the forms thus obtained permitt comparison of male and female inflorescences in corn and related grasses. A detailed discussion of the botanical aspect shall be given shortly. The genetic apect, finally, is the subject of the present publication. Pod corn has been obtained twice: São Paulo Pod Corn and Bolivia Pod Corn. The former came from one half ear left in our laboratory by a student and belongs to the type of corn cultivated in the State of São Paulo, while the other belongs to the Andean group, and has been received both through Dr. CARDENAS, President of the University at Cochabamba, Bolivia, and through Dr. H. C. CUTLER, Harvard University, who collected material in the Andes. The results of the studies may be summarized as follows: 1) In both cases, pod corn is characterized by the presence of a dominant Tu factor, localized in the fourth chromosome and linked with sul. The crossover value differs somewhat from the mean value of 29% given by EMERSON, BEADLE and FRAZER (1935) and was 25% in 1217 plants for São Paulo Pod Corn and 36,5% in 345 plants for Bolivia Pod Corn. However not much importance should be attributed to the quantitative differences. 2) Segregation was completely normal in Bolivia Pod Corn while São Paulo Pod Corn proved to be heterozygous for a new com uma eliminação forte, funcionam apenas 8% em vez de 50%. Existem cerca de 30% de "jcrossing-over entre o gen doce (Su/su) e o fator gametofítico; è cerca de 5% entre o gen Tu e o fator gametofítico. A ordem dos gens no cromosômio IV é: Ga4 - Tu - Sul. 3) Using BRIEGER'S formulas (1930, 1937a, 1937b) the following determinations were made. a) the elimination of ga4 pollen tubes may be strong or weak. In the former case only about 8% and in the latter 37% of ga4 pollen tubes function, instead of the 50% expected in normal heterozygotes. b) There is about 30,4% crossing-over between sul and ga4 and 5,3% between Tu and ga3, the order of the factors beeing Su 1 - Tu - Ga4. 4) The new gametophyte factor differs from the two others factors in the same chromosome, causing competition between pollen tubes. The factor Gal, ocupies another locus, considerably to the left of Sul (EMERSON, BEADLE AND FRAZSER, 1935). The gen spl ocupies another locus and causes a difference of the size of the pollen grains, besides an elimination of pollen tubes, while no such differences were observed in the case of the new factor Ga4. 5) It may be mentioned, without entering into a detailed discussion, that it seems remarquable that three of the few gametophyte factors, so far studied in detail are localized in chromosome four. Actuality there are a few more known (BRIEGER, TIDBURY AND TSENG 1938), but only one other has been localized so far, Ga2, in chromosome five between btl and prl. (BRIEGER, 1935). 6) The fourth chromosome of corn seems to contain other pecularities still. MANGELSDORF AND REEVES (1939) concluded that it carries two translocations from Tripsacum chromosomes, and BRIEGER (1944b) suggested that the tu allel may have been introduced from a tripsacoid ancestor in substitution of the wild type gene Tu at the beginning of domestication. Serious disturbances in the segregation of fourth chromosome factors have been observed (BRIEGER, unpublished) in the hybrids of Brazilian corn and Mexican teosinte, caused by gametophytic and possibly zygotic elimination. Future studies must show wether there is any relation between the frequency of factors, causing gametophyte elimination and the presence of regions of chromosomes, tranfered either from Tripsacum or a related species, by translocation or crossing-over.

Competição entre megaspórios em milho

The experiments reported were started as early as 1933, when indications were found in class material that the factor for small pollen, spl, causes not only differences in the size of pollen grains and in the growth of pollen tubes, but also a competition between megaspores, as first observed by RENNER (1921) in Oenothera. Dr. P. C. MANGELSDORF, who had kindly furnished the original seeds, was informed and the final publication delayed untill his publication in 1940. A further delay was caused by other circunstances. The main reason for the differences of the results obtained by SINGLETON and MANGELSDORF (1940) and those reported here, seems to be the way the material was analysed. I applied methods of a detailed statistical analysis, while MANGELSDORF and SINGLETON analysed pooled data. 1) The data obtained on pollen tube competition indicate .that there is about 3-4% of crossing-over between the su and sp factors in chromosome IV. The elimination is not always complete, but from 0 to 10% of the sp pollen tubes may function, instead of the 50% expected without elimination. These results are, as a whole, in accordance with SINGLETON and MANGELSDORF's data. 2) Female elimination is weaker and transmission determined as between 16 to 49,5%, instead of 50% without competition, the values being calculated by a special formula. 3) The variability of female elimination is partially genotypical, partially phenotypical. The former was shown by the difference in the behavior of the two progenies tested, while the latter was very evident when comparing the upper and lower halves of ears. For some unknown physiological reason, the elimination is generally stronger in the upper than in the lower half of the ear. 4) The female elimination of the sp gene may be caused theoretically, by either of two processes: a simple lethal effect in the female gametophyte or a competition between megaspores. The former would lead not only to the abortion of the individual megaspores, but of the whole uniovulate ovary. In the case of the latter, the abortive megaspore carrying the gene sp will be substituted in each ovule by one of the Sp megaspores and no abortion of ovaries may be observed. My observations are completely in favor of the second explication: a) The ears were as a whole very well filled except for a few incomplete ears which always appear in artificial pollinations. b) Row arrangement was always very regular. c) The number of kernels on ears with elimination is not smaller than in normal ears, but is incidentally higher : with elimnation, in back-crosses 354 kernels and in selfed ears 390 kernels, without elimination 310 kernels per ear. d) There is no correlation between the intensity of elimination and the number of grains in individual ears; the coefficient; of linear correlation, equal to 0,24, is small and insignificant. e) Our results are in complete disagreement whit those reported by SINGLETON and MANGELSDORF (1940). Since these authors present only pooled date, a complete and detailed analysis which may explain the cause of these divergences is impossible.

A ação dos gens gametofíticos com referência especial ao milho

1) The first part deals with the different processes which may complicate Mendelian segregation and which may be classified into three groups, according to BRIEGER (1937b) : a) Instability of genes, b) Abnormal segregation due to distur- bances during the meiotic divisions, c) obscured segregation, after a perfectly normal meiosis, caused by elimination or during the gonophase (gametophyte in higher plants), or during zygophase (sporophyte). Without entering into detail, it is emphasized that all the above mentioned complications in the segregation of some genes may be caused by the action of other genes. Thus in maize, the instability of the Al factor is observed only when the gene dt is presente in the homozygous conditions (RHOADES 1938). In another case, still under observation in Piracicaba, an instability is observed in Mirabilis with regard to two pairs of alleles both controlling flower color. Several cases are known, especially in corn, where recessive genes, when homozigous, affect the course of meiosis, causing asynapsis (asyndesis) (BEADLE AND MC CLINTOCK 1928, BEADLE 1930), sticky chromosomes (BEADLE 1932), supermunmerary divisions (BEADLE 1931). The most extreme case of an obscured segregatiou is represented by the action of the S factors in self stetrile plants. An additional proof of EAST AND MANGELSDORF (1925) genetic formula of self sterility has been contributed by the studies on Jinked factors in Nicotina (BRIEGER AND MANGELSDORF (1926) and Antirrhinum (BRIEGER 1930, 1935), In cases of a incomplete competition and selection between pollen tubes, studies of linked indicator-genes are indispensable in the genetic analysis, since it is impossible to analyse the factors for gametophyte competition by direct aproach. 2) The flower structure of corn is explained, and stated that the particularites of floral biology make maize an excellent object for the study of gametophyte factors. Since only one pollen tube per ovule may accomplish fertilization, the competition is always extremely strong, as compared with other species possessing multi-ovulate ovaries. The lenght of the silk permitts the study of pollen tube competitions over a varying distance. Finally the genetic analysis of grains characters (endosperm and aleoron) simpliflen the experimental work considerably, by allowing the accumulation of large numbers for statistical treatment. 3) The four methods for analyzing the naturing of pollen tube competition are discussed, following BRIEGER (1930). Of these the first three are: a) polinization with a small number of pollen grains, b) polinization at different times and c) cut- ting the style after the faster tubes have passe dand before the slower tubes have reached the point where the stigma will be cut. d) The fourth method, alteration of the distatice over which competition takes place, has been applied largely in corn. The basic conceptions underlying this process, are illustrated in Fig. 3. While BRINK (1925) and MANGELSDORF (1929) applied pollen at different levels on the silks, the remaining authors (JONES, 1922, MANGELSDORF 1929, BRIEGER, at al. 1938) have used a different process. The pollen was applied as usual, after removing the main part of the silks, but the ears were divided transversally into halves or quarters before counting. The experiments showed generally an increase in the intensity of competition when there was increase of the distance over which they had to travel. Only MANGELSDORF found an interesting exception. When the distance became extreme, the initially slower tubes seemed to become finally the faster ones. 4) Methods of genetic and statistical analysis are discussed, following chiefly BRIEGER (1937a and 1937b). A formula is given to determine the intensity of ellimination in three point experiments. 5) The few facts are cited which give some indication about the physiological mechanism of gametophyte competition. They are four in number a) the growth rate depends-only on the action of gametophyte factors; b) there is an interaction between the conductive tissue of the stigma or style and the pollen tubes, mainly in self-sterile plants; c) after self-pollination necrosis starts in the tissue of the stigma, in some orchids after F. MÜLLER (1867); d) in pollon mixtures there is an inhibitory interaction between two types of pollen and the female tissue; Gossypium according to BALLS (1911), KEARNEY 1923, 1928, KEARNEY AND HARRISON (1924). A more complete discussion is found in BRIEGER 1930). 6) A list of the gametophyte factors so far localized in corn is given. CHROMOSOME IV Ga 1 : MANGELSDORF AND JONES (1925), EMERSON 1934). Ga 4 : BRIEGER (1945b). Sp 1 : MANGELSDORF (1931), SINGLETON AND MANGELSDORF (1940), BRIEGER (1945a). CHROMOSOME V Ga 2 : BRIEGER (1937a). CHROMOSOME VI BRIEGER, TIDBURY AND TSENG (1938) found indications of a gametophyte factor altering the segregation of yellow endosperm y1. CHROMOSOME IX Ga 3 : BRIEGER, TIDBURY AND TSENG (1938). While the competition in these six cases is essentially determined by one pair of factors, the degree of elimination may be variable, as shown for Ga2 (BRIEGER, 1937), for Ga4 (BRIEGER 1945a) and for Spl (SINGLETON AND MANGELSDORF 1940, BRIEGER 1945b). The action of a gametophyte factor altering the segregation of waxy (perhaps Ga3) is increased by the presence of the sul factor which thus acts as a modifier (BRINCK AND BURNHAM 1927). A polyfactorial case of gametophyte competition has been found by JONES (1922) and analysed by DEMEREC (1929) in rice pop corn which rejects the pollen tubes of other types of corn. Preference for selfing or for brothers-sister mating and partial elimination of other pollen tubes has been described by BRIEGER (1936). 7) HARLAND'S (1943) very ingenious idea is discussed to use pollen tube factors in applied genetics in order to build up an obstacle to natural crossing as a consequence of the rapid pollen tube growth after selfing. Unfortunately, HARLAND could not obtain the experimental proof of the praticability of his idea, during his experiments on selection for minor modifiers for pollen tube grouth in cotton. In maize it should be possible to employ gametophyte factors to build up lines with preference for crossing, though the method should hardly be of any practical advantage.

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.

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.

Efeitos do arsênico sôbre a cultura do algodoeiro em terra arenosa

The authors studied the action of arsenic, in the form of lead arsenate and sodium arsenite, on cotton in white sandy soil of Piracicaba, State of S. Paulo, Brazil. The experiment was carried out in Mitscherlich pots, applying increasing quantities of the above mentioned compounds. The following conclusions were reached: sodium arsenite is more toxic than lead arsenate. 48 pounds per acre of lead arsenate and 16 pounds per acre of sodium arsenite reduced the vegetative development and the production of cotton. The roots were more seriously affected than the aerial parts. Sandy soils were sensitive to arsenic toxicity. The arsenic mobilization in the soil seems to depend upon factors such as, the a- cidity, the concentration of Fe2O3, CaO, P2O5 and soil colloids, both clay and humus components. The authors suggest, based on their own experiment and after a detailed study of the literature, the use of organic insecticids which may not leave toxic residues, rotation of crops, application of lime and reduction of arsenical sprays to a mini mum. Arsenic compounds should not be used in soils destined to the cultivation of food plants. Rice should not be planted in soils contaminated by arsenic compounds during several years of cotton cultivation. Future experiments are planed, using other soils such as "terra roxa", in Mitscherlich pots and in field plots.

Espiguetas de dois grãos no milho

A morfologia, ocorrência, utilidade e genética das flores funcionais inferiores em espiguetas de milho, são examinadas ligeiramente. Em regra, somente a flor superior em cada espigueta numa espiga de milho se desenvolve e contém um grão, porém nos exemplos em foco a flor inferior se desenvolve tão bem como a superior. O embrião no milho geralmente se acha voltado na mesma direção que a ponta da espiga, ao passo que o embrião do grão proveniente da flor inferior se volta na direção da base. São raras, não só na América do Norte e Central, como na maior parte da América do Sul, as espigas nas quais os grãos provêm da flor inferior das espiguetas, constituindo uma exceção o milho doce Country Gentleman, no qual se encontram grãos em ambas as flores na maioria das espiguetas. No Brasil e na Bolívia, entretanto, são mais comuns as espigas com espiguetas de dois grãos. Sendo o milho proveniente da América do Sul, é de esperar-se que se encontrem mais variedades e tipos mais primitivos próximo do centro de origem. No milho Pipoca Pontudo Paulista, o Dr. BRIEGER encontrou espigas com ambas as flores funcionais em algumas espiguetas. Em alguns casos, ambos os grãos eram de tamanho normal, porém, mais comumente, um dos dois grãos era bem menor que o outro. Em espigas encontradas pelo Dr. MARTIN CARDENAS, algumas espiguetas apresentam grãos provindos somente das flores inferiores, uma circunstância característica do grupo "Poaceae", e não do "Panicaceae" a que pertence o milho. Muitos gens que influenciam os característicos do pendão, também influenciam os das espigas. Alguns destes controlam a formação de grãos na flor inferior da espigueta-fêmea. A maioria dos gens conhecidos como afetando as espiguetas inferiores, são recessivos, tal como no caso das espigas brasileira e boliviana estudadas, e no Country Gentleman. Um exemplo de espiguetas gêmeas foi encontrado entre o material tunicata do Dr. BRIEGER. Aí, em vez de uma só espi-gueta, o que é o normal, havia duas espiguetas completas, simétricas, sendo uma em posição oposta ao normal. Os grãos, em ambas, achavam-se na flor superior. Prosseguem os estudos sobre a espigueta do milho. O Dr. GONÇALVES DRUMOND, da Escola Superior de Viçosa, Minas Gerais, encontrou recentemente algumas espigas de "Cateto", nas quais a flor inferior é funcional e está estudando as mesmas. Parece que o mais interessante material para os novos estudos é o que o Dr. BRIEGER encontrou no seu milho "Pipoca Pontudo Paulista, pois há ai graus variáveis de desenvolvimento tanto superiores como inferiores.

Gramados para parques avícolas: nota prévia

Na Seção de Avicultura da Escola Superior de Agricultura "Luiz de Queiroz", da Universidade de São Paulo, foi iniciada uma experiência de pastagens para galinhas, para determinação das espécies mais adequadas ao fim visado. Os resultados obtidos neste primeiro ano de experiência indicaram a seguinte classificação: 1.o - Consociação de Grama Seda (Cynodon dactylon Pers.) var.? com Capim Quicúio (Pennisetum clandestinum Chiov.). 2.0 - Grama Seda (Cynodon dactylon Pers.) var.? 3.0 - Capim Quicúio (Pennisetum clandestinum Chiov.). 4.O - Grama de Batatais (Palpalum notatum Flügge.). 5.o - Uma grama ainda não determinada. 6.o - Grama Paulista (Cynodon dactylon Pers.) var.? A variedade Gigante de Cynodon dactylon Pers. não deu resultados satisfatórios. A experiência será continuada.