Spatio-temporal dynamics and transition from asymptotic equilibrium to bounded oscillations in Chrysomya albiceps (Diptera, Calliphoridae)

The sensitivity of parameters that govern the stability of population size in Chrysomya albiceps and describe its spatial dynamics was evaluated in this study. The dynamics was modeled using a density-dependent model of population growth. Our simulations show that variation in fecundity and mainly in survival has marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations. C. albiceps exhibits a two-point limit cycle, but the introduction of diffusive dispersal induces an evident qualitative shift from two-point limit cycle to a one fixed-point dynamics. Population dynamics of C. albiceps is here compared to dynamics of Cochliomyia macellaria, C. megacephala and C. putoria.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Are there evidences of a complex mimicry system among Asclepias curassavica (Apocynaceae), Epidendrum fulgens (Orchidaceae), and Lantana camara (Verbenaceae) in Southern Brazil?

The goal of this paper was to test the presence of mimicry in Asclepias curassavica L., Epidendrum fulgens Brong., and Lantana camara L. The study was carried out at the Parque Estadual de Itapeva, RS, southern Brazil, from 2004 to 2006. Flowering period of each of the three species was followed up; focal observations of butterflies visiting flowers, from fixed point and during random walks were carried out. We also estimated the frequency of pollinaria removal in the orchid, as well as its mode of reproduction. All these variables were important for testing the mimicry hypothesis. Despite some temporal coincidences in the flowering period of two plants in the system, there was no statistical association among the three plants as to flowering period. Twenty-nine species of butterflies, as potential pollinators, were recorded, particularly Agraulis vanillae maculosa, Dryas iulia alcionea, Urbanus simplicius, Tegosa claudina, and Heliconius erato phyllis, which were the more frequent visitors of the three plants. There was association between the number of visits to L. camara and E. fulgens, based on Pearson correlation (r = 0.4603; n = 19; P = 0.0473). Pollinaria removal of E. fulgens was low, as measured by the percentage of removal (range: 0 - 10%). The analysis of the mode of reproduction of this orchid showed its pollinator-dependence, since no fruits were formed by spontaneous self-pollination. In contrast, the percentage of fruit set that resulted from geitonogamy and xenogamy was, in average, 86%. The results here shown are not conclusive as to the occurrence of a mimicry system among the three plants.

Effect of point mutations on Herbaspirillum seropedicae NifA activity

NifA is the transcriptional activator of the nif genes in Proteobacteria. It is usually regulated by nitrogen and oxygen, allowing biological nitrogen fixation to occur under appropriate conditions. NifA proteins have a typical three-domain structure, including a regulatory N-terminal GAF domain, which is involved in control by fixed nitrogen and not strictly required for activity, a catalytic AAA+ central domain, which catalyzes open complex formation, and a C-terminal domain involved in DNA-binding. In Herbaspirillum seropedicae, a β-proteobacterium capable of colonizing Graminae of agricultural importance, NifA regulation by ammonium involves its N-terminal GAF domain and the signal transduction protein GlnK. When the GAF domain is removed, the protein can still activate nif genes transcription; however, ammonium regulation is lost. In this work, we generated eight constructs resulting in point mutations in H. seropedicae NifA and analyzed their effect on nifH transcription in Escherichia coli and H. seropedicae. Mutations K22V, T160E, M161V, L172R, and A215D resulted in inactive proteins. Mutations Q216I and S220I produced partially active proteins with activity control similar to wild-type NifA. However, mutation G25E, located in the GAF domain, resulted in an active protein that did not require GlnK for activity and was partially sensitive to ammonium. This suggested that G25E may affect the negative interaction between the N-terminal GAF domain and the catalytic central domain under high ammonium concentrations, thus rendering the protein constitutively active, or that G25E could lead to a conformational change comparable with that when GlnK interacts with the GAF domain.

Mid-point for open-ended income category and the effect of equivalence scales on the income-health relationship

To estimate the mid-point of an open-ended income category and to assess the impact of two equivalence scales on income-health associations. Data were obtained from the 2010 Brazilian Oral Health Survey ( Pesquisa Nacional de Saúde Bucal – SBBrasil 2010). Income was converted from categorical to two continuous variables ( per capita and equivalized) for each mid-point. The median mid-point was R$ 14,523.50 and the mean, R$ 24,507.10. When per capita income was applied, 53% of the population were below the poverty line, compared with 15% with equivalized income. The magnitude of income-health associations was similar for continuous income, but categorized equivalized income tended to decrease the strength of association.

Cut-off point for WHOQOL-bref as a measure of quality of life of older adults

OBJECTIVE To propose a cut-off for the World Health Organization Quality of Life-Bref (WHOQOL-bref) as a predictor of quality of life in older adults. METHODS Cross-sectional study with 391 older adults registered in the Northwest Health District in Belo Horizonte, MG, Southeastern Brazil, between October 8, 2010 and May 23, 2011. The older adults’ quality of life was measured using the WHOQOL-bref. The analysis was rationalized by outlining two extreme and simultaneous groups according to perceived quality of life and satisfaction with health (quality of life good/satisfactory – good or very good self-reported quality of life and being satisfied or very satisfied with health – G5; and poor/very poor quality of life – poor or very poor self-reported quality of life and feeling dissatisfied or very dissatisfied with health – G6). A Receiver-Operating Characteristic curve (ROC) was created to assess the diagnostic ability of different cut-off points of the WHOQOL-bref. RESULTS ROC curve analysis indicated a critical value 60 as the optimal cut-off point for assessing perceived quality of life and satisfaction with health. The area under the curve was 0.758, with a sensitivity of 76.8% and specificity of 63.8% for a cut-off of ≥ 60 for overall quality of life (G5) and sensitivity 95.0% and specificity of 54.4% for a cut-off of < 60 for overall quality of life (G6). CONCLUSIONS Diagnostic interpretation of the ROC curve revealed that cut-off < 60 for overall quality of life obtained excellent sensitivity and negative predictive value for tracking older adults with probable worse quality of life and dissatisfied with health.

Metabolic syndrome in fixed-shift workers

OBJECTIVE To analyze if metabolic syndrome and its altered components are associated with demographic, socioeconomic and behavioral factors in fixed-shift workers.METHODS A cross-sectional study was conducted on a sample of 902 shift workers of both sexes in a poultry processing plant in Southern Brazil in 2010. The diagnosis of metabolic syndrome was determined according to the recommendations from Harmonizing the Metabolic Syndrome. Its frequency was evaluated according to the demographic (sex, skin color, age and marital status), socioeconomic (educational level, income and work shift), and behavioral characteristics (smoking, alcohol intake, leisure time physical activity, number of meals and sleep duration) of the sample. The multivariate analysis followed a theoretical framework for identifying metabolic syndrome in fixed-shift workers.RESULTS The prevalence of metabolic syndrome in the sample was 9.3% (95%CI 7.4;11.2). The most frequently altered component was waist circumference (PR 48.4%; 95%CI 45.5;51.2), followed by high-density lipoprotein. Work shift was not associated with metabolic syndrome and its altered components. After adjustment, the prevalence of metabolic syndrome was positively associated with women (PR 2.16; 95%CI 1.28;3.64), workers aged over 40 years (PR 3.90; 95%CI 1.78;8.93) and those who reported sleeping five hours or less per day (PR 1.70; 95%CI 1.09;2.24). On the other hand, metabolic syndrome was inversely associated with educational level and having more than three meals per day (PR 0.43; 95%CI 0.26;0.73).CONCLUSIONS Being female, older and deprived of sleep are probable risk factors for metabolic syndrome, whereas higher educational level and higher number of meals per day are protective factors for metabolic syndrome in fixed-shift workers.

Immunoperoxidase for the detection for the detection of antibodies in cerebrospinal fluid in neurocysticercosis: use of Cysticercus cellulosae and Cysticercus longicollis particles fixed on microscopy slides

The ORF strain of Cysticercus longicollis represents an important model for the study of heterologous antigens in the immunodiagnosis of neurocysticercosis (NC). The immunoperoxidase (IP) technique was standardized using a particulate antigen suspension of Cysticercus longicollis (Cl) and Cysticercus cellulosae (Cc). Cerebrospinal fluid (CSF) samples were incubated on the antigen fixed to microscopy slides; the conjugate employed was anti-IgG-peroxidase and the enzymatic reaction was started by covering the slides with chromogen solution (diaminobenzidine/H2O2). After washing with distilled water, the slide was stained with 2% malachite green in water. Of the CSF samples from 21 patients with NC, 19 (90.5%) were positive, whereas the 8 CSF samples from the control group (100%) were negative. The results of the IP-Cl test applied to 127 CSF samples from patients with suspected NC showed 28.3% reactivity as opposed to 29.1 % for the IP-Cc test. The agreement index for the IP test (Cl x Cc) was 94.2%, with no significant difference between the two antigens.

Detection of parvovirus B19 infection in formalin-fixed and paraffin-embedded placenta and fetal tissues

Parvovirus B19 infection was first discovered in 1975 and it is implicated in fetal death from hydrops fetalis the world over. Diagnosis is usually made through histological identification of the intranuclear inclusion in placenta and fetal organs. However, these cells may be scarce or uncharacteristic, making definitive diagnosis difficult. We analyzed histologically placentas and fetal organs from 34 cases of non-immune hydrops fetalis, stained with Hematoxylin and Eosin (HE) and submitted to immunohistochemistry and polymerase chain reaction (PCR). Of 34 tissue samples, two (5.9%) presented typical intranuclear inclusion in circulating normoblasts seen in Hematoxylin and Eosin stained sections, confirmed by immunohistochemistry and PCR. However, PCR of fetal organs was negative in one case in which the placenta PCR was positive. We concluded that parvovirus B19 infection frequency is similar to the literature and that immunohistochemistry was the best detection method. It is highly specific and sensitive, preserves the morphology and reveals a larger number of positive cells than does HE with the advantage of showing cytoplasmic and nuclear positivity, making it more reliable. Although PCR is more specific and sensitive in fresh or ideally fixed material it is not so in formalin-fixed paraffin-embedded tissues, frequently the only one available in such cases.

Effects of tissue handling and processing steps on PCR for detection of Mycobacterium tuberculosis in formalin-fixed paraffin-embedded samples

Development and standardization of reliable methods for detection of Mycobacterium tuberculosis in clinical samples is an important goal in laboratories throughout the world. In this work, lung and spleen fragments from a patient who died with the diagnosis of miliary tuberculosis were used to evaluate the influence of the type of fixative as well as the fixation and paraffin inclusion protocols on PCR performance in paraffin embedded specimens. Tissue fragments were fixed for four h to 48 h, using either 10% non-buffered or 10% buffered formalin, and embedded in pure paraffin or paraffin mixed with bee wax. Specimens were submitted to PCR for amplification of the human beta-actin gene and separately for amplification of the insertion sequence IS6110, specific from the M. tuberculosis complex. Amplification of the beta-actin gene was positive in all samples. No amplicons were generated by PCR-IS6110 when lung tissue fragments were fixed using 10% non-buffered formalin and were embedded in paraffin containing bee wax. In conclusion, combined inhibitory factors interfere in the detection of M. tuberculosis in stored material. It is important to control these inhibitory factors in order to implement molecular diagnosis in pathology laboratories.

Detection of codon 12 mutation in the k-ras oncogene in pancreatic tumors

Mutations at codons 12, 13, or 61 of the H-ras, K-ras, and N-ras have been detected in human neoplasias by a variety of techniques. Some of these techniques are very sensitive and can detect K-ras mutation in 90% of the cases of pancreatic adenocarcinomas. We analyzed 11 samples of pancreatic adenocarcinoma, three samples of pancreatic mucinous cystadenoma, and two samples without tumors in formalin-fixed paraffin embedded tissue sections. K-ras mutations at codon 12 were detected by a two-step PCR-enriched technique in all the samples of pancreatic adenocarcinoma, but not in cystadenoma or control samples. This technique may be useful for early detection of pancreatic cancer.

Exercise and heart failure. Relation of the severity of the disease to the anaerobic threshold and the respiratory compensation point

OBJECTIVE - To identify, the anaerobic threshold and respiratory compensation point in patients with heart failure. METHODS - The study comprised 42 Men,divided according to the functional class (FC) as follows: group I (GI) - 15 patients in FC I; group II (GII) - 15 patients in FC II; and group III (GIII) - 12 patients in FC III. Patients underwent a treadmill cardiopulmonary exercise test, where the expired gases were analyzed. RESULTS - The values for the heart rate (in bpm) at the anaerobic threshold were the following: GI, 122±27; GII, 117±17; GIII, 114±22. At the respiratory compensation point, the heart rates (in bpm) were as follows: GI, 145±33; GII, 133±14; GIII 123±22. The values for the heart rates at the respiratory compensation point in GI and GIII showed statistical difference. The values of oxygen consumption (VO2) at the anaerobic threshold were the following (in ml/kg/min): GI, 13.6±3.25; GII, 10.77±1.89; GIII, 8.7±1.44 and, at the respiratory compensation point, they were as follows: GI, 19.1±2.2; GII, 14.22±2.63; GIII, 10.27±1.85. CONCLUSION - Patients with stable functional class I, II, and III heart failure reached the anaerobic threshold and the respiratory compensation point at different levels of oxygen consumption and heart rate. The role played by these thresholds in physical activity for this group of patients needs to be better clarified.

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.

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.

Os anofelinos do sub-gênero kerteszia em relação à distribuição das bromeliáceas em comunidades florestais do município de Brusque, Estado de Santa Catarina

The present work is part of the studies realized under the authority of the National Service of Malaria (Brazil), with the collaboration of scientists of the Oswaldo Cruz Institute, in some forests of the southern part of Brazil.This is the first of a series and its subject is the development of the Anopheles mosquitoes of the kerteszia in water collected in Bromeliaceae leaves. The ecology of Bromeliaceae was studied in a previous work. The botanical material was classified by specialists from several botanical institutions from Europe and the United States of America. The most important ecological relations of the “bromeliad-kerteszia” problem were presented through four indices: 1st Positivity index – Relative frequency of bromeliad with watery forms in the bromeliad examined. 2nd Larval index – Mean number of watery forms in the positive bromeliad. 3rd Ovoposition index – Product of the Positivy index by the Larval index. 4th MK index – Product of the Ovoposition index by the total number of bromeliad, positive or not, in a unity of area (1.000 m²). The capture of flying forms in relation to the relative humidity was also studied. From the several forests of the Brusque region we have selected one community of each type, which were the most representative forests in Southern Brazil. Conclusions on the “bromeliad-kerteszia” problem – From a general point of view only a few factors are really important and these are listed below: 1°) The volum of water on the bromeliad. 2°) The level where the bromeliad is fixed. 3°) The number of bromeliad in unity of area. The distribution of microclimas in the forest through the considered levels has a direct influence on the species of subgenus Kerteszia (qualitative influence) and an indirect influence through the ecological distribution of the more frequent bromeliad with best qualities as biotope for the watery forms (qualitative influence). The MK index is roughly proportional to the square of half the total number of Bromeliaceae in a certain type of forest. Then the MK index would be a certain function of the ecological type of the forest and of the total number of bromeliad in a unity of area. MK approximately α x (x/10)² . x = n° of bromeliad in a unity of área (1.000 m²); α = qualitative factor. It would be interesting to see if this proportion is maintained when we have examined a greater number of forests of different types.