Critical points in logistic growth curves and treatment comparisons

Several biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the maintenance of a less productive phase results in uneconomical activity. In this report we present methods of determining critical points in logistic functions that separate the early stages of growth from the asymptotic phase, with the aim of establishing a stopping critical point in the growth and on this basis determine differences in treatments. The logistic growth model is fitted to experimental data of imbibition of arariba seeds (Centrolobium tomentosum). To determine stopping critical points the following methods were used: i) accelerating growth function, ii) tangent at the inflection point, iii) segmented regression; iv) modified segmented regression; v) non-significant difference; and vi) non-significant difference by simulation. The analysis of variance of the abscissas and ordinates of the breakpoints was performed with the objective of comparing treatments and methods used to determine the critical points. The methods of segmented regression and of the tangent at the inflection point lead to early stopping points, in comparison with other methods, with proportions ordinate/asymptote lower than 0.90. The non-significant difference method by simulation had higher values of abscissas for stopping point, with an average proportion ordinate/asymptote equal to 0.986. An intermediate proportion of 0.908 was observed for the acceleration function method.

Avaliação de substratos na emergência de plântulas de araticum-de-terra-fria (Annona emarginata (Schltdl.) H. Rainer)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Determination of a point sufficiently close to the asymptote in nonlinear growth functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Growth and juvenile development of Uca maracoani Latreille 1802-1803 in laboratory conditions (Crustacea, Decapoda, Brachyura, Ocypodidae).

The life cycle of decapod crustaceans can be classified into three distinct morphological phases: larval, juvenile and adult. Despite its recognized importance, studies of the juvenile phase have been neglected. The present Study aimed to analyze the growth of juveniles from a single population of Uca maracoani under laboratory conditions, and also to describe the morphological differentiation of pleopods in each sex. Megalopae and juvenile crabs or U. maracoani obtained on a Mud beach at Jabaquara, Paraty, on the southern coast of the state of Rio de Janeiro (Brazil), were reared in the laboratory. The specimens were checked daily for molts and deaths. The carapace widths (CW) of intact exuviae and dead individuals were measured under a stereoscopic microscope provided with a micrometer rule. These data allowed the definition of a growth equation as well as the stages related to the beginning of pleopod development, which begins when females reach 3.0 mill CW (6th juvenile developmental stage), similar to the sizes reported for other species of the genus. In males, however, pleopods appear when the crabs reach 3.5 mm CW, equivalent to the 7th developmental stage. This difference may be related to differential growth between sexes. It also may be a consequence of laboratory rearing, or may represent an actual feature of the species.

Growth curves for ostriches (Struthio camelus) in a Brazilian population

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Modelo de Fisher-Kolmogorov em dinâmica populacional com capacidade de suporte espacialmente dependente

Pós-graduação em Física - IFT

A morphometric study of the mud crab, Panopeus austrobesus Williams, 1983 (Decapoda, Brachyura) from a subtropical mangrove in South America

The relative growth of the xanthid crab, Panopeus austrobesus was investigated by means of the allometric method. Crabs were obtained in the mangrove formed by the estuary of the rivers Comprido and Escuro (23degrees29'24S 45degrees10'12W), Ubatuba, São Paulo State, Brazil. All crabs were measured to obtain their carapace width (CW) and length (CL), abdomen width (AW) at the basis of the 5(th) somite, and major cheliped propodus length (PL) and height (PH). Males were also measured for their gonopod length (GL). The size of crabs based on CW ranged from 4.0 to 44.8 mm for males and 3.1 to 34.5 mm for females. The relative growth equation (Y = aX(b)) based on the relationship between GL and CW suggested that males reach their sexual maturity near 14.6 mm CW. Such relationship shows a positive allometry during the juvenile phase and an isometric growth in adult life. In females, the estimated size at 50% maturity is 13.0 mm CW, based on the relationship AW vs. CW. Males reach larger sizes than females, which probably provides them better conditions to protect females during courtship. Concerning cheliped size, approximately 73% of the crabs analysed (N = 209), disregarding sex, have the right PL larger than the left. The PL growth shows that specimens with a left major cheliped (26%) have a higher allometric coefficient, despite being smaller considering their CW. Such a difference may compensate the smaller size of the crab during defense or prey capture.

Morphometry of the crab Hexapanopeus schmitti (Decapoda : Xanthoidea) on the northern coast of the state of São Paulo, Brazil

A morphometric study of the xanthoid crab Hexapanopeus schmitti was carried out, using the allometric method. Samples were taken monthly for two years (1998-1999) in the Ubatuba region, northern coast of São Paulo, Brazil. Sex and size were assessed for each specimen, and all crabs were measured to obtain their carapace width (CW) and length (CL), abdomen width (AW) of females, major cheliped propodus length and height (PL and PH), and gonopod length (GL) of males. A total of 301 crabs were analyzed, 209 males and 92 females. The CWs of the crabs ranged from 2.5 to 9.8 mm for males and from 2.8 to 9.4 mm for females. The relative growth equation (y=ax(b)) based on the relationship between GL and CW suggested that males reach their morphological sexual maturity near 6.1 mm CW. In females, the estimated size at 50 % maturity was 4.8 mm CW, based on the relationship of AW vs. CW. Males reach larger sizes than females, which probably favors their ability to guard the females during courtship. In approximately 83 % of the crabs (n= 371), disregarding sex, the right cheliped was larger.

Caracterização e análise do sistema de abastecimento de água potável no município de Botucatu, SP

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Solving the Levins' paradox in the logistic model to the population growth

We introduce a new method to improve Markov maps by means of a Bayesian approach. The method starts from an initial map model, wherefrom a likelihood function is defined which is regulated by a temperature-like parameter. Then, the new constraints are added by the use of Bayes rule in the prior distribution. We applied the method to the logistic map of population growth of a single species. We show that the population size is limited for all ranges of parameters, allowing thus to overcome difficulties in interpretation of the concept of carrying capacity known as the Levins paradox. © Published under licence by IOP Publishing Ltd.

The relative growth and sexual maturity of the freshwater crab Dilocarcinus pagei (Brachyura, Trichodactylidae) in the northwestern region of the state of São Paulo

The aim of the present study was to determine the size at sexual maturity in the freshwater crab Dilocarcinus pagei Stimpson, 1861, from a population located in Mendonça, state of São Paulo, Brazil. The crabs were sampled monthly (July 2005 to June 2007), at Barra Mansa reservoir. The specimens were captured manually or in sieves passed through the aquatic vegetation. The crabs were captured and separated by sex based on morphology of the pleon and on the number of pleopods. The following dimensions were measured: carapace width (CW); carapace length (CL); propodus length (PL); and abdomen width (AW). The morphological analysis of the gonads was used to identify and categorize individuals according to their stage of development. The morphological maturity was estimated based on the analysis of relative growth based on the allometric equation y = ax b. The gonadal maturity was based on the morphology of the gonads by the method CW50 which indicates the size at which 50% of the individuals in the population showed gonads morphologically mature to reproduction. The biometric relationships that best demonstrated the different patterns of growth for the juvenile and adult stages were CW vs. PL for males and CW vs. AW for females (p<0.001). Based on these relationships, the estimated value to morphological sexual maturity was 21.5 mm (CW) in males and 19.7 mm (CW) in females. The determination of the size at sexual maturity and the adjustment of the data based on the logistic curve (CW50) resulted in a size of 38.2 mm for males and 39.4 mm for females (CW). Based on the data obtained for sexual maturity for D. pagei, we can estimate a minimum size for capture of 40 mm (CW). This minimum size allows at least half of the population to reproduce and retains the juveniles and a portion of the adults in the population.

Multiplicity of solutions for a biharmonic equation with subcritical or critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Inflection and stability points of diphasic logistic analysis of growth

Growth functions with inflection points following a diphasic model, can be adjusted by two approaches using segmented regression or the sum of two functions. In both cases, there are two functions, one for each phase, with inflection and stability points. However, when they are summed, the result is a new function and the points of inflection and stability are different from those obtained from using each function individually. A method to determine these points in a diphasic logistics sum of functions is suggested and the results obtained from fitting the models to eucalyptus growth data showed a better fit of the logistic diphasic sum as compared with segmented regression and monophasic logistic models.

Growth and body nutrient deposition of two broiler commercial genetic lines

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Maturation and growth curves of Macrobrachium Carcinus (Linnaeus) (Crustacea, Decapoda, Palaemonidae) from Ribeira de Iguape River, southern Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)