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.

Evaluation of substrates on the emergence of "araticum-de-terra-fria" (Annona emarginata (Schltdl.) H. Rainer) Seedlings

Choosing a substrate is the determinant factor for the seedling producer; thus, the aim of this study was to evaluate the effect of different types of substrates on the emergence of "araticum-de-terra-fria" (Annona emarginata (Schltdl.) H. Rainer) seedlings. The experiment was carried out in a greenhouse and the experimental design was in randomized blocks, with three treatments and five replicates of 72 seeds per plot. The treatments consisted of the following substrates: coconut fiber, vermiculite and Plantmax® Citrus. The number of emerged seedlings was weekly counted for 105 days. Data regarding seedling height were obtained, and the emergence velocity index and mean time, besides total emergence percentage and that over time were calculated. Results from total mean emergence percentage, seedling height, emergence velocity index (EVI), and mean emergence time (MET) were subjected to analysis of variance and means were compared by the Tukey's test at 5% significance. The curves concerning the emergence percentage over time were fit by the logistic growth equation for each treatment and the means of each parameter (A, B, C) were compared by the Duncan's test at 5% significance. The substrates vermiculite led to the highest values of emergence percentage differing from the PlantMax® Citrus, but not of the coconut fiber, however the vermiculite promoted seedling height in a shorter time; therefore, this substrate is recommended for the initial development of "araticum-de-terra-fria" (Annona emarginata (Schltdl.) H. Rainer) seedlings.

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)

Synchronization in Von Bertalanffy’s models

Many data have been useful to describe the growth of marine mammals, invertebrates and reptiles, seabirds, sea turtles and fishes, using the logistic, the Gom-pertz and von Bertalanffy's growth models. A generalized family of von Bertalanffy's maps, which is proportional to the right hand side of von Bertalanffy's growth equation, is studied and its dynamical approach is proposed. The system complexity is measured using Lyapunov exponents, which depend on two biological parameters: von Bertalanffy's growth rate constant and the asymptotic weight. Applications of synchronization in real world is of current interest. The behavior of birds ocks, schools of fish and other animals is an important phenomenon characterized by synchronized motion of individuals. In this work, we consider networks having in each node a von Bertalanffy's model and we study the synchronization interval of these networks, as a function of those two biological parameters. Numerical simulation are also presented to support our approaches.

Age, growth and population dynamics of lemon sole Microstomus kitt (Walbaum 1792) sampled off the West Coast of Ireland

The age, growth, maturity and population dynamics of lemon sole (Microstomus kitt), captured off the west coast of Ireland (ICES division Vllb), were determined for the period November 2000 to February 2002. The maximum age recorded was 14 years. Males of the population were dominated by 4 year olds, while females were dominated by 5 year olds. Females dominated the sex ratio in the overall sample, each month sampled, at each age and from 22cm in total length onwards (when N > 20). Possible reasons for the dominance of females in the sex ratio are discussed. Three models were used to obtain the parameters of the von Bertalanfly growth equation. These were the Ford-Walford plot (Beverton and Holt 1957), the Gulland and Holt plot (1959) and the Rafail (1973) method. Results of the fitted von Bertalanffy growth curves showed that female lemon sole o f f the west coast of Ireland grew faster than males and attained a greater size. Male and female lemon sole mature from 2 years of age onwards. There is evidence in the population o f a smaller asymptotic length (L«, = 34.47cm), faster growth rate (K = 0.1955) and younger age at first maturity, all of which are indicative o f a decrease in population size, when present results are compared to data collected in the same area 22 years earlier. Results of the yield per recruit curve indicate that lemon sole are currently being over-fished o f f the west coast of Ireland. Problems of selectivity within the sampling method, particularly at the discarding stage, may have influenced the outcome of results of the models used in the assessment of this stock. Therefore, additional/future work on this species should include catch data which incorporates discards and not landings data alone.

Economic growth and inequality: the role of fiscal policies

This paper analyses the impact of different instruments of fiscal policy on economic growth as well as on income inequality, using an unbalanced panel of 43 upper-middle and high income countries for the period 1972-2006. We consider and estimate two individual equations explaining growth and inequality in order to assess the incidence of different fiscal policies. Firstly, our approach considers imposing orthogonal assumptions between growth and inequality in both equations, and secondly, it allows growth to be included in the inequality equation, and inequality to be included in the growth equation. The empirical results suggest that an increase in the size of government measured through current expenditures and direct taxes diminishes economic growth while reducing inequality, being public investment the only fiscal policy that may break this trade-off between efficiency and equity, since increases in this item reduces inequality without harming output. Therefore, the results reflect that the trade-off between efficiency and equity that governments often confront when designing their fiscal policies may be avoided.

Growth of champa fruit under agroecological conditions of Miraflores, Boyacá, Colombia

The objective of this work was to analyze the growth of champa fruit (Campomanesia lineatifolia) as a function of growing-degree days (GDD) in the municipality of Miraflores, in Boyacá, Colombia. Thirty trees were selected at random, and 100 flowers in full bloom were marked in each tree. From the 26th day after flowering until harvest, 10 samples were taken every 15 days to determine the fruit parameters and growth rate. Temperature was recorded to calculate the GDD. From flowering until harvest, 1,489.1 GDD were accumulated over 145 days. Dry and fresh matter mass of pulp, seed, and total fruit were fitted to a logistic growth model, and three growth stages (S1, S2 and S3) were defined. In the S1, growth was slow, and the relative growth remained nearly stable, whereas the absolute growth rate (AGR) increased slowly. In the S2, maximum growth was observed. In the S3, which corresponds to maturation, dry mass increased gradually, and the AGR decreased, while the fresh pulp and total mass did not cease to increase. The polar and equatorial diameters increased linearly, while the volume followed an exponential model. Champa fruit show a simple sigmoid growth curve.

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

Effects of Initial Fat Thickness, Hip Height, and Concentration of Dietary Energy on Growth of Area of the Longissimus dorsi Muscle and Subcutaneous Fat of Yearling Steers

Steers were sorted into four groups based on hip height and fat cover at the start of the finishing period. Each group of sorted steers was fed diets containing 0.59 or 0.64 Mcal NEg per lb. of diet dry matter. Steers with less initial fat cover (0.08 in.) compared with those with more (0.17) had less carcass fat cover 103 days later. The steers with less fat cover accumulated fat at a faster rate, but this was not apparent prior to 80 days. Accretion of fat was best predicted by an exponential growth equation, and was not affected by the two concentrations of energy fed in this study. Steers with greater initial height accumulated fat cover at a slower rate than shorter steers. This difference was interpreted to mean that large-frame steers accumulate subcutaneous fat at a slower rate than medium-frame steers. Increase in area of the ribeye was best described by a linear equation. Initial fat cover, hip height, and concentrations of energy in the diet did not affect rate of growth of this muscle. Predicting carcass fat cover from the initial ultrasound measurement of fat thickness found 46 of the 51 carcasses with less than 0.4 in. of fat cover. Twelve carcasses predicted to have less than 0.4 in. of fat cover had more than 0.4 in. Five carcasses predicted to have more than 0.4 in. actually had less than that. Accurate initial measurements of initial fat thickness with ultrasound might be a useful measurement to sort cattle for specific marketing grids.

Stabilization in a two-species chemotaxis system with logistic source

We study a system of three partial differential equations modelling the spatiotemporal behaviour of two competitive populations of biological species both of which are attracted chemotactically by the same signal substance. For a range of the parameters the system possesses a uniquely determined spatially homogeneous positive equilibrium (u?, v?) globally asymptotically stable within a certain nonempty range of the logistic growth coefficients.

What determines the finance-growth nexus? Empirical evidence for threshold models

This paper elaborates the notion of balanced'' financial development that is contingent on a country's general level of development. We develop an empirical framework to address this point, referring to threshold regressions and a bootstrap test for structural shift in a growth equation. We find that countries gain less from financial activity, if the latter fails to keep up with or exceeds what would follow from a balanced expansion path. These analyses contribute to the finance and growth literature in providing empirical support for the balanced'' financial development hypothesis.