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The Snowball is a diffusion-type, nonlinear autoregressive process. Its solution for the time variable (which is available only in certain cases) yields a growth function with saturation level, similar to the logistic, or the Gompertz functions. First time, the snowball process was described by me, in the 70-s, but this trial remained without any echoes of the model-builders. In the last 40 years, the rapid development of informatics made us possible to analyse problems that are difficult to handle analytically. So, the possibility to analyse some problems of the snowball process has been realized. The article gives an example of these, but its focus is on the application of the snowball model. Three different social-economic events (the diffusion of the mobile phones, the COVID, and the war-inducted inflation of the last years) are examined here. [ABSTRACT FROM AUTHOR]

The inflection point is an important feature of sigmoidal height-diameter (H-D) models. It is often cited as one of the properties favoring sigmoidal model forms. However, there are very few studies analyzing the inflection points of H-D models. The goals of this study were to theoretically and empirically examine the behaviors of inflection points of six common H-D models with a regional dataset. The six models were the Wykoff (WYK), Schumacher (SCH), Curtis (CUR), Hossfeld IV (HOS), von Bertalanffy-Richards (VBR), and Gompertz (GPZ) models. The models were first fitted in their base forms with tree species as random effects and were then expanded to include functional traits and spatial distribution. The distributions of the estimated inflection points were similar between the two-parameter models WYK, SCH, and CUR, but were different between the three-parameter models HOS, VBR, and GPZ. GPZ produced some of the largest inflection points. HOS and VBR produced concave H-D curves without inflection points for 12.7% and 39.7% of the tree species. Evergreen species or decreasing shade tolerance resulted in larger inflection points. The trends in the estimated inflection points of HOS and VBR were entirely opposite across the landscape. Furthermore, HOS could produce concave H-D curves for portions of the landscape. Based on the studied behaviors, the choice between two-parameter models may not matter. We recommend comparing several three-parameter model forms for consistency in estimated inflection points before deciding on one. Believing sigmoidal models to have inflection points does not necessarily mean that they will produce fitted curves with one. Our study highlights the need to integrate analysis of inflection points into modeling H-D relationships.

We employ properties of high-dimensional geometry to obtain some insights into capabilities of deep perceptron networks to classify large data sets. We derive conditions on network depths, types of activation functions, and numbers of parameters that imply that approximation errors behave almost deterministically. We illustrate general results by concrete cases of popular activation functions: Heaviside, ramp sigmoid, rectified linear, and rectified power. Our probabilistic bounds on approximation errors are derived using concentration of measure type inequalities (method of bounded differences) and concepts from statistical learning theory. [ABSTRACT FROM AUTHOR]

Suppose [Formula: see text] and [Formula: see text] are finite complexes, with [Formula: see text] simply connected. Gromov conjectured that the number of mapping classes in [Formula: see text] which can be realized by [Formula: see text]-Lipschitz maps grows asymptotically as [Formula: see text], where [Formula: see text] is an integer determined by the rational homotopy type of [Formula: see text] and the rational cohomology of [Formula: see text]. This conjecture was disproved in a recent paper of the author and Weinberger; we gave an example where the “predicted” growth is [Formula: see text] but the true growth is [Formula: see text]. Here we show, via a different mechanism, that the universe of possible such growth functions is quite large. In particular, for every rational number [Formula: see text], there is a pair [Formula: see text] for which the growth of [Formula: see text] is essentially [Formula: see text].

In this note, we will focus on the relationships between the growth rates of several functions that describe the topological shape at infinity of discrete groups. In particular, we will consider, in detail, the notion of the rate of vanishing of the simple connectivity at infinity for some geometric classes of finitely presented groups. [ABSTRACT FROM AUTHOR]

Understanding the effect of dispersal on fragmented populations has drawn the attention of ecologists and managers in recent years, and great efforts have been made to understand the impact of dispersal on the total population size. All previous numerical and theoretical findings determined that the possible response scenarios of the overall population size to increasing dispersal are monotonic or hump-shaped, which has become a common assumption in ecology. Against this, we show in this paper that many other response scenarios are possible by using a simple two-patch discrete-time model. This fact evidences the interplay of local dynamics and dispersal and has significant consequences from a management perspective that will be discussed., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

In this note, we will focus on the relationships between the growth rates of several functions that describe the topological shape at infinity of discrete groups. In particular, we will consider, in detail, the notion of the rate of vanishing of the simple connectivity at infinity for some geometric classes of finitely presented groups.

Inspired by the recently emerging Wolfram Physics Project where “Multiway Systems,” graph representations of abstract rewriting systems equipped with a causal structure, have played an important role in discrete models of spacetime and quantum mechanics, this paper establishes several more fundamental properties about the growth (number of states over steps in a system’s evolution) of string rewriting systems in general. While proving the undecidability of exactly determining a system’s growth function, we show several asymptotic properties all growth functions of arbitrary string rewriting systems share. Through an explicit construction, it is proven that string rewriting systems, while never exceeding exponential functions in their growth, are capable of growing arbitrarily slowly, that is, slower than the asymptotic inverse of every Turing-computable function. Additionally, an elementary classification scheme partitioning the set of string rewriting systems into finitely many nontrivial subsets is provided. By introducing arithmetic-like operations under which Multiway Systems form a weakened semiring structure, it is furthermore demonstrated that their growth functions, while always being primitively recursive, can approximate many well-known elementary functions classically used in calculus, which underlines the complexity and computational diversity of Multiway Systems. In the context of the Wolfram Physics Project, some implications of these findings are discussed as well. [ABSTRACT FROM AUTHOR]

In recent years, aquaculture of the African catfish Clarias gariepinus (Burchell 1882) has experienced rapid growth in Africa, Asia and Europe. In order to improve its rearing systems, it is imperative to determine the individual growth patterns of the species. Individual fish growth is relevant when evaluating commercial viability, planning the time of harvest or projecting profits. In this study, we analysed the growth data of African catfish juveniles reared in an indoor freshwater recirculation aquaculture system and fed five different commercial aquafeeds over a period of 111 days. We fitted five nonlinear growth models—von Bertalanffy, Gompertz, Brody, Richards and logistic—to the weight data and applied the Akaike information criterion, the sum of squares and the maximum likelihood to determine the model that best describes the growth data of the species under the controlled culture conditions. According to the goodness‐of‐fit criteria, the Gompertz model was consistently the one that best described the growth of African catfish. The F‐test showed significant differences (p = 0.05) for one of the experimental feeds (T1,2) that produced the superior growth in terms of rate and biomass. [ABSTRACT FROM AUTHOR]

The climate is changing and these changes may affect tree growth. Diameter growth models are one of the essential inputs for many growth and yield projection systems. Therefore, diameter growth models that can be used to estimate inside bark diameter at breast height (DBH) for red pine plantations in a changing climate were developed. One hundred and fifty red pine (Pinus resinosa Ait.) trees were sampled from 30 even-aged monospecific plantations (sites) (5 trees/site) across Ontario, Canada. Stem analysis data collected from these trees was used to develop and evaluate the growth models using a mixed effects modeling approach. Site and climate effects on diameter growth were examined by incorporating site and climate variables in the models. Including climate variables improved the fit statistics.Inside bark DBHs were predicted for 4 geographic areas of Ontario for the period 2021 to 2080. Three emissions trajectories known as representative concentration pathways (RCPs), each reflecting different levels of heat at the end of the century (i.e., 2.6, 4.5, and 8.5 W m−2), were evaluated. At the end of the 2021 to 2080 growth period, projected diameters were wider by 11% and 23% for trees in the southeastern and southwestern parts, respectively, and narrower by 6% for those in the central west part of Ontario (under all climate change scenarios relative to those under a no change scenario). However, no pronounced difference in projected diameters was evident for trees in the far west part of the province regardless of climate change scenario (relative to the no change scenario). In the absence of climate data, the model fitted without climate variables can be used to estimate inside bark DBH.

• We propose a method to obtain functional frames of growth functions from experimental data. • Data points are wrapped by graphs of 2 functions without requiring any assumption on the unkwown growth function. • Some additional flexibilities of the method are introduced. • The approach is illustrated on synthetic and real data for robust predictions. We address the problem of determining functional framing from experimental data points in view of robust time-varying predictions, which is of crucial importance in bioprocess monitoring. We propose a method that provides guaranteed functional bounds, instead of sets of parameters values for growth functions such as the classical Monod or Haldane functions commonly used in bioprocess modeling. We illustrate the applicability of the method with bioreactor simulations in batch and continuous mode, as well as on real data. We also present two extensions of the method adding flexibility in its application, and discuss its efficiency in providing guaranteed state estimations. [ABSTRACT FROM AUTHOR]

Because of the relatively long growing cycle and the high cost of research into turkey production and nutrition, the potential benefits from modelling growth in this avian species are considerable. Though there are many studies aimed at evaluating animal growth models, the number of studies targeting growth models in turkeys is quite limited. In this paper we present a sinusoidal function to describe the evolution of growth in turkeys as a function of time based on data published by Aviagen. The new function was evaluated with regard to its ability to describe the relationship between body weight and age in turkeys and was compared to four standard growth functions: the Gompertz, logistic, Lopez, and Richards. The results of this study show that the new sinusoidal function precisely describes the growth dynamics of turkeys. Fitting the functions to different data profiles nearly always led to the same or less maximized log-likelihood values for the sinusoidal equation, indicating its suitability in describing growth data from turkeys.

1. The objective of the present study is to introduce fresh insight into modelling of egg production by applying classical growth functions to egg production records reported by Aviagen Management Guide to laying hens and the parent stock of broiler chickens. 2. The functions (monomolecular, logistic, Gompertz, Richards and Morgan) were fitted using nonlinear regression procedures of SAS software, and their performance was assessed using goodness-of-fit statistics (coefficient of determination, residual mean squares, Akaike information criterion and Bayesian information criterion). 3. Overall, except for the logistic and Gompertz, the growth functions evaluated gave an acceptable fit to the cumulative egg production curves, with the Morgan equation ranking first followed by the Richards equation. The Morgan and Richards equations provided satisfactory predictions of weekly egg yield at different egg production stages, from early to late production, whereas the least accurate estimates were obtained with the logistic equation. 4. In conclusion, classical growth functions proved feasible alternatives to fit cumulative egg production curves of laying hens and parent stock of broiler chickens, resulting in suitable statistical performance and accurate estimates of production. [ABSTRACT FROM AUTHOR]

The notion of a generalized scale emerged in recent joint work with Afsar–Brownlowe–Larsen on equilibrium states on C ∗ -algebras of right Least Common Multiple (LCM) monoids, where it features as the key datum for the dynamics under investigation. This work provides the structure theory for such monoidal homomorphisms. We establish the uniqueness of the generalized scale and characterize its existence in terms of a simplicial graph arising from a new notion of irreducibility inside right LCM monoids. In addition, the method yields an explicit construction of the generalized scale if existent. We discuss applications for graph products as well as algebraic dynamical systems and reveal a striking connection to Saito's degree map. [ABSTRACT FROM AUTHOR]

Abstract Cortical auditory evoked potential (CAEP) thresholds have been shown to correlate well with behaviourally determined hearing thresholds. Growth functions of CAEPs show promise as an alternative to single level detection for objective hearing threshold estimation; however, the accuracy and clinical relevance of this method is not well examined. In this study, we used temporal and spectral CAEP features to generate feature growth functions. Spectral features may be more robust than traditional peak-picking methods where CAEP morphology is variable, such as in children or hearing device users. Behavioural hearing thresholds were obtained and CAEPs were recorded in response to a 1 kHz puretone from twenty adults with no hearing loss. Four features, peak-to-peak amplitude, root-mean-square, peak spectral power and peak phase-locking value (PLV) were extracted from the CAEPs. Functions relating each feature with stimulus level were used to calculate objective hearing threshold estimates. We assessed the performance of each feature by calculating the difference between the objective estimate and the behaviourally-determined threshold. We compared the accuracy of the estimates using each feature and found that the peak PLV feature performed best, with a mean threshold error of 2.7 dB and standard deviation of 5.9 dB from behavioural threshold across subjects. We also examined the relation between recording time, data quality and threshold estimate errors, and found that on average for a single threshold, 12.7 minutes of recording was needed for a 95% confidence that the threshold estimate was within 20 dB of the behavioural threshold using the peak-to-peak amplitude feature, while 14 minutes is needed for the peak PLV feature. These results show that the PLV of CAEPs can be used to find a clinically relevant hearing threshold estimate. Its potential stability in differing morphology may be an advantage in testing infants or cochlear implant users. Highlights • Growth functions provide clinically viable objective estimates of hearing threshold. • Cortical response peak-to-peak amplitudes and phase locking values are suitable. • Best threshold estimates are consistently within 6 dB of behavioural threshold. • 13 min testing time for ±20 dB accuracy with single electrode recording. [ABSTRACT FROM AUTHOR]

Non-destructive monitoring of chick embryonic growth can provide vital management insights for poultry farmers and other stakeholders. Although non-destructive studies on fertility, hatching time and gender have been conducted recently, there has been no available method for embryonic growth observation, especially during the second half of incubation. Therefore, this work investigated the feasibility of using near-infrared (NIR) sensor-based egg opacity values—the amount of light lost when passing through the egg—for indirectly observing embryo growth during incubation. ROSS 308 eggs were selected based on size, mass and shell color for this experiment. To estimate the embryo size precisely, we fit various mathematical growth functions during incubation, based on the opacity value of incubated eggs. Although all the growth models tested performed similarly in fitting the data, the exponential and power functions had better performances in terms of co-efficient of determination (0.991 and 0.994 respectively) and RMSE to explain embryo growth during incubation. From these results, we conclude that the modeling paradigm adopted provides a simple tool to non-invasively investigate embryo growth. These models could be applied to resolving developmental biology, embryonic pathology, industrial and animal welfare issues in the near future.

Abstract Growth of multichambered foraminifera can be studied by investigation of chamber volumes. This approach is applicable to the vast majority of living and fossil species. Cell growth is represented by the test volume, whereby chamber volumes exhibit the increase in cell volume by growth stages. Two models fit foraminiferal growth, the unlimited linear and the limited sigmoidal function. The growth stage, in which reproduction begins, is represented in sigmoidal growth by the point of inflection; this stage cannot be determined in the unlimited linear growth model. The timing of chamber building is apparently correlated with cell growth, thus the "chamber building rate" remains constant in linearly growing cells whereas it decreases and ultimately approximates zero in limited growth. Longevity can be estimated for living individuals with sigmoidal growth by the inverse of the chamber building function at the inflection point of the cell growth function. Calculating the mean chamber building function for a species inhabiting a distinct geographical region, its inverse can be used in this region to estimate the individual lifetime based on the final growth state (= chamber number). Deviations of observed chamber volumes from theoretical values determined by the chamber building function can be irregular or oscillating. Periods of oscillating functions in larger foraminifera may point to tidal, lunar and seasonal cycles. Based on the determination of seasonal oscillations in the test by stable isotopes, lifetime ≥1 year can also be estimated for fossil species. The development in foraminifera is expressed in a huge variability of test forms with different wall textures depending on functional and constructional aspects. The historical-phylogenetic approach enables a differentiation into three groups, the Tubothalamea, Globothalamea and the Nodosariids. Within the Tubothalamea and Globothalamea, several subgroups feature symbiont-bearing foraminifera with large tests designed to optimize the surface/volume ratio allowing the symbiotic microalgae to occupy an optimal position near the test surface. [ABSTRACT FROM AUTHOR]

Differential equations and advanced statistical models have been used to predict growth phenomena. In the present study, general nonlinear growth functions such as von Bertalanffy, Gompertz, logistic, and Brody, along with hierarchical modeling were applied to investigate the phenotypic growth pattern of Iranian Lori-Bakhtiari sheep. Growth data from 1410 Lori- Bakhtiari lambs were used in the present study. The results showed that the Brody function outperformed the other three nonlinear growth functions. In addition, including hierarchical growth modeling results allowed the adoption of many random effect structures, suggesting that hierarchical growth modeling has a useful role in growth data modeling. This method provides an estimation of growth parameters based on individual animals, improving individual growth selection. The results suggest this approach for growth modeling. Combining the strength of individual growth modeling with general growth modeling, e.g., von Bertalanffy, Gompertz, logistic, and Brody would be deeply appealing in the future. In this regard, dealing with sheep growth phenomenon using pure mathematical models, i.e. grey system theory models that could be new powerful prediction tools for breeders and experts, has not been done yet. However, running the analysis on large datasets will require significantly higher computational power than is ordinarily available. [ABSTRACT FROM AUTHOR]

Buccinanops globulosus is an edible marine gastropod that is being captured by artisanal fishermen without management regulations. As basic knowledge on population features is required in case a sustained commercial exploitation of this species is established, we estimated and compared the age and growth of B. globulosus in two populations separated by 16 km, inhabiting similar physical environments but different anthropic influence. Our results, based on stable oxygen isotope analysis and best fitted models by likelihood ratio tests, detected differences in age and growth between both samplings. Maximum shell marks suggest one year difference between populations. Richards was chosen as the best fitting model for both sampling sites and significant differences were observed between them. Human activities could be causing the age reduction among other irreversible effects on the population under anthropic influence. This should be considered when developing sustainable management regulations for this fishery resource, especially those based on shell/age size. [ABSTRACT FROM AUTHOR]

There has been much recent interest in mathematical developments for the analysis of growth in poultry. In this paper, we present a sinusoidal function to describe the evolution of growth as a function of time based on real life experiments. The function was evaluated with regard to its ability to describe the relationship between body weight and age in broilers and was compared to 4 standard growth functions: Gompertz, logistic, Lopez, and Richards. In order to estimate the model parameters, we adopted a global optimization method based on a direct search method instead of using gradient-based techniques. The results of this study show that both the sinusoidal function and the direct search method precisely describe the growth dynamics of broiler chickens. Fitting the growth functions to different data profiles nearly always led to the same or less maximized log-likelihood values for the sinusoidal equation, which is an indication of its superiority in describing growth data from broiler chickens. [ABSTRACT FROM AUTHOR]

Copyright of Bulletin of the Faculty of Forestry, University of Banja Luka / Glasnik Šumarskog Fakulteta Univerziteta u Banjoj Luci is the property of University of Banja Luka, Faculty of Forestry and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of World's Poultry Science Journal is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Theoretical models of populations on a system of two connected patches previously have shown that when the two patches differ in maximum growth rate and carrying capacity, and in the limit of high diffusion, conditions exist for which the total population size at equilibrium exceeds that of the ideal free distribution, which predicts that the total population would equal the total carrying capacity of the two patches. However, this result has only been shown for the Pearl-Verhulst growth function on two patches and for a single-parameter growth function in continuous space. Here, we provide a general criterion for total population size to exceed total carrying capacity for three commonly used population growth rates for both heterogeneous continuous and multi-patch heterogeneous landscapes with high population diffusion. We show that a sufficient condition for this situation is that there is a convex positive relationship between the maximum growth rate and the parameter that, by itself or together with the maximum growth rate, determines the carrying capacity, as both vary across a spatial region. This relationship occurs in some biological populations, though not in others, so the result has ecological implications. [ABSTRACT FROM AUTHOR]

We prove that an arbitrary countable dimensional Lie algebra over a field of characteristic that is locally of subexponential growth is embeddable in a finitely generated Lie algebra of subexponential growth. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate tree-ring width variability and to distinguish groups of trees with similar growth trends in order to study tree growth responses to various stand and site conditions. The methods of cluster analysis were employed for this purpose. Four distinct groups of trees were identified. For each group, the mean tree-ring curve was calculated in order to look for the main signals that distinguish the groups from one another. The idea behind this was to divide the samples into homogeneous groups with similar growth trends, representing typical examples of variability of the studied Norway spruce population. In the next step, several regression functions were studied and compared for their ability to fit the ring-width-age data applied to the mean ring-width curve of each group. Fischer's F-test was used to test the differences in goodness of fit between the equations in each group. From all examined/applied equations, smoothing spline, polynomial of degree 5, and Šmelko-Burgan functions were found to be the most universal and suitable for detrending of all examined ring width curves. Hugershoff function was found to be suitable for curves with one local maximum only. Exponential and Korf's functions were unsatisfactory for the purposes of tree ring curves detrending.

Reliable information related to vegetation phenology is required to improve understanding of land–atmosphere coupling and the biosphere's response and feedbacks to climate change. The logistic function is commonly used to model bounded growth and decay and extract phenological information from remotely sensed vegetation indices. However, several other growth functions can also model bounded growth and decay and may have more desirable properties than the logistic function for capturing deciduous forest phenology. We employed three complimentary criteria and evaluated the suitability of the Gompertz, logistic, mirror-Gompertz, and Richards functions to reliably capture remotely sensed phenology of deciduous forests. Our analyses showed that although all the four growth functions fit remotely sensed data equally well, their ability to capture rapidly changing phenology early in spring and late in fall differs significantly. Using 10 years of field measurements from two deciduous forest sites in the northeastern United States, we showed that dynamics in the fraction of absorbed photosynthetically active radiation (FAPAR) phenology is asymmetric in both spring and fall. It develops more rapidly early in spring and decays more rapidly late in fall. A flexible function that can capture these asymmetric dynamics is likely to capture the phenological development and the transition dates better. Comparison with field measurements of start-of-season (SOS), end-of-season (EOS), and growing period length (GPL) confirmed this. Mean differences between modeled and observed GPL was 13.5 and 18.5 days for the Richards and logistic function, respectively, at Harvard Forest and 2.6 and 7.1 days, respectively at Hubbard Brook Forest. Our analyses also showed that FAPAR and normalized difference vegetation index have a strong linear relationship in spring, but correlate poorly in fall. Our results suggest that a flexible function line Richards is likely to be more reliable for modeling phenology and retrieving information of transitions events from remotely sensed NDVI. [ABSTRACT FROM AUTHOR]

Funções de crescimento não-lineares foram ajustados a dados de peso-idade de 40 cordeiros das raças Santa Inês e Bergamácia. Pelos testes de Hartley e de Bartlett, verificou-se que os dados apresentavam heterogeneidade de variâncias; em função disso, ajustaram-se as funções de crescimento pelo método dos quadrados mínimos ponderado pelo inverso da variância dos pesos a cada pesagem utilizando a opção WEIGTH do PROC MODEL (SAS INSTITUTE, 1996). As funções de crescimento foram comparadas pela interpretação biológica dos parâmetros e pelos indicadores de qualidade do ajuste (coeficiente de determinação ajustado, quadrado médio do resíduo e teste de Durbin-Watson). As funções de von Bertalanffy e Gompertz apresentaram a melhor qualidade de ajuste, ao passo que as funções de Richards, Logística e Brody não se mostraram adequadas para descrever o crescimento dos animais por apresentarem estimativas não condizentes com a realidade.Non linear growth functions were fitted to weight-age data of 40 Santa Inês and Bergamacy lambs. The Hartley and Bartlett tests indicated that the data presented heteroscedastic variance, so the growth functions were fitted through weighted minimum square method by the inverse variance weight in each sampler using the WEIGHT option in PROC MODEL (SAS INSTITUTE, 1996). The functions were compared using the biological interpretation of the parameters and the quality indicators of fit (adjusted determination coefficient, mean square error and Durbin-Watson test). The von Bertalanffy and Gompertz functions provided the best fittings, whereas Richards, Logistic and Brody functions turned out not to be suitable for describing growth behavior, became estimates based on them do not agree with observation.

We present a tool (KORFit) for fitting growth functions to empirical data, primarily for forest management applications, but also can be applied in other biological fields. KORFit fits data using 12 growth functions. Increment curves are produced, and growth magnitude and increment values can be predicted for a given age. KORFit implements an efficient and robust algorithm of Levenberg–Marquardt non-linear least squares fitting method utilizing MATLAB libraries. Criteria for evaluating goodness of fit (e.g. Akaike information criterion, Bayesian information criterion, leave-one-out cross-validation) are implemented. Individualized curves for individual data point can be modeled. [ABSTRACT FROM AUTHOR]

The objective of the present study was to compare alternative growth functions fitted to pig live weight data, with particular emphasis on the function׳s ability to predict future animal live weight. The final dataset consisted of 51,893 live weight records from 10,201 pigs aged between 61 and 200 days. Fixed effects models and mixed models were applied to the three different growth functions: von Bertalanffy, Gompertz, and Richards; fixed and mixed model polynomial equations were also considered. The growth function׳s ability to predict future live weight was determined by excluding a selection of animal live weight records post 160 days of age and comparing the predicted live weight to actual live weight. Irrespective of whether a fixed or mixed model framework was used, the Gompertz function best modelled the full dataset, with an accuracy squared for the full dataset ( r w 2 ) of 0.997 and root mean square error (RMSE) of 1.60 kg for the fixed effects model and r w 2 of 0.995 and RMSE of 2.25 kg for the mixed model equation. The Gompertz mixed model also achieved the greatest accuracy squared of predicting ( r w w ^ 2 ) future live weight records, with an r w w ^ 2 of 0.846 and RMSE of 5.35 kg. A strong positive correlation was estimated between asymptotic mature weight ( A ; r =0.83 to 0.96) across the three growth functions for all considered equations. A strong negative correlation was estimated between parameters A and k (rate of maturation) for the Gompertz fixed effects model (−0.88) and mixed model (−0.70). Results from this study could be used to implement a decision support tool for pork producers, offering extra information when they are making important feeding, slaughter and breeding decisions. [ABSTRACT FROM AUTHOR]

Four novel growth functions, namely, Pareto, extreme value distribution (EVD), Lomolino, and cumulative β-P distribution (CBP), are derived, and their ability to describe ostrich growth curves is evaluated. The functions were compared with standard growth equations, namely, the monomolecular, Michaelis-Menten (MM), Gompertz, Richards, and generalized MM (gMM). For this purpose, 2 separate comparisons were conducted. In the first, all the functions were fitted to 40 individual growth curves (5 males and 35 females) of ostriches using nonlinear regression. In the second, performance of the functions was assessed when data from 71 individuals were composited (570 data points). This comparison was undertaken using nonlinear mixed models and considering 3 approaches: 1) models with no random effect, 2) random effect incorporated as the intercept, and 3) random effect incorporated into the asymptotic weight parameter (Wf). The results from the first comparison showed that the functions generally gave acceptable values of R2 and residual variance. On the basis of the Akaike information criterion (AIC), CBP gave the best fit, whereas the Gompertz and Lomolino equations were the preferred functions on the basis of corrected AIC (AICc). Bias, accuracy factor, the Durbin-Watson statistic, and the number of runs of sign were used to analyze the residuals. CBP gave the best distribution of residuals but also produced more residual autocorrelation (significant Durbin-Watson statistic). The functions were applied to sample data for a more conventional farm species (2 breeds of cattle) to verify the results of the comparison of fit among functions and their applicability across species. In the second comparison, analysis of mixed models showed that incorporation of a random effect into Wf gave the best fit, resulting in smaller AIC and AICc values compared with those in the other 2 approaches. On the basis of AICc, best fit was achieved with CBP, followed by gMM, Lomolino, and Richards functions, respectively. The exponential, MM, Pareto, and EVD equations produced negative values for initial weight (W0) if left unconstrained. The Gompertz equation, in spite of having a fixed inflection point and therefore being less flexible, gave accurate estimates of both W0 and Wf and an acceptable goodness of fit favored by having fewer parameters than the other sigmoidal functions. Nevertheless, all the sigmoidal functions appeared appropriate in describing the growth trajectory of male and female ostriches to a reasonable level of accuracy. [ABSTRACT FROM AUTHOR]

This research aims to study the performance of Pinus elliottii Engelm. and Pinus taeda L. in the arenizated and degraded areas by antropic action in the western of Rio Grande do Sul state. In stands were selected medium trees, which were harvested and sectioned by Smalian method to obtain wood discs for dendro chronological analysis to determine the diameter by age. The diameter growth compared between species showed different levels of development over time. The use of dummy variables in the growth model enables a single equation to estimate the diameter as a function of age for both species, considering the medium and low levels of soil degradation, as variables necessary to estimate the growth of these species in these types of arenizated degraded soils. [ABSTRACT FROM AUTHOR]

We prove that in the pure mapping class group of the 3-punctured projective plane equipped with the word metric induced by certain generating set, the ratio of the number of pseudo-Anosov elements to the number of all elements in a ball centered at the identity tends to one, as the radius of the ball tends to infinity. We also compute growth functions of the sets of reducible and pseudo-Anosov elements. [ABSTRACT FROM AUTHOR]

• A better knowledge of the growth of horses can facilitate sounder intervention in their health control, nutrition and management. • Five nonlinear functions were compared for describing the growth curves of horses. • Horse growth curves are better represented by diminishing returns functions. • A point of inflexion seems to be not noticeable during horse postnatal growth. • Nonsigmoidal functions are adequate for describing the growth curves in horses. A better knowledge of the growth of horses can facilitate sounder intervention in their health control, nutrition and management. This study compared five growth functions with either diminishing returns (monomolecular and Michaelis-Menten) or asymptotic sigmoidal (Gompertz, Richards and Lopez) behavior for describing the growth curves of horses, based on the relationship between a given somatic growth trait (body weight, withers height, or body weight to withers height ratio) and age. Data used in this study were those available in the literature for quarter horse males and thoroughbred foals and fillies from birth to maturity. Estimates of the model parameters were obtained using nonlinear regression procedures and the Marquardt-Levenberg algorithm. Functions were compared using goodness-of-fit statistics such as adjusted coefficient of determination and root mean square error. The results obtained with the Richards, Lopez and Gompertz equations suggest that curves are not sigmoidal, and that the diminishing returns models are adequate for describing the growth curves in horses. [ABSTRACT FROM AUTHOR]

Studies on maturation and body composition mention age at peak height velocity (PHV) as an important measure that could predict adulthood outcome. The age at PHV is often derived from growth models such as the triple logistic fitted to the stature (height) data. Theoretically, for a well-behaved growth function, age at PHV could be obtained by setting the second derivative of the growth function to zero and solving for age. Such a solution obviously depends on the parameters of the growth function. Therefore, the uncertainty in the estimation of age at PHV resulting from the uncertainty in the estimation of the growth model, need to be accounted for in the models in which it is used as a predictor. Explicit expressions for the age at PHV and, consequently the variance of the estimate of the age at PHV, do not exist for some of the commonly used nonlinear growth functions, such as the triple logistic function. Once an estimate of this variance is obtained, it could be incorporated in subsequent modeling either through measurement error models or by using the inverse variances as weights. A numerical method for estimating the variance is implemented. The accuracy of this method is demonstrated through comparisons in models where explicit solution for the variance exists. The method of estimating the variance is illustrated by applying to growth data from the Fels study and subsequently used as weights in modeling two adulthood outcomes from the same study. [ABSTRACT FROM AUTHOR]

Abstract: Despite the fact that heterochronic processes seem to be an important process determining morphological evolution of the delphinid skull, previous workers have not found allometric scaling as relevant factor in the differentiation within the genus Sotalia. Here we analyzed the skull ontogeny of the estuarine dolphin S. guianensis and investigate differential growth and shape changes of two cranial regions – the neurocranium and the face – in order to evaluate the relevance of cranial compartmentalization on the ontogeny of this structure. Our results show that, even though both cranial regions stop growing at adulthood, the face has higher initial growth rates than the neurocranium. The rate of shape changes is also different for both regions, with the face showing a initially higher, but rapidly decreasing rate of change, while the neurocranium shows a slow decreasing rate, leading to persistent and localized shape changes throughout adult life, a pattern that could be related to epigenetic regional factors. The pattern of ontogenetic shape change described here is similar to those described for other groups of Delphinidae and also match intra and interspecific variation found within the family, suggesting that mosaic heterochrony could be an important factor in the morphological evolution of this group. [Copyright &y& Elsevier]

Generating ecological production functions, including harvest yield functions, is a high priority research area. Most yield functions used in economics and ecology rely on convexity properties of species growth functions, but convexity is shown here to depend on whether realistic biology is incorporated. Optimizing behavior by individual organisms is connected with species population dynamics in order to derive growth functions in a general equilibrium ecosystem model. Non convexities are shown to be an inherent property of the growth functions owing to familiar biological processes including predator-prey and competitive relations, predator satiation and prey substitution. The growth functions generate yield functions that are problematic for management, because they exhibit kinked average revenue curves, discontinuous marginal revenue curves, and knife edge optimum effort levels where a small increase above the optimum effort can rapidly deplete the stock. These phenomena can be explained entirely by the underlying biological processes. [ABSTRACT FROM AUTHOR]

Poultry industries face various decisions in the production cycle that affect the profitability of an operation. Predictions of growth when the birds are ready for sale are important factors that contribute to the economy of poultry operations. Mathematical functions called ‘growth functions’ have been used to relate body weight (W) to age or cumulative feed intake. These can also be used as response functions to predict daily energy and protein dietary requirements for maintenance and growth (France et al., 1989). When describing growth versus age in poultry, a fixed point of inflexion can be a limitation with equations such as the Gompertz and logistic. Inflexion points vary depending on age, sex, breed and type of animal, so equations such as the Richards and López are generally recommended. For describing retention rate against daily intake, which generally does not exhibit an inflexion point, the monomolecular would appear the function of choice. [ABSTRACT FROM PUBLISHER]