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Ontogenetic growth reflects the changes of biomass, height (or body length) of a biological organism as a function of time. Many growth equations have been built but few can accurately predict the ending time of growth. Here we are attempting to provide two growth equations for predicting the time when growth terminates. Meanwhile, these models are also expected to apply to different growth patterns of biological organisms. Two time-dependent growth equations with four parameters each were obtained by replacing temperature with time in two non-linear mathematical models that describe the temperature-dependent developmental and growth rates of poikilotherms. Both models can generate a skewed or symmetrical bell-shaped curve. We obtained the growth equations by integrating these two temperature-dependent developmental rate models with temperature replaced by time. The dry weight data of six species of agricultural crops, the height data of four bamboo species, the tree-ring width data of two coniferous species, and the fresh weight data of 16 animals were used to fit these growth equations. Both growth equations agree well with the actual growth data of animals and plants. Additionally, one equation exhibits wide applicability and is better than the other in describing the tree-ring width. The time of reaching the maximal biomass or height can be predicted by these two models. The growth equations are valuable for predicting the time when the maximal biomass and height (or body length) are reached. Parameters of theses equations can directly reflect the growth rate: the conceptual starting time of growth, the ending time of growth, the maximal growth, and the time associated with the maximal growth rate that is actually the inflection point of the growth equation. We show that these two equations apply to many diverse species. It is worthwhile to explore and compare the growth patterns of biological organisms. In addition, the prediction of tree-ring width of conifers will be helpful to accurately predict the carbon storage in forest ecosystems. [ABSTRACT FROM AUTHOR]

The equation describing a power–law relationship between the mean and variance of population abundance in space or time is known as Taylor’s power law (TPL), initially observed in samples of insects. Factors determining the TPL exponent are of particular concern to ecologists because the observations of the exponent usually range 1–2. Recent studies have suggested that TPL is caused solely by statistical artifacts rather than biological processes, with the corresponding statistical models lacking linkages to explicit population demography. In this study, we used two special forms of the Neyman–Scott cluster point process to study the effect of offspring dispersal distance from the parents on the TPL exponent. Results showed that dispersal distance could largely affect the TPL exponent. The response curve of TPL exponent to dispersal distance is similar to the shape of the left-skewed gamma distribution function multiplied by a constant which can permit its maximum value to exceed 1. That means, short-distance dispersals could produce large TPL exponents relative to the whole response curve. However, the TPL exponent will decline in the case that the dispersal is extremely short or long. To better understand the function of the exponent of TPL on fitness, we attempted to link plant seed dispersal ability to the TPL exponent, and we discussed the trade-off between investing in propagation energy and in performance energy of plants. Dispersal overlap of offspring each other to an extent can cause a large TPL exponent, providing maximum fitness in a population. A novel theoretical frame was proposed to explain the role of spatial TPL relationships in affecting the fitness of plants. [ABSTRACT FROM AUTHOR]

Of the many mathematical models proposed for capturing the dynamics of plant growth, the beta sigmoid function (BSF) is the newest and consequently is not well known to ecologists. A recent software package based on the Microsoft Excel macro, LEAF-E, was designed to promote the use of BSF, even though the performance of BSF and other growth models had not been compared. We developed R functions for fitting the BSF with a freer option for choosing the parametric number, and illustrated their performance using simulated data generated by four equations (the exponential, logistic, Gompertz, and von Bertalanffy equations), as well as dry weights of six crop species measured in growing seasons. Compared to other growth models, the BSF allowed for both symmetric and asymmetric growth curves, and thus the simulated data modeled the actual data quite well. It was demonstrated that the BSF was better than the above four traditional growth equations. In addition, the R functions developed here can facilitate future data fitting and model comparison for capturing plant growth dynamics. And the time when plants reach their maximum body size can be accurately obtained by using the BSF. [ABSTRACT FROM AUTHOR]

Highlights: [•] There is no universal metabolic scaling exponent (α) for different species or taxa in the von Bertalanffy equation. [•] Use of 2/3 or 3/4 value for the scaling exponent α should not be decided merely based on the goodness-of-fit. [•] The logistic equation is a better model for describing the ontogenetic growth of animals and plants. [Copyright &y& Elsevier]

Highlights: [•] Ontogenetic growth model does not interpret the crop ontogenetic growth. [•] Logistic model is applicable to both animal and plant ontogenetic growth. [•] Logistic model is in fact universal for the ontogenetic growth of creature. [Copyright &y& Elsevier]