A unified approach to the Richards-model family for use in growth analyses: Why we need only two model forms

Tjørve, Even; Tjørve, Kathleen M. C.

doi:10.1016/j.jtbi.2010.09.008

Cited by 158 publications

(181 citation statements)

References 23 publications

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“…The Gompertz equation is one of the expressions of the Richards model of growth [22] and has been used to study the growth of many vertebrate groups, including dinosaurs [23]. The Richards model has other popular forms, such as the von Bertalanffy growth equation, but the analytical solution of the von Bertalanffy equation is complicated [24], and its application to allometry has yet to be established.…”

Section: (D) Gompertz Allometrymentioning

confidence: 99%

Adult sex ratio, sexual dimorphism and sexual selection in a Mesozoic reptile

et al. 2015

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The evolutionary history of sexual selection in the geologic past is poorly documented based on quantification, largely because of difficulty in sexing fossil specimens. Even such essential ecological parameters as adult sex ratio (ASR) and sexual size dimorphism (SSD) are rarely quantified, despite their implications for sexual selection. To enable their estimation, we propose a method for unbiased sex identification based on sexual shape dimorphism, using size-independent principal components of phenotypic data. We applied the method to test sexual selection in Keichousaurus hui, a Middle Triassic (about 237 Ma) sauropterygian with an unusually large sample size for a fossil reptile. Keichousaurus hui exhibited SSD biased towards males, as in the majority of extant reptiles, to a minor degree (sexual dimorphism index 20.087). The ASR is about 60% females, suggesting higher mortality of males over females. Both values support sexual selection of males in this species. The method may be applied to other fossil species. We also used the Gompertz allometric equation to study the sexual shape dimorphism of K. hui and found that two sexes had largely homogeneous phenotypes at birth except in the humeral width, contrary to previous suggestions derived from the standard allometric equation.

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Section: (D) Gompertz Allometrymentioning

confidence: 99%

Adult sex ratio, sexual dimorphism and sexual selection in a Mesozoic reptile

et al. 2015

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“…where A is the asymptotic value, T is the inflection point, R is the rate of growth, and M is the shape parameter (Tjørve and Tjørve, 2010). Each of the four parameters could be simultaneously modeled as a linear function of multiple covariates to test hypotheses about the effect of environmental and management variables on the different components of growth:…”

Section: Chick Growthmentioning

confidence: 99%

Can river management improve the piping plover’s long-term survival on the Missouri River?

Catlin

Milenkaya

Hunt

et al. 2014

Biological Conservation

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“…7. The confidence intervals clearly suggest that the proposed model (18) gives the best fit in all locations. The bootstrap confidence intervals are provided in the table for all locations for all models with different bootstrap samples.…”

Section: A Confirmatory Test Using a Bootstrap Techniquementioning

confidence: 81%

“…5 ISRP is plotted for Gompertz, logistic and two proposed models (17) and (18). Figure 5 suggests that, using the ISRP metric we can rank our preferences as model (17,18), Gompertz and logistic. However, there is very little difference observed between the Gompertz and logistic profiles of ISRPG and ISRPL with the corresponding constant rate parameter.…”

Section: Two New Proposed Growth Lawsmentioning

confidence: 99%

“…Particularly in the fisheries literature much has been discussed on models using von Bertalanffy growth law, including criticisms [12,13], testing for parameter differences [14,15], bioenergetic applications [16] and re-parameterizations (see also [17,18]). There have also been theoretical approaches to define a general framework to study growth models and a new family of sigmoid growth functions has been introduced, namely, Trans-General Logistic, Trans-General von Bertalanffy and Trans-Gompertz [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

2014

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Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, "Average Relative Growth Rate" is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.Keywords Growth curve models · Average relative growth rate · Interval specific rate parameter · Overall rate parameter · Model selection

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A unified approach to the Richards-model family for use in growth analyses: Why we need only two model forms

Cited by 158 publications

References 23 publications

Adult sex ratio, sexual dimorphism and sexual selection in a Mesozoic reptile

Adult sex ratio, sexual dimorphism and sexual selection in a Mesozoic reptile

Can river management improve the piping plover’s long-term survival on the Missouri River?

Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

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