The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family

<div><p>The Gompertz model is well known and widely used in many aspects of biology. It has been frequently used to describe the growth of animals and plants, as well as the number or volume of bacteria and cancer cells. Numerous parametrisations and re-parametrisations of varying usefulness are found in the literature, whereof the Gompertz-Laird is one of the more commonly used. Here, we review, present, and discuss the many re-parametrisations and some parameterisations of the Gompertz model, which we divide into <i>T</i>_<i>i</i> (type I)- and <i>W</i>₀ (type II)-forms. In the <i>W</i>₀-form a starting-point parameter, meaning birth or hatching value (<i>W</i>₀), replaces the inflection-time parameter (<i>T</i>_<i>i</i>). We also propose new “unified” versions (U-versions) of both the traditional <i>T</i>_<i>i</i> -form and a simplified <i>W</i>₀-form. In these, the growth-rate constant represents the relative growth rate instead of merely an unspecified growth coefficient. We also present U-versions where the growth-rate parameters return absolute growth rate (instead of relative). The new U-Gompertz models are special cases of the Unified-Richards (U-Richards) model and thus belong to the Richards family of U-models. As U-models, they have a set of parameters, which are comparable across models in the family, without conversion equations. The improvements are simple, and may seem trivial, but are of great importance to those who study organismal growth, as the two new U-Gompertz forms give easy and fast access to all shape parameters needed for describing most types of growth following the shape of the Gompertz model.</p></div

Planktonic larval duration, age and growth of Ostorhinchus doederleini (Pisces: Apogonidae) on the southern Great Barrier Reef, Australia

Cardinalfishes (Apogonidae) are abundant on corals reefs, but there are few data on demography to understand trophodynamics and population dynamics. Ostorhinchus doederleini is a small and abundant apogonid on the Great Barrier Reef (GBR) and throughout the western Pacific Ocean. We present key demographic parameters for the entire life history from the southern GBR. Daily deposition of increments in otoliths was validated. Fish had a Planktonic Larval Duration (PLD) of 16–26 days. PLD was established from fish collected immediately prior to settlement as no settlement mark was found. Fish grew at about 0.35 mm day−1 for the first 20 days after settlement. Fish reached a maximum standard length at about 200 days, and no fish lived longer than 368 days at four reefs separated by kilometers to tens of kilometers. There was no evidence for differences in size at age between sexes. Mortality was very high, and for fish greater than 60 days old, mortality rates ranged from 2.9 to 4.6 % day−1. Short lives and high mortality rates make O. doederleini, and potentially other apogonids, vulnerable to recruitment failure. Here, we review data on the demographic characteristics of other reef fishes. Although some taxa live to over 50 years, the short lives of apogonids are most aligned with the Gobiidae and Blenniidae (i.e., typically <1.5 years). Descriptions of fish size, age, longevity, growth and mortality, from hatching to age maxima, are very rare for most taxa, even at the level of family