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A new four-parameter, generalized logistic equation and its applications to mammalian somatic growth

100%

Wan X., Wang M., Wang G., Zhong W.

Acta Theriologica

2000

tom 45

nr 2

A new mathematical equation is introduced in this paper: w = f - 1/(b/f +(1/(f-s)-b-f)exp(kt)) where W is the size at any convenient unit of time /, s is the initial size, f is the upper asympotic size, k is the growth coefficient (k > 0), and b is the constant. The new equation encompasses the logistic equation and therefore should be considered as a generalized version of the classical logistic equation. With its additional fourth parameter 6, the new equation yields an unfixed value of inflexion point which enables it to possess good flexibility for depicting diverse growth patterns. In order to evaluate the fitness of the new growth equation, some commonly encountered models are compared to the new one using 12 sets of somatic growth data of mammalian species including hamster, rat, vole, pika, mouse, rabbit, cattle, and bear, The new equation possesses excellent fitness to each data set, suggesting that it is worth being considered by growth data analysts.

Varied somatic growth and sex cell development in reciprocal hybrids of roach Rutilus rutilus [L.] and ide Leuciscus idus [L.]

51%

Kopiejewska W., Terlecki J., Chybowski L.

Archives of Polish Fisheries

2003

tom 11

nr 1

Body length and weight and the developmental stage of sex cells were determined in 1.5- and 3-year-old specimens of the F₁ generation of reciprocal hybrids of roach Rutilus rutilus and ide Leuciscus idus. Body length and weight and the developmental stage of sex cell varied in reciprocal hybrids of roach and ide. The hybrids obtained from crossing R. rutilus females with L. idus males (R. rutilus x L. idus) were larger than those obtained from crossing L. idus females with R. rutilus males (L. idus x R. rutilus) (P < 0.001). At the ages of 1.5 and 3 years the hybrids had a similar body length and weight to L. idus (P>0.05) and a greater body length and weight than R. rutilus (P<0.001). The hybrids of L. idus x R. rutilus were smaller than L. idus and larger than R. rutilus (P < 0.001). Two-thirds of the studied L. idus x R. rutilus hybrid females were sexually mature at age 3, and only one R. rutilus x L. idus hybrid female exhibited signs of cytological maturation. In the control samples, roach females reached sexual maturity, while ide females were immature. The testes of 3-year-old R. rutilus x L. idus hybrid males contained spermatogonia and spermatocytes, while those of L. idus X R. rutilus hybrid males most often contained spermatocytes. The ovaries of female reciprocal hybrids of R. rutilus and L. idus contained not only developing oocytes, but also sex cells which stopped developing at an early stage of gametogenesis. These constituted approximately 50-60% of the area of ovary sections in 13% of the studied females, while in other females they were observed singly. The results obtained indicate that rapid somatic growth exhibited by L. idus is inherited by hybrids to a greater extent through L. idus males than through females. The differences in achieving sexual maturity exhibited by the females of reciprocal hybrids of R. rutilus and L. idus suggest that male genomes may have an important impact on this process.

Ograniczanie wyników

1 Acta Theriologica

1 Archives of Polish Fisheries

1 Chybowski L.

1 Kopiejewska W.

1 Terlecki J.

1 Wan X.

1 Wang G.

1 Wang M.

1 Zhong W.

1 2003

1 2000

Wyniki wyszukiwania

A new four-parameter, generalized logistic equation and its applications to mammalian somatic growth

Varied somatic growth and sex cell development in reciprocal hybrids of roach Rutilus rutilus [L.] and ide Leuciscus idus [L.]