Color inheritance and pigment characterization of red (wild-type), greenish-brown, and green strains of Gracilaria birdiae (Gracilariales, Rhodophyta)

Species of Gracilaria are some of the most useful algae in the world for the production of agar. As a consequence of its economic importance, the genus has been the subject of many studies worldwide. Color variants of Gracilaria birdiae have been found in the natural population on the Brazilian coast, and they have also been isolated from plants cultivated in laboratory. These findings raised new questions regarding intraspecific variation and the prospects of cultivating such variants for their agar production. Therefore, this work aimed to determine the mode of color inheritance for two G. birdiae strains: a greenish-brown strain (gb) found in a natural population and a green strain (gr) which had arisen as a spontaneous mutation in a red plant cultured in the laboratory. The pigment contents of these strains, as well as the red wildtype (rd), were also characterized. Crosses between female and male plants of the same color (rd, gr, or gb) and between different colors were performed. Crosses between plants of the same color showed tetrasporophytic and gametophytic descendents of the parental color. Recessive nuclear inheritance was found in the greenish-brown strain, and cytoplasmic maternal inheritance was found in the green strain; both had lower phycoerythrin and higher concentrations of allophycocyanin and phycocyanin than the wild-type. Chlorophyll a contents were similar among all strains. Taken together, our results contribute to knowledge about the variability of this important red algae. In addition, since greenish-brown and green strains showed stability of color, both could be selected and tested in experimental sea cultivation to evaluate if mutants have advantageous performance when compared with red strain.

Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.