All Green, But Equal? Morphological Traits And Ecological Implications On Spores Of Three Species Of Mosses In The Brazilian Atlantic Forest.

Spores of the tropical mosses Pyrrhobryum spiniforme, Neckeropsis undulata and N. disticha were characterized regarding size, number per capsule and viability. Chemical substances were analyzed for P. spiniforme and N. undulata spores. Length of sporophyte seta (spore dispersal ability) was analyzed for P. spiniforme. Four to six colonies per species in each site (lowland and highland areas of an Atlantic Forest; Serra do Mar State Park, Brazil) were visited for the collection of capsules (2008 - 2009). Neckeropsis undulata in the highland area produced the largest spores (ca. 19 µm) with the highest viability. The smallest spores were found in N. disticha in the lowland (ca. 13 µm). Pyrrhobryum spiniforme produced more spores per capsule in the highland (ca. 150,000) than in lowland (ca. 40,000); longer sporophytic setae in the lowland (ca. 64 mm) than in the highland (ca. 43 mm); and similar sized spores in both areas (ca. 16 µm). Spores of N. undulata and P. spiniforme contained lipids and proteins in the cytoplasm, and acid/neutral lipids and pectins in the wall. Lipid bodies were larger in N. undulata than in P. spiniforme. No starch was recorded for spores. Pyrrhobryum spiniforme in the highland area, different from lowland, was characterized by low reproductive effort, but presented many spores per capsule.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.