Melvin A. Nyman

Population modelling of Gelidium sesquipedale (Rhodophyta, Gelidiales)

A matrix population model of Gelidium sesquipedale, a commercial agarophyte from the Northeast Atlantic, was developed based on demographic data obtained during two years in a commercial stand of Cape Espichel, Portugal. G. sesquipedale individuals were classified into categories such as life cycle phase, spores, juveniles and adult frond size, because the species vital rates, fecundity, fertility, survival, growth and breakage depend on them. We also exemplify the use of a user-friendly modelling software, Stella, to develop a structured-population model. This is the first time this software has been used to model the demography of seaweed populations. The Stella model developed here behaved very similarly to the matrix model, because of its particular construction, which causes the forcing functions to be discrete rather than continuous. The relative importance of spore recruitment and vegetative growth of new fronds in both population growth and population structure was investigated. Elasticity analysis suggests that vegetative recruitment is the most important demographic parameter controlling population growth together with survival and transitions between juveniles (1–6 cm fronds) and class 1 fronds (6–9 cm fronds). On the other hand, sexual reproduction may, by itself, efficiently control the relative proportion of gametophytes and tetrasporophytes in the population, even though its contribution to recruitment is extremely small. A 40% difference in the growth rates of gametophyte and tetrasporophyte submatrices resulted from natural differences in spore recruitment rates.

Student connections of linear algebra concepts: an analysis of concept maps

This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernauds theory of conceptual fields and Pirie and Kierens model for the growth of mathematical understanding. In addition to the existing techniques for analysing concept maps, two new techniques are developed for analysing qualitative data based on student-constructed concept maps: (1) temporal clumping of concepts and (2) the use of adjacency matrices of an undirected graph representation of the concept map. Findings suggest that students may find it more difficult to make connections between concepts like eigenvalues and eigenvectors and concepts from other parts of the conceptual field such as basis and dimension. In fact, eigenvalues and eigenvectors seemed to be the most disconnected concepts within all of the students’ concept maps. In addition, the relationships between link types and certain clumps are suggested as well as directions for future study and curriculum design.

Introducing mathematical modelling skills to students and the use of posters in assessment

ABSTRACT A well balanced mathematics curriculum consists of a mixture of concepts, context, and skills. It is now recognized that ones ability to use mathematics in problem solving is equally important as developing mathematical skills. Developing good problem solving skills is not easy. In this paper we describe the outcomes of an intensive one month mathematical modelling course and the use of posters in peer assessment of the student work.

Macrocystis pyrifera in New Zealand: testing two mathematical models for whole plant growth

A Leslie-Lewis matrix projection model and a Markov chain model for whole plant growth in the giant Kelp,Macrocystis pyrifera, are developed and compared. Parameters of the models are estimated from field data gathered from several plants in New Zealand over a four-month period. Interpretations of the results are discussed.

Mass distribution in the fronds of macrocystis pyrifera from New Zealand and California

The mass distribution along the fronds of Macrocystis is examined for plants collected from California and New Zealand. Analysis of fronds classified according to length and condition yields polynomial curves for cumulative mass as a function of distance above the holdfast. Models for this functional relationship are discussed. Similarities and differences between the deep-water California plant and the shallow-water New Zealand plant are highlighted.