Aspects of the biology of Lutraria lutraria (L.) (bivalvia : Mactracea)

The life history of a population of Lutraria lutraria in a depth of 7m at Hunterston, Ayrshire is discussed. Much of the present population Is thought to have settled in 1967. The functional morphology of Lutraria is described and related to its life as a large, deep-burrowing bivalve. Lutraria spawned in late spring and continued to do so through the summer in 1979 and 1980. Animals became spent in August and September. Unsuccessful attempts were made to induce spawning in the laboratory. Artificial fertilization was successful but development did not proceed beyond the ciliated gastrula stage. Larvae of Lutraria were not identified in plankton samples and young stages were not encountered in sieved sediment samples. The biochemical cycle of the total animal and five component parts (gonad and visceral mass, digestive gland, adductor muscle, siphon and 'other' tissue) is investigated. A marked increase in weight, reflected in an increase in weight of the component parts, was recorded in Autumn 1979. This is thought to be related to an exceptional increase in the phytoplankton at this time. Although a relationship between the biochemical cycle and reproductive cycle remains uncertain, definite seasonal changes were recorded in the respiration rate of Lutraria. At 10°C, the maximum rate of a standard 20g animal was 0.1283m1s 02/g. dry wt./hr. in May 1980 and the minimum rate was 0.O59mls 02/g. dry wt./hr. in October 1980. The effect of temperature on respiration rate was also investigated. Significant differences were recorded for five experimental temperatures (10°C, 15°C, 20°C, 25°C and 30 °C) in August and October but only between two temperatures (10 C and 30 C) in April. There was a decrease in respiration rate at 30 C in August and October, but an increase in April. Respiration rate is affected by a reduction in oxygen tension. A variety of responses were recorded with a small degree of regulation shown. Individuals of Lutraria were able to survive 48 hours under anaerobic conditions. In fully oxygenated conditions heart rate ranged from 4-15 beats per minute with an average of 8 beats per minute. Heart beat was markedly affected by changes in temperature and oxygen tension, increasing to a maximum 22 beats per minute at 25 C, and decreasing to a minimum 2 beats per minute in anaerobic conditions. Heart rate is reduced (12 beats per minute to 5 beats per minute) on exposure to air. Lutraria exhibits an intermittent pattern of pumping activity. Under normal conditions 35% of the time is spent pumping and this Increases as oxygen is reduced (3.00mls 02/litre) to 65% of the time spent pumping. 15. Under normal conditions the respiratory flow varies between 0.382 litres per hour and 1.023 litres per hxir. Adult Lutraria maintain their ability to burrow, albeit slowly.

Optimal static and sequential design : a critical review

The aim of this thesis is to review and augment the theory and methods of optimal experimental design. In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure. It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated. In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue. Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem. A necessary and sufficient condition for optimality of a design measure is given. Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested. Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter. In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed. A new algorithm is presented with illustrations of how it should be used in practice. It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design. In situations where this is not satisfactory algorithms for improvement of this design are reviewed. Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference. In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures. Alternative suggestions are made along with conjectures as to how these might improve performance. Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5. The results of this study provide empirical support for these conjectures. In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially. Further examples are considered which stress the importance of the use of prior information in situations of this type. Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time. In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold.