The covarion model of molecular evolution : a thesis presented in partial fulfilment of the requirements for the degree of Master of Philosophy in Biology at Massey University

Current methods for constructing evolutionary trees generally do not work well for sequences in which multiple substitutions have occurred. The covarion hypothesis may provide a solution to this problem. This hypothesis states that only a limited number of the codons in a given sequence are free to vary, but that the set of variable codons may change as mutations are fixed in the population. Although this is reasonable from a biological point of view, it is a difficult hypothesis to test scientifically because the apparent large number of parameters involved makes it very hard to analyse statistically. In this study, computer simulations were carried out on up to 51 machines running in parallel, using a simple covarion model based on a hidden Markov model (HMM) approach. This model required two new parameters—the proportion of sites that are variable at any given time, and the rate of exchange between fixed and variable states. These two parameters were both varied in the simulations. Sequence and distance data were simulated on a given tree under this covarion model, and these data were used to test the performance of standard tree-building methods at recovering the original tree The neighbour joining and maximum likelihood methods tested were found to perform better with data generated under the covarion model than with data generated under a simpler model in which all sites vary at the same rate. This suggests that current tree-building methods may perform better with biological data than computer simulation studies suggest

Verifiable control of a swarm of unmanned aerial vehicles

This article considers the distributed control of a swarm of unmanned aerial vehicles (UAVs) investigating autonomous pattern formation and reconfigurability. A behaviour-based approach to formation control is considered with a velocity field control algorithm developed through bifurcating potential fields. This new approach extends previous research into pattern formation using potential field theory by considering the use of bifurcation theory as a means of reconfiguring a swarm pattern through a free parameter change. The advantage of this kind of system is that it is extremely robust to individual failures, is scalpable, and also flexible. The potential field consists of a steering and repulsive term with the bifurcation of the steering potential resulting in a change of the swarm pattern. The repulsive potential ensures collision avoidance and an equally spaced final formation. The stability of the system is demonstrated to ensure that desired behaviours always occur, assuming that at large separation distances the repulsive potential can be neglected through a scale separation that exists between the steering and repulsive potential. The control laws developed are applied to a formation of ten UAVs using a velocity field tracking approach, where it is shown numerically that desired patterns can be formed safely ensuring collision avoidance

Pattern transition in spacecraft formation flying via the artificial potential field method and bifurcation theory

In recent years many new and exciting space concepts have developed around spacecraft formation flying. This form of distributed system has the advantages of being extremely flexible and robust. This paper considers the development of new control methodologies based on the artificial potential function method and extends previous research in this area by considering bifurcation theory as a means of controlling the transition between different formations. For real, safety critical applications it is important to prove the stability of the system. This paper therefore aims to replace algorithm validation with mathematical proof through dynamical systems theory. Finally we consider the transition of formations at the Sun-Earth L2 point

Spacecraft formation flying using bifurcating potential fields

The distributed control of spacecraft flying in formation has been shown to have advantages over conventional single spacecraft systems. These include scalability, flexibility and robustness to failures. This paper considers the real problem of actuator saturation and shows how bound control laws can be developed that allow pattern formation and reconfigurability in a formation of spacecraft using bifurcating potential fields. In addition the stability of the system is ensured mathematically through dynamical systems theory

Distributed control of multi-robot systems using bifurcating potential fields

The distributed control of multi-robot systems has been shown to have advantages over conventional single robot systems. These include scalability, flexibility and robustness to failures. This paper considers pattern formation and reconfigurability in a multi-robot system using bifurcating potential fields. It is shown how various patterns can be achieved through a simple free parameter change. In addition the stability of the system of robots is proven to ensure that desired behaviours always occur

Pattern transition in spacecraft formation flying using bifurcating potential field

Many new and exciting space mission concepts have developed around spacecraft formation flying, allowing for autonomous distributed systems that can be robust, scalable and flexible. This paper considers the development of a new methodology for the control of multiple spacecraft. Based on the artificial potential function method, research in this area is extended by considering the new approach of using bifurcation theory as a means of controlling the transition between different formations. For real, safety or mission critical applications it is important to ensure that desired behaviours will occur. Through dynamical systems theory, this paper also aims to provide a step in replacing traditional algorithm validation with mathematical proof, supported through simulation. This is achieved by determining the non-linear stability properties of the system, thus proving the existence or not of desired behaviours. Practical considerations such as the issue of actuator saturation and communication limitations are addressed, with the development of a new bounded control law based on bifurcating potential fields providing the key contribution of this paper. To illustrate spacecraft formation flying using the new methodology formation patterns are considered in low-Earth-orbit utilising the Clohessy-Wiltshire relative linearised equations of motion. It is shown that a formation of spacecraft can be driven safely onto equally spaced projected circular orbits, autonomously reconfiguring between them, whilst satisfying constraints made regarding each spacecraft