An accurate evaluation of total population density is required in many ecological and biological field. To protect crops from pest attacks, the population density of pests must be evaluated adequately. Accurate information obtained as a result of trapping in ecological monitoring is beneficial for decision-making purposes when implementing a control action. In pest monitoring, a classic technique of evaluating density based on a statistical method may result in poor accuracy. Accuracy can be optimised by applying alternative numerical integration methods to the problem. We explain how insufficient information regarding population density negatively affects the accuracy of estimation. Consequently, a coarse grid problem arises where the numerical integration methods are no longer valid. The evaluation of integration error is now a random variable and the probabilistic approach is used, due to the uncertainty in sampling data. In this thesis several population models have been considered to explain that the value of correlation coefficient on a coarse sampling grid is lost even if the true value is close to one. Phenomenon of ghost synchronization has been observed when the value of correlation coefficient on a coarse sampling grid is close to one but in reality the dynamics are not correlated.

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Theoretical modelling of the microtubule-Dam1-ring force generation mechanism and the pulling of tubes from surface-supported lipid bilayers are presented and discussed. Atomic force microscopy (AFM) force data of tube pulling experiments is analysed and compared with theoretical predictions. Featurescommonto recent computational models are simplified and examined independently where possible. In particular, the steric confinement of the Dam1 ring on a microtubule (MT) by protofilaments (PFs), the powerstroke produced by curling PFs, the depolymerisation of the MT, and the binding attraction between Dam1 and the MT are modelled. Model parameters are fitted to data. Functional force generation is equally demonstrated when attachment is maintained by steric confinement alone (protofilament model) or by a binding attraction alone (binding model). Moreover, parameters amenable to experimental modification are shown to induce differences between the protofilament model and the binding model. Changing the depolymerisation rate of MTs, the diffusion coefficient of the Dam1 ring, or applying an oscillating load force will allow discrimination of these two different mechanisms of force generation and kinetochore attachment. A previously described theoretical model of pulling lipid bilayer tubes from vesicles is modified for the case of pulling tubes from surface-supported lipid bilayers. A shape equation for axisymmetric membranes is derived variationally and solved numerically for zero pressure. Free energy profiles and force curves are calculated for various AFM probe sizes and compared to experimental data where a ground flat AFM probe is used to pull tubes from surface-supported lipid bilayers. The predicted force curves partially fit the experimental data, although not at short distances, and estimates of the bilayer surface tension are given. Pressure and volume profiles are calculated for the extension of the model to the nonzero pressure case.

Phytoplankton aggregations come in a wide range of space and time scales and, as such, simulating such behavior is computationally restrictive. I present a Large-eddy simulation of the upper mixed layer, resolving scales of o(1m). I then show how aggregations are promoted by nutrient upwellings (something which macroscale models struggle to emulate), facilitated primarily by Langmuir circulations. I then demonstrate how certain levels of turbulent mixing encourage planktonic thin layering, a phenomenon which is widely observed.

Collective movements are ubiquitous in biological systems, occurring at all scales; from the sub-organismal movements of groups of cells, to the far-ranging movements of bird flocks and herds of large herbivores. Movement patterns at these vastly different scales often exhibit surprisingly similar patterns, suggesting that mathematically similar mechanisms may drive collective movements across many systems. The aims of this study were three-fold. First, to develop mechanistic movement models capable of producing the observed wealth of spatial patterns. Second, to tailor statistical inference approaches to these models that are capable of identifying drivers of collective movement that could be applied to a wide range of study systems. Third, to validate the approaches by fitting the mechanistic models to data from diverse biological systems. These study systems included two small-scale in vitro cellular systems, involving movement of groups of human melanoma cells and Dictyostelium discoideum (slime mould) cells, and a third much larger-scale system, involving wildebeest in the Serengeti ecosystem. I developed a series of mechanistic movement models, based on advection-diffusion partial differential equations and integro-differential equations, that describe changes in the spatio-temporal distribution of the study population as a consequence of various movement drivers, including environmental gradients, environmental depletion, social behaviour, and spatial and temporal heterogeneity in the response of the individuals to these drivers. I also developed a number of approaches to statistical inference (comprising both parameter estimation and model comparison) for these models that ranged from frequentist, to pseudo-Bayesian, to fully Bayesian. These inference approaches also varied in whether they required numerical solutions of the models, or whether the need for numerical solutions was bypassed by using gradient matching methods. The inference methods were specifically designed to be effective in the face of the many difficulties presented by advection-diffusion models, particularly high computational costs and instabilities in numerical model solutions, which have previously prevented these models from being fitted to data. It was also necessary for these inference methods to be able to cope with data of different qualities; the cellular data provided accurate information on the locations of all individuals through time, while the wildebeest data consisted of coarse ordinal abundance categories on a spatial grid at monthly intervals. By applying the developed models and inference methods to data from each study system, I drew a number of conclusions about the mechanisms driving movement in these systems. In all three systems, for example, there was evidence of a saturating response to an environmental gradient in a resource or chemical attractant that the individuals could deplete locally. I also found evidence of temporal dependence in the movement parameters for all systems. This indicates that the simplifying assumption that behaviour is constant, which has been made by many previous studies that have modelled movement, is unlikely to be justified. Differences between the systems were also demonstrated, such as overcrowding affecting the movements of melanoma and wildebeest, but not Dictyostelium, and wildebeest having a much greater range of perception than cells, and thus being able to respond to environmental conditions tens of kilometres away. The toolbox of methods developed in this thesis could be applied to increase understanding of the mechanisms underlying collective movement in a wide range of systems. In their current form, these methods are capable of producing very close matches between models and data for our simple cell systems, and also produce a relatively good model fit in the more complex wildebeest system, where there is, however, still some room for improvement. While more work is required to make the models generalisable to all taxa, particularly through the addition of memory-driven movement, inter-individual differences in behaviour, and more complex social dynamics, the advection-diffusion modelling framework is flexible enough for these additional behaviours to be incorporated in the future. A greater understanding of what drives collective movements in different systems could allow management of these movements to prevent the collapse of important migrations, control pest species, or prevent the spread of cancer.

The use of distributional models in forestry is investigated, in terms of their capability of modelling distributions of forest mensurational attributes, for modelling and inventory purposes. Emphasis is put on: (i) the univariate and bivariate modelling of tree diameters and heights for stand-level modelling work, and (ii) heuristic methods for use and analysis of distributions which occur in multi-temporal EO imagery, (for the inventory-related tasks of land-use mapping, change detection and growth modelling). In univariate distribution modelling, a new parameterization of the widely-used Johnson’s SB distribution is given, and new Logit-Logistic, generalised Weibull and the Burr system (XII, III, IV) models are introduced into forest modelling. The Logit-Logistic distribution is found to be the best among those compared. The use of regression-based methods of parameter estimation is also investigated. In the domain of bivariate distribution modelling of tree diameters and heights the Plackett method (a particular form of copula) is used to construct Plackett-based bivariate Beta, S­B and Logit-Logistic distributions, (the latter two are new), which are compared with each other and the SBB­ distribution. Other copula functions, including the normal copula, are further employed (for the first time in forest modelling) to construct bivariate distributional models. With the normal copula, the superiority of the Logit-Logistic in the univariate domain is extended into the bivariate domain. To use multi-temporal EO imagery, two pre-processing procedures are necessary: image to image co-registration, and radiometric correction. A spectral correlation-based pixel-matching method is developed to “refine” manually selected control points to achieve very accurate image co-registration. A robust non-parametric method of spectral-distribution standardization is used for relative radiometric correction between images. Finally, possibilities for further research are discussed.