Time series modelling methods to forecast the volume of self-assessment tax returns in the UK.

Her Majesty's Revenue and Customs (HMRC) has the ambitious target of making tax digital for all its customers and collecting tax in a more efficient, effective and accurate manner for both the government and UK taxpayers. Self-assessment tax returns, the biggest key business event for HMRC, is also one of the most popular digital services with over 90% of the approximately 12 million taxpayers in self assessment filing their return online each year. The majority of returns are filed in January immediately prior to the self-assessment deadline (31st January), putting significant pressure not only on the self-assessment digital service but also on all other HMRC digital services. Hence, understanding and predicting demand for the system is vital to provide a robust and responsive service. We therefore developed mathematical models with Bayesian inference techniques to forecast volumes of Self-assessment (SA) returns submitted online during January, providing accurate hourly predictions of traffic on the digital system in the run up to the SA deadline. Because none of the models being considered is believed to be the true model, we use an ensemble modelling technique that combines forecasts from different models to develop a less risky demand forecast.

Evidence for Active Uptake and Deposition of Si-based Defenses in Tall Fescue.

Silicon (Si) is taken up from the soil as monosilicic acid by plant roots, transported to leaves and deposited as phytoliths, amorphous silica (SiO2) bodies, which are a key component of anti-herbivore defense in grasses. Silicon transporters have been identified in many plant species, but the mechanisms underpinning Si transport remain poorly understood. Specifically, the extent to which Si uptake is a passive process, driven primarily by transpiration, or has both passive and active components remains disputed. Increases in foliar Si concentration following herbivory suggest plants may exercise some control over Si uptake and distribution. In order to investigate passive and active controls on Si accumulation, we examined both genetic and environmental influences on Si accumulation in the forage grass Festuca arundinacea. We studied three F. arundinacea varieties that differ in the levels of Si they accumulate. Varieties not only differed in Si concentration, but also in increases in Si accumulation in response to leaf damage. The varietal differences in Si concentration generally reflected differences in stomatal density and stomatal conductance, suggesting passive, transpiration-mediated mechanisms underpin these differences. Bagging plants after damage was employed to minimize differences in stomatal conductance between varieties and in response to damage. This treatment eliminated constitutive differences in leaf Si levels, but did not impair the damage-induced increases in Si uptake: damaged, bagged plants still had more leaf Si than undamaged, bagged plants in all three varieties. Preliminary differential gene expression analysis revealed that the active Si transporter Lsi2 was highly expressed in damaged unbagged plants compared with undamaged unbagged plants, suggesting damage-induced Si defenses are regulated at gene level. Our findings suggest that although differences in transpiration may be partially responsible for varietal differences in Si uptake, they cannot explain damage-induced increases in Si uptake and deposition, suggesting that wounding causes changes in Si uptake, distribution and deposition that likely involve active processes and changes in gene expression.

Defending the leaf surface: intra- and inter-specific differences in silicon deposition in grasses in response to damage and silicon supply.

Understanding interactions between grasses and their herbivores is central to the conservation of species-rich grasslands and the protection of our most important crops against pests. Grasses employ a range of defenses against their natural enemies; silicon-based defenses have been shown to be one of the most effective. Silicon (Si) is laid down on the leaf surface as spines and other sharp bodies, known as phytoliths, making grasses abrasive and their foliage indigestible to herbivores. Previous studies on Si defenses found that closely related species may have similar levels of Si in the leaves but differ markedly in abrasiveness. Here we show how the number, shape and distribution of Si-rich phytoliths and spines differ within and between different grass species and demonstrate that species also differ in their ability to change the deposition and distribution of these defenses in response to damage or increases in Si supply. Specifically, we tested the response of two genotypes of Festuca arundinacea known to differ in their surface texture and three different grass species (F. ovina, F. rubra, and Deschampsia cespitosa) differing in their abrasiveness to combined manipulation of leaf damage and Si supply. F. arundinacea plants with a harsh leaf surface had higher Si content and more spines on their leaf surface than soft varieties. F. ovina and D. cespitosa plants increased their leaf Si concentration and produced an increase in the number of leaf spines and phytoliths on the leaf surface in response to Si addition. F rubra also increased leaf Si content in response to treatments, particularly in damaged leaves, but did not deposit this in the form of spines or increased densities of phytoliths. We discuss how the form in which grasses deposit Si may affect their anti-herbivore characteristics and consider the ecological and agricultural implications of the differences in allocation to Si-based defenses between grass species.