Modelling leaf development in Oxalis latifolia

This study was carried to develop functions that could explain the growth of Oxalis latifolia, in both early stages and throughout the season, contributing to the improvement of its cultural control. Bulbs of the Cornwall form of O. latifolia were buried at 1 and 8 cm in March 1999 and 2000. Samples were destructive at fixed times, and at each time the corresponding BBCH scale codes as well as the absolute number of growing and adult leaves were noted. Using the absolute number of adult leaves (transformed to percentages), a Gaussian curve of three parameters that explains the growth during the season (R2=0.9355) was developed. The BBCH scale permitted the fit of two regression lines that were accurately adjusted for each burial depth (R2=0.9969 and R2=0.9930 respectively for 1 and 8 cm). The best moment for an early defoliation in Northern Spain could be calculated with these regression lines, and was found to be the second week of May. In addition, it was observed that a burial depth of 8 cm does not affect the growing pattern of the weed, but it affects the number of leaves they produce, which decreases to less than a half of those produced at 1 cm.

Modelling bird species richness with neural networks for forest landscape management in NE Spain

Para preservar la biodiversidad de los ecosistemas forestales de la Europa mediterránea en escenarios actuales y futuros de cambio global mediante una gestión forestal sostenible es necesario determinar cómo influye el medio ambiente y las propias características de los bosques sobre la biodiversidad que éstos albergan. Con este propósito, se analizó la influencia de diferentes factores ambientales y de estructura y composición del bosque sobre la riqueza de aves forestales a escala 1 × 1 km en Cataluña (NE de España). Se construyeron modelos univariantes y multivariantes de redes neuronales para respectivamente explorar la respuesta individual a las variables y obtener un modelo parsimonioso (ecológicamente interpretable) y preciso. La superficie de bosque (con una fracción de cabida cubierta superior a 5%), la fracción de cabida cubierta media, la temperatura anual y la precipitación estival medias fueron los mejores predictores de la riqueza de aves forestales. La red neuronal multivariante obtenida tuvo una buena capacidad de generalización salvo en las localidades con una mayor riqueza. Además, los bosques con diferentes grados de apertura del dosel arbóreo, más maduros y más diversos en cuanto a su composición de especies arbóreas se asociaron de forma positiva con una mayor riqueza de aves forestales. Finalmente, se proporcionan directrices de gestión para la planificación forestal que permitan promover la diversidad ornítica en esta región de la Europa mediterránea.

Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure

Magneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a 'chain deformation gradient' and a 'chain magnetic field'. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading.

Intravoxel incoherent motion diffusion-weighted imaging in the liver: comparison of mono-, bi- and tri-exponential modelling at 3.0-T.

PURPOSE: To determine whether a mono-, bi- or tri-exponential model best fits the intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) signal of normal livers. MATERIALS AND METHODS: The pilot and validation studies were conducted in 38 and 36 patients with normal livers, respectively. The DWI sequence was performed using single-shot echoplanar imaging with 11 (pilot study) and 16 (validation study) b values. In each study, data from all patients were used to model the IVIM signal of normal liver. Diffusion coefficients (Di ± standard deviations) and their fractions (fi ± standard deviations) were determined from each model. The models were compared using the extra sum-of-squares test and information criteria. RESULTS: The tri-exponential model provided a better fit than both the bi- and mono-exponential models. The tri-exponential IVIM model determined three diffusion compartments: a slow (D1 = 1.35 ± 0.03 × 10(-3) mm(2)/s; f1 = 72.7 ± 0.9 %), a fast (D2 = 26.50 ± 2.49 × 10(-3) mm(2)/s; f2 = 13.7 ± 0.6 %) and a very fast (D3 = 404.00 ± 43.7 × 10(-3) mm(2)/s; f3 = 13.5 ± 0.8 %) diffusion compartment [results from the validation study]. The very fast compartment contributed to the IVIM signal only for b values ≤15 s/mm(2) CONCLUSION: The tri-exponential model provided the best fit for IVIM signal decay in the liver over the 0-800 s/mm(2) range. In IVIM analysis of normal liver, a third very fast (pseudo)diffusion component might be relevant. KEY POINTS: ? For normal liver, tri-exponential IVIM model might be superior to bi-exponential ? A very fast compartment (D = 404.00 ± 43.7 × 10 (-3)  mm (2) /s; f = 13.5 ± 0.8 %) is determined from the tri-exponential model ? The compartment contributes to the IVIM signal only for b ≤ 15 s/mm (2.)

Statistical modelling of CSP solving algorithms performance

The goal of this work is to try to create a statistical model, based only on easily computable parameters from the CSP problem to predict runtime behaviour of the solving algorithms, and let us choose the best algorithm to solve the problem. Although it seems that the obvious choice should be MAC, experimental results obtained so far show, that with big numbers of variables, other algorithms perfom much better, specially for hard problems in the transition phase.

On diversity effects of alternative agricultural policy reforms in Finland : an agricultural sector modelling approach

Selostus: Maatalouspolitiikkauudistusten vaikutuksista pellonkäytön diversiteettiin

Fire management, climate change and their interacting effects on birds in complex Mediterranean landscapes: dynamic distribution modelling of an early-successional species - the near-threatened Dartford Warbler (Sylvia undata)

The current challenge in a context of major environmental changes is to anticipate the responses of species to future landscape and climate scenarios. In the Mediterranean basin, climate change is one the most powerful driving forces of fire dynamics, with fire frequency and impact having markedly increased in recent years. Species distribution modelling plays a fundamental role in this challenge, but better integration of available ecological knowledge is needed to adequately guide conservation efforts. Here, we quantified changes in habitat suitability of an early-succession bird in Catalonia, the Dartford Warbler (Sylvia undata) ― globally evaluated as Near Threatened in the IUCN Red List. We assessed potential changes in species distributions between 2000 and 2050 under different fire management and climate change scenarios and described landscape dynamics using a spatially-explicit fire-succession model that simulates fire impacts in the landscape and post-fire regeneration (MEDFIRE model). Dartford Warbler occurrence data were acquired at two different spatial scales from: 1) the Atlas of European Breeding Birds (EBCC) and 2) Catalan Breeding Bird Atlas (CBBA). Habitat suitability was modelled using five widely-used modelling techniques in an ensemble forecasting framework. Our results indicated considerable habitat suitability losses (ranging between 47% and 57% in baseline scenarios), which were modulated to a large extent by fire regime changes derived from fire management policies and climate changes. Such result highlighted the need for taking the spatial interaction between climate changes, fire-mediated landscape dynamics and fire management policies into account for coherently anticipating habitat suitability changes of early succession bird species. We conclude that fire management programs need to be integrated into conservation plans to effectively preserve sparsely forested and early succession habitats and their associated species in the face of global environmental change.

Modelling additional costs caused by a new product feature

Työn tavoitteena oli mallintaa uuden tuoteominaisuuden aiheuttamat lisäkustannukset ja suunnitella päätöksenteon työkalu Timberjack Oy:n kuormatraktorivalmistuksen johtoryhmälle. Tarkoituksena oli luoda karkean tason malli, joka sopisi eri tyyppisten tuoteominaisuuksien kustannuksien selvittämiseen. Uuden tuoteominaisuuden vaikutusta yrityksen eri toimintoihin selvitettiin haastatteluin. Haastattelukierroksen tukena käytettiin kysymyslomaketta. Haastattelujen tavoitteena oli selvittää prosessit, toiminnot ja resurssit, jotka ovat välttämättömiä uuden tuoteominaisuuden tuotantoon saattamisessa ja tuotannossa. Malli suunniteltiin haastattelujen ja tietojärjestelmästä hankitun tiedon pohjalta. Mallin rungon muodostivat ne prosessit ja toiminnot, joihin uudella tuoteominaisuudella on vaikutusta. Huomioon otettiin sellaiset resurssit, joita uusi tuoteominaisuus kuluttaa joko välittömästi, tai välillisesti. Tarkasteluun sisällytettiin ainoastaan lisäkustannukset. Uuden tuoteominaisuuden toteuttamisesta riippumattomat, joka tapauksessa toteutuvat yleiskustannukset jätettiin huomioimatta. Malli on yleistys uuden tuoteominaisuuden aiheuttamista lisäkustannuksista, koska tarkoituksena on, että se sopii eri tyyppisten tuoteominaisuuksien aiheuttamien kustannusten selvittämiseen. Lisäksi malli soveltuu muiden pienehköjen tuotemuutosten kustannusten kartoittamiseen.

Object-Oriented Modelling of Multilayer Networks

Tämä diplomityökuuluu tietoliikenneverkkojen suunnittelun tutkimukseen ja pohjimmiltaan kohdistuu verkon mallintamiseen. Tietoliikenneverkkojen suunnittelu on monimutkainen ja vaativa ongelma, joka sisältää mutkikkaita ja aikaa vieviä tehtäviä. Tämä diplomityö esittelee ”monikerroksisen verkkomallin”, jonka tarkoitus on auttaa verkon suunnittelijoita selviytymään ongelmien monimutkaisuudesta ja vähentää verkkojen suunnitteluun kuluvaa aikaa. Monikerroksinen verkkomalli perustuu yleisille objekteille, jotka ovat yhteisiä kaikille tietoliikenneverkoille. Tämä tekee mallista soveltuvan mielivaltaisille verkoille, välittämättä verkkokohtaisista ominaisuuksista tai verkon toteutuksessa käytetyistä teknologioista. Malli määrittelee tarkan terminologian ja käyttää kolmea käsitettä: verkon jakaminen tasoihin (plane separation), kerrosten muodostaminen (layering) ja osittaminen (partitioning). Nämä käsitteet kuvataan yksityiskohtaisesti tässä työssä. Monikerroksisen verkkomallin sisäinen rakenne ja toiminnallisuus ovat määritelty käyttäen Unified Modelling Language (UML) -notaatiota. Tämä työ esittelee mallin use case- , paketti- ja luokkakaaviot. Diplomityö esittelee myös tulokset, jotka on saatu vertailemalla monikerroksista verkkomallia muihin verkkomalleihin. Tulokset osoittavat, että monikerroksisella verkkomallilla on etuja muihin malleihin verrattuna.

Supporting Business Model Modelling: a Compromise between Creativity and Constraints

Diagrams and tools help to support task modelling in engi- neering and process management. Unfortunately they are unfit to help in a business context at a strategic level, because of the flexibility needed for creative thinking and user friendly interactions. We propose a tool which bridges the gap between freedom of actions, encouraging creativity, and constraints, allowing validation and advanced features.

Modelling the curing process in magneto-sensitive polymers: Rate-dependence and shrinkage

This paper deals with a phenomenologically motivated magneto-viscoelastic coupled finite strain framework for simulating the curing process of polymers under the application of a coupled magneto-mechanical road. Magneto-sensitive polymers are prepared by mixing micron-sized ferromagnetic particles in uncured polymers. Application of a magnetic field during the curing process causes the particles to align and form chain-like structures lending an overall anisotropy to the material. The polymer curing is a viscoelastic complex process where a transformation from fluid. to solid occurs in the course of time. During curing, volume shrinkage also occurs due to the packing of polymer chains by chemical reactions. Such reactions impart a continuous change of magneto-mechanical properties that can be modelled by an appropriate constitutive relation where the temporal evolution of material parameters is considered. To model the shrinkage during curing, a magnetic-induction-dependent approach is proposed which is based on a multiplicative decomposition of the deformation gradient into a mechanical and a magnetic-induction-dependent volume shrinkage part. The proposed model obeys the relevant laws of thermodynamics. Numerical examples, based on a generalised Mooney-Rivlin energy function, are presented to demonstrate the model capacity in the case of a magneto-viscoelastically coupled load.

Three-dimensional hydrodynamic numerical modelling of fold nappe formation, basement-cover deformation and slab detachment with applications to the helvetic nappe system (W Switzerland)

Many three-dimensional (3-D) structures in rock, which formed during the deformation of the Earth's crust and lithosphere, are controlled by a difference in mechanical strength between rock units and are often the result of a geometrical instability. Such structures are, for example, folds, pinch-and-swell structures (due to necking) or cuspate-lobate structures (mullions). These struc-tures occur from the centimeter to the kilometer scale and the related deformation processes con-trol the formation of, for example, fold-and-thrust belts and extensional sedimentary basins or the deformation of the basement-cover interface. The 2-D deformation processes causing these structures are relatively well studied, however, several processes during large-strain 3-D defor-mation are still incompletely understood. One of these 3-D processes is the lateral propagation of these structures, such as fold and cusp propagation in a direction orthogonal to the shortening direction or neck propagation in direction orthogonal to the extension direction. Especially, we are interested in fold nappes which are recumbent folds with amplitudes usually exceeding 10 km and they have been presumably formed by ductile shearing. They often exhibit a constant sense of shearing and a non-linear increase of shear strain towards their overturned limb. The fold axes of the Morcles fold nappe in western Switzerland plunges to the ENE whereas the fold axes in the more eastern Doldenhorn nappe plunges to the WSW. These opposite plunge direc-tions characterize the Rawil depression (Wildstrubel depression). The Morcles nappe is mainly the result of layer parallel contraction and shearing. During the compression the massive lime-stones were more competent than the surrounding marls and shales, which led to the buckling characteristics of the Morcles nappe, especially in the north-dipping normal limb. The Dolden-horn nappe exhibits only a minor overturned fold limb. There are still no 3-D numerical studies which investigate the fundamental dynamics of the formation of the large-scale 3-D structure including the Morcles and Doldenhorn nappes and the related Rawil depression. We study the 3-D evolution of geometrical instabilities and fold nappe formation with numerical simulations based on the finite element method (FEM). Simulating geometrical instabilities caused by sharp variations of mechanical strength between rock units requires a numerical algorithm that can accurately resolve material interfaces for large differences in material properties (e.g. between limestone and shale) and for large deformations. Therefore, our FE algorithm combines a nu-merical contour-line technique and a deformable Lagrangian mesh with re-meshing. With this combined method it is possible to accurately follow the initial material contours with the FE mesh and to accurately resolve the geometrical instabilities. The algorithm can simulate 3-D de-formation for a visco-elastic rheology. The viscous rheology is described by a power-law flow law. The code is used to study the 3-D fold nappe formation, the lateral propagation of folding and also the lateral propagation of cusps due to initial half graben geometry. Thereby, the small initial geometrical perturbations for folding and necking are exactly followed by the FE mesh, whereas the initial large perturbation describing a half graben is defined by a contour line inter-secting the finite elements. Further, the 3-D algorithm is applied to 3-D viscous nacking during slab detachment. The results from various simulations are compared with 2-D resulats and a 1-D analytical solution. -- On retrouve beaucoup de structures en 3 dimensions (3-D) dans les roches qui ont pour origines une déformation de la lithosphère terrestre. Ces structures sont par exemple des plis, des boudins (pinch-and-swell) ou des mullions (cuspate-lobate) et sont présentés de l'échelle centimétrique à kilométrique. Mécaniquement, ces structures peuvent être expliquées par une différence de résistance entre les différentes unités de roches et sont généralement le fruit d'une instabilité géométrique. Ces différences mécaniques entre les unités contrôlent non seulement les types de structures rencontrées, mais également le type de déformation (thick skin, thin skin) et le style tectonique (bassin d'avant pays, chaîne d'avant pays). Les processus de la déformation en deux dimensions (2-D) formant ces structures sont relativement bien compris. Cependant, lorsque l'on ajoute la troisiéme dimension, plusieurs processus ne sont pas complètement compris lors de la déformation à large échelle. L'un de ces processus est la propagation latérale des structures, par exemple la propagation de plis ou de mullions dans la direction perpendiculaire à l'axe de com-pression, ou la propagation des zones d'amincissement des boudins perpendiculairement à la direction d'extension. Nous sommes particulièrement intéressés les nappes de plis qui sont des nappes de charriage en forme de plis couché d'une amplitude plurikilométrique et étant formées par cisaillement ductile. La plupart du temps, elles exposent un sens de cisaillement constant et une augmentation non linéaire de la déformation vers la base du flanc inverse. Un exemple connu de nappes de plis est le domaine Helvétique dans les Alpes de l'ouest. Une de ces nap-pes est la Nappe de Morcles dont l'axe de pli plonge E-NE tandis que de l'autre côté de la dépression du Rawil (ou dépression du Wildstrubel), la nappe du Doldenhorn (équivalent de la nappe de Morcles) possède un axe de pli plongeant O-SO. La forme particulière de ces nappes est due à l'alternance de couches calcaires mécaniquement résistantes et de couches mécanique-ment faibles constituées de schistes et de marnes. Ces différences mécaniques dans les couches permettent d'expliquer les plissements internes à la nappe, particulièrement dans le flanc inver-se de la nappe de Morcles. Il faut également noter que le développement du flanc inverse des nappes n'est pas le même des deux côtés de la dépression de Rawil. Ainsi la nappe de Morcles possède un important flanc inverse alors que la nappe du Doldenhorn en est presque dépour-vue. A l'heure actuelle, aucune étude numérique en 3-D n'a été menée afin de comprendre la dynamique fondamentale de la formation des nappes de Morcles et du Doldenhorn ainsi que la formation de la dépression de Rawil. Ce travail propose la première analyse de l'évolution 3-D des instabilités géométriques et de la formation des nappes de plis en utilisant des simulations numériques. Notre modèle est basé sur la méthode des éléments finis (FEM) qui permet de ré-soudre avec précision les interfaces entre deux matériaux ayant des propriétés mécaniques très différentes (par exemple entre les couches calcaires et les couches marneuses). De plus nous utilisons un maillage lagrangien déformable avec une fonction de re-meshing (production d'un nouveau maillage). Grâce à cette méthode combinée il nous est possible de suivre avec précisi-on les interfaces matérielles et de résoudre avec précision les instabilités géométriques lors de la déformation de matériaux visco-élastiques décrit par une rhéologie non linéaire (n>1). Nous uti-lisons cet algorithme afin de comprendre la formation des nappes de plis, la propagation latérale du plissement ainsi que la propagation latérale des structures de type mullions causé par une va-riation latérale de la géométrie (p.ex graben). De plus l'algorithme est utilisé pour comprendre la dynamique 3-D de l'amincissement visqueux et de la rupture de la plaque descendante en zone de subduction. Les résultats obtenus sont comparés à des modèles 2-D et à la solution analytique 1-D. -- Viele drei dimensionale (3-D) Strukturen, die in Gesteinen vorkommen und durch die Verfor-mung der Erdkruste und Litosphäre entstanden sind werden von den unterschiedlichen mechani-schen Eigenschaften der Gesteinseinheiten kontrolliert und sind häufig das Resulat von geome-trischen Istabilitäten. Zu diesen strukturen zählen zum Beispiel Falten, Pich-and-swell Struktu-ren oder sogenannte Cusbate-Lobate Strukturen (auch Mullions). Diese Strukturen kommen in verschiedenen Grössenordungen vor und können Masse von einigen Zentimeter bis zu einigen Kilometer aufweisen. Die mit der Entstehung dieser Strukturen verbundenen Prozesse kontrol-lieren die Entstehung von Gerbirgen und Sediment-Becken sowie die Verformung des Kontaktes zwischen Grundgebirge und Stedimenten. Die zwei dimensionalen (2-D) Verformungs-Prozesse die zu den genannten Strukturen führen sind bereits sehr gut untersucht. Einige Prozesse wäh-rend starker 3-D Verformung sind hingegen noch unvollständig verstanden. Einer dieser 3-D Prozesse ist die seitliche Fortpflanzung der beschriebenen Strukturen, so wie die seitliche Fort-pflanzung von Falten und Cusbate-Lobate Strukturen senkrecht zur Verkürzungsrichtung und die seitliche Fortpflanzung von Pinch-and-Swell Strukturen othogonal zur Streckungsrichtung. Insbesondere interessieren wir uns für Faltendecken, liegende Falten mit Amplituden von mehr als 10 km. Faltendecken entstehen vermutlich durch duktile Verscherung. Sie zeigen oft einen konstanten Scherungssinn und eine nicht-lineare zunahme der Scherverformung am überkipp-ten Schenkel. Die Faltenachsen der Morcles Decke in der Westschweiz fallen Richtung ONO während die Faltenachsen der östicher gelegenen Doldenhorn Decke gegen WSW einfallen. Diese entgegengesetzten Einfallrichtungen charakterisieren die Rawil Depression (Wildstrubel Depression). Die Morcles Decke ist überwiegend das Resultat von Verkürzung und Scherung parallel zu den Sedimentlagen. Während der Verkürzung verhielt sich der massive Kalkstein kompetenter als der Umliegende Mergel und Schiefer, was zur Verfaltetung Morcles Decke führ-te, vorallem in gegen Norden eifallenden überkippten Schenkel. Die Doldenhorn Decke weist dagegen einen viel kleineren überkippten Schenkel und eine stärkere Lokalisierung der Verfor-mung auf. Bis heute gibt es keine 3-D numerischen Studien, die die fundamentale Dynamik der Entstehung von grossen stark verformten 3-D Strukturen wie den Morcles und Doldenhorn Decken sowie der damit verbudenen Rawil Depression untersuchen. Wir betrachten die 3-D Ent-wicklung von geometrischen Instabilitäten sowie die Entstehung fon Faltendecken mit Hilfe von numerischen Simulationen basiert auf der Finite Elemente Methode (FEM). Die Simulation von geometrischen Instabilitäten, die aufgrund von Änderungen der Materialeigenschaften zwischen verschiedenen Gesteinseinheiten entstehen, erfortert einen numerischen Algorithmus, der in der Lage ist die Materialgrenzen mit starkem Kontrast der Materialeigenschaften (zum Beispiel zwi-schen Kalksteineinheiten und Mergel) für starke Verfomung genau aufzulösen. Um dem gerecht zu werden kombiniert unser FE Algorithmus eine numerische Contour-Linien-Technik und ein deformierbares Lagranges Netz mit Re-meshing. Mit dieser kombinierten Methode ist es mög-lich den anfänglichen Materialgrenzen mit dem FE Netz genau zu folgen und die geometrischen Instabilitäten genügend aufzulösen. Der Algorithmus ist in der Lage visko-elastische 3-D Ver-formung zu rechnen, wobei die viskose Rheologie mit Hilfe eines power-law Fliessgesetzes beschrieben wird. Mit dem numerischen Algorithmus untersuchen wir die Entstehung von 3-D Faltendecken, die seitliche Fortpflanzung der Faltung sowie der Cusbate-Lobate Strukturen die sich durch die Verkürzung eines mit Sediment gefüllten Halbgraben bilden. Dabei werden die anfänglichen geometrischen Instabilitäten der Faltung exakt mit dem FE Netz aufgelöst wäh-rend die Materialgranzen des Halbgrabens die Finiten Elemente durchschneidet. Desweiteren wird der 3-D Algorithmus auf die Einschnürung während der 3-D viskosen Plattenablösung und Subduktion angewandt. Die 3-D Resultate werden mit 2-D Ergebnissen und einer 1-D analyti-schen Lösung verglichen.

Mixed and Hybrid Models of Public Service Delivery

This symposium presents research from different contexts to improve our collective understanding of a variety of aspects of mixed forms of service delivery, be they mixed contracting at the level of the market (which is more common in the U.S.), or mixed management and ownership at the level of the firm (which is more common in Europe). The articles included in this special symposium examine the factors that give rise to mixed forms of service delivery (e.g., economic and fiscal stress, regulatory flexibility, geography, management) and how these factors impact their design and operation. Articles also explore the performance of mixed forms of service delivery relative to more conventional arrangements like contracted or direct service delivery. The articles contribute to a better theoretical and conceptual understanding of mixed/hybrid forms of services delivery.

Modelling the Evolution and Spread of HIV Immune Escape Mutants.

During infection with human immunodeficiency virus (HIV), immune pressure from cytotoxic T-lymphocytes (CTLs) selects for viral mutants that confer escape from CTL recognition. These escape variants can be transmitted between individuals where, depending upon their cost to viral fitness and the CTL responses made by the recipient, they may revert. The rates of within-host evolution and their concordant impact upon the rate of spread of escape mutants at the population level are uncertain. Here we present a mathematical model of within-host evolution of escape mutants, transmission of these variants between hosts and subsequent reversion in new hosts. The model is an extension of the well-known SI model of disease transmission and includes three further parameters that describe host immunogenetic heterogeneity and rates of within host viral evolution. We use the model to explain why some escape mutants appear to have stable prevalence whilst others are spreading through the population. Further, we use it to compare diverse datasets on CTL escape, highlighting where different sources agree or disagree on within-host evolutionary rates. The several dozen CTL epitopes we survey from HIV-1 gag, RT and nef reveal a relatively sedate rate of evolution with average rates of escape measured in years and reversion in decades. For many epitopes in HIV, occasional rapid within-host evolution is not reflected in fast evolution at the population level.