Bayesian fisheries stock assessment: integrating and updating knowledge

In this thesis the use of the Bayesian approach to statistical inference in fisheries stock assessment is studied. The work was conducted in collaboration of the Finnish Game and Fisheries Research Institute by using the problem of monitoring and prediction of the juvenile salmon population in the River Tornionjoki as an example application. The River Tornionjoki is the largest salmon river flowing into the Baltic Sea. This thesis tackles the issues of model formulation and model checking as well as computational problems related to Bayesian modelling in the context of fisheries stock assessment. Each article of the thesis provides a novel method either for extracting information from data obtained via a particular type of sampling system or for integrating the information about the fish stock from multiple sources in terms of a population dynamics model. Mark-recapture and removal sampling schemes and a random catch sampling method are covered for the estimation of the population size. In addition, a method for estimating the stock composition of a salmon catch based on DNA samples is also presented. For most of the articles, Markov chain Monte Carlo (MCMC) simulation has been used as a tool to approximate the posterior distribution. Problems arising from the sampling method are also briefly discussed and potential solutions for these problems are proposed. Special emphasis in the discussion is given to the philosophical foundation of the Bayesian approach in the context of fisheries stock assessment. It is argued that the role of subjective prior knowledge needed in practically all parts of a Bayesian model should be recognized and consequently fully utilised in the process of model formulation.

Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Biological data and model development for management of longfinned eels

Objectives: 1. Estimate population parameters required for a management model. These include survival, density, age structure, growth, age and size at maturity and at recruitment to the adult eel fishery. Estimate their variability among individuals in a range of habitats. 2. Develop a management population dynamics model and use it to investigate management options. 3. Establish baseline data and sustainability indicators for long-term monitoring. 4. Assess the applicability of the above techniques to other eel fisheries in Australia, in collaboration with NSW. Distribute developed tools via the Australia and New Zealand Eel Reference Group.

Studies on Plant Demography: Ranunculus Repens L., R. Bulbosus L. and R. Acris L.: III. A Mathematical Model Incorporating Multiple Modes of Reproduction

This paper presents a comparative population dynamics study of three closely related species of buttercups (Ranunculus repens, R. acris, and R. bulbosus). The study is based on an investigation of the behaviour of the seeds in soil under field conditions and a continuous monitoring of survival and reproduction of some 9000 individual plants over a period of 21/2 years in a coastal grassland in North Wales. The data were analysed with the help of an extension of Leslie's matrix method which makes possible an simultaneous treatment of vegetative and sexual reproduction. It was found that R. repens (a) depends more heavily on vegetative as compared with sexual reproduction, (b) shows indications of negatively density-dependent population regulation, and (c) exhibits little variation in population growth rates from site to site and from one year to the next. In contrast, R. bulbosus (a) depends exclusively on sexual reproduction, (b) shows indications of a positively density-dependent population behaviour, and (c) exhibits great variation in population growth rates from site to site and from one year to the next. R. acris exhibits an intermediate behaviour in all these respects. It is suggested that the attributes of R. repens are those expected of a species inhabiting a stable environment, while R. bulbosus exhibits some of the characteristics of a fugitive species.

Food intake, growth and social interactions of signal crayfish, Pacifastacus leniusculus (Dana)

The knowledge about the optimal rearing conditions, such as water temperature and quality, photoperiod and density, with the understanding of animal nutritional requirements forms the basis of economically stable aquaculture for freshwater crayfish. However, the shift from a natural environment to effective culture conditions induces several changes, not only at the population level, but also at the individual level. The social contacts between conspecifics increase with increasing animal density. The competition for limited resources (e.g. food, shelter, mates) is more severe with the presence of agonistic behaviour and may lead to unequal distribution of these. The objectives of this study were to: 1) study the distribution of a common food resource between communally reared signal crayfish (Pacifastacus leniusculus) and to assign potential feeding hierarchy on the basis of individual food intake measurements, 2) explore the possibilities of size distribution manipulations to affect population dynamics and food intake to improve growth and survival in culture and 3) study the effect of food ration and spatial distribution on food intake and to explore the effect of temperature and food ration on growth and body composition of freshwater crayfish. The feeding ranks between animals were assigned with a new method for individual food intake measurement of communally reared crayfish. This technique has a high feasibility and a great potential to be applied in crayfish aquaculture studies. In this study, signal crayfish showed high size-related variability in food consumption both among individuals within a group (inter-individual) and within individual day-to-day variation (intra-individual). Increased competition for food led to an unequal distribution of this resource and this may be a reason for large growth differences between animals. The consumption was significantly higher when reared individually in comparison with communal housing. These results suggest that communally housed crayfish form a feeding hierarchy and that the animal size is the major factor controlling the position in this hierarchy. The optimisation of the social environment ( social conditions ) was evaluated in this study as a new approach to crayfish aquaculture. The results showed that the absence of conspecifics (individual rearing vs. communal housing) affects growth rate, food intake and the proportion of injured animals, whereas size variation between animals influences the number and duration of agonistic encounters. In addition, animal size had a strong influence on the fighting success of signal crayfish reared in a social milieu with a wide size variation of conspecifics. Larger individuals initiated and won most of the competitions, which suggests size-based social hierarchy of P. leniusculus. This is further supported by the fact that the length and weight gain of smaller animals increased after size grading, maybe because of a better access to the food resource due to diminished social pressure. However, the high dominance index was not based on size under conditions of limited size variation, e.g. those characteristic of restocked natural populations and aquaculture, indicating the important role of behaviour on social hierarchy.

Modeling ecological and evolutionary processes in spatially structured populations

Many species inhabit fragmented landscapes, resulting either from anthropogenic or from natural processes. The ecological and evolutionary dynamics of spatially structured populations are affected by a complex interplay between endogenous and exogenous factors. The metapopulation approach, simplifying the landscape to a discrete set of patches of breeding habitat surrounded by unsuitable matrix, has become a widely applied paradigm for the study of species inhabiting highly fragmented landscapes. In this thesis, I focus on the construction of biologically realistic models and their parameterization with empirical data, with the general objective of understanding how the interactions between individuals and their spatially structured environment affect ecological and evolutionary processes in fragmented landscapes. I study two hierarchically structured model systems, which are the Glanville fritillary butterfly in the Åland Islands, and a system of two interacting aphid species in the Tvärminne archipelago, both being located in South-Western Finland. The interesting and challenging feature of both study systems is that the population dynamics occur over multiple spatial scales that are linked by various processes. My main emphasis is in the development of mathematical and statistical methodologies. For the Glanville fritillary case study, I first build a Bayesian framework for the estimation of death rates and capture probabilities from mark-recapture data, with the novelty of accounting for variation among individuals in capture probabilities and survival. I then characterize the dispersal phase of the butterflies by deriving a mathematical approximation of a diffusion-based movement model applied to a network of patches. I use the movement model as a building block to construct an individual-based evolutionary model for the Glanville fritillary butterfly metapopulation. I parameterize the evolutionary model using a pattern-oriented approach, and use it to study how the landscape structure affects the evolution of dispersal. For the aphid case study, I develop a Bayesian model of hierarchical multi-scale metapopulation dynamics, where the observed extinction and colonization rates are decomposed into intrinsic rates operating specifically at each spatial scale. In summary, I show how analytical approaches, hierarchical Bayesian methods and individual-based simulations can be used individually or in combination to tackle complex problems from many different viewpoints. In particular, hierarchical Bayesian methods provide a useful tool for decomposing ecological complexity into more tractable components.

Climate forcing on avian life history

In the 21st century, human-induced global climate change has been highlighted as one of the most serious threats to ecosystems worldwide. According to global climate scenarios, the mean temperature in Finland is expected to increase by 1.8 4.0°C by the end of the century. The regional and seasonal change in temperature has predicted to be spatially and temporally asymmetric, where the High-Arctic and Antarctic areas and winter and spring seasons have been projected to face the highest temperature increase. To understand how species respond to the ongoing climate change, we need to study how climate affects species in different phases of their life cycle. The impact of climate on breeding and migration of eight large-sized bird species was studied in this thesis, taking food availability into account. The findings show that climatic variables have considerable impact on the life-history traits of large-sized birds in northern Europe. The magnitude of climatic effects on migration and breeding was comparable with that of food supply, conventionally regarded as the main factor affecting these life-history traits. Based on the results of this thesis and the current climate scenarios, the following not mutually exclusive responses are possible in the near future. Firstly, asymmetric climate change may result in a mistiming of breeding because mild winters and early spring may lead to earlier breeding, whereas offspring are hatching into colder conditions which elevate mortality. Secondly, climate induced responses can differ between species with different breeding tactics (income vs. capital breeding), so that especially capital breeders can gain advantage on global warming as they can sustain higher energy resources. Thirdly, increasing precipitation has the potential to reduce the breeding success of many species by exposing nestlings to more severe post-hatching conditions and hampering the hunting conditions of parents. Fourthly, decreasing ice cover and earlier ice-break in the Baltic Sea will allow earlier spring migration in waterfowl. In eiders, this can potentially lead to more productive breeding. Fifthly, warming temperatures can favour parents preparing for breeding and increase nestling survival. Lastly, the climate-induced phenological changes in life history events will likely continue. Furthermore, interactions between climate and food resources can be complex and interact with each other. Eiders provide an illustrative example of this complexity, being caught in the crossfire between more benign ice conditions and lower salinity negatively affecting their prime food resource. The general conclusion is that climate is controlling not only the phenology of the species but also their reproductive output, thus affecting the entire population dynamics.

The ecology of the mountain hare (Lepus timidus L.) in managed boreal forests: habitat associations at different forest scales

Aims of this thesis This study is part of a larger hare project in Finland, which provides answers to basic ecological questions regarding the mountain hare. This study of the ecology of the mountain hare focuses in particular on different levels of managed boreal forest. The feeding habits and intensity of mountain hares in winter are explored, and the connections between mountain hares versus the forest structure are also studied (e.g. habitat use and the importance of different forest layers for hares). The use of the environment by hares at the landscape level was examined (forest patch structures), and the home ranges of mountain hares were studied. Finally, the productivity and survival rate of mountain hare populations were also studied (discussion e.g. predator effects on hare populations). Conclusions Feeding intensity seemed to be highest in the spring-winter, when home ranges were also largest. Favourable food species are covered by snow in winter and the mobility of hares is highest during late winter. A shortage of suitable food species may be problematic for hares, especially during the winter period. In this study mountain hares preferred a dense shrub layer at local level and deciduous and mixed tree forest over coniferous forest at the landscape level. Food and shelter are vital for hares and the preference for particular habitats may also affect the population dynamics of the mountain hare. It would be possible to improve the quality of food and shelter or at least prevent the most negative habitat changes through forest management. At a local level it is also possible to add supplementary food for hares through the winter period. The intensive clearing of young sapling stands and especially the removal of deciduous shrubs and trees reduces the quality of habitats for the mountain hare. Mountain hares primarily live in forest habitat and it is possible that changes in the forest structure play a crucial role in mountain hare habitat preference. Ecological knowledge of the mountain hare is vital to create habitat structure more suitable for the species. More deciduous trees should be saved in managing forests and the mechanical clearing of the shrub layer should be done carefully.

Ecological consequences of genetic modifications - an invasion analysis approach

Biological invasions are considered as one of the greatest threats to biodiversity, as they may lead to disruption and homogenization of natural communities, and in the worst case, to native species extinctions. The introduction of gene modified organisms (GMOs) to agricultural, fisheries and forestry practices brings them into contact with natural populations. GMOs may appear as new invasive species if they are able to (1) invade into natural habitats or (2) hybridize with their wild relatives. The benefits of GMOs, such as increased yield or decreased use of insecticides or herbicides in cultivation, may thus be reduced due the potential risks they may cause. A careful ecological risk analysis therefore has to precede any responsible GMO introduction. In this thesis I study ecological invasion in relation to GMOs, and what kind of consequences invasion may have in natural populations. A set of theoretical models that combine life-history evolution, population dynamics, and population genetics were developed for the hazard identification part of ecological risks assessment of GMOs. In addition, the potential benefits of GMOs in management of an invasive pest were analyzed. In the first study I showed that a population that is fluctuating due to scramble-type density dependence (due to, e.g., nutrient competition in plants) may be invaded by a population that is relatively more limited by a resource (e.g., light in plants) that is a cause of contest-type density dependence. This result emphasises the higher risk of invasion in unstable environments. The next two studies focused on escape of a growth hormone (GH) transgenic fish into a natural population. The results showed that previous models may have given too pessimistic a view of the so called Trojan gene -effect, where the invading genotype is harmful for the population as a whole. The previously suggested population extinctions did not occur in my studies, since the changes in mating preferences caused by the GH-fish were be ameliorated by decreased level of competition. The GH-invaders may also have to exceed a threshold density before invasion can be successful. I also showed that the prevalence of mature parr (aka. sneaker) strategy among GH-fish may have clear effect on invasion outcome. The fourth study assessed the risks and developed methods against the invasion of the Colorado Potato Beetle (CPB, Leptinotarsa decemlineata). I showed that the eradication of CPB is most important for the prevention of their establishment, but the cultivation of transgenic Bt-potato could also be effective. In general, my results emphasise that invasion of transgenic species or genotypes to be possible under certain realistic conditions and resulting in competitive exclusion, population decline through outbreeding depression and genotypic displacement of native species. Ecological risk assessment should regard the decline and displacement of the wild genotype by an introduced one as a consequence that is as serious as the population extinction. It will also be crucial to take into account different kinds of behavioural differences among species when assessing the possible hazards that GMOs may cause if escaped. The benefits found of GMO crops effectiveness in pest management may also be too optimistic since CPB may evolve resistance to Bt-toxin. The models in this thesis could be further applied in case specific risk assessment of GMOs by supplementing them with detailed data of the species biology, the effect of the transgene introduced to the species, and also the characteristics of the populations or the environments in the risk of being invaded.

The influence of eutrophication on sexual selection in sticklebacks

Jordens ekologiska system undergår för tillfället stora förändringar pga. människans aktiviteter. Ett växande antal studier visar att dessa förändringar påverkar naturliga och sexuella urvalet och därmed evolutiva processer. Målet med detta arbete var att undersöka effekterna av omgivningsförändringar på sexuella urvalet genom att använda den ökade övergödningen inom storpiggen Gasterosteus aculeatus lekområden som modell system. Sexuella urvalet är en viktig evolutiv kraft med följder på populations- och artnivå (Kapitel 1). Avhandlingens olika delar fokuserar på övergödningens effekter på upptäckandet av partners, användningen av visuella- och doftsignaler i partnersval, och fördelningen av parningsframgången mellan bobyggande hanar. I Kapitel II och III simuleras hur grumlighet orsakad av fytoplankton påverkar hastigheten med vilken potentiella partners påträffas, genom effekter på synligheten. Resultaten visar att normala algblomningar i Östersjön har en måttlig effekt på finnandet av potentiella partners. Detta tyder på att algblomningarna troligen inte kommer att minska på selektiva parningen pga. ökade sökkostnader. I Kapitel IV visas att storspiggen ändrar relativa användningen av olika signaler när vattnets grumlighet ökar; visuella signaler minskar i betydelse medan doftsignaler ökar i betydelse. Samtidigt underlättas användandet av doftsignaler av ändringar i vattnets kemiska sammansättning då fotosyntesen intensifieras (Kapitel V). Lek i övergödda vatten kan ändå vara kostsamt både på individ- och populationsnivån, då parasiterade hanar, som troligen är dåligt genetiskt anpassade till sin miljö, lyckas få mer ägg i sina bon än friskare hanar som troligen är av högre genetisk kvalitet (Kapitel VI). Övergödningen påverkar således partnersval och konkurrensen om partners genom att påverka upptäckandet av potentiella partners, evalueringen av partners och fördelningen av partners inom lekområdena. De följder detta kan ha för evolutionen av sexuellt selekterad egenskaper och för populationers dynamik och livskraft är dock oklara. Avhandlingen visar på svårigheten att förutse följderna av omgivningsförändringar för sexuella urvalet och effekterna på individ och populationsnivå.

Photophysics of conjugated polymers: interplay between Forster energy migration and defect concentration in shaping a photochemical funnel in PPV

Recent single molecule experiments have suggested the existence of a photochemical funnel in the photophysics of conjugated polymers, like poly[2-methoxy-5-(2'-ethylhexyl)oxy-1,4-phenylenevinylene] (MEH-PPV). The funnel is believed to be a consequence of the presence of conformational or chemical defects along the polymer chain and efficient non-radiative energy transfer among different chromophore segments. Here we address the effect of the excitation energy dynamics on the photophysics of PPV. The PPV chain is modeled as a polymer with the length distribution of chromophores given either by a Gaussian or by a Poisson distribution. We observe that the Poisson distribution of the segment lengths explains the photophysics of PPV better than the Gaussian distribution. A recently proposed version of an extended particle-in-a-box' model is used to calculate the exciton energies and the transition dipole moments of the chromophores, and a master equation to describe the excitation energy transfer among different chromophores. The rate of energy transfer is assumed to be given here, as a first approximation, by the well-known Forster expression. The observed excitation population dynamics confirms the photochemical funneling of excitation energy from shorter to longer chromophores of the polymer chain. The time scale of spectral shift and energy transfer for our model polymer, with realistic values of optical parameters, is in the range of 200-300 ps. We find that the excitation energy may not always migrate towards the longest chromophore segments in the polymer chain as the efficiency of energy transfer between chromophores depends on the separation distance between the two and their relative orientation.

Host-parasitoid relationship in different Cotesia melitaearum and Melitaea cinxia populations around the Baltic Sea

The relationship between hosts and parasites is one of the most studied interactions between living organisms, and it is both universal and common in nature. Parasitoids are special type of parasites whose offspring develop attached to or within a single host organism that it ultimately consumes and kills. Hosts are arthropods and most parasitoids belong to the insect order Hymenoptera. For almost two decades metapopulation research on the Glanville fritillary butterfly (Melitaea cinxia) has been conducted in the Åland Islands, Finland. The studies have been concerned with the population dynamics, evolution, genetics, behavior, natural history and life history characteristics of M. cinxia, as well as with species interacting with the butterfly. The parasitoids of M. cinxia have been under long term studies and much has been learned about specific host-parasitoid interactions during the past decade. The research for this Master s thesis was done in the Åland Islands during summer 2010. I conducted a reciprocal transplant style experiment in order to compare the performance of host butterflies (M. cinxia) under attack by different parasitoid wasps (C. melitaearum). I used hosts and parasitoids from five origins around the Baltic Sea: Öland, Uppland, Åland, Saaremaa and Pikku-Tytärsaari. The host-parasitoid relationship was studied in terms of host susceptibility and parasitoid virulence, addressing specifically the possible effects of inbreeding and local adaptation of both parasitoids and their hosts. I compared various factors such as host defence ratio, parasitoid development rate, cocoon production rate etc. I also conducted a small scale C. melitaearum egg development experiment and C. melitaearum external morphology comparison between different parasitoid populations. The results show that host resistance and parasitoid virulence differ between both host and parasitoid populations. For example, Öland hosts were most susceptible to parasitoids and especially vulnerable to Pikku-Tytärsaari wasps. Pikku-Tytärsaari wasps were most successful in terms of parasitoids virulence and efficiency except in Saaremaa hosts, where the wasp did not succeed. Saaremaa hosts were resistant except towards Åland parasitoids. I did not find any simple pattern concerning host resistance and parasitoid virulence between inbred and outbred populations. Also, the effect of local adaptation was not detected, perhaps because metapopulation processes disturb local adaptation of the studied populations. Morphological comparisons showed differences between studied wasp populations and sexual dimorphism was obvious with females being bigger that males. There were also interesting differences among populations in male and female wing shapes. The results raise many further questions. Especially interesting were Pikku-Tytärsaari wasps that did well in terms of efficiency and virulence. Pikku-Tytärsaari is a small, isolated island in the Gulf of Finland and both the host and parasitoids are extremely inbred. For the host and parasitoid to persist in the island, the host has to have some mechanisms to escape the parasitoid. Further research will be done on the subject to discover the mechanisms of Pikku-Tytärsaari host s ability to escape parasitism. Also, genetic analyses will be conducted in the near future to determine the relatedness of used C. melitaearum populations.

Optimal multispecies fishery management in the Baltic Sea: A bioeconomic analysis

The aim of the thesis is to assess the fishery of Baltic cod, herring and sprat by simulation over 50 years time period. We form a bioeconomic multispecies model for the species. We include species interactions into the model because especially cod and sprat stocks have significant effects on each other. We model the development of population dynamics, catches and profits of the fishery with current fishing mortalities, as well as with the optimal profit maximizing fishing mortalities. Thus, we see how the fishery would develop with current mortalities, and how the fishery should be developed in order to yield maximal profits. Especially cod stock has been quite low recently and by optimizing the fishing mortality it could get recovered. In addition, we assess what would happen to the fisheries of the species if more favourable environmental conditions for cod recruitment dominate in the Baltic Sea. The results may yield new information for the fisheries management. According to the results the fishery of Baltic cod, herring and sprat are not at the most profitable level. The fishing mortalities of each species should be lower in order to maximize the profits. By fishing mortality optimizing the net present value would be almost three times higher in the simulation period. The lower fishing mortality of cod would result in a cod stock recovery. If the environmental conditions in the Baltic Sea improved, cod stock would recover even without a decrease in the fishing mortality. Then the increased cod stock would restrict herring and sprat stock remarkably, and harvesting of these species would not be as profitable anymore.

Ribavirin-Induced Anemia in Hepatitis C Virus Patients Undergoing Combination Therapy

The current standard of care for hepatitis C virus (HCV) infection - combination therapy with pegylated interferon and ribavirin - elicits sustained responses in only similar to 50% of the patients treated. No alternatives exist for patients who do not respond to combination therapy. Addition of ribavirin substantially improves response rates to interferon and lowers relapse rates following the cessation of therapy, suggesting that increasing ribavirin exposure may further improve treatment response. A key limitation, however, is the toxic side-effect of ribavirin, hemolytic anemia, which often necessitates a reduction of ribavirin dosage and compromises treatment response. Maximizing treatment response thus requires striking a balance between the antiviral and hemolytic activities of ribavirin. Current models of viral kinetics describe the enhancement of treatment response due to ribavirin. Ribavirin-induced anemia, however, remains poorly understood and precludes rational optimization of combination therapy. Here, we develop a new mathematical model of the population dynamics of erythrocytes that quantitatively describes ribavirin-induced anemia in HCV patients. Based on the assumption that ribavirin accumulation decreases erythrocyte lifespan in a dose-dependent manner, model predictions capture several independent experimental observations of the accumulation of ribavirin in erythrocytes and the resulting decline of hemoglobin in HCV patients undergoing combination therapy, estimate the reduced erythrocyte lifespan during therapy, and describe inter-patient variations in the severity of ribavirin-induced anemia. Further, model predictions estimate the threshold ribavirin exposure beyond which anemia becomes intolerable and suggest guidelines for the usage of growth hormones, such as erythropoietin, that stimulate erythrocyte production and avert the reduction of ribavirin dosage, thereby improving treatment response. Our model thus facilitates, in conjunction with models of viral kinetics, the rational identification of treatment protocols that maximize treatment response while curtailing side effects.