| 1. |
- Ghersheen, Samia, 1985-
(författare)
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Dynamics of Coinfection : Complexity and Implications
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Living beings are always on risk from multiple infectious agents in individual or in groups. Though multiple pathogens' interactions have widely been studied in epidemiology. Despite being well known, the co-existence of these pathogens and their coinfection remained a mystery to be uncovered. Coinfection is one of the important and interesting phenomenon in multiple interactions when two infectious agents coexist at a time in a host. The aim of this thesis is to understand the complete dynamics of coinfection and the role of different factors affecting these interactions.Mathematical modelling is one of the tools to study the coinfection dynamics. Each model has its own limitations and choice of the model depends on the questions to be addressed. There is always a crosstalk between the choice of model and limitation of their solvability. The complexity of the problem defines the restriction in analytical possibilities.In this thesis we formulate and analyse the mathematical models of coinfection with different level of complexities. Since viral infections are a major class of infectious diseases, in the first three papers we formulated a susceptible, infected, recovered (SIR) model for coinfection of the two viral strains in a single host population introducing carrying capacity as limited growth factor in susceptible class. In the first study, we made some assumptions for the transmission of coinfection in the model. In the following papers, the analysis is expanded by relaxing these assumptions which has generated the complexity in dynamics. We showed that the dynamics of stable equilibrium points depends on the fundamental parameters including carrying capacity K. A parameter dependent transition dynamics exists starting from disease free state to a level where coinfection can persists only with susceptible class. A disease-free equilibrium point is stable only when K is small. With increase in carrying capacity to a level where only single infection can invade and persists. Further increase in carrying capacity becomes large enough for the existence and persistence of coinfection due to the high density of susceptible class. In paper I, we proved the existence of a globally stable equilibrium point for any set of parameter values, revealing persistence of disease in a population. This shows a close relationship between the intensity of infection and carrying capacity as a crucial parameter of the population. So there is always a positive correlation between risk of infection and carrying capacity which leads to destabilization of the population.In paper IV, we formulated mathematical models using different assumptions and multiple level of complexities to capture the effect of additional phenomena such as partial cross immunity, density dependence in each class and a role of recovered population in the dynamics. We found the basic reproduction number for each model which is the threshold that describes the invasion of disease in population. The basic reproduction number in each model shows that the persistence of disease or strains depends on the carrying capacity K. In the first model of this paper, we have also shown the local stability analysis of the boundary equilibrium points and showed that the recovered population is not uniformly bounded with respect to K.Paper V uses simulations to analyse the dynamics and specifically studies how temporal variation in the carrying capacity of the population affects its dynamics. The degree of autocorrelation in variability of carrying capacity influences whether the different classes exhibit temporal variation or not. The fact that the different classes respond differently to the variation depends in itself on whether their equilibrium densities show a dependence on the carrying capacity or not. An important result is that at high autocorrelation, the healthy part of the population is not affected by the external variation and at the same time the infected part of the population exhibits high variation. A transition to lower autocorrelation, more randomness, means that the healthy population varies over time and the size of the infected population decreases in variation.
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| 2. |
- Liu-Helmersson, Jing, 1960-
(författare)
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Climate Change, Dengue and Aedes Mosquitoes : Past Trends and Future Scenarios
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Background Climate change, global travel and trade have facilitated the spread of Aedes mosquitoes and have consequently enabled the diseases they transmit (dengue fever, Chikungunya, Zika and yellow fever) to emerge and re-emerge in uninfected areas. Large dengue outbreaks occurred in Athens in 1927 and in Portuguese island, Madeira in 2012, but there are almost no recent reports of Aedes aegypti, the principal vector, in Europe. A dengue outbreak needs four conditions: sufficient susceptible humans, abundant Aedes vector, dengue virus introduction, and conducive climate. Can Aedes aegypti establish themselves again in Europe in the near future if they are introduced? How do the current and future climate affect dengue transmission globally, and regionally as in Europe? This thesis tries to answer these questions.Methods Two process-based mathematical models were developed in this thesis. Model 1 describes a vector’s ability to transmit dengue – vectorial capacity – based on temperature and diurnal temperature range (DTR). Model 2 describes vector population dynamics based on the lifecycle of Aedes aegypti. From this model, vector abundance was estimated using both climate as a single driver, and climate together with human population and GDP as multiple drivers; vector population growth rate was derived as a threshold condition to estimate the vector’s invasion to a new place.Results Using vectorial capacity, we estimate dengue epidemic potential globally for Aedes aegypti and in Europe for Aedes aegypti and Aedes albopictus. We show that mean temperature and DTR are both important in modelling dengue transmission, especially in a temperate climate zone like Europe. Currently, South Europe is over the threshold for dengue epidemics if sufficient dengue vectors are present. Aedes aegypti is on the borderline of invasion into the southern tip of Europe. However, by end of this century, the invasion of Aedes aegypti may reach as far north as the middle of Europe under the business-as-usual climate scenario. Or it may be restricted to the south Europe from the middle of the century if the low carbon emission – Paris Agreement – is implemented to limit global warming to below 2°C.Conclusion Climate change will increase the area and time window for Aedes aegypti’s invasion and consequently the dengue epidemic potential globally, and in Europe in particular. Successfully achieving the Paris Agreement would considerably change the future risk scenario of a highly competent vector – Aedes aegypti’s – invasion into Europe. Therefore, the risk of transmission of dengue and other infectious diseases to the mainland of Europe depends largely on human efforts to mitigate climate change.
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| 3. |
- Fransson, Peter, 1988-
(författare)
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Optimal thinning : a theoretical investigation on individual-tree level
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Paper I: In paper I, we asked how a tree should optimally allocate its resources to maximize its fitness. We let a subject tree grow in an environment shaded by nearby competing trees. The competitors were assumed to have reached maturity and had stopped growing, thus creating a static light environment for the subject tree to grow in. The light environment was modeled as a logistic function. For the growth model we used the pipe model as a foundation, linking tree width and leaf mass. This allowed us to construct a dynamic tree-growth model where the tree can allocate biomass from photosynthesis (net productivity) to either stem-height growth, crown-size growth, or reproduction (seed production). Using Pontryagin's maximum principle we derived necessary conditions for optimal biomass allocation, and on that built a heuristic allocation model. The heuristic model states that the tree should first invest into crown-size and then switch to tree height-growth, and lastly invest into crown-size before the growth investments stop and all investments are allocated to reproduction. To test our heuristic method, we used it to determine the growth in several different light environments. The results were then compared to the optimal growth trajectories. The optimal growth was determined by applying dynamic programming. Our less computationally demanding heuristic performed very well in comparison. We also found there exist a critical crown-size: if the subject tree possessed a larger crown-size, the tree would be unable to reach up to the canopy height.Paper II: One of the most important aspects of modelling forest growth, and modelling growth of individual trees in general, is the competition between trees. A high level of competition pressure has a negative impact on the growth of individual trees. There are many ways of modelling competition, the most common one is by using a competition index. In this paper we tested 16 competition indices, in conjunction with a log-linear growth model, in terms of the mean squared error and the coefficient of determination. 5 competition indices are distance-independent (i.e. distance between the competitors are not taken into consideration) and 11 are distance-dependent. The data we used to fit our growth model, with accompanying competition index, was taken from an experimental site, in northern Sweden, of Norway spruce. The growth data for the Norway spruce comes from stands which were treated with one of two treatments, solid fertilization, liquid fertilization, or no treatment (control stand). We found that the distance-dependent indices perform better than the distance-independent. However, both the best distance-dependent and independent index performed overall well. We also found that the ranking of the indices was unaffected by the stand treatment, i.e. indices that work well for one treatment will work well for the others.Paper III: In this paper we studied how spatial distribution and size selection affect the residual trees, after a thinning operation, in terms of merchantable wood production and stand economy. We constructed a spatially explicit individual-based forest-growth model and fitted and validated the model against empirical data for Norway spruce stands in northern Sweden. To determine the cost for the forest operation we employed empirical cost functions for harvesting and forwarding. The income from the harvested timber is calculated from volume-price lists. The thinnings were determined by three parameters: the spatial evenness of residual trees, the size selection of removed trees, and the basal area reduction. In order to find tree selections fulfilling these constraints we used the metropolis algorithm. We varied these three constrains and applied them for thinning of different initial configurations of Norway spruce stands. The initial configurations for the stands where collected from empirical data. We found that changing the spatial evenness and size selection improved the net wood production and net present value of the stand up to 8%. However, the magnitude of improvement was dependent on the initial configuration (the magnitude of improvement varied between 1.7%—8%).Paper IV: With new technology and methods from remote sensing, such as LIDAR, becoming more prevalent in forestry, the ability to assess information on a detailed scale has become more available. Measurements for each individual tree can be more easily gathered on a larger scale. This type of data opens up for using individual-based model for practical precision forestry planning. In paper IV we used the individual-based model constructed in paper III to find the optimal harvesting time for each individual tree, such that the land expectation value is maximized. We employed a genetic algorithm to find a near optimal solution to our optimization. We optimized a number of initial Norway spruce stands (data obtained from field measurements). The optimal management strategy was to apply thinning from above. We also found that increasing the discount rate will decrease the time for final felling and increase basal area reduction for the optimal strategy. Decreasing relocation costs (the cost to bring machines to the stand) led to an increase in the number of optimal thinnings and postponed the first thinning. Our strategy was superior to both the unthinned strategy and a conventional thinning strategy, both in terms of land expectation value (>20% higher) and merchantable wood production.
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| 4. |
- Wickman, Jonas, 1985-
(författare)
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Evolution of Ecological Communities in Spatially Heterogeneous Environments
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Evolutionarily stable communities are the endpoints of evolution, and ecological communities whose traits are under selection will eventually settle into them. Hence, the properties of such communities are of particular interest, as they can persist over long evolutionary time scales. The notion of an evolutionarily stable strategy - an evolved strategy that cannot be beat by any other once established - has now been part of theoretical ecology for almost 50 years, and the theory for evolutionarily stable strategies and communities, and how they are reached has become increasingly versatile. However, for environments where conditions vary in space, so-called heterogeneous environments, efficient analytical and numerical tools for studying evolutionarily stable communities and how they come about have been lacking. Hence, many questions regarding how evolutionarily stable diversity is generated and maintained when ecological and evolutionary forces vary in space remain unexplored. In particular, how spatially averaged selection and selective forces derived from spatial variability can act together to either promote or inhibit evolutionarily stable diversity is not well understood. In this thesis, I use a two-pronged approach towards answering such questions by developing the necessary analytical and numerical tools for assembling and analyzing evolutionarily stable communities in heterogeneous environments, and by then employing these tools to study communities of resource competitors and food webs. Specifically, I derive expressions for directional and stabilizing/disruptive selection when the spatially heterogeneous ecological dynamics of a community are described by reaction-diffusion equations. These expressions allow us to understand selection across an environment in terms of local selection pressures, and also enable efficient numerical implementations of evolutionary community assembly procedures that lead to evolutionarily stable communities. Applied to the communities of resource competitors and food webs I find that the selective forces derived from spatially averaged selection and those derived from spatial variability can act both in concert or in opposition. If these forces act in opposition and if the spatial variability of local selection is high, a high diversity of organisms can form even when spatially averaged selection is stabilizing. In contrast, if spatially averaged selection is disruptive, it can prevent more diverse communities from forming by creating few globally unbeatable strategies. However, these forces can also act disruptively in concert to create more diverse communities. Together, these results demonstrate a surprising variety of qualitatively different outcomes when evolutionarily stable communities are assembled in heterogeneous environments.
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| 5. |
- Lindh, Magnus, 1973-
(författare)
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Evolution of Plants : a mathematical perspective
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The Earth harbors around 300 000 plant species. The rich and complex environment provided by plants is considered a key factor for the extraordinary diversity of the terrestrial fauna by, for example, providing food and shelter. This thesis contributes to the understanding of these questions by investigating how the interplay of physiology, demography, and evolution gives rise to variation and diversity in fundamental plant traits. This will help us answer questions such as: How has this amazing diversity of plant species emerged? Which mechanisms maintain diversity? How are plant strategies and plant diversity influenced by variations in the environment?A plant faces multiple problems to survive and reproduce successfully. These problems can be modeled by considering traits, trade-offs and a fitness measure. For example: How to maximize growth rate, while maximizing structural stability? I will investigate four plant models in order to understand the function of plants, and mechanisms promoting diversity. Paper I: We study how annual plants with and without growth constraints should optimize their flowering time when productivity or season length changes. With a dynamic ontogenetic growth model and optimal control theory we prove that a bang-bang reproductive control is optimal under constrained growth and constant mortality rate. We find that growth constraints can flip the direction of optimal phenological response for increasing productivity. The reason is that the growth rate of vegetative mass saturates at high productivity and therefore it is better to flower earlier and take advantage of a longer reproductive period. If season length extends equally both in the beginning and the end of the season, growth constraints control the direction of the optimal response as well. Our theory can help explaining phenological patterns along productivity gradients, and can be linked to empirical observations made on a calendar scale.Paper II: We introduce a new measure of tree crown-rise efficiency based on the loss of biomass of the tree during growth. The more mass the tree looses during growth, the less crown-rise efficient it is. Top-heavy shapes loose more biomass than bottom-heavy shapes. Light-use efficiency is defined as the mean light assimilation of the leaves in the crown times the ratio of leaf mass and total mass. We then study the trade-off between light-use efficiency to crown-rise efficiency for tree crown shapes. We assume that the total tree mass is constant, and a constant vertical light gradient represent the shading from a surrounding forest. We find large differences in crown shapes at intermediate vertical light gradient, when both self-shading and mean-field shading are important, suggesting light-use vs crown-rise efficiency as a new trade-off that can explain tree diversity. Our crown-rise efficiency measure could easily be integrated into existing forest models.Paper III: We extend an evolutionary tree crown model, where trees with different heights compete for light, with drought-induced mortality rates depending on ground-water availability and the depth of an optional taproot. The model does not include competition for ground water. Our model explains how ground-water availability can shape plant communities, when taproot and non-taproot strategies can coexist, and when only one of these strategies can persist. We investigate how emerging plant diversity varies with water table depth, soil water gradient and drought-induced mortality rate. The taproot enables plants to reach deep water, thus reducing mortality, but also carries a construction cost, thus inducing a trade-off. We find that taproots maintain plant diversity under increasing drought mortality, and that taproots evolve when groundwater is accessible at low depths. There are no viable strategies at high drought mortality and deep water table. Red Queen evolutionary dynamics appear at intermediate drought mortality in mixed communities with and without taproots, as the community never reaches a final evolutionarily stable composition.Paper IV: We extend a size-structured plant model, with self-shading and two evolving traits, crown top-heaviness and crown width-to-height ratio. The model allows us to identify salient trade-offs for the crown shape. The most important trade-off for top-heaviness is light-use efficiency vs crownrise efficiency, and the most important trade-off for width-to-height ratio is self-shading vs branch costs. We find that when the two traits coevolve; the outcome is a single common evolutionarily stable strategy (ESS), far away from the highest net primary production (NPP). When only sun angle is decreasing with increasing latitude both the crown width-to-height ratio and crown top-heaviness decrease. However, when light response in addition to the sun angle decreases with increasing latitude, the crown width-to-height ratio is nearly invariant of latitude except at low site productivity when the ratio decreases with latitude. Top-heaviness is always decreasing with increasing latitude. Finally, we find that crown top-heaviness increases with the NPP or leaf-area index (LAI) at ESS, but crown width-to-height ratio is maximal at an intermediate NPP or LAI.
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