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- Austin, Brian, et al.
(author)
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Sliding window discretization : A new method for multiple band matching of bacterial genotyping fingerprints
- 2004
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In: Bulletin of Mathematical Biology. - : Springer Science and Business Media LLC. - 0092-8240 .- 1522-9602. ; 66:6, s. 1575-1596
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Journal article (peer-reviewed)abstract
- Microbiologists have traditionally applied hierarchical clustering algorithms as their mathematical tool of choice to unravel the taxonomic relationships between micro-organisms. However, the interpretation of such hierarchical classifications suffers from being subjective, in that a variety of ad hoc choices must be made during their construction. On the other hand, the application of more profound and objective mathematical methods - such as the minimization of stochastic complexity - for the classification of bacterial genotyping fingerprints data is hampered by the prerequisite that such methods only act upon vectorized data. In this paper we introduce a new method, coined sliding window discretization, for the transformation of genotypic fingerprint patterns into binary vector format. In the context of an extensive amplified fragment length polymorphism (AFLP) data set of 507 strains from the Vibrionaceae family that has previously been analysed, we demonstrate by comparison with a number of other discretization methods that this new discretization method results in minimal loss of the original information content captured in the banding patterns. Finally, we investigate the implications of the different discretization methods on the classification of bacterial genotyping fingerprints by minimization of stochastic complexity, as it is implemented in the BinClass software package for probabilistic clustering of binary vectors. The new taxonomic insights learned from the resulting classification of the AFLP patterns will prove the value of combining sliding window discretization with minimization of stochastic complexity, as an alternative classification algorithm for bacterial genotyping fingerprints.
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- Björklund, Mats, et al.
(author)
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Environmental Fluctuations and Level of Density-Compensation Strongly Affects the Probability of Fixation and Fixation Times
- 2011
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In: Bulletin of Mathematical Biology. - : Springer Science and Business Media LLC. - 0092-8240 .- 1522-9602. ; 73:7, s. 1666-1681
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Journal article (peer-reviewed)abstract
- The probability of, and time to, fixation of a mutation in a population has traditionally been studied by the classic Wright-Fisher model where population size is constant. Recent theoretical expansions have covered fluctuating populations in various ways but have not incorporated models of how the environment fluctuates in combination with different levels of density-compensation affecting fecundity. We tested the hypothesis that the probability of, and time to, fixation of neutral, advantageous and deleterious mutations is dependent on how the environment fluctuates over time, and on the level of density-compensation. We found that fixation probabilities and times were dependent on the pattern of autocorrelation of carrying capacity over time and interacted with density-compensation. The pattern found was most pronounced at small population sizes. The patterns differed greatly depending on whether the mutation was neutral, advantageous, or disadvantageous. The results indicate that the degree of mismatch between carrying capacity and population size is a key factor, rather than population size per se, and that effective population sizes can be very low also when the census population size is far above the carrying capacity. This study highlights the need for explicit population dynamic models and models for environmental fluctuations for the understanding of the dynamics of genes in populations.
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- Bodin, Mats, et al.
(author)
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A systematic overview of Harvesting-Induced Maturation Evolution in Predator-Prey systems with three different Life-History Tradeoffs
- 2012
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In: Bulletin of Mathematical Biology. - : Springer. - 0092-8240 .- 1522-9602. ; 74:12, s. 2842-2860
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Journal article (peer-reviewed)abstract
- There are concerns that anthropogenic harvesting may cause phenotypic adaptive changes in exploited wild populations, in particular maturation at a smaller size and younger age. In this paper, we study the evolutionarily stable size at maturation of prey subjected to size-selective harvesting in a simple predator-prey model, taking into account three recognized life-history costs of early maturation, namely reduced fecundity, reduced growth, and increased mortality. Our analysis shows that harvesting large individuals favors maturation at smaller size compared to the unharvested system, independent of life-history tradeoff and the predator's prey-size preference. In general, however, the evolutionarily stable maturation size can either increase or decrease relative to the unharvested system, depending on the harvesting regime, the life-history tradeoff, and the predator's preferred size of prey. Furthermore, we examine how the predator population size changes in response to adaptive change in size at maturation of the prey. Surprisingly, in some situations, we find that the evolutionarily stable maturation size under harvesting is associated with an increased predator population size. This occurs, in particular, when early maturation trades off with growth rate. In total, we determine the evolutionarily stable size at maturation and associated predator population size for a total of forty-five different combinations of tradeoff, harvest regime, and predated size class.
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- Britton, Tom, et al.
(author)
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A Network Epidemic Model with Preventive Rewiring : Comparative Analysis of the Initial Phase
- 2016
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In: Bulletin of Mathematical Biology. - : Springer Science and Business Media LLC. - 0092-8240 .- 1522-9602. ; 78:12, s. 2427-2454
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Journal article (peer-reviewed)abstract
- This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate (and reconnect to non-infectious individuals with probability or else simply drop the edge if ), so-called preventive rewiring. The models are denoted SIR- and SEIR-, and we focus attention on the early stages of an outbreak, where we derive the expressions for the basic reproduction number and the expected degree of the infectious nodes using two different approximation approaches. The first approach approximates the early spread of an epidemic by a branching process, whereas the second one uses pair approximation. The expressions are compared with the corresponding empirical means obtained from stochastic simulations of SIR- and SEIR- epidemics on Poisson and scale-free networks. Without rewiring of exposed nodes, the two approaches predict the same epidemic threshold and the same for both types of epidemics, the latter being very close to the mean degree obtained from simulated epidemics over Poisson networks. Above the epidemic threshold, pairwise models overestimate the value of computed from simulations, which turns out to be very close to the one predicted by the branching process approximation. When exposed individuals also rewire with (perhaps unaware of being infected), the two approaches give different epidemic thresholds, with the branching process approximation being more in agreement with simulations.
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| 8. |
- Britton, Tom, et al.
(author)
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Stochastic Epidemics in Growing Populations
- 2014
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In: Bulletin of Mathematical Biology. - : Springer Science and Business Media LLC. - 0092-8240 .- 1522-9602. ; 76:5, s. 985-996
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Journal article (peer-reviewed)abstract
- Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that three different scenarios may occur: (i) an epidemic never takes off, (ii) an epidemic gets going and grows but at a slower rate than the community thus still being negligible in terms of population fractions, or (iii) an epidemic takes off and grows quicker than the community eventually leading to an endemic equilibrium. Depending on the parameter values, either scenario (i) is the only possibility, both scenarios (i) and (ii) are possible, or scenarios (i) and (iii) are possible.
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- Brännström, Åke, et al.
(author)
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Coupled map lattice approximations for spatially explicit individual-based models of ecology
- 2005
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In: Bulletin of Mathematical Biology. - : Springer Science and Business Media LLC. - 0092-8240 .- 1522-9602. ; 67:4, s. 663-682
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Journal article (peer-reviewed)abstract
- Spatially explicit individual-based models are widely used in ecology but they are often difficult to treat analytically. Despite their intractability they often exhibit clear temporal and spatial patterning. We demonstrate how a spatially explicit individual-based model of scramble competition with local dispersal can be approximated by a stochastic coupled map lattice. The approximation disentangles the deterministic and stochastic element of local interaction and dispersal. We are thus able to understand the individual-based model through a simplified set of equations. In particular, we demonstrate that demographic noise leads to increased stability in the dynamics of locally dispersing single-species populations. The coupled map lattice approximation has general application to a range of spatially explicit individual-based models. It provides a new alternative to current approximation techniques, such as the method of moments and reaction–diffusion approximation, that captures both stochastic effects and large-scale patterning arising in individual-based models.
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- Camitz, Martin, et al.
(author)
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The effect of time distribution shape on a complex epidemic model
- 2009
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In: Bulletin of Mathematical Biology. - : Springer Science and Business Media LLC. - 0092-8240 .- 1522-9602. ; 71:8, s. 1902-1913
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Journal article (peer-reviewed)abstract
- In elaborating a model of the progress of an epidemic, it is necessary to make assumptions about the distributions of latency times and infectious times. In many models, the often implicit assumption is that these times are independent and exponentially distributed. We explore the effects of altering the distribution of latency and infectious times in a complex epidemic model with regional divisions connected by a travel intensity matrix. We show a delay in spread with more realistic latency times. More realistic infectiousness times lead to faster epidemics. The effects are similar but accentuated when compared to a purely homogeneous mixing model.
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