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From Genetics to Mathematics.
Title:
From Genetics to Mathematics.
Author:
Miekisz, Jacek.
ISBN:
9789812837257
Personal Author:
Physical Description:
1 online resource (242 pages)
Series:
Series on Advances in Mathematics for Applied Sciences
Contents:
Contents -- Preface -- References -- 1. To understand nature D. Mackiewicz and S. Cebrat -- Contents -- 1.1 Introduction -- 1.2 Evolution of the DNA coding sequences -- 1.2.1 DNA double helix. -- 1.2.2 Chromosomes -- 1.2.3 Genomes -- 1.2.4 Topology of DNA replication -- 1.2.5 DNA asymmetry -- 1.2.6 Transcription -- 1.2.7 Genetic code, degeneracy, redundancy -- 1.2.8 Topology of coding sequences -- 1.2.9 Mutational pressure -- 1.3 Evolution of coding sequences. -- 1.3.1 Conditions for computer simulation of coding sequences evolution. -- 1.3.2 Dynamics of mutation accumulation and gene's elimination -- 1.3.3 The relation between the mutation rate and sequence divergence -- 1.4 Evolution of whole genomes -- Acknowledgements -- References -- 2. Evolution of the age-structured populations A. Laszkiewicz, P. Biecek, K. Borikowska, and S. Cebrat -- Contents -- 2.1 Introduction -- 2.2 The Penna model. -- 2.2.1 Description of the standard Penna model. -- 2.2.2 Results of standard simulations -- 2.2.3 The role of parameters in modeling the age-structured populations -- 2.2.3.1. Random death -- 2.2.3.2. Threshold T -- 2.3 The noisy Penna model -- 2.4 Mother care -- 2.5 Adaptation to the environmental conditions - learning -- 2.6 Additional risk factors -- 2.7 Ageing and the loss of complexity -- 2.8 Why women live longer than men -- 2.8.1 The role of the crossover rate for the strategies of evolution -- Acknowledgements -- References -- 3. Complementing haplotypes versus purifying selection W. Waga, M. Zawierta, J. Kowalski, and S. Cebrat -- Contents -- 3.1. Introduction -- 3.2. Mutations, frequency of defective alleles in the populations and complementation -- 3.3. Assumptions of the model -- 3.4. Positive selection for heterozygosity -- 3.5. Is the complementation strategy possible without an advantage of heterozygosity?.

3.6. Phase transition between purifying selection and complementation strategy -- 3.7. Simulations on a square lattice -- 3.7.1. Sympatric speciation -- 3.7.2. Some snapshots of expanding populations -- 3.7.3. Expansion rate and crossover frequency -- 3.7.4. Geographical distribution of defective genes -- 3.7.5. Distribution of accepted crossover events -- 3.7.6. How selection shapes the distribution of recombination spots along the chromosomes? -- 3.8. Phase transition and the length of chromosomes -- 3.9. Kinship and fecundity in the human population -- Acknowledgements -- References -- 4. Models of population dynamics and genetics R. Rudnicki -- Contents -- 4.1. Introduction -- 4.2. History of mathematical modeling in biology -- 4.3. Discrete models -- 4.4. TiIne continuous discrete structure models -- 4.5. Continuous structure generation models -- 4.6. Continuous time-structure models -- 4.7. Conclusion -- Acknowledgements -- References -- 5. Age-structured population models with genetics M. R. Dudek and T. Nadzieja -- Contents -- 5.1. Introduction -- 5.2. One-variable models, single species -- 5.3. A few-variable model -- 5.4. Models with genetics -- 5.5. Solving ODE and DDE in population model -- References -- 6. Computational modeling of evolutionary systems A. Lipowski and D. Lipowska -- Contents -- 6.1. Introduction -- 6.2. Coarse-grained versus individual-based modeling of an ecosystem -- 6.3. Lattice prey-predator models -- 6.4. Modeling of complex ecosystems -- 6.5. Multispecies prey-predator model and periodicity of extinctions -- 6.5.1. Model -- 6.5.2. Extinctions -- 6.5.3. Unique genetic code and the emergence of a multispecies ecosystem -- 6.5.4. Multispecies prey-predator model - summary and perspectives -- 6.6. Computational approaches to the evolution of language -- 6.6.1. Evolution and language development.

6.6.2. Language as a complex adapting system -- 6.6.3. Evolutionary naming game -- 6.6.4. Baldwin effect -- 6.7. Conclusions -- Acknowledgments -- References -- Biological Glossary -- Author Index -- Subject Index -- Photos.
Abstract:
This volume contains pedagogical and elementary introductions to genetics for mathematicians and physicists as well as to mathematical models and techniques of population dynamics. It also offers a physicist's perspective on modeling biological processes. Each chapter starts with an overview followed by the recent results obtained by authors. Lectures are self-contained and are devoted to various phenomena such as the evolution of the genetic code and genomes, age-structured populations, demography, sympatric speciation, the Penna model, Lotka-Volterra and other predator-prey models, evolutionary models of ecosystems, extinctions of species, and the origin and development of language. Authors analyze their models from the computational and mathematical points of view.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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