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2047:. The presence of these special steady-state points at certain values of a parameter (e.g. mass) is represented by a point and once the parameter passes a certain value, a qualitative change occurs, called a bifurcation, in which the nature of the space changes, with profound consequences for the protein concentrations: the cell cycle has phases (partially corresponding to G1 and G2) in which mass, via a stable point, controls cyclin levels, and phases (S and M phases) in which the concentrations change independently, but once the phase has changed at a bifurcation event ( 1966:. It is possibly a good example of a mathematical model as it deals with simple calculus but gives valid results. Two research groups have produced several models of the cell cycle simulating several organisms. They have recently produced a generic eukaryotic cell cycle model that can represent a particular eukaryote depending on the values of the parameters, demonstrating that the idiosyncrasies of the individual cell cycles are due to different protein concentrations and affinities, while the underlying mechanisms are conserved (Csikasz-Nagy et al., 2006). 203: 1923:, and its applications were developed in mathematical biology and especially in mathematical medicine. In a more general sense, MST is the theory of molecular categories defined as categories of molecular sets and their chemical transformations represented as set-theoretical mappings of molecular sets. The theory has also contributed to biostatistics and the formulation of clinical biochemistry problems in mathematical formulations of pathological, biochemical changes of interest to Physiology, Clinical Biochemistry and Medicine. 2013: 5067: 5728: 973: 5716: 1216: 960: 5748: 5738: 260: 1355:
of published authors contributing to this field. Many of the included examples are characterised by highly complex, nonlinear, and supercomplex mechanisms, as it is being increasingly recognised that the result of such interactions may only be understood through a combination of mathematical, logical, physical/chemical, molecular and computational models.
2051:), the system cannot go back to the previous levels since at the current mass the vector field is profoundly different and the mass cannot be reversed back through the bifurcation event, making a checkpoint irreversible. In particular the S and M checkpoints are regulated by means of special bifurcations called a 1902:
A model of a biological system is converted into a system of equations, although the word 'model' is often used synonymously with the system of corresponding equations. The solution of the equations, by either analytical or numerical means, describes how the biological system behaves either over time
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Several areas of specialized research in mathematical and theoretical biology as well as external links to related projects in various universities are concisely presented in the following subsections, including also a large number of appropriate validating references from a list of several thousands
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for ultrasensitive transcription factors, afterwards the parameters of the equations (rate constants, enzyme efficiency coefficients and Michaelis constants) must be fitted to match observations; when they cannot be fitted the kinetic equation is revised and when that is not possible the wiring
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Abstract relational biology (ARB) is concerned with the study of general, relational models of complex biological systems, usually abstracting out specific morphological, or anatomical, structures. Some of the simplest models in ARB are the Metabolic-Replication, or (M,R)--systems introduced by
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For example, abstract relational biology (ARB) is concerned with the study of general, relational models of complex biological systems, usually abstracting out specific morphological, or anatomical, structures. Some of the simplest models in ARB are the Metabolic-Replication, or
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to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.
1907:. There are many different types of equations and the type of behavior that can occur is dependent on both the model and the equations used. The model often makes assumptions about the system. The equations may also make assumptions about the nature of what may occur. 1931:
Theoretical approaches to biological organization aim to understand the interdependence between the parts of organisms. They emphasize the circularities that these interdependences lead to. Theoretical biologists developed several concepts to formalize this idea.
1648:. Phylogenetics is an area that deals with the reconstruction and analysis of phylogenetic (evolutionary) trees and networks based on inherited characteristics Traditional population genetic models deal with alleles and genotypes, and are frequently 1988:
To obtain these equations an iterative series of steps must be done: first the several models and observations are combined to form a consensus diagram and the appropriate kinetic laws are chosen to write the differential equations, such as
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A fixed mapping between an initial state and a final state. Starting from an initial condition and moving forward in time, a deterministic process always generates the same trajectory, and no two trajectories cross in state space.
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Baianu IC, Brown R, Georgescu G, Glazebrook JF (2006). "Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks".
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In analysis, the properties of the equations are used to investigate the behavior of the system depending on the values of the parameters and variables. A system of differential equations can be represented as a
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research. Describing systems in a quantitative manner means their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter. This requires precise
2024:, where each vector described the change (in concentration of two or more protein) determining where and how fast the trajectory (simulation) is heading. Vector fields can have several special points: a 2952: 1419:
An elaboration of systems biology to understand the more complex life processes was developed since 1970 in connection with molecular set theory, relational biology and algebraic biology.
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of biomolecular reactions in terms of sets of molecules and their chemical transformations represented by set-theoretical mappings between molecular sets. It was introduced by
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Many population genetics models assume that population sizes are constant. Variable population sizes, often in the absence of genetic variation, are treated by the field of
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Evolutionary biology has been the subject of extensive mathematical theorizing. The traditional approach in this area, which includes complications from genetics, is
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To fit the parameters, the differential equations must be studied. This can be done either by simulation or by analysis. In a simulation, given a starting
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diagram is modified. The parameters are fitted and validated using observations of both wild type and mutants, such as protein half-life and cell size.
1694:, selection acts directly on inherited phenotypes, without genetic complications. This approach has been mathematically refined to produce the field of 1427:
A monograph on this topic summarizes an extensive amount of published research in this area up to 1986, including subsections in the following areas:
3778: 2009:(list of the values of the variables), the progression of the system is calculated by solving the equations at each time-frame in small increments. 2196: 1793: â€“ continuous time with memory of past events, discrete state space, waiting times of events (or transitions between states) discretely occur. 1280: 3306:
Wolkenhauer O, Ullah M, Kolch W, Cho KH (September 2004). "Modeling and simulation of intracellular dynamics: choosing an appropriate framework".
3854: 3753: 1862: 1252: 2938: 2551: 6271: 5784: 2069: 230: 1259: 4156: 4057: 2104: 1672: 2981: 2581:"Complex Systems Analysis of Arrested Neural Cell Differentiation during Development and Analogous Cell Cycling Models in Carcinogenesis" 3614: 3589: 3564: 1004: 2891: 1266: 6250: 4283: 3639: 2666: 1739: 296: 3450: 3419:
13th International Conference on Computational Intelligence Methods for Bioinformatics and Biostatistics, Stirling, UK, 1–3 Sep 2016
3412:"Inference in a Partial Differential Equations Model of Pulmonary Arterial and Venous Blood Circulation using Statistical Emulation" 1752: 2749: 1640:, via his work on quantitative genetics. Another important branch of population genetics that led to the extensive development of 2815: 1248: 3091: 1345:
experimentation due to ethical considerations, risk, unreliability and other complications involved in human and animal research
6245: 4242: 3548: 3492: 2129: 1941: 910: 5075: 4215: 1857: 905: 17: 2633: 4663: 3734: 2778: 2465: 2442: 1100:, theoretical biology employs several fields of mathematics, and has contributed to the development of new techniques. 1981:(whereas a model describing a statistical distribution of protein concentrations in a population of cells is called a 1671:
are another famous example. Population dynamics overlap with another active area of research in mathematical biology:
1571:(also known as theoretical neuroscience or mathematical neuroscience) is the theoretical study of the nervous system. 5777: 4688: 4029: 4010: 3969: 3946: 3927: 3904: 3885: 3821: 3805: 3521: 3434: 3028: 2791: 1299: 223: 2164: 1159:: Malthus argued that growth would be exponential (he uses the word "geometric") while resources (the environment's 1827: 3349: 1273: 1998: 1732: 1052:
to investigate the principles that govern the structure, development and behavior of the systems, as opposed to
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have been proposed and analyzed, and provide important results that may be applied to health policy decisions.
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which deals with the conduction of experiments to test scientific theories. The field is sometimes called
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Fussenegger M, Bailey JE, Varner J (July 2000). "A mathematical model of caspase function in apoptosis".
3250: 2109: 2089: 2056: 1668: 1645: 59: 31: 2837: 2193: 1130: 5139: 2266:"Modeling mammary organogenesis from biological first principles: Cells and their physical constraints" 1831: 1812: 1568: 3757: 5174: 5134: 5099: 4711: 4290: 4267: 4235: 2558: 1994: 1625: 990: 275: 181: 171: 161: 4195: 5741: 4454: 4263: 2552:"Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models" 1782: 1683: 1129:' 1789 essay on the growth of the human population was based on the concept of exponential growth. 900: 3173:
Oprisan SA, Oprisan A (2006). "A Computational Model of Oncogenesis using the Systemic Approach".
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Research Report Communicated to the Institute of Genomic Biology, University of Illinois at Urbana
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Robert Rosen in 1957–1958 as abstract, relational models of cellular and organismal organization.
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in spirals consisting of 21 (blue) and 13 (aqua). Such arrangements have been noticed since the
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Interest in the field has grown rapidly from the 1960s onwards. Some reasons for this include:
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The Theoretical Biologist's Toolbox. Quantitative Methods for Ecology and Evolutionary Biology
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Wang Y, Brodin E, Nishii K, Frieboes HB, Mumenthaler SM, Sparks JL, Macklin P (January 2021).
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A random mapping between an initial state and a final state, making the state of the system a
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is very complex and has been the subject of intense study, since its misregulation leads to
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Algebraic biology (also known as symbolic systems biology) applies the algebraic methods of
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Making Sense of Life: Explaining Biological Development with Models, Metaphors and Machines
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Nonlinear Dynamics and Chaos: Applications to Physics, Biology, Chemistry, and Engineering
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A better representation, which handles the large number of variables and parameters, is a
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Kuznetsov AV, Avramenko AA (April 2009). "A macroscopic model of traffic jams in axons".
2139: 2124: 2114: 2040: 1920: 1816: 1675:, the study of infectious disease affecting populations. Various models of the spread of 1656: 1590: 1404: 1077: 1045: 943: 933: 721: 593: 285: 4128: 4079: 3133: 2685: 2392: 1609:, and changes in the frequencies of existing alleles and genotypes at a small number of 6240: 6194: 6174: 6159: 5984: 5979: 5636: 5616: 5601: 5428: 5423: 5221: 5169: 5052: 5047: 4962: 4917: 4844: 4766: 4716: 4278: 4273: 4099: 3999: 3916: 3681: 3392: 3331: 3190: 3150: 3117: 2928: 2760: 2745: 2705: 2532: 2349: 2324: 2300: 2277: 2265: 2241: 2044: 2029: 2025: 1982: 1872: 1808: 1765: 1758: 1687: 1663:
formulated the first principle of population dynamics, which later became known as the
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effects at a large number of gene loci are considered, together with the assumption of
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Life Itself: A Comprehensive Inquiry Into the Nature, Origin, and Fabrication of Life
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in 1957–1958 as abstract, relational models of cellular and organismal organization.
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in 1879, in an account notable for being the first use of a mathematical argument in
938: 821: 701: 558: 391: 329: 202: 4148: 4103: 3396: 1383:'s Work-Constraints cycles, and more recently the notion of closure of constraints. 5904: 5731: 5348: 5035: 4922: 4532: 4495: 4380: 4350: 4170: 4132: 4083: 3720: 3673: 3422: 3376: 3335: 3315: 3280: 3182: 3145: 3137: 3066:"Computer models and automata theory in biology and medicine | KLI Theory Lab" 2709: 2689: 2588: 2536: 2524: 2494: 2406: 2396: 2344: 2336: 2295: 2287: 2236: 2228: 2084: 2052: 1974: 1613: 1557: 1376: 1147:
to show how powerful the effect of natural selection would be, unless one includes
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revolution, which are difficult to understand without the use of analytical tools
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applied mathematics to describe the effect of smallpox on the human population.
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Proceedings of the National Academy of Sciences of the United States of America
2144: 1953: 1891: 1835: 1823: 1479: 1156: 1126: 964: 688: 498: 156: 3284: 3186: 2838:"Computer Simulations and the Question of Computability of Biological Systems" 2528: 1977:) of the protein inside a single typical cell; this type of model is called a 6265: 6124: 6019: 5909: 5884: 5879: 5566: 5463: 5353: 5328: 5323: 5216: 5164: 5159: 4937: 4854: 4756: 4721: 4490: 3825: 3708: 3538: 2953:"bibliography for category theory/algebraic topology applications in physics" 2759:. Computer Algebra in Biology. Tokyo: Universal Academy Press. Archived from 2648: 2593: 2580: 2119: 2079: 1990: 1878: 1852: 1633: 1617: 1191: 1183: 1081: 1072:
Mathematical biology aims at the mathematical representation and modeling of
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The following is a list of mathematical descriptions and their assumptions.
1462:, abstract categories in relational biology, metabolic-replication systems, 6169: 6149: 6114: 6109: 6099: 6094: 6074: 6054: 5964: 5934: 5894: 5874: 5864: 5844: 5839: 5834: 5829: 5611: 5591: 5556: 5551: 5541: 5536: 5516: 5496: 5408: 5378: 5338: 5318: 5308: 5288: 5283: 5278: 5273: 5154: 5144: 5119: 4776: 4610: 4527: 4485: 4346: 4095: 3704: 3388: 3327: 3292: 3159: 2701: 2420: 2401: 2372: 2358: 2340: 2309: 2250: 2033: 2021: 1915:
Molecular set theory (MST) is a mathematical formulation of the wide-sense
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Mathematical Theories of Populations: Demographics, Genetics and Epidemics
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The earlier stages of mathematical biology were dominated by mathematical
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Mathematics has been used in biology as early as the 13th century, when
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and can be used to make mathematical models of a wide variety of plants.
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The term "theoretical biology" was first used as a monograph title by
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May RM (February 2004). "Uses and abuses of mathematics in biology".
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have traditionally been the dominant fields of mathematical biology.
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Hurlbert SH (1990). "Spatial Distribution of the Montane Unicorn".
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to describe a growing population of rabbits. In the 18th century,
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This area has received a boost due to the growing importance of
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MontĂŠvil M, Speroni L, Sonnenschein C, Soto AM (October 2016).
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Modelling electrical properties of muscle interactions, as in
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Mathematical Modeling : Mathematical Models in Medicine
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Life's Other Secret: The New Mathematics of the Living World
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to help understand complex, non-linear mechanisms in biology
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The rapid growth of data-rich information sets, due to the
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Computer Models and Automata Theory in Biology and Medicine
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SIAM and Society of Mathematical Biology, National Meeting
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described the evolutionary benefits of what is now called
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The Evolution of Complexity by Means of Natural Selection
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Noè U, Chen WW, Filippone M, Hill N, Husmeier D (2017).
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Modelling the movement of interacting cell populations
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Charles Ehresmann's Centennial Conference Proceedings
2869:"Natural Transformations Models in Molecular Biology" 1174: in 1920. One founding text is considered to be 4164: 3748: 3746: 3409: 2335:(3). The American Society for Cell Biology: 227–40. 3981:"Biologist Salary | Payscale". Payscale.Com, 2021, 2667:"Biological organisation as closure of constraints" 2323:Robeva R, Davies R, Hodge T, Enyedi A (Fall 2010). 1395:to the study of biological problems, especially in 1240:. Unsourced material may be challenged and removed. 3998: 3957: 3918:Modelling Biological Populations in Space and Time 3915: 3508:Churchland PS, Koch C, Sejnowski TJ (March 1994). 3270: 3743: 3516:. Vol. 3. World Scientific. pp. 25–34. 3045:"Dual Tessellation â€“ from Wolfram MathWorld" 2507: 1636:made fundamental advances in statistics, such as 1431:in biology and medicine, arterial system models, 1323:Recent development of mathematical tools such as 6263: 4216:The Collection of Biostatistics Research Archive 3875: 3698: 2721: 2719: 1947: 1888:Spatial distribution modeling using plot samples 1523:Mathematical modelling of intracellular dynamics 3855:Budapest University of Technology and Economics 3851:"The Molecular Network Dynamics Research Group" 2578: 1863:Philosophical Transactions of the Royal Society 1811:for numerical simulation methods, specifically 1773:Stochastic processes (random dynamical systems) 1520:Mathematical modelling of scar tissue formation 3251:"Jonathan Sherratt's Research: Scar Formation" 3172: 2664: 2483:"Mathematical Biology is Good for Mathematics" 1729: â€“ discrete time, continuous state space. 1486:, relational biology and organismic theories. 1358: 1133:formulated the logistic growth model in 1836. 5778: 4236: 3615:"The mechanochemical theory of morphogenesis" 3590:"Leah Edelstein-Keshet: Research Interests f" 3514:Biology And Computation: A Physicist's Choice 3453:. Integrativebiology.ox.ac.uk. Archived from 3209:"MCRTN â€“ About tumour modelling project" 2892:"Quantum Interactomics and Cancer Mechanisms" 2716: 2070:Biological applications of bifurcation theory 1761: â€“ discrete time, discrete state space. 1563: 998: 224: 4157:Notices of the American Mathematical Society 4058:Notices of the American Mathematical Society 4047: 3894: 3451:"Integrative Biology â€“ Heart Modelling" 2270:Progress in Biophysics and Molecular Biology 2221:Progress in Biophysics and Molecular Biology 2105:Mathematical modelling of infectious disease 3474: 3068:. Theorylab.org. 2009-05-26. Archived from 3016: 2980:. PlanetPhysics. 2009-01-24. Archived from 1717:Deterministic processes (dynamical systems) 5785: 5771: 4243: 4229: 3899:(Reprinted ed.). Philadelphia: SIAM. 3479:Fundamentals of Computational Neuroscience 1701: 1414: 1334:power, which facilitates calculations and 1005: 991: 231: 217: 6251:Timeline of biology and organic chemistry 4050:"Getting Started in Mathematical Biology" 4005:. Princeton: Princeton University Press. 3149: 2937:) CS1 maint: location missing publisher ( 2592: 2498: 2410: 2400: 2365: 2348: 2299: 2281: 2240: 2211: 1926: 1869:Travelling waves in a wound-healing assay 1740:Numerical ordinary differential equations 1300:Learn how and when to remove this message 3955: 3663: 3230:"Jonathan Sherratt's Research Interests" 2776: 2011: 1753:Numerical partial differential equations 1526:Mathematical modelling of the cell cycle 1016: 5792: 4165:Kroc J, Balihar K, Matejovic M (2019). 3936: 3913: 2744: 1910: 1897: 1759:Logical deterministic cellular automata 1574: 1478:models and complete self-reproduction, 1367:Other approaches include the notion of 14: 6264: 4149:"Why Is Mathematical Biology So Hard?" 4110: 4019: 3996: 3536: 2911: 2889: 2813: 2725: 2631: 2549: 2453: 2371: 1973:these models show the change in time ( 1669:Lotka–Volterra predator-prey equations 1466:applications in biology and medicine, 1249:"Mathematical and theoretical biology" 6246:Nobel Prize in Physiology or Medicine 5766: 4224: 3795: 3512:. In Gutfreund H, Toulouse G (eds.). 3510:"What Is Computational Neuroscience?" 3089: 6272:Mathematical and theoretical biology 5737: 4211:The Society for Mathematical Biology 4143: 3939:Introduction to Mathematical Biology 2914:"Category Theory and Living Systems" 2579:Baianu I, Prisecaru V (April 2012). 2480: 2130:Spring school on theoretical biology 1842: 1386: 1349: 1238:adding citations to reliable sources 1209: 1064:to stress the mathematical side, or 1044:which employs theoretical analysis, 1034:Mathematical and theoretical biology 5747: 4065: 3779:"Abstract Relational Biology (ARB)" 3308:IEEE Transactions on NanoBioscience 3047:. Mathworld.wolfram.com. 2010-03-03 2835: 1997:for enzyme substrate reactions and 1858:The Chemical Basis of Morphogenesis 1529:Mathematical modelling of apoptosis 1490:Modeling cell and molecular biology 1423:Computer models and automata theory 1182:, and other early pioneers include 24: 4664:Evolutionary developmental biology 4040: 3468: 2612:"Research in Mathematical Biology" 1163:) could only grow arithmetically. 1021:Yellow chamomile head showing the 25: 6283: 4689:Post-transcriptional modification 4204: 4137:10.1038/scientificamerican0388-80 4113:"How the leopard gets its spots?" 4048:Hoppensteadt F (September 1995). 3094:. Maths.gla.ac.uk. Archived from 3017:Preston K, Duff MJ (1985-02-28). 2665:MontĂŠvil M, Mossio M (May 2015). 2212:Longo G, Soto AM (October 2016). 1847:One classic work in this area is 1828:stochastic differential equations 1096:Because of the complexity of the 5746: 5736: 5727: 5726: 5714: 5065: 3642:. Maths.ox.ac.uk. Archived from 3617:. Maths.ox.ac.uk. Archived from 3567:. Maths.ox.ac.uk. Archived from 2755:. In Anai H, Horimoto K (eds.). 2292:10.1016/j.pbiomolbio.2016.08.004 2233:10.1016/j.pbiomolbio.2016.06.005 1214: 1205: 1151:'s discussion of the effects of 1108: 1076:, using techniques and tools of 972: 971: 958: 258: 201: 3843: 3814: 3789: 3771: 3756:. PlanetPhysics. Archived from 3692: 3657: 3632: 3607: 3582: 3557: 3530: 3501: 3443: 3403: 3360: 3342: 3299: 3264: 3243: 3222: 3201: 3166: 3109: 3083: 3058: 3037: 3010: 2995: 2970: 2955:. PlanetPhysics. Archived from 2945: 2905: 2883: 2861: 2847: 2829: 2807: 2780:Cancer Modelling and Simulation 2770: 2738: 2732:Mathematical Models in Medicine 2658: 2625: 2572: 2543: 1971:ordinary differential equations 1789:Non-Markovian processes â€“ 1733:Ordinary differential equations 1534:Modelling physiological systems 1502:Mechanics of biological tissues 1225:needs additional citations for 4024:. Cambridge University Press. 3878:Mathematical Models in Biology 3640:"Biological pattern formation" 2879:. Bethesda, MD: 230–232. 1983. 2674:Journal of Theoretical Biology 2474: 2447: 2427: 2316: 2257: 2205: 2194:Careers in theoretical biology 2186: 2157: 2095:Journal of Theoretical Biology 1993:for stoichiometric reactions, 1746:Partial differential equations 13: 1: 3868: 3800:. Columbia University Press. 3565:"Travelling waves in a wound" 1948:Model example: the cell cycle 1546:Multi-scale modelling of the 3427:10.1007/978-3-319-67834-4_15 2460:. Harvard University Press. 2329:CBE: Life Sciences Education 1884:Biological pattern formation 1877:A mechanochemical theory of 7: 4250: 4175:10.13140/RG.2.2.29919.30887 3983:Biologist Salary | PayScale 3876:Edelstein-Keshet L (2004). 3543:. Oxford University Press. 2110:Metabolic network modelling 2062: 2057:infinite period bifurcation 1999:Goldbeter–Koshland kinetics 1861:, published in 1952 in the 1791:generalized master equation 1505:Theoretical enzymology and 1359:Abstract relational biology 1170:in 1901, and soon after by 1080:. It can be useful in both 1048:and abstractions of living 32:Biological Theory (journal) 10: 6288: 3142:10.1038/s41598-020-78780-7 2786:. Chapman Hall/CRC Press. 2694:10.1016/j.jtbi.2015.02.029 2647:(1): 11–36. Archived from 2214:"Why do we need theories?" 1951: 1813:dynamic Monte Carlo method 1569:Computational neuroscience 1564:Computational neuroscience 1341:An increasing interest in 1103: 141:Relationship with sciences 29: 6233: 5800: 5708: 5677: 5239: 5209: 5175:Polymerase chain reaction 5135:Green fluorescent protein 5085: 5074: 5063: 4971: 4903: 4835: 4775: 4712:Earliest known life forms 4697: 4644: 4561: 4468: 4308: 4299: 4258: 3285:10.1016/j.mbs.2009.01.005 3187:10.1007/s10516-005-4943-x 2529:10.1007/s10516-005-3973-8 1995:Michaelis-Menten kinetics 1727:Difference equations/Maps 1673:mathematical epidemiology 1626:quasi-linkage equilibrium 911:List of unsolved problems 3895:Hoppensteadt F (1993) . 3754:"molecular set category" 3273:Mathematical Biosciences 3020:Modern Cellular Automata 2933:: CS1 maint: location ( 2919:. In Ehresmann A (ed.). 2594:10.1038/npre.2012.7101.1 2481:Reed M (November 2015). 2437:, New York: John Wiley, 2151: 2090:Ewens's sampling formula 1969:By means of a system of 1940:--systems introduced by 1783:probability distribution 1684:evolutionary game theory 1601:, the appearance of new 1514:modelling and simulation 1435:models, biochemical and 1131:Pierre François Verhulst 906:List of research methods 5227:species discovery curve 4355:Response to environment 4088:10.1126/science.1094442 3727:Oxford University Press 3475:Trappenberg TP (2002). 3320:10.1109/TNB.2004.833694 2032:, either a source or a 1702:Mathematical biophysics 1665:Malthusian growth model 1415:Complex systems biology 1338:not previously possible 379:Response to environment 5860:Biological engineering 5700:Plant morphology terms 5304:Biological engineering 4986:Biological interaction 4190:Cite journal requires 3985:. Accessed 3 May 2021. 3796:Rosen R (2005-07-13). 3092:"rwo_research_details" 3090:Ogden R (2004-07-02). 2814:Witten M, ed. (1986). 2757:Algebraic Biology 2005 2632:Jungck JR (May 1997). 2402:10.1073/pnas.171326298 2341:10.1187/cbe.10-03-0019 2016: 1927:Organizational biology 1832:Fokker–Planck equation 1030: 896:List of biology awards 504:Biological engineering 5945:Developmental biology 5920:Computational biology 5900:Cellular microbiology 5389:Developmental biology 5364:Computational biology 5344:Cellular microbiology 4684:Mendelian inheritance 4596:Energy transformation 3002:"Cellular Automata". 2730:. In Witten M (ed.). 2049:Cell cycle checkpoint 2015: 1979:deterministic process 1781:with a corresponding 1686:, developed first by 1630:quantitative genetics 1200:Conrad Hal Waddington 1020: 589:Developmental biology 564:Computational biology 544:Cellular microbiology 6165:Reproductive biology 6050:Mathematical biology 5975:Evolutionary biology 5925:Conservation biology 5607:Reproductive biology 5493:Mathematical biology 5419:Evolutionary biology 5369:Conservation biology 5180:Two-hybrid screening 5150:Protein purification 4981:Biogeochemical cycle 4943:Internal environment 4591:Cellular respiration 3956:Strogatz SH (2001). 3719:, Sprevak M (eds.). 3369:Nature Biotechnology 2433:Ian Stewart (1998), 2135:Statistical genetics 1911:Molecular set theory 1898:Mathematical methods 1638:analysis of variance 1584:evolutionary biology 1575:Evolutionary biology 1454:, cancer modelling, 1442:, quantum automata, 1405:molecular structures 1393:symbolic computation 1234:improve this article 1145:evolutionary ecology 1074:biological processes 1058:mathematical biology 1054:experimental biology 929:Agricultural science 807:Reproductive biology 693:Mathematical biology 619:Evolutionary biology 569:Conservation biology 106:Discrete mathematics 5950:Ecological genetics 5794:Branches of biology 5394:Ecological genetics 5105:Gel electrophoresis 5095:Genetic engineering 5048:Population dynamics 4958:Reproductive system 4129:1988SciAm.258c..80M 4117:Scientific American 4080:2004Sci...303..790M 3990:Theoretical biology 3937:Rubinow SI (1975). 3211:. Calvino.polito.it 3134:2021NatSR..11.1710W 2777:Preziosi L (2003). 2686:2015JThBi.372..179M 2393:2001PNAS...98.8928M 2140:Theoretical ecology 2125:Population genetics 2115:Molecular modelling 2041:bifurcation diagram 1921:Anthony Bartholomay 1817:Gillespie algorithm 1657:population dynamics 1622:linkage equilibrium 1591:population genetics 1091:mathematical models 1078:applied mathematics 1066:theoretical biology 1046:mathematical models 934:Biomedical sciences 594:Ecological genetics 246:Part of a series on 40:Part of a series on 18:Theoretical biology 6241:History of biology 6175:Structural biology 6160:Relational biology 5985:Generative biology 5980:Freshwater biology 5721:Biology portal 5617:Structural biology 5602:Relational biology 5429:Generative biology 5424:Freshwater biology 5222:mark and recapture 5170:Restriction enzyme 4963:Respiratory system 4918:Circulatory system 4845:Epidermis (botany) 4111:Murray JD (1988). 3997:Bonner JT (1988). 3914:Renshaw E (1991). 3822:"The JJ Tyson Lab" 3122:Scientific Reports 3004:Los Alamos Science 2912:Kainen PC (2005). 2890:Baianu IC (2004). 2803:on March 10, 2012. 2726:Baianu IC (1987). 2550:Baianu IC (2004). 2487:Notices of the AMS 2454:Keller EF (2002). 2199:2019-09-14 at the 2045:bifurcation theory 2017: 1983:stochastic process 1873:Swarming behaviour 1809:Monte Carlo method 1766:Cellular automaton 1688:John Maynard Smith 1176:On Growth and Form 1031: 965:Biology portal 817:Structural biology 802:Relational biology 629:Generative biology 624:Freshwater biology 207:Mathematics Portal 6259: 6258: 6180:Synthetic biology 6060:Molecular biology 5915:Cognitive biology 5760: 5759: 5622:Synthetic biology 5502:Molecular biology 5359:Cognitive biology 5235: 5234: 5061: 5060: 4752:Natural selection 4533:Organic compounds 4430:Scientific method 4420:Emergent property 4361:Hierarchy of life 4331:Energy processing 4020:Mangel M (2006). 3550:978-0-19-850942-4 3540:SAC Phylogenetics 3537:Semple C (2003). 3494:978-0-19-851582-1 3356:on July 28, 2007. 2614:. Maths.gla.ac.uk 2585:Nature Precedings 2493:(10): 1172–1176. 2100:Logistic function 1917:chemical kinetics 1843:Spatial modelling 1696:adaptive dynamics 1642:coalescent theory 1558:monodomain models 1496:molecular biology 1472:cellular automata 1448:molecular biology 1444:quantum computers 1429:computer modeling 1387:Algebraic biology 1350:Areas of research 1310: 1309: 1302: 1284: 1196:Nicolas Rashevsky 1188:Hans Leo Przibram 1172:Jakob von UexkĂźll 1161:carrying capacity 1153:population growth 1141:MĂźllerian mimicry 1040:, is a branch of 1023:Fibonacci numbers 1015: 1014: 939:Health technology 822:Synthetic biology 702:Molecular biology 559:Cognitive biology 354:Energy processing 241: 240: 196: 195: 27:Branch of biology 16:(Redirected from 6279: 5905:Chemical biology 5787: 5780: 5773: 5764: 5763: 5750: 5749: 5740: 5739: 5730: 5729: 5723: 5719: 5718: 5695:Ecological terms 5349:Chemical biology 5210:Field techniques 5083: 5082: 5069: 4928:Digestive system 4923:Endocrine system 4496:Chemical element 4455:Biology journals 4351:Self-replication 4306: 4305: 4245: 4238: 4231: 4222: 4221: 4199: 4193: 4188: 4186: 4178: 4161: 4153: 4140: 4107: 4062: 4054: 4035: 4016: 4004: 3975: 3963: 3952: 3933: 3921: 3910: 3891: 3863: 3862: 3857:. 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Archived from 2161: 2085:Entropy and life 2053:Hopf bifurcation 1975:dynamical system 1460:genetic networks 1305: 1298: 1294: 1291: 1285: 1283: 1242: 1218: 1210: 1155:that influenced 1123:Daniel Bernoulli 1119:Fibonacci series 1117:used the famous 1007: 1000: 993: 980: 975: 974: 967: 963: 962: 901:List of journals 549:Chemical biology 262: 243: 242: 233: 226: 219: 205: 69: 68: 37: 36: 21: 6287: 6286: 6282: 6281: 6280: 6278: 6277: 6276: 6262: 6261: 6260: 6255: 6229: 6190:Systems biology 6155:Quantum biology 5796: 5791: 5761: 5756: 5713: 5712: 5704: 5690:Botanical terms 5673: 5672: 5671: 5632:Systems biology 5597:Quantum biology 5231: 5205: 5087: 5077: 5070: 5057: 4967: 4948:Muscular system 4905: 4899: 4890:Vascular tissue 4837: 4831: 4771: 4732:History of life 4693: 4674:Gene regulation 4669:Gene expression 4640: 4557: 4464: 4295: 4254: 4249: 4207: 4202: 4191: 4189: 4180: 4179: 4151: 4074:(5659): 790–3. 4052: 4043: 4041:Further reading 4038: 4032: 4013: 3978: 3972: 3949: 3930: 3907: 3888: 3871: 3866: 3849: 3848: 3844: 3835: 3833: 3820: 3819: 3815: 3808: 3794: 3790: 3777: 3776: 3772: 3763: 3761: 3752: 3751: 3744: 3737: 3697: 3693: 3678:10.2307/3545216 3662: 3658: 3649: 3647: 3638: 3637: 3633: 3624: 3622: 3613: 3612: 3608: 3599: 3597: 3588: 3587: 3583: 3574: 3572: 3563: 3562: 3558: 3551: 3535: 3531: 3524: 3506: 3502: 3495: 3473: 3469: 3460: 3458: 3449: 3448: 3444: 3437: 3414: 3408: 3404: 3365: 3361: 3348: 3347: 3343: 3304: 3300: 3269: 3265: 3256: 3254: 3249: 3248: 3244: 3235: 3233: 3228: 3227: 3223: 3214: 3212: 3207: 3206: 3202: 3171: 3167: 3114: 3110: 3101: 3099: 3088: 3084: 3075: 3073: 3064: 3063: 3059: 3050: 3048: 3043: 3042: 3038: 3031: 3015: 3011: 3001: 3000: 2996: 2987: 2985: 2976: 2975: 2971: 2962: 2960: 2951: 2950: 2946: 2926: 2925: 2916: 2910: 2906: 2894: 2888: 2884: 2867: 2866: 2862: 2853: 2852: 2848: 2840: 2836:Lin HC (2004). 2834: 2830: 2818: 2812: 2808: 2800: 2794: 2783: 2775: 2771: 2763: 2752: 2743: 2739: 2724: 2717: 2669: 2663: 2659: 2651: 2636: 2630: 2626: 2617: 2615: 2610: 2609: 2602: 2577: 2573: 2564: 2562: 2554: 2548: 2544: 2523:(1–2): 65–122. 2512: 2508: 2479: 2475: 2468: 2452: 2448: 2432: 2428: 2387:(16): 8928–30. 2370: 2366: 2321: 2317: 2262: 2258: 2216: 2210: 2206: 2201:Wayback Machine 2191: 2187: 2178: 2176: 2163: 2162: 2158: 2154: 2149: 2065: 1958:The eukaryotic 1956: 1950: 1929: 1913: 1900: 1892:Turing patterns 1845: 1802:master equation 1779:random variable 1775: 1719: 1704: 1692:George R. Price 1577: 1566: 1507:enzyme kinetics 1480:chaotic systems 1468:automata theory 1464:category theory 1425: 1417: 1389: 1361: 1352: 1330:An increase in 1306: 1295: 1289: 1286: 1243: 1241: 1231: 1219: 1208: 1180:D'Arcy Thompson 1168:Johannes Reinke 1111: 1106: 1011: 970: 957: 956: 949: 948: 924: 916: 915: 882: 874: 873: 872: 871: 832:Systems biology 797:Quantum biology 442: 434: 433: 398: 383: 345: 334: 310: 302: 267: 265:Science of life 237: 192: 191: 142: 134: 133: 129:Decision theory 77: 35: 28: 23: 22: 15: 12: 11: 5: 6285: 6275: 6274: 6257: 6256: 6254: 6253: 6248: 6243: 6237: 6235: 6231: 6230: 6228: 6227: 6222: 6217: 6212: 6207: 6202: 6197: 6192: 6187: 6182: 6177: 6172: 6167: 6162: 6157: 6152: 6147: 6142: 6137: 6132: 6127: 6122: 6117: 6112: 6107: 6102: 6097: 6092: 6087: 6082: 6077: 6072: 6067: 6062: 6057: 6052: 6047: 6045:Marine biology 6042: 6037: 6032: 6027: 6022: 6017: 6012: 6007: 6002: 5997: 5992: 5987: 5982: 5977: 5972: 5967: 5962: 5957: 5952: 5947: 5942: 5937: 5932: 5927: 5922: 5917: 5912: 5907: 5902: 5897: 5892: 5887: 5882: 5877: 5872: 5867: 5862: 5857: 5855:Bioinformatics 5852: 5847: 5842: 5837: 5832: 5827: 5822: 5817: 5812: 5807: 5801: 5798: 5797: 5790: 5789: 5782: 5775: 5767: 5758: 5757: 5755: 5754: 5744: 5734: 5724: 5709: 5706: 5705: 5703: 5702: 5697: 5692: 5687: 5681: 5679: 5675: 5674: 5670: 5669: 5664: 5659: 5654: 5649: 5644: 5639: 5634: 5629: 5624: 5619: 5614: 5609: 5604: 5599: 5594: 5589: 5584: 5579: 5574: 5569: 5564: 5559: 5554: 5549: 5544: 5539: 5534: 5529: 5524: 5519: 5514: 5509: 5504: 5499: 5494: 5491: 5489:Marine biology 5486: 5481: 5476: 5471: 5466: 5461: 5456: 5451: 5446: 5441: 5436: 5431: 5426: 5421: 5416: 5411: 5406: 5401: 5396: 5391: 5386: 5381: 5376: 5371: 5366: 5361: 5356: 5351: 5346: 5341: 5336: 5331: 5326: 5321: 5316: 5311: 5306: 5301: 5299:Bioinformatics 5296: 5291: 5286: 5281: 5276: 5271: 5266: 5261: 5256: 5251: 5245: 5244: 5243: 5241: 5237: 5236: 5233: 5232: 5230: 5229: 5224: 5219: 5213: 5211: 5207: 5206: 5204: 5203: 5196: 5189: 5182: 5177: 5172: 5167: 5162: 5157: 5152: 5147: 5142: 5137: 5132: 5130:DNA microarray 5127: 5125:DNA sequencing 5122: 5117: 5115:Centrifugation 5112: 5110:Chromatography 5107: 5102: 5100:Transformation 5097: 5091: 5089: 5080: 5072: 5071: 5064: 5062: 5059: 5058: 5056: 5055: 5050: 5045: 5040: 5039: 5038: 5028: 5023: 5018: 5013: 5011:Climate change 5008: 5003: 4998: 4993: 4988: 4983: 4977: 4975: 4969: 4968: 4966: 4965: 4960: 4955: 4953:Nervous system 4950: 4945: 4940: 4935: 4930: 4925: 4920: 4915: 4909: 4907: 4901: 4900: 4898: 4897: 4892: 4887: 4885:Vascular plant 4882: 4877: 4872: 4867: 4862: 4857: 4852: 4847: 4841: 4839: 4833: 4832: 4830: 4829: 4824: 4823: 4822: 4817: 4812: 4807: 4802: 4792: 4787: 4781: 4779: 4773: 4772: 4770: 4769: 4764: 4759: 4754: 4749: 4744: 4742:Microevolution 4739: 4737:Macroevolution 4734: 4729: 4724: 4719: 4714: 4709: 4703: 4701: 4695: 4694: 4692: 4691: 4686: 4681: 4676: 4671: 4666: 4661: 4656: 4650: 4648: 4642: 4641: 4639: 4638: 4633: 4631:Photosynthesis 4628: 4623: 4618: 4613: 4608: 4603: 4598: 4593: 4588: 4586:Cell signaling 4583: 4578: 4573: 4567: 4565: 4559: 4558: 4556: 4555: 4550: 4545: 4540: 4535: 4530: 4525: 4520: 4515: 4514: 4513: 4503: 4498: 4493: 4488: 4483: 4478: 4472: 4470: 4469:Chemical basis 4466: 4465: 4463: 4462: 4457: 4452: 4447: 4442: 4437: 4435:Taxonomic rank 4432: 4427: 4422: 4417: 4415:Reductionistic 4412: 4358: 4323: 4318: 4312: 4310: 4303: 4297: 4296: 4294: 4293: 4288: 4287: 4286: 4276: 4271: 4262:Introduction ( 4259: 4256: 4255: 4248: 4247: 4240: 4233: 4225: 4219: 4218: 4213: 4206: 4205:External links 4203: 4201: 4200: 4192:|journal= 4162: 4147:(March 2004). 4141: 4108: 4063: 4044: 4042: 4039: 4037: 4036: 4030: 4017: 4011: 3993: 3992: 3991: 3987: 3986: 3977: 3976: 3970: 3953: 3947: 3941:. John Wiley. 3934: 3928: 3911: 3905: 3892: 3886: 3872: 3870: 3867: 3865: 3864: 3861:on 2012-02-10. 3842: 3813: 3806: 3788: 3785:on 2016-01-07. 3770: 3742: 3736:978-0198747826 3735: 3691: 3672:(3): 257–271. 3656: 3631: 3606: 3581: 3556: 3549: 3529: 3522: 3500: 3493: 3467: 3442: 3435: 3402: 3359: 3341: 3298: 3263: 3242: 3221: 3200: 3165: 3108: 3082: 3057: 3036: 3029: 3009: 2994: 2969: 2944: 2904: 2882: 2860: 2846: 2828: 2806: 2792: 2769: 2766:on 2006-06-16. 2737: 2715: 2657: 2654:on 2009-03-26. 2624: 2600: 2571: 2542: 2506: 2473: 2467:978-0674012509 2466: 2446: 2443:978-0471158455 2426: 2364: 2315: 2256: 2204: 2185: 2169:www.bath.ac.uk 2155: 2153: 2150: 2148: 2147: 2145:Turing pattern 2142: 2137: 2132: 2127: 2122: 2117: 2112: 2107: 2102: 2097: 2092: 2087: 2082: 2077: 2072: 2066: 2064: 2061: 2030:unstable point 1954:Cellular model 1952:Main article: 1949: 1946: 1928: 1925: 1912: 1909: 1899: 1896: 1895: 1894: 1889: 1886: 1881: 1875: 1870: 1844: 1841: 1840: 1839: 1836:Wiener process 1824:Markov process 1820: 1798:Markov process 1794: 1774: 1771: 1770: 1769: 1756: 1743: 1730: 1718: 1715: 1703: 1700: 1661:Thomas Malthus 1628:, one derives 1576: 1573: 1565: 1562: 1561: 1560: 1550: 1544: 1531: 1530: 1527: 1524: 1521: 1518: 1515: 1509: 1503: 1424: 1421: 1416: 1413: 1403:, analysis of 1388: 1385: 1360: 1357: 1351: 1348: 1347: 1346: 1339: 1328: 1321: 1308: 1307: 1222: 1220: 1213: 1207: 1204: 1157:Charles Darwin 1127:Thomas Malthus 1110: 1107: 1105: 1102: 1098:living systems 1062:biomathematics 1038:biomathematics 1013: 1012: 1010: 1009: 1002: 995: 987: 984: 983: 982: 981: 968: 951: 950: 947: 946: 941: 936: 931: 925: 922: 921: 918: 917: 914: 913: 908: 903: 898: 893: 883: 880: 879: 876: 875: 870: 869: 864: 859: 854: 849: 844: 839: 834: 829: 824: 819: 814: 809: 804: 799: 794: 789: 784: 779: 774: 769: 764: 759: 754: 749: 744: 739: 734: 729: 724: 719: 714: 709: 704: 699: 694: 691: 689:Marine biology 686: 681: 676: 671: 666: 661: 656: 651: 646: 641: 636: 631: 626: 621: 616: 611: 606: 601: 596: 591: 586: 581: 576: 571: 566: 561: 556: 551: 546: 541: 536: 531: 526: 521: 516: 511: 506: 501: 499:Bioinformatics 496: 491: 486: 481: 476: 471: 466: 461: 456: 451: 445: 444: 443: 440: 439: 436: 435: 432: 431: 409: 404: 397: 396: 382: 381: 376: 371: 366: 361: 356: 351: 344: 343: 338:Properties of 333: 332: 327: 322: 317: 311: 309:Key components 308: 307: 304: 303: 301: 300: 289: 288: 283: 278: 272: 269: 268: 263: 255: 254: 248: 247: 239: 238: 236: 235: 228: 221: 213: 210: 209: 198: 197: 194: 193: 190: 189: 184: 179: 174: 169: 164: 159: 154: 149: 143: 140: 139: 136: 135: 132: 131: 122: 117: 108: 103: 94: 89: 84: 78: 73: 72: 65: 64: 63: 62: 57: 49: 48: 42: 41: 26: 9: 6: 4: 3: 2: 6284: 6273: 6270: 6269: 6267: 6252: 6249: 6247: 6244: 6242: 6239: 6238: 6236: 6232: 6226: 6223: 6221: 6218: 6216: 6213: 6211: 6208: 6206: 6203: 6201: 6198: 6196: 6193: 6191: 6188: 6186: 6183: 6181: 6178: 6176: 6173: 6171: 6168: 6166: 6163: 6161: 6158: 6156: 6153: 6151: 6148: 6146: 6143: 6141: 6138: 6136: 6133: 6131: 6128: 6126: 6125:Phylogenetics 6123: 6121: 6118: 6116: 6113: 6111: 6108: 6106: 6103: 6101: 6098: 6096: 6093: 6091: 6088: 6086: 6083: 6081: 6078: 6076: 6073: 6071: 6068: 6066: 6063: 6061: 6058: 6056: 6053: 6051: 6048: 6046: 6043: 6041: 6038: 6036: 6033: 6031: 6028: 6026: 6023: 6021: 6020:Human biology 6018: 6016: 6013: 6011: 6008: 6006: 6003: 6001: 5998: 5996: 5993: 5991: 5988: 5986: 5983: 5981: 5978: 5976: 5973: 5971: 5968: 5966: 5963: 5961: 5958: 5956: 5953: 5951: 5948: 5946: 5943: 5941: 5938: 5936: 5933: 5931: 5928: 5926: 5923: 5921: 5918: 5916: 5913: 5911: 5910:Chronobiology 5908: 5906: 5903: 5901: 5898: 5896: 5893: 5891: 5888: 5886: 5885:Biotechnology 5883: 5881: 5880:Biostatistics 5878: 5876: 5873: 5871: 5868: 5866: 5863: 5861: 5858: 5856: 5853: 5851: 5848: 5846: 5843: 5841: 5838: 5836: 5833: 5831: 5828: 5826: 5823: 5821: 5818: 5816: 5813: 5811: 5808: 5806: 5803: 5802: 5799: 5795: 5788: 5783: 5781: 5776: 5774: 5769: 5768: 5765: 5753: 5745: 5743: 5735: 5733: 5725: 5722: 5717: 5711: 5710: 5707: 5701: 5698: 5696: 5693: 5691: 5688: 5686: 5683: 5682: 5680: 5676: 5668: 5665: 5663: 5660: 5658: 5655: 5653: 5650: 5648: 5645: 5643: 5640: 5638: 5635: 5633: 5630: 5628: 5625: 5623: 5620: 5618: 5615: 5613: 5610: 5608: 5605: 5603: 5600: 5598: 5595: 5593: 5590: 5588: 5585: 5583: 5580: 5578: 5575: 5573: 5570: 5568: 5567:Phylogenetics 5565: 5563: 5560: 5558: 5555: 5553: 5550: 5548: 5545: 5543: 5540: 5538: 5535: 5533: 5530: 5528: 5525: 5523: 5520: 5518: 5515: 5513: 5510: 5508: 5505: 5503: 5500: 5498: 5495: 5492: 5490: 5487: 5485: 5482: 5480: 5477: 5475: 5472: 5470: 5467: 5465: 5464:Human biology 5462: 5460: 5457: 5455: 5452: 5450: 5447: 5445: 5442: 5440: 5437: 5435: 5432: 5430: 5427: 5425: 5422: 5420: 5417: 5415: 5412: 5410: 5407: 5405: 5402: 5400: 5397: 5395: 5392: 5390: 5387: 5385: 5382: 5380: 5377: 5375: 5372: 5370: 5367: 5365: 5362: 5360: 5357: 5355: 5354:Chronobiology 5352: 5350: 5347: 5345: 5342: 5340: 5337: 5335: 5332: 5330: 5329:Biotechnology 5327: 5325: 5324:Biostatistics 5322: 5320: 5317: 5315: 5312: 5310: 5307: 5305: 5302: 5300: 5297: 5295: 5292: 5290: 5287: 5285: 5282: 5280: 5277: 5275: 5272: 5270: 5267: 5265: 5262: 5260: 5257: 5255: 5252: 5250: 5247: 5246: 5242: 5238: 5228: 5225: 5223: 5220: 5218: 5217:Belt transect 5215: 5214: 5212: 5208: 5202: 5201: 5197: 5195: 5194: 5190: 5188: 5187: 5183: 5181: 5178: 5176: 5173: 5171: 5168: 5166: 5165:Southern blot 5163: 5161: 5160:Northern blot 5158: 5156: 5153: 5151: 5148: 5146: 5143: 5141: 5138: 5136: 5133: 5131: 5128: 5126: 5123: 5121: 5118: 5116: 5113: 5111: 5108: 5106: 5103: 5101: 5098: 5096: 5093: 5092: 5090: 5084: 5081: 5079: 5073: 5068: 5054: 5051: 5049: 5046: 5044: 5041: 5037: 5034: 5033: 5032: 5029: 5027: 5024: 5022: 5019: 5017: 5014: 5012: 5009: 5007: 5004: 5002: 4999: 4997: 4994: 4992: 4989: 4987: 4984: 4982: 4979: 4978: 4976: 4974: 4970: 4964: 4961: 4959: 4956: 4954: 4951: 4949: 4946: 4944: 4941: 4939: 4938:Immune system 4936: 4934: 4931: 4929: 4926: 4924: 4921: 4919: 4916: 4914: 4911: 4910: 4908: 4902: 4896: 4893: 4891: 4888: 4886: 4883: 4881: 4878: 4876: 4873: 4871: 4868: 4866: 4863: 4861: 4858: 4856: 4855:Ground tissue 4853: 4851: 4848: 4846: 4843: 4842: 4840: 4834: 4828: 4825: 4821: 4818: 4816: 4813: 4811: 4808: 4806: 4803: 4801: 4798: 4797: 4796: 4793: 4791: 4788: 4786: 4783: 4782: 4780: 4778: 4774: 4768: 4765: 4763: 4760: 4758: 4757:Phylogenetics 4755: 4753: 4750: 4748: 4745: 4743: 4740: 4738: 4735: 4733: 4730: 4728: 4725: 4723: 4722:Genetic drift 4720: 4718: 4715: 4713: 4710: 4708: 4705: 4704: 4702: 4700: 4696: 4690: 4687: 4685: 4682: 4680: 4677: 4675: 4672: 4670: 4667: 4665: 4662: 4660: 4657: 4655: 4652: 4651: 4649: 4647: 4643: 4637: 4634: 4632: 4629: 4627: 4624: 4622: 4619: 4617: 4614: 4612: 4609: 4607: 4604: 4602: 4599: 4597: 4594: 4592: 4589: 4587: 4584: 4582: 4579: 4577: 4574: 4572: 4569: 4568: 4566: 4564: 4560: 4554: 4551: 4549: 4546: 4544: 4541: 4539: 4536: 4534: 4531: 4529: 4528:Nucleic acids 4526: 4524: 4521: 4519: 4516: 4512: 4509: 4508: 4507: 4504: 4502: 4499: 4497: 4494: 4492: 4491:Chemical bond 4489: 4487: 4486:Carbohydrates 4484: 4482: 4479: 4477: 4474: 4473: 4471: 4467: 4461: 4458: 4456: 4453: 4451: 4448: 4446: 4443: 4441: 4438: 4436: 4433: 4431: 4428: 4426: 4423: 4421: 4418: 4416: 4413: 4410: 4406: 4402: 4398: 4394: 4390: 4386: 4382: 4378: 4374: 4370: 4366: 4362: 4359: 4356: 4352: 4348: 4344: 4340: 4336: 4332: 4328: 4324: 4322: 4319: 4317: 4314: 4313: 4311: 4307: 4304: 4302: 4298: 4292: 4289: 4285: 4282: 4281: 4280: 4277: 4275: 4272: 4269: 4265: 4261: 4260: 4257: 4253: 4246: 4241: 4239: 4234: 4232: 4227: 4226: 4223: 4217: 4214: 4212: 4209: 4208: 4197: 4184: 4176: 4172: 4168: 4163: 4159: 4158: 4150: 4146: 4142: 4138: 4134: 4130: 4126: 4122: 4118: 4114: 4109: 4105: 4101: 4097: 4093: 4089: 4085: 4081: 4077: 4073: 4069: 4064: 4060: 4059: 4051: 4046: 4045: 4033: 4031:0-521-53748-7 4027: 4023: 4018: 4014: 4012:0-691-08493-9 4008: 4003: 4002: 3995: 3994: 3989: 3988: 3984: 3980: 3979: 3973: 3971:0-7382-0453-6 3967: 3962: 3961: 3954: 3950: 3948:0-471-74446-8 3944: 3940: 3935: 3931: 3929:0-521-44855-7 3925: 3920: 3919: 3912: 3908: 3906:0-89871-017-0 3902: 3898: 3893: 3889: 3887:0-07-554950-6 3883: 3879: 3874: 3873: 3860: 3856: 3852: 3846: 3832:on 2007-07-28 3831: 3827: 3826:Virginia Tech 3823: 3817: 3809: 3807:9780231075657 3803: 3799: 3792: 3784: 3780: 3774: 3760:on 2016-01-07 3759: 3755: 3749: 3747: 3738: 3732: 3728: 3724: 3723: 3718: 3714: 3710: 3706: 3702: 3695: 3687: 3683: 3679: 3675: 3671: 3667: 3660: 3646:on 2004-11-12 3645: 3641: 3635: 3621:on 2008-06-06 3620: 3616: 3610: 3596:on 2007-06-12 3595: 3591: 3585: 3571:on 2008-06-06 3570: 3566: 3560: 3552: 3546: 3542: 3541: 3533: 3525: 3523:9789814504140 3519: 3515: 3511: 3504: 3496: 3490: 3486: 3481: 3480: 3471: 3457:on 2009-01-13 3456: 3452: 3446: 3438: 3436:9783319678337 3432: 3428: 3424: 3420: 3413: 3406: 3398: 3394: 3390: 3386: 3382: 3381:10.1038/77589 3378: 3375:(2): 768–74. 3374: 3370: 3363: 3355: 3351: 3345: 3337: 3333: 3329: 3325: 3321: 3317: 3313: 3309: 3302: 3294: 3290: 3286: 3282: 3279:(2): 142–52. 3278: 3274: 3267: 3253:. Ma.hw.ac.uk 3252: 3246: 3232:. Ma.hw.ac.uk 3231: 3225: 3210: 3204: 3196: 3192: 3188: 3184: 3180: 3176: 3169: 3161: 3157: 3152: 3147: 3143: 3139: 3135: 3131: 3127: 3123: 3119: 3112: 3098:on 2009-02-02 3097: 3093: 3086: 3072:on 2011-07-28 3071: 3067: 3061: 3046: 3040: 3032: 3030:9780306417375 3026: 3022: 3021: 3013: 3005: 2998: 2984:on 2016-01-07 2983: 2979: 2973: 2959:on 2016-01-07 2958: 2954: 2948: 2940: 2936: 2930: 2922: 2915: 2908: 2900: 2893: 2886: 2878: 2874: 2870: 2864: 2856: 2850: 2839: 2832: 2824: 2817: 2810: 2799: 2795: 2793:1-58488-361-8 2789: 2782: 2781: 2773: 2762: 2758: 2751: 2747: 2741: 2733: 2729: 2722: 2720: 2711: 2707: 2703: 2699: 2695: 2691: 2687: 2683: 2679: 2675: 2668: 2661: 2650: 2646: 2642: 2635: 2628: 2613: 2607: 2605: 2595: 2590: 2586: 2582: 2575: 2561:on 2007-07-13 2560: 2553: 2546: 2538: 2534: 2530: 2526: 2522: 2518: 2510: 2501: 2496: 2492: 2488: 2484: 2477: 2469: 2463: 2459: 2458: 2450: 2444: 2440: 2436: 2430: 2422: 2418: 2413: 2408: 2403: 2398: 2394: 2390: 2386: 2382: 2378: 2375:(July 2001). 2374: 2368: 2360: 2356: 2351: 2346: 2342: 2338: 2334: 2330: 2326: 2319: 2311: 2307: 2302: 2297: 2293: 2289: 2284: 2279: 2275: 2271: 2267: 2260: 2252: 2248: 2243: 2238: 2234: 2230: 2226: 2222: 2215: 2208: 2202: 2198: 2195: 2189: 2175:on 2018-09-23 2174: 2170: 2166: 2160: 2156: 2146: 2143: 2141: 2138: 2136: 2133: 2131: 2128: 2126: 2123: 2121: 2120:Morphometrics 2118: 2116: 2113: 2111: 2108: 2106: 2103: 2101: 2098: 2096: 2093: 2091: 2088: 2086: 2083: 2081: 2080:Biostatistics 2078: 2076: 2073: 2071: 2068: 2067: 2060: 2058: 2054: 2050: 2046: 2042: 2037: 2035: 2031: 2027: 2023: 2014: 2010: 2008: 2003: 2000: 1996: 1992: 1991:rate kinetics 1986: 1984: 1980: 1976: 1972: 1967: 1965: 1961: 1955: 1945: 1943: 1939: 1933: 1924: 1922: 1918: 1908: 1906: 1893: 1890: 1887: 1885: 1882: 1880: 1879:morphogenesis 1876: 1874: 1871: 1868: 1867: 1866: 1864: 1860: 1859: 1854: 1853:morphogenesis 1850: 1837: 1833: 1829: 1825: 1821: 1818: 1814: 1810: 1807: 1803: 1799: 1795: 1792: 1788: 1787: 1786: 1784: 1780: 1767: 1764: 1760: 1757: 1754: 1751: 1747: 1744: 1741: 1738: 1734: 1731: 1728: 1725: 1724: 1723: 1714: 1711: 1709: 1699: 1697: 1693: 1689: 1685: 1680: 1678: 1674: 1670: 1666: 1662: 1658: 1653: 1651: 1647: 1646:phylogenetics 1643: 1639: 1635: 1634:Ronald Fisher 1631: 1627: 1623: 1619: 1618:infinitesimal 1615: 1612: 1608: 1607:recombination 1604: 1600: 1596: 1592: 1587: 1585: 1581: 1572: 1570: 1559: 1555: 1551: 1549: 1545: 1542: 1539:Modelling of 1538: 1537: 1536: 1535: 1528: 1525: 1522: 1519: 1516: 1513: 1510: 1508: 1504: 1501: 1500: 1499: 1497: 1492: 1491: 1487: 1485: 1481: 1477: 1473: 1469: 1465: 1461: 1457: 1453: 1449: 1445: 1441: 1438: 1434: 1430: 1420: 1412: 1410: 1407:and study of 1406: 1402: 1398: 1394: 1384: 1382: 1378: 1374: 1371:developed by 1370: 1365: 1356: 1344: 1340: 1337: 1333: 1329: 1326: 1322: 1319: 1315: 1314: 1313: 1304: 1301: 1293: 1282: 1279: 1275: 1272: 1268: 1265: 1261: 1258: 1254: 1251: â€“  1250: 1246: 1245:Find sources: 1239: 1235: 1229: 1228: 1223:This article 1221: 1217: 1212: 1211: 1206:Recent growth 1203: 1201: 1197: 1193: 1192:Vito Volterra 1189: 1185: 1184:Ronald Fisher 1181: 1177: 1173: 1169: 1164: 1162: 1158: 1154: 1150: 1146: 1142: 1138: 1134: 1132: 1128: 1124: 1120: 1116: 1109:Early history 1101: 1099: 1094: 1092: 1087: 1083: 1079: 1075: 1070: 1067: 1063: 1059: 1055: 1051: 1047: 1043: 1039: 1035: 1028: 1024: 1019: 1008: 1003: 1001: 996: 994: 989: 988: 986: 985: 979: 969: 966: 961: 955: 954: 953: 952: 945: 942: 940: 937: 935: 932: 930: 927: 926: 920: 919: 912: 909: 907: 904: 902: 899: 897: 894: 892: 888: 885: 884: 878: 877: 868: 865: 863: 860: 858: 855: 853: 850: 848: 845: 843: 840: 838: 835: 833: 830: 828: 825: 823: 820: 818: 815: 813: 810: 808: 805: 803: 800: 798: 795: 793: 790: 788: 785: 783: 780: 778: 775: 773: 770: 768: 767:Phylogenetics 765: 763: 760: 758: 755: 753: 750: 748: 745: 743: 740: 738: 735: 733: 730: 728: 725: 723: 720: 718: 715: 713: 710: 708: 705: 703: 700: 698: 695: 692: 690: 687: 685: 682: 680: 677: 675: 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Perseus. 3709:Copeland BJ 3699:Wooley TE, 3350:"Tyson Lab" 3128:(1): 1710. 2227:(1): 4–10. 1905:equilibrium 1849:Alan Turing 1822:Continuous 1456:neural nets 1437:oscillation 1369:autopoiesis 1336:simulations 1082:theoretical 1027:Middle Ages 862:Xenobiology 857:Virophysics 827:Systematics 782:Primatology 727:Ornithology 669:Ichthyology 654:Herpetology 649:Gerontology 614:Epigenetics 574:Cryobiology 464:Agrostology 454:Aerobiology 449:Abiogenesis 315:Cell theory 172:Linguistics 162:Computation 157:Geosciences 120:Probability 46:Mathematics 6205:Toxicology 6200:Teratology 6145:Proteomics 6130:Physiology 6070:Neontology 6035:Lipidology 6030:Immunology 6000:Geobiology 5960:Embryology 5940:Dendrology 5870:Biophysics 5850:Biogeology 5678:Glossaries 5647:Toxicology 5642:Teratology 5587:Proteomics 5572:Physiology 5512:Neontology 5479:Lipidology 5474:Immunology 5444:Geobiology 5404:Embryology 5384:Dendrology 5314:Biophysics 5294:Biogeology 5088:techniques 5043:Microbiome 4870:Plant stem 4762:Speciation 4707:Adaptation 4636:Prokaryote 4616:Metabolism 4576:Cell cycle 4407:>  4403:>  4399:>  4397:Population 4395:>  4391:>  4387:>  4383:>  4379:>  4375:>  4371:>  4367:>  4343:Regulation 4327:Adaptation 3869:References 3836:2008-09-10 3764:2010-03-17 3650:2010-03-17 3625:2010-03-17 3600:2005-02-26 3575:2010-03-17 3461:2010-03-17 3257:2010-03-17 3236:2010-03-17 3215:2010-03-17 3175:Axiomathes 3102:2010-03-17 3076:2010-03-17 3051:2010-03-17 2988:2010-03-17 2963:2010-03-17 2746:Barnett MP 2680:: 179–91. 2618:2008-09-10 2565:2011-08-07 2517:Axiomathes 2283:1702.03337 2179:2018-06-07 2075:Biophysics 1960:cell cycle 1708:biophysics 1677:infections 1650:stochastic 1401:proteomics 1290:March 2020 1260:newspapers 1178:(1917) by 847:Toxicology 842:Teratology 787:Proteomics 772:Physiology 712:Neontology 679:Lipidology 674:Immunology 644:Geobiology 604:Embryology 584:Dendrology 514:Biophysics 494:Biogeology 369:Regulation 349:Adaptation 182:Philosophy 125:Statistics 115:Set theory 6120:Phycology 6105:Pathology 6090:Osteology 6080:Nutrition 6040:Mammalogy 6015:Histology 5562:Phycology 5547:Pathology 5532:Osteology 5522:Nutrition 5484:Mammalogy 5459:Histology 5200:in silico 5076:Research 5053:Resources 5026:Ecosystem 5016:Community 5001:Biosphere 4913:Breathing 4795:Eukaryote 4777:Diversity 4727:Gene flow 4699:Evolution 4606:Eukaryote 4518:Molecules 4409:Biosphere 4405:Ecosystem 4401:Community 4373:Organelle 4268:Evolution 3922:. 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SIAM. 3717:Wilson R 3713:Bowen JP 3705:Maini PK 3701:Baker RE 3397:52802267 3389:10888847 3328:15473072 3293:19563741 3160:33462259 2748:(2006). 2702:25752259 2641:Bioscene 2421:11481461 2373:Mallet J 2359:20810955 2310:27544910 2251:27390105 2197:Archived 2063:See also 1826: â€“ 1800: â€“ 1599:mutation 1554:bidomain 1541:arterial 1452:genetics 1440:networks 1397:genomics 1381:Kauffman 1373:Maturana 1318:genomics 978:Category 944:Pharming 881:Research 852:Virology 837:Taxonomy 777:Pomology 707:Mycology 639:Genomics 634:Genetics 459:Agronomy 441:Branches 428:Protists 407:Bacteria 392:Kingdoms 297:timeline 286:Glossary 101:Analysis 97:Calculus 87:Geometry 6225:Zoology 5955:Ecology 5825:Anatomy 5742:Commons 5685:Biology 5667:Zoology 5399:Ecology 5269:Anatomy 5186:in vivo 5078:methods 5031:Habitat 5006:Climate 4991:Biomass 4973:Ecology 4820:Protist 4785:Archaea 4679:Genomes 4626:Mitosis 4621:Meiosis 4543:Polymer 4523:Monomer 4511:Quantum 4345:,  4341:,  4337:,  4333:,  4329:,  4316:Science 4301:Biology 4279:History 4274:Outline 4252:Biology 4145:Reed MC 4125:Bibcode 4076:Bibcode 4068:Science 3686:3545216 3336:1829220 3151:7813881 3130:Bibcode 2857:. 1986. 2710:4654439 2682:Bibcode 2537:9907900 2389:Bibcode 2350:2931670 2301:5563449 2242:5501401 2055:and an 1964:cancers 1616:. 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