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In [[mathematical biology]], the '''community matrix''' is the [[linearization]] of a [[generalized L ...4 =Petchey | first14= O.|title=Interaction Strengths in Food Webs: Issues and Opportunities |journal= Journal of Animal Ecology|volume=73|issue=5|pages=5 ...

...30 |doi=10.1017/S0013091500034428 |issn=1464-3839|doi-access=free }}</ref> and subsequently independently in 1959 by [[biophysics]] professor [[Heinz von ==Mathematical formula== ...

{{Short description|Mathematical model to describe the outbreak of an infectious disease}} ...ure is it was a model where the age-of-infection affected the transmission and removal rates. {{cn|date=May 2023}} ...

..., pharmaceutical drugs, or boundary species affect the steady-state fluxes and species concentrations. The flux response coefficient is defined by: The flux response coefficient is related to control coefficients and [[Elasticity coefficient|elasticities]] through the following relationship: ...

...asic form, one species grows best under equilibrium competitive conditions and another performs better under variable competitive conditions. Like all coe ...with zero curvature, positive effects on species with positive curvature, and negative effects on species with negative curvature. Thus, <math display="i ...

...ll |journal=In Proceedings of the 2 Nd International Conference on Systems Biology |date=2001 |pages=291–300 |citeseerx=10.1.1.324.922 }}</ref> ...and their importance in the analysis of eigenvectors, state observability and controllability of the continuous stirred tank reactor |journal=Chemical En ...

...on of [[heterozygosity]], or [[genetic diversity]], in a finite population and for the estimation of [[genetic distance]]s between populations of interest ...genetical models without recombination | journal = Theoretical Population Biology | volume = 7 | issue = 2| pages = 256–276 | doi=10.1016/0040-5809(75)90020- ...

{{Short description|Mathematical framework}} ...e="Sigmund1936">{{cite journal |last=Sigmund |first=Karl |title=Kolmogorov and population dynamics |journal=Giornale Istituto Ital. Attuari |volume=7 |pag ...

...tions of observables, can be defined using a control coefficient; but flux and concentration control coefficients are by far the most commonly used. ...n in terms of [[percentage]]s makes control coefficients easier to measure and more intuitively understandable. ...

...tion)|Kolmogorov forward equations]]'''<!--intentional link to DAB page--> and '''[[Kolmogorov backward equations]]''', characterize [[Markov process|cont ...kov processes, which are described by the [[Chapman–Kolmogorov equation]], and sought to derive a theory of continuous time Markov processes by extending ...

...| first2 = L.C. | last3 = Jones | first3 = D.S. | title = Fossil bivalves and the sclerochronological reawakening | date = 2021 | journal = Paleobiology ...al Issue: Age and Growth of Chondrichthyan Fishes: New Methods, Techniques and Analysis|url=https://books.google.com/books?id=ESUyc2dMrnEC&pg=PA301|date=5 ...

...Variables Characterizing Metabolic Systems |journal=Journal of Theoretical Biology |date=October 1996 |volume=182 |issue=3 |pages=259–268 |doi=10.1006/jtbi.19 The summation of the [[Control coefficient (biochemistry)|flux and concentration control coefficients]] were discovered independently by the ...

...le in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc. This list presents differential equations that h * [[Sturm–Liouville theory]] of [[orthogonal polynomials]] and separable partial differential equations ...

...|predator–prey]] dynamics. Where ''N'' is the population of a prey species and ''P'' that of a predator, the population dynamics are described by the foll .../S0022-5193(89)80211-5|volume=139|issue = 3|journal=Journal of Theoretical Biology|pages=311–326|year = 1989|last1 = Arditi|first1 = Roger|last2 = Ginzburg|fi ...

...th>K</math>, with <math>N</math> being the length of a string of evolution and <math>K</math> determining the level of landscape ruggedness. ...ring the organizational structure), which tend to interact with each other and affect profit in a complex fashion.<ref>{{cite journal | last1 = Levinthal ...

...competition, and it can prevent stronger species from becoming too common and crowding out other species. ...nisms of Maintenance of Species Diversity|journal=Annual Review of Ecology and Systematics|date=November 2000|volume=31|issue=1|pages=343–366|doi=10.1146/ ...

...a model]], which describes the dynamics of antagonistic populations (preys and predators) using [[differential equation]]s. ...mes that parasitoids search for hosts at random, and that both parasitoids and hosts are assumed to be distributed in a non-contiguous ("clumped") fashion ...

...ompetition-colonization trade-off in microbial communities | journal = BMC Biology | volume = 20 | issue = 1 | pages = 262 | date = November 2022 | pmid = 364 ...3C }}</ref> In which case some species are particularly good at colonizing and others have well-established survival abilities.<ref>{{cite journal | vauth ...

| work_institution = [[Courant Institute of Mathematical Sciences]] | thesis_title = Scheduling and Load Balancing ...

...or certain Markov chains arising in [[thermodynamics]],{{r|williams|hill}} and proved in full generality by {{harvtxt|Leighton|Rivest|1986}}, motivated by ...and end in that state have [[greatest common divisor]] one. An irreducible and aperiodic Markov chain necessarily has a stationary distribution, a probabi ...