Populations with interaction and environmental dependence: From few, (almost) independent, members into deterministic evolution of high densities

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Chigansky, PavelThe Hebrew University Of Jerusalem (författare)

Populations with interaction and environmental dependence: From few, (almost) independent, members into deterministic evolution of high densities

Artikel/kapitelEngelska2019

Förlag, utgivningsår, omfång ...

2019-03-05
Informa UK Limited,2019
electronicrdacarrier

Nummerbeteckningar

LIBRIS-ID:oai:research.chalmers.se:9faf4c48-b50a-48d8-b1de-1ebdc8858573
https://doi.org/10.1080/15326349.2019.1575755DOI
https://research.chalmers.se/publication/509309URI
https://research.chalmers.se/publication/510770URI
https://gup.ub.gu.se/publication/282304URI

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Språk:engelska
Sammanfattning på:engelska

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Anmärkningar

Many populations, e.g. not only of cells, bacteria, viruses, or replicating DNA molecules, but also of species invading a habitat, or physical systems of elements generating new elements, start small, from a few lndividuals, and grow large into a noticeable fraction of the environmental carrying capacity K or some corresponding regulating or system scale unit. Typically, the elements of the initiating, sparse set will not be hampering each other and their number will grow from Z0 = z0 in a branching process or Malthusian like, roughly exponential fashion, Zt ~atW, where Z t is the size at discrete time t → ∞, a > 1 is the offspring mean per individual (at the low starting density of elements, and large K), and W a sum of z0 i.i.d. random variables. It will, thus, become detectable (i.e. of the same order as K) only after around K generations, when its density Xt := Z t /K will tend to be strictly positive. Typically, this entity will be random, even if the very beginning was not at all stochastic, as indicated by lower case z0 , due to variations during the early development. However, from that time onwards, law of large numbers effects will render the process deterministic, though inititiated by the random density at time log K, expressed through the variable W. Thus, W acts both as a random veil concealing the start and a stochastic initial value for later, deterministic population density development. We make such arguments precise, studying general density and also system-size dependent, processes, as K → ∞. As an intrinsic size parameter, K may also be chosen to be the time unit. The fundamental ideas are to couple the initial system to a branching process and to show that late densities develop very much like iterates of a conditional expectation operator. The “random veil”, hiding the start, was first observed in the very concrete special case of finding the initial copy number in quantitative PCR under Michaelis-Menten enzyme kinetics, where the initial individual replication variance is nil if and only if the efficiency is one, i.e. all molecules replicate.

Ämnesord och genrebeteckningar

NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
TEKNIK OCH TEKNOLOGIER Industriell bioteknik Bioprocessteknik hsv//swe
ENGINEERING AND TECHNOLOGY Industrial Biotechnology Bioprocess Technology hsv//eng
NATURVETENSKAP Matematik Sannolikhetsteori och statistik hsv//swe
NATURAL SCIENCES Mathematics Probability Theory and Statistics hsv//eng
NATURVETENSKAP Matematik hsv//swe
NATURAL SCIENCES Mathematics hsv//eng
carrying capacity
threshold size
population dynamics
density dependence
Branching processes
Branching processes
carrying capacity
density dependence
population dynamics
threshold size
Mathematics

Biuppslag (personer, institutioner, konferenser, titlar ...)

Jagers, Peter,1941Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences(Swepub:cth)jagers (författare)
Klebaner, Fima C.Monash University (författare)
The Hebrew University Of JerusalemInstitutionen för matematiska vetenskaper (creator_code:org_t)

Sammanhörande titlar

Ingår i:Stochastic Models: Informa UK Limited35:2, s. 108-1181532-63491532-4214

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Av författaren/redakt...: Chigansky, Pavel; Jagers, Peter, 1 ...; Klebaner, Fima C ...

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NATURVETENSKAP: NATURVETENSKAP; och Matematik; och Beräkningsmatema ...

TEKNIK OCH TEKNOLOGIER: TEKNIK OCH TEKNO ...; och Industriell biot ...; och Bioprocessteknik

NATURVETENSKAP: NATURVETENSKAP; och Matematik; och Sannolikhetsteor ...

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Artiklar i publikationen: Stochastic Model ...

Av lärosätet: Chalmers tekniska högskola; Göteborgs universitet

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