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3.3: Eenvoudige kwantitatiewe genetika-modelle vir Browniese beweging - Biologie

3.3: Eenvoudige kwantitatiewe genetika-modelle vir Browniese beweging - Biologie


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Brownse beweging onder Genetiese Drift

Die eenvoudigste manier om Browniese evolusie van karakters te verkry, is wanneer evolusionêre verandering neutraal is, met eienskappe wat slegs verander as gevolg van genetiese drywing (bv. Hierdie aannames lyk waarskynlik onrealisties, veral as jy dink aan 'n eienskap soos die liggaamsgrootte van 'n akkedis! Maar ons sal later sien dat ons ook Brownse beweging kan aflei onder ander modelle, waarvan sommige seleksie behels.

Beskou die gemiddelde waarde van hierdie eienskap, $ar{z}$, in 'n populasie met 'n effektiewe populasiegrootte van Ne (dit is tegnies die variansie effektiewe populasie)2. Aangesien daar geen seleksie is nie, sal die fenotipiese karakter verander slegs as gevolg van mutasies en genetiese drywing. Ons kan hierdie proses op 'n aantal maniere modelleer, maar die eenvoudigste gebruik 'n "oneindige allele"-model. Onder hierdie model vind mutasies lukraak plaas en het ewekansige fenotipiese effekte. Ons neem aan dat mutasies ewekansig getrek word uit 'n verspreiding met gemiddelde 0 en mutasievariansie σm2. Hierdie model neem aan dat die aantal allele so groot is dat daar effektief geen kans is dat mutasies meer as een keer met dieselfde alleel gebeur nie - dus "oneindige allele." Die allele in die populasie verander dan in frekwensie deur tyd as gevolg van genetiese drywing. Dryf en mutasie saam bepaal dan die dinamika van die gemiddelde eienskap deur tyd.

As ons hierdie oneindige allele-model baie keer sou simuleer, sou ons 'n stel geëvolueerde populasies hê. Hierdie populasies sou gemiddeld dieselfde gemiddelde eienskapwaarde hê, maar sou van mekaar verskil. Kom ons probeer om af te lei presies hoe hierdie populasies3 ontwikkel.

As ons 'n bevolking oorweeg wat onder hierdie model ontwikkel, is dit nie moeilik om aan te toon dat die verwagte bevolkingsfenotipe na enige tyd gelyk is aan die beginfenotipe nie. Dit is omdat die fenotipes nie saak maak vir oorlewing of voortplanting nie, en daar word aanvaar dat mutasies ewekansig en simmetries is. Dus,

$$ E[ar{z}(t)] = ar{z}(0) label{3.1}$$

Let daarop dat hierdie vergelyking reeds ooreenstem met die eerste eienskap van Brownse beweging.

Vervolgens moet ons ook die variansie van hierdie gemiddelde fenotipes oorweeg, wat ons die tussen-populasie fenotipiese variansie sal noem (σB2). Wat belangrik is, σB2 is dieselfde hoeveelheid wat ons vroeër beskryf het as die "variansie" van eienskappe oor tyd - dit wil sê, die variansie van gemiddelde eienskapwaardes oor baie onafhanklike "lopies" van evolusionêre verandering oor 'n sekere tydperk.

Om te bereken σB2, moet ons variasie binne ons modelbevolkings oorweeg. As gevolg van ons vereenvoudigende aannames, kan ons op een of ander tyd uitsluitlik fokus op additiewe genetiese variansie binne elke populasie t, wat ons kan aandui as σa2. Additiewe genetiese variansie meet die totale hoeveelheid genetiese variasie wat additief optree (m.a.w. die bydraes van elke alleel tel bymekaar om die finale fenotipe te voorspel). Dit sluit genetiese variasie uit wat interaksies tussen allele behels, soos dominansie en epistase (sien Lynch en Walsh 1998 vir 'n meer gedetailleerde bespreking). Additiewe genetiese variansie in 'n populasie sal oor tyd verander as gevolg van genetiese drywing (wat geneig is om af te neem σa2) en mutasie-insette (wat geneig is om toe te neem σa2). Ons kan die verwagte waarde van modelleer σa2 van een generasie na die volgende as (Clayton en Robertson 1955; Lande 1979, 1980):

$$ E[sigma_a^2 (t+1)]=(1-frac{1}{2 N_e})E[sigma_a^2 (t)]+sigma_m^2 label{3.2}$$

waar t die verloop van tyd in geslagte is, Ne is die effektiewe bevolkingsgrootte, en σm2 is die mutasievariansie. Daar is twee dele aan hierdie vergelyking. Die eerste, ((1-frac{1}{2 N_e})E[sigma_a^2 (t)]), toon die afname in additiewe genetiese variansie elke generasie as gevolg van genetiese drywing. Die tempo van afname hang af van effektiewe bevolkingsgrootte, Ne, en die huidige vlak van bykomende variasie. Die tweede deel van die vergelyking beskryf hoe additiewe genetiese variansie toeneem as gevolg van nuwe mutasies (σm2) elke generasie.

As ons aanneem dat ons die beginwaarde by tyd 0 ken, σaStart2, kan ons die verwagte additiewe genetiese variansie te eniger tyd bereken t soos:

$$ E[sigma_a^2 (t)]={(1-frac{1}{2 N_e})}^t [sigma_{aStart}^2 - 2 N_e sigma_m^2 ]+ 2 N_e sigma_m^2 label{3.3}$$

Let daarop dat die eerste term in die vergelyking hierbo, ({(1-frac{1}{2 N_e})}^t), na nul gaan as t groot word. Dit beteken dat additiewe genetiese variasie in die ontwikkelende bevolkings uiteindelik 'n ewewig tussen genetiese drywing en nuwe mutasies sal bereik, sodat additiewe genetiese variasie ophou verander van een generasie na die volgende. Ons kan hierdie ewewig vind deur die limiet van Vergelyking ef{3.3} as te neem t groot word.

[lim_{t → ∞}E[σ_a^2(t)] = 2N_eσ_m^2 label{3.4}]

Dus hang die ewewigsgenetiese variansie af van beide bevolkingsgrootte en mutasie-insette.

Ons kan nou die tussen-populasie fenotipiese variansie op tyd aflei t, σB2(t). Ons sal dit aanneem σa2 is in ewewig en dus konstant (vergelyking 3.4). Gemiddelde eienskapwaardes in onafhanklik ontwikkelende bevolkings sal van mekaar verskil. Slaan 'n paar calculus oor, na 'n sekere tydperk t verloop het, sal die verwagte onderbevolkingsafwyking wees (vanaf Lande 1976):

$$ sigma_B^2 (t)=frac{t sigma_a^2}{N_e} label{3.5} $$

Vervanging van die ewewigswaarde van σa2 van vergelyking 3.4 na vergelyking 3.5 gee (Lande 1979, 1980):

$$ sigma_B^2 (t)=frac{t sigma_a^2}{N_e} = frac{t cdot 2 N_e sigma_m^2}{N_e} = 2 t sigma_m^2 label{3.6 }$$

Hierdie vergelyking stel dat die variasie tussen twee uiteenlopende populasies afhang van twee keer die tyd sedert hulle gedivergeer het en die tempo van mutasie-insette. Let daarop dat vir hierdie model, die hoeveelheid variasie tussen bevolkings onafhanklik is van beide die begintoestand van die bevolkings en hul effektiewe bevolkingsgrootte. Hierdie model voorspel dus dat langtermyn-tempo's van evolusie oorheers word deur die voorsiening van nuwe mutasies aan 'n bevolking.

Alhoewel ons spesifieke aannames vir daardie afleiding moes maak, toon Lynch en Hill (1986) dat Vergelyking ef{3.6} 'n algemene resultaat is wat geld onder 'n reeks modelle, selfs dié wat dominansie, koppeling, nie-ewekansige paring insluit, en ander prosesse. Vergelyking ef{3.6} is ietwat nuttig, maar ons kan nie dikwels die mutasievariansie meet nie σm2 vir enige natuurlike bevolkings (maar sien Turelli 1984). Daarenteen ken ons soms wel die oorerflikheid van 'n bepaalde eienskap. Oorerflikheid beskryf die proporsie van totale fenotipiese variasie binne 'n populasie (σw2) wat te wyte is aan bykomende genetiese effekte (σa2):

[h^2=frac{sigma_a^2}{sigma_w^2}.]

Ons kan die verwagte eienskap-oorerflikheid vir die oneindige allele-model by mutasie-ewewig bereken. Deur Vergelyking ef{3.4} te vervang, vind ons dat:

$$ h^2 = frac{2 N_e sigma_m^2}{sigma_w^2} label{3.7}$$

Sodat:

$$ sigma_m^2 = frac{h^2 sigma_w^2}{2 N_e} label{3.8} $$

Hier, h2 is oorerflikheid, Ne die effektiewe bevolkingsgrootte, en σw2 die binne-bevolking fenotipiese variansie, wat verskil van σa2 omdat dit alle bronne van variasie binne bevolkings insluit, insluitend beide nie-additiewe genetiese effekte en omgewingseffekte. Vervang hierdie uitdrukking vir σw2 in vergelyking ef{3.6}, het ons:

$$ sigma_B^2 (t) = 2 sigma_m^2 t = frac{h^2 sigma_w^2 t}{N_e} label{3.9}$$

Dus, na 'n tydsinterval t, het die gemiddelde fenotipe van 'n populasie 'n verwagte waarde gelyk aan die beginwaarde, en 'n variansie wat positief afhang van tyd, oorerflikheid en eienskapvariansie, en negatief van effektiewe populasiegrootte.

Om hierdie resultaat te verkry, moes ons spesifieke aannames maak oor normaliteit van nuwe mutasies wat nogal onrealisties kan lyk. Dit is opmerklik dat indien fenotipes deur genoeg mutasies geraak word, die sentrale limietstelling waarborg dat die verspreiding van fenotipes binne populasies normaal sal wees - maak nie saak wat die onderliggende verspreiding van daardie mutasies mag wees nie. Ons moes ook aanneem dat eienskappe neutraal is, 'n meer twyfelagtige aanname dat ons hieronder ontspan - waar ons ook sal wys dat daar ander maniere is om Brownse bewegingsevolusie te kry as net genetiese drywing!

Let ten slotte op dat hierdie kwantitatiewe genetika-model voorspel dat eienskappe onder 'n Brownse bewegingsmodel sal ontwikkel. Dus, ons kwantitatiewe genetika-model het dieselfde statistiese eienskappe van Brownse beweging. Ons hoef net een parameter te vertaal: σ2 = h2σw2/Ne4.

Brownse beweging onder seleksie

Ons het getoon dat dit moontlik is om 'n Brownse bewegingsmodel direk met 'n kwantitatiewe genetiese model van drif in verband te bring. Trouens, daar is 'n mate van versoeking om die twee gelyk te stel, en tot die gevolgtrekking te kom dat eienskappe wat soos Brownse beweging ontwikkel, nie onder keuse is nie. Dit is egter verkeerd. Meer spesifiek, 'n waarneming dat 'n eienskap ontwikkel soos verwag onder Brownse beweging is nie gelykstaande daaraan om te sê dat daardie eienskap nie onder seleksie is nie. Dit is omdat karakters ook as 'n Brownse stap kan ontwikkel, selfs al is daar sterk seleksie - solank seleksie op bepaalde maniere optree wat die eienskappe van die Brownse bewegingsmodel handhaaf.

Oor die algemeen hang die pad wat gevolg word deur populasie gemiddelde eienskapwaardes onder mutasie, seleksie en wegdrywing af van die spesifieke manier waarop hierdie prosesse plaasvind. 'n Verskeidenheid van sulke modelle word deur Hansen en Martins (1996) oorweeg. Hulle identifiseer drie baie verskillende modelle wat seleksie insluit waar gemiddelde eienskappe steeds onder 'n ongeveer Brownse model ontwikkel. Hier bied ek eenveranderlike weergawes van die Hansen-Martins-modelle aan, vir eenvoud; raadpleeg die oorspronklike vraestel vir meerveranderlike weergawes. Let daarop dat al hierdie modelle vereis dat die sterkte van seleksie relatief swak is, of anders sal genetiese variasie van die karakter uitgeput word deur seleksie met verloop van tyd en die dinamika van eienskap-evolusie sal verander.

Een model neem aan dat populasies ontwikkel as gevolg van rigtingseleksie, maar die sterkte en rigting van seleksie wissel ewekansig van een generasie na die volgende. Ons modelleer seleksie elke generasie as getrek uit 'n normale verspreiding met gemiddelde 0 en variansie σs2. Soortgelyk aan ons drifmodel, sal bevolkings weer onder Brownse beweging ontwikkel. In hierdie geval het die Brownse bewegingsparameters egter 'n ander interpretasie:

$$ sigma_B^2=(frac{h^2 sigma_W^2}{N_e} +sigma_s^2)t label{3.10}$$

In die spesifieke geval waar variasie in seleksie veel groter is as variasie as gevolg van drywing, dan:

[σ_B^2 ≈ σ_s^2 label{3.11}]

Dit wil sê, wanneer seleksie (gemiddeld) baie sterker is as drywing, word die tempo van evolusie heeltemal oorheers deur die seleksieterm. Dit is nie so vergesog nie, aangesien baie studies seleksie in die natuur getoon het wat beide sterker is as drif en wat gewoonlik in beide rigting en grootte van een generasie na die volgende verander.

In 'n tweede model beskou Hansen en Martins (1996) 'n populasie wat onderhewig is aan sterk stabiliserende seleksie vir 'n bepaalde optimale waarde, maar waar die posisie van die optimum self ewekansig verander volgens 'n Brownse bewegingsproses. In hierdie geval kan populasiegemiddeldes weer deur Brownse beweging beskryf word, maar nou weerspieël die tempo-parameter beweging van die optimum eerder as die aksie van mutasie en drywing. Spesifiek, as ons beweging van die optimum beskryf deur 'n Brownse tempo parameter σE2, dan:

[σ_B^2 ≈ σ_E^2 label{3.12}]

Om hierdie resultaat te verkry moet ons aanvaar dat daar ten minste 'n bietjie stabiliserende seleksie is (ten minste in die orde van 1/tij waar tij is die aantal generasies wat pare bevolkings van mekaar skei; Hansen en Martins 1996).

Weereens in hierdie geval is die populasie onder sterk seleksie in enige generasie, maar langtermynpatrone van eienskapverandering kan deur Brownse beweging beskryf word. Die tempo van die lukrake stap word totaal bepaal deur die aksie van seleksie eerder as dryf.

Die belangrike wegneempunt van beide hierdie modelle is dat die patroon van eienskap-evolusie deur tyd onder hierdie model steeds 'n Brownse bewegingsmodel volg, al word veranderinge oorheers deur seleksie en nie deur drywing nie. Met ander woorde, Brownse bewegingsevolusie impliseer nie dat karakters nie onder keuse is nie!

Laastens oorweeg Hansen en Martins (1996) die situasie waar bevolkings ontwikkel volgens 'n tendens. In hierdie geval kry ons evolusie wat verskil van Brownse beweging, maar 'n paar sleutelkenmerke deel. Beskou 'n populasie onder konstante rigtingseleksie, s, sodat:

$$ E[ar{z}(t+1)]=ar{z}(t) + h^2 s label{3.13}$$

Die variansie tussen populasies as gevolg van genetiese drywing na 'n enkele generasie is dan:

$$ sigma_B^2 = frac{h^2 sigma_w^2}{N_e} label{3.14}$$

Oor 'n langer tydperk sal eienskappe ontwikkel sodat hulle gemiddelde eienskapwaarde verwag het wat normaal is met gemiddelde:

$$ E[ar{z}(t)]=t cdot (h^2 s) label{3.15}$$

Ons kan ook variansie tussen spesies bereken as:

$$ sigma_B^2(t) = frac{h^2 sigma_w^2 t}{N_e} label{3.16}$$

Let daarop dat die variansie van hierdie proses presies identies is aan die variansie tussen populasies in 'n suiwer drifmodel (vergelyking 3.9). Seleksie verander net die verwagting vir die spesiegemiddelde (natuurlik neem ons aan dat variasie binne populasies en oorerflikheid konstant is, wat slegs waar sal wees as seleksie redelik swak is). Verder, met vergelykende metodes, oorweeg ons dikwels 'n stel spesies en hul eienskappe in die huidige dag, in welke geval hulle almal dieselfde hoeveelheid evolusionêre tyd sal beleef het (t) en dieselfde verwagte eienskapwaarde het. Trouens, vergelykings ef{3.14} en ef{3.16} is presies dieselfde as wat ons sou verwag onder 'n suiwer-dryfmodel in dieselfde populasie, maar begin met 'n eienskapwaarde gelyk aan (ar{z} (0) = t cdot (h^2 s)). Dit wil sê, vanuit die perspektief van data slegs oor lewende spesies, is hierdie twee suiwer drif- en lineêre seleksiemodelle statisties ononderskeibaar. Die implikasies hiervan is treffend: ons kan nooit bewyse vind vir tendense in evolusie wat slegs lewende spesies bestudeer nie (Slater et al. 2012).

Samevattend kan ons drie baie verskillende maniere beskryf waarop eienskappe onder Brownse beweging kan ontwikkel - suiwer drywing, ewekansig variërende seleksie en wisselende stabiliserende seleksie - en een model, konstante rigtingseleksie, wat patrone onder bestaande spesies skep wat nie van Brownse beweging onderskei kan word nie . En daar is meer moontlike modelle daar buite wat dieselfde patrone voorspel. Mens kan nooit hierdie modelle van mekaar onderskei deur die kwalitatiewe patroon van evolusie oor spesies heen te evalueer nie – hulle voorspel almal dieselfde patroon van Brownse bewegingsevolusie. Die besonderhede verskil deurdat die modelle Browniese bewegingtempo-parameters het wat van mekaar verskil en verband hou met meetbare hoeveelhede soos bevolkingsgrootte en die sterkte van seleksie. Slegs deur iets van hierdie parameters te weet, kan ons tussen hierdie moontlike scenario's onderskei.

Jy sal dalk agterkom dat nie een van hierdie "Brownian" modelle besonder gedetailleerd is nie, veral vir die modellering van evolusie oor lang tydskale. Jy kan selfs kla dat hierdie modelle onrealisties is. Dit is moeilik om 'n geval voor te stel waar 'n eienskap slegs deur ewekansige mutasies van klein effek oor baie allele beïnvloed kan word, of waar seleksie op 'n werklik ewekansige manier van een generasie na die volgende vir miljoene jare sou optree. En jy sou reg wees! Daar is egter geweldige statistiese voordele verbonde aan die gebruik van Brownse modelle vir vergelykende ontledings. Baie van die resultate wat in hierdie boek verkry word, is byvoorbeeld eenvoudig onder Brownse beweging, maar baie meer kompleks en anders onder ander modelle. En dit is ook so dat sommige (maar nie alle) metodes robuust is vir beskeie oortredings van Brownse beweging, op dieselfde manier dat baie standaard statistiese ontledings robuust is vir geringe variasies van die aannames van normaliteit. In elk geval sal ons voortgaan met modelle gebaseer op Brownse beweging, met inagneming van hierdie belangrike waarskuwings.


Een bydrae van 15 tot 'n besprekingsvergadering-uitgawe 'Dateer spesie-divergensies met behulp van rotse en horlosies'.

Gepubliseer deur die Royal Society onder die bepalings van die Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, wat onbeperkte gebruik toelaat, mits die oorspronklike outeur en bron gekrediteer word.

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Moderne filogenetiese vergelykende metodes en hul toepassing in evolusionêre biologie: konsepte en praktyk. — Geredigeer deur László Zsolt Garamszegi

Matthew W. Pennell, Moderne filogenetiese vergelykende metodes en hul toepassing in evolusionêre biologie: konsepte en praktyk. — Geredigeer deur László Zsolt Garamszegi, Sistematiese Biologie, Volume 64, Uitgawe 1, Januarie 2015, Bladsye 161–163, https://doi.org/10.1093/sysbio/syu075

As gevolg van die proses van afkoms met modifikasie, deel naverwante spesies baie eienskappe. Filogenieë verskaf dus inligting wat nie net in ag geneem moet word wanneer interspesifieke vergelykings gemaak word nie, maar wat ook aangewend kan word om insig in makro-evolusionêre vrae te verkry. Statistiese benaderings vir die gebruik van hierdie inligting, genoem filogenetiese vergelykende metodes (PCM's), het die afgelope paar dekades geweldig gegroei. Die nuwe boek, Moderne filogenetiese vergelykende metodes en hul toepassings in evolusionêre biologie, hersien baie van hierdie ontwikkelings.

Die boek het 22 hoofstukke, wat in drie afdelings gerangskik is, wat meestal bestaan ​​uit resensies van betroubare onderwerpe in vergelykende biologie. Dit sluit in: filogenetiese regressie-passingsmodelle vir beide kontinue en diskrete karakters gemeenskap en ko-evolusionêre filogenetiese metodes sowel as 'n paar meer algemene hoofstukke oor die voorbereiding van data vir afleiding, boombou, simulering en plot van bome en eienskappe, ens. Die primêre klem van die boek, is egter op die meganika van gepaste eienskap-evolusionêre modelle.

Alhoewel dit in sommige dele 'n bietjie teenstrydig is (soos tipies van geredigeerde versamelings), doen die verskillende skrywers oor die algemeen 'n prysenswaardige werk om die talle statistiese nuanses en wiskundige truuks te verduidelik wat betrokke is by modelpassing en 'n opsomming van 'n groeiende en dikwels intimiderend digte liggaam van literatuur. Baie min hierin is nuut (slegs Nunn en Zhu, in hoofstuk 21, wyk af van hierdie draaiboek, en bied 'n nuwe en intrige benadering vir die ondersoek van "evolusionêre singulariteite"), maar ek dink die boek is 'n nuttige hulpbron vir beide ervare hande en nuwelinge in die veld – alhoewel ek eerlikwaar, gegewe die duur prys van die boek en die feit dat dit meestal 'n resensie van voorheen gepubliseerde werk is, sal ek aanbeveel om dit uit 'n biblioteek te kyk eerder as om 'n kopie vir jou lessenaar te koop.

Die skrywers se fokus is egter feitlik uitsluitlik op statistiese kwessies. By die deurlees van hierdie versameling kan ek nie anders as om 'n sentiment te herroep wat deur Houle et al. (2011) in hul helder oorsig van metingteorie en die toepassings daarvan in biologie. Hulle kritiseer statistici wat voorstaan ​​dat datatransformasies regverdigbaar is wanneer dit ook al lei tot verspreidings wat aan die aannames van 'n bepaalde analise voldoen: "As dit statistiek is, wil ons geen deel daarvan hê nie, aangesien wetenskap oor die natuur gaan, nie oor getalle nie" [p. 18].

N ( 0 , V ) waar V is die verwagte variansie-kovariansie matriks vir die eienskappe wat 'n evolusionêre model gegee word. Met ander woorde, die evolusionêre model word gebruik om die struktuur van die residue te modelleer en nie die werklike eienskappe nie. Soos bespreek in nie minder nie as nege uit die 22 hoofstukke van die boek, stel die formulering van die model op so 'n manier ons in staat om gebruik te maak van goed gevestigde statistiese teorie van veralgemeende kleinste kwadrate (GLS) en veralgemeende lineêre gemengde effekte (GLM). modelle. Die insluiting van die filogenetiese struktuur in die foutafwyking is nie anders as om enige ander tipe kovariansie in te sluit nie. By recognizing this equivalence, we can now fit phylogenetic regression models with a variety of distributions for the response variable Y [Ives and Garland, Chapter 9 Villemereuil and Nakagawa, Chapter 11], incorporate measurement error [Garamszegi, Chapter 7], perform model averaging [Garamszegi and Mundry, Chapter 12] and path-analysis [Gonzalez-Voyer and von Hardenberg, Chapter 8], identify outliers [Nunn and Zhu, Chapter 21], and use standard model diagnostics [Mundry, Chapter 6].

A number of the authors suggest that a λ tree transformation ( Freckleton et al. 2002) is often more appropriate than simply assuming Brownian motion (BM) for constructing the error variance term V. (The λ transformation involves multiplying the off-diagonals of V by an estimated parameter between 0 and 1.) This is a purely phenomenological construct — by shrinking every branch except those leading to the tips, it implies that there is something special about extant taxa, which is clearly not the case. Nonetheless, researchers (including the authors of the current volume) often use such models to claim that one trait is adapted to the value of another. In Chapter 14, Hansen clearly articulates (recapitulating arguments he has made elsewhere see Hansen and Orzack 2005), that these types of models do not actually capture the process of adaptation at all: “any adaptive process that is sufficiently slow to generate a phylogenetic signal in model residuals will also generate systematic deviations from the optimal state” [p. 360]. Effectively, standard regression models assume that adaptation to a new environment is instantaneous, and that maladaption is phylogenetically structured — closely related species will have similar deviations from the optimal trait value even if the optimum differs between them. From a biological perspective, this seems very odd.

Perhaps even more confusing is the use of Ornstein-Uhlenbeck (OU) models to construct the error variance term. OU is attractive for modeling the residual variance because, unlike the λ transformation, it is a coherent stochastic process and is directly analogous to a population level model from quantitative genetics — quadratic stabilizing selection on a fixed adaptive landscape ( Lande 1976 Hansen and Martins 1996). While the λ transformation is obviously just a statistical construct, OU seems to be biologically motivated. Indeed, a number of authors suggest that including an OU error variance captures “constraints” [Paradis, p. 9], “stabilizing selection” [Ives and Garland, p. 234], or “selective regimes” [Symonds and Blomberg, p. 122] but this does not get around Hansen's criticisms. These models still assume phylogenetically structured maladapation, and they do not allow researchers to make specific inferences about stabilizing selection or evolutionary constraints. OU error structures may often fit data better than BM error structures, but it is likely that this is simply because OU can accommodate more variance towards the tips of the phylogeny than a BM model can (including λ has a similar effect). The evolutionary argument here seems to be merely window dressing for a purely statistical argument.

OU models are further treated in depth in three different chapters. Each of these chapters [Hansen, Chapter 14 O'Meara and Beaulieu, Chapter 15 Mahler and Ingram, Chapter 18] offers an interpretation as to what the parameters of an OU model actually represent. The differences between them are nuanced (and I will not dissect them here), but importantly they all share the perspective that a simple quantitative genetics explanation — i.e., clade-wide stabilizing selection where some species are further from the optima than are others — is almost certainly naïve and unreasonable. Rather, OU models likely reflect in some way the structure and dynamics of the macroevolutionary adaptive landscape ( Simpson 1944 Arnold et al. 2001 Hansen 2012), upon which lie population-level adaptive landscapes.

How are we to reconcile these different uses and interpretations of the same core models, and make sense of comparative analyses? In my view, there are three possible frameworks with which to think about comparative biology. First, we can take the view that what we are measuring are strictly patterns, and that we are not necessarily making inferences about specific evolutionary processes. This is certainly a defensible position: the patterns may be interesting in and of themselves, and documenting commonalities and differences among clades and through time may provide a broader picture of the history of life on earth. In practice, this is what researchers are often actually doing, even if they are hesitant to admit it. A benefit of openly adopting this perspective is that we can consider a much broader suite of models that may provide a much better fit to our data and more predictive power than current models — if we are not interested in making specific evolutionary inferences, then we need not be beholden to specific evolutionary models. Such alternatives may include macroevolutionary diffusion processes (e.g., Clauset and Erwin 2008), models derived from macroecological theories, or making use of statistical learning approaches divorced from any process whatsoever.

The second framework is the quantitative genetics view: the models we fit in comparative biology should be taken as literally representing microevolutionary hypotheses. Many of the commonly used models can be directly interpreted in terms of population-level parameters ( Hansen and Martins 1996 Pennell and Harmon 2013). We can compare the estimated model parameters to within-population measures, in order to test whether macroevolutionary divergences are consistent with evolution by drift, stabilizing selection, etc. This project is certainly interesting and worth pursuing. But given the results of studies that have explicitly examined this connection using rather simple models ( Lynch 1990 Estes and Arnold 2007 Hohenlohe and Arnold 2008), it appears that translating the parameters estimated from comparative data to the terms of quantitative genetics (i.e., if we assume that BM is strictly a model of drift, the estimated rate parameter σ 2 is equal to the additive genetic variance G divided by the effective population size N e ⁠ ) will often result in nonsensical numbers.

The third perspective is to take seriously the idea that macroevolutionary models reflect the dynamics of adaptive landscapes through deep time ( Arnold et al. 2001 Hansen 2012). This is in line with the views of chapter authors Hansen, O'Meara & Beaulieu, and Ingram & Mahler. Comparative biologists have a tendency to discuss many of these ideas in quotation marks. The optimum of OU models is referred to as “clade level optimum”. A model with decelerating rates of change depicts an “early burst”. I argue that a much richer and more meaningful connection can potentially be made. Theoretical work over the last century has produced a beautiful and fairly comprehensive understanding of how populations move across adaptive landscapes, and empiricists have tested the theoretical predictions in a wide variety of systems and contexts. In contrast, we have only a preliminary understanding of how the landscapes themselves evolve at longer time scales. This is a fundamentally important question in evolutionary biology, and one which I believe phylogenetic comparative biology and paleobiology can help address.

There is a lot of work to be done before we will really be able to get at these types of questions. Once we recognize that some of the classic concepts in evolutionary biology — such as adaptive zones, adaptive radiations and key innovations — are actually hypotheses about the structure and dynamics of adaptive landscapes, we can start developing statistical models that actually capture their essential properties. Current models are, at best, loosely tied to these ideas (and hence the scare quotes). Additionally, there are a number of existing mathematical frameworks that make predictions about these higher-order processes and trait evolution over longer time periods (see e.g., Gavrilets 2004 Doebeli 2011) but there is currently no way to estimate the relevant parameters of these models from comparative data.

Both the development of new PCMs and the interest in using them has grown tremendously over the past decade. Nevertheless, I feel that we, as a field, are somewhat stuck. First, the same handful of statistical models are employed over and over again, with most of the progress representing relatively minor variations on similar themes (that is not to say that such improvements are not challenging or worthwhile). Second, we are often much too vague about what exactly we want to explain with PCMs — this is apparent in both this current book collection and in the literature more broadly. I argue that these two problems are deeply intertwined. The standard collection of models available today, namely those based on BM and OU, have had such staying power in part because they can be useful for detecting patterns, can be interpreted in light of evolutionary genetics, and can loosely be tied to questions about adaptive landscapes. Requiring this sort of conceptual flexibility is also a limitation. More focused, question-specific approaches to modeling that are directly tied to the inferences we actually want to make will likely get us much further than sticking to models that are more general but address no questions particularly well.


Consequences of local selection on covariance among selected loci

Box 2 illustrates how θW en θB are built up in simplified examples of two populations undergoing local stabilizing selection. θW is negative in a population undergoing directional or stabilizing selection. This build-up of negative covariance under selection is known as the Bulmer effect ( Bulmer 1980, 1989 ). On the opposite, θB will be positive when selection is divergent among populations. The example given in Box 2 corresponds to a simplified case where the variance between populations (VB) is initially zero. In a more general context, the sign of θB depends on the difference between the value of the genetic variance among populations before the onset of selection and the variance of phenotypic optima VOPT ( Latta 1998 ).

Under divergent local selection, the genetic variance among populations increases towards VOPT. This response is permitted by two processes: first, the build-up of covariance of additive effects among loci second, a change in allele frequencies that results in a change in the genic variance. The build-up of positive covariance among loci (θB) contributes to a larger decoupling between differentiation at QTL (FSTQ) and phenotypic differentiation VST, as predicted by (eqn 1). Conversely, a change in allele frequencies will affect both FSTQ en VST in parallel, thus reducing the discrepancy between differentiation at QTL and phenotypic differentiation.


Models of Life

This book has been cited by the following publications. This list is generated based on data provided by CrossRef.
  • Publisher: Cambridge University Press
  • Online publication date: October 2014
  • Print publication year: 2014
  • Online ISBN: 9781107449442
  • DOI: https://doi.org/10.1017/CBO9781107449442
  • Subjects: Genomics, Bioinformatics and Systems Biology, Life Sciences, Physiology and Biological Physics

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Book description

Reflecting the major advances that have been made in the field over the past decade, this book provides an overview of current models of biological systems. The focus is on simple quantitative models, highlighting their role in enhancing our understanding of the strategies of gene regulation and dynamics of information transfer along signalling pathways, as well as in unravelling the interplay between function and evolution. The chapters are self-contained, each describing key methods for studying the quantitative aspects of life through the use of physical models. They focus, in particular, on connecting the dynamics of proteins and DNA with strategic decisions on the larger scale of a living cell, using E. coli and phage lambda as key examples. Encompassing fields such as quantitative molecular biology, systems biology and biophysics, this book will be a valuable tool for students from both biological and physical science backgrounds.

Resensies

'Models of Life is an insight of a physicist into biological regulatory mechanisms. It provides a quantitative basis of how many of the biological systems work. Using simple logic and mathematics, Kim Sneppen, a world renowned scientist and thinker, has created a must-read for investigators in quantitative biology. The book provides a clear explanation of triumphant experiments in a lucid way with crisp figures. The brilliance of the author’s analytical mind is on display when one sees how he explains some of the exciting paradigmatic regulatory systems, beginning with the basics of molecular biology. The book is also replete with intellectually challenging problem questions for readers, making the book an excellent text for students as well.'

Sankar Adhya - National Cancer Institute, Maryland

'Kim Sneppen’s insightful book covers lots of ground in describing biological systems at different time and length scales and levels of resolution. Its different chapters unified by the author’s modeling philosophy are sure to be of interest to a very diverse group of readers … Readers interested in agent-based modeling will find it applies to systems as diverse as epigenetics, propagation of information and evolutionary patterns in fossil records. Dedicated chapters combine biophysics and systems biology of gene regulation and protein-protein interactions. The book provides especially deep coverage of biology of phages, bacteria and their interactions within ecosystems. It would make an excellent textbook for one or even several university courses on systems or evolutionary biology. In fact when teaching these courses I will use it heavily myself and recommend it to my students.'

Sergei Maslov - Brookhaven National Laboratory, New York

'Sneppen has written a wonderfully friendly and readable book on the principles of biological cells for physicists. He presents concepts and models at a level that is sufficiently deep to convey powerful insights, while keeping the math to the absolutely minimal level that is needed to be clear and informative. This book is pioneering in covering scientific terrain that is largely not covered much elsewhere, but will be in the future - including feedback, regulation, networks, bistability in the lambda-phage switch, DNA looping, diffusion in cells, epigenetic regulation and cellular evolution. I highly recommend it as a deeply insightful book about the principles of biology and a great read.'


Active fluid with Acidithiobacillus ferrooxidans: correlations between swimming and the oxidation route

To explore engineering platforms towards ‘active bacterial baths’, we grow and characterize native and commercial strains of Acidithiobacillus ferrooxidans to promote swimming locomotion. Three different energy sources were used, namely elemental sulfur, ferrous sulfate, and pyrite. The characteristics of the culture, such as pH, Eh, and the concentration of cells and ions, are monitored to seek correlations between the oxidation route and the transport mechanism. We found that only elemental sulfur induces swimming mobility in the commercial DSMZ – 24,419 strain, while ferrous sulfate and the sulfide mineral, pyrite, did not activate swimming on any strain. The bacterial mean squared displacement and the mean velocity are measured to provide a quantitative description of the bacterial mobility. We found that, even if the A. ferrooxidans strain is grown in a sulfur-rich environment, it preferentially oxidizes iron when an iron-based material is included in the media. Similar to other species, once the culture pH decreases below 1.2, the active locomotion is inhibited. The engineering control and activation of swimming in bacterial cultures offer fertile grounds towards applications of active suspensions such as energy-efficient bioleaching, mixing, drug delivery, and bio-sensing.

Dit is 'n voorskou van intekeninginhoud, toegang via jou instelling.


Genetic architecture and selective sweeps after polygenic adaptation to distant trait optima

Understanding the genetic basis of phenotypic adaptation to changing environments is an essential goal of population and quantitative genetics. While technological advances now allow interrogation of genome-wide genotyping data in large panels, our understanding of the process of polygenic adaptation is still limited. To address this limitation, we use extensive forward-time simulation to explore the impacts of variation in demography, trait genetics, and selection on the rate and mode of adaptation and the resulting genetic architecture. We simulate a population adapting to an optimum shift, modeling sequence variation for 20 QTL for each of 12 different demographies for 100 different traits varying in the effect size distribution of new mutations, the strength of stabilizing selection, and the contribution of the genomic background. We then use random forest regression approaches to learn the relative importance of input parameters in determining a number of aspects of the process of adaptation including the speed of adaptation, the relative frequency of hard sweeps and sweeps from standing variation, or the final genetic architecture of the trait. We find that selective sweeps occur even for traits under relatively weak selection and where the genetic background explains most of the variation. Though most sweeps occur from variation segregating in the ancestral population, new mutations can be important for traits under strong stabilizing selection that undergo a large optimum shift. We also show that population bottlenecks and expansion impact overall genetic variation as well as the relative importance of sweeps from standing variation and the speed with which adaptation can occur. We then compare our results to two traits under selection during maize domestication, showing that our simulations qualitatively recapitulate differences between them. Overall, our results underscore the complex population genetics of individual loci in even relatively simple quantitative trait models, but provide a glimpse into the factors that drive this complexity and the potential of these approaches for understanding polygenic adaptation.

Author summary Many traits are controlled by a large number of genes, and environmental changes can lead to shifts in trait optima. How populations adapt to these shifts depends on a number of parameters including the genetic basis of the trait as well as population demography. We simulate a number of trait architectures and population histories to study the genetics of adaptation to distant trait optima. We find that selective sweeps occur even in traits under relatively weak selection and our machine learning analyses find that demography and the effect sizes of mutations have the largest influence on genetic variation after adaptation. Maize domestication is a well suited model for trait adaptation accompanied by demographic changes. We show how two example traits under a maize specific demography adapt to a distant optimum and demonstrate that polygenic adaptation is a well suited model for crop domestication even for traits with major effect loci.


Description of the data set

I surveyed the literature for studies reporting genetic correlations between two or more of the traits, development time, growth rate, size at maturity (which I shall also refer to as simply adult size) and fecundity. I include only data for nondomesticated species. To avoid pseudoreplication I used mean values per species unless the data were highly discrepant in which case I report both individual values and means. If both male and female estimates were given I used only the female estimates. If possible, I used the heritability estimate for adult size that was reported in the same paper as the other trait (Gkoers, Dtyd, Feiers): this means that in a few cases the heritability estimate for adult size may differ among comparisons. Where multiple indexes of size were given (e.g. head width, femur length) I used the averaged value of the heritability or correlation. Where possible, estimates were only used for animals reared in the laboratory under ‘normal’ conditions (e.g. not an obviously novel food source). Traits were defined as follows:

1 Development time: For insects, which are the majority of organisms, the time from hatching to final eclosion. For the other invertebrate (Helix aspersa, a snail), hatching to first reproduction. For vertebrates, the time from ‘hatching’ to first reproduction. For plants, the time from seedling emergence to flowering.

2 Size at maturity: For insects, this is either the size at eclosion or a closely correlated trait such as pupal weight. For other organisms it is the size at first reproduction.

3 Growth rate: The ideal measure would be the slope of the linearized relationship between size at age t en t. In the absence of this measure I have used size at some immature age as a surrogate. In some papers growth rate is defined as adult size/development time: this would only be ‘growth rate’ as defined previously if the growth trajectory were linear. Because no evidence is presented for this, and because this measure is confounded with the other two traits (adult size, development time) under study, I have not used this measure of growth rate.

4 Fecundity: Some measure of the number of propagules produced during some defined period.

The phenotypic correlation is a complex function of the genetic correlation and therefore it has been suggested that the phenotypic correlation cannot be assumed to be a reliable guide to the evolutionary importance of a trade-off ( 50 79 60 , 62 69 ). To see if this admonition holds true across different categories of trade-offs I compare the genetic (ra) and phenotypic (rbl) correlations, asking first if there is a correspondence between the signs, which at least indicates that the phenotypic correlation is a guide to the presence of a trade-off, and, second, if the value of rbl is a reasonable surrogate for ra.


10 - Evolutionary quantitative genetics of sperm

Evolution requires two separate conditions selection, resulting from differences in traits associated with variation in fitness, and additive genetic variation underlying the morphological, physiological or behavioral variation. By far, most evolutionary studies have focused on the selection. The ability to fertilize eggs clearly influences male fitness and so studying variation in sperm traits that are related to fertilization success—that is, the covariance between fitness and sperm characteristics—has led to a good understanding of the types of selection that influence sperm. The evolutionarily relevant aspects of genetics of sperm traits, which is the evolutionarily relevant source of this variation, are less well studied. Additive genetic effects are those effects of genes that are independent of the effects of any other genes that affect the trait of interest—in other words, the effects of genes that can be transmitted across generations without any dependence on the transmission of any other genes. For most complex traits, multiple additive effects sum to give an overall genetic contribution.


Kyk die video: Biologija,. SŠ - Diferencijacija i specijalizacija stanica (Oktober 2022).