fitness and prediction in evolutionary theory

Fitness and Prediction

in Evolutionary Theory

London School of Economics, 25/1/2017

Charles H. Pence

Department of Philosophy

Outline

1. Fundamentals of Selection2. Two Roles for Fitness3. e Claim4. Predictive Fitness

4.1 From the PIF to Predictive Fitness4.2 Ways Out?

5. e Moral

e take-home: A common conceptual analysis of tnessin the philosophy of biology is mistaken.

Charles H. Pence 2 / 53

Natural Selection

Charles H. Pence Fundamentals of Selection 3 / 53

t = 0

t = 1 t = 2


t = 0 t = 1

t = 2


t = 0 t = 1 t = 2


Fitness


>


Blue organisms leave more ospringthan red organisms.

A circle: the tautology problem


Blue organisms will probably (aredisposed to) leave more ospring than

red organisms.


The Propensity

Interpretation of

Fitness


Two Notions of

Fitness

Charles H. Pence Two Roles for Fitness 11 / 53

Matthen and Ariew (2002)

[F]or many this notion of an organism’s overall competitiveadvantage traceable to heritable traits is at the heart of thetheory of natural selection. Recognizing this, we shall callthis measure of an organism’s selective advantage itsvernacular tness. According to one standard way ofunderstanding natural selection, vernacular tness – orrather the variation thereof – is a cause of evolutionarychange. (p. 56)



Fitness occurs also in equations of population geneticswhich predict, with some level of probability, thefrequency with which a gene occurs in a population ingeneration n + 1 given its frequency in generation n. Inpopulation genetics, predictive tness (as we shall call it) isa statistical measure of evolutionary change, the expectedrate of increase (normalized relative to others) of a gene . . .in future generations. . . . (p. 56)


Causal (vernacular) tness: general(causal) notion in natural selection

Predictive (mathematical) tness:predict future representation fromcentral tendency/expected value



[N]atural selection is not a process driven byvarious evolutionary factors taken as forces;rather, it is a statistical “trend” with these factors(vernacular tness excluded) as predictors.ese theses demand a radical revision ofreceived conceptions of causal relations inevolution. (p. 57)


The Claim

Charles H. Pence The Claim 16 / 53

ContraMatthen and Ariew, predictivetness is not a fruitful way tounderstand tness in biology.

By extension, neither is the dichotomybetween causal and predictive tness.


It fails in a way that should lead us toquestion not only the predictive-causaldichotomy, but the relationship betweenshort-term and long-term evolutionary

processes.


Predictive Fitness

Charles H. Pence Predictive Fitness 19 / 53

Standard view: predictive tness trackssomething like a central tendencyextracted from the distribution of

outcomes of interest



e basic principle of statistical thermodynamics is thatless probable thermodynamic states give way in time tomore probable ones, simply by the underlying entitiesparticipating in fundamental processes. [. . . ]e same istrue of evolution. (p. 80)


Lewontin (1974)

When we say that we have an evolutionary perspective ona system or that we are interested in the evolutionarydynamics of some phenomenon, we mean that we areinterested in the change of state of some universe in time.[. . . ]e sucient set of state variables for describing anevolutionary process within a population must include someinformation about the statistical distribution of genotypicfrequencies. (pp. 6, 16; orig. emph.)


Among other reasons, this is to be usefulfor grounding medium- to long-termpredictions about evolutionary change

in tness comparisons.


Fitness

Maximization


One way to get these predictions:

Evolution as a process that maximizestness over time


Birch (2016)

Neither [of the approaches surveyed] establishes amaximization principle with biological meaning, and Iconclude that it may be a mistake to look for universalmaximization principles justied by theory alone. (p. 714)


But this isn’t the only way to generatepredictions. What about buildingpredictions from the PIF itself?


From Causal to

Predictive

Charles H. Pence From the PIF to Predictive Fitness 29 / 53

How should defenders of the PIFrespond to M&A’s emphasis on

predictive tness?


Millstein (2016)

Fitness is an organism’s propensity to survive andreproduce (based on its heritable physical traits) in aparticular environment and a particular population over aspecied number of generations.at is what tness is.[. . . ] Expected reproductive success is not the propensityinterpretation of tness and it never was; it was just oneway of trying to grapple with probability distributions andassign tness values. (p. 615)


e basic idea: Dene the propensityinterpretation in terms of facts about thepossible lives an organism (with a givengenotype, in a given environment) could

have lived.


F(G , E) = exp( limt→∞

1t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω)

Having our cake and eating it, too:

• Gives you a mathematical model. . .• . . . that’s grounded in a specic dispositionalproperty


Can we draw any conclusions about thequality of predictions from the Pence &

Ramsey model?




A long-run limit: perfect for prediction! But itrelies on an assumption: non-chaotic populationdynamics


Question: How common is non-chaoticdynamics in evolving systems?

My assumption: Won’t be able to answerthis – model is far too general.


Approach of Doebeli & Ispolatov (2014):Investigate by simulating populations

with two features:

1. Density-dependent selectionpressures

2. High-dimensional phenotype space


Doebeli & Ispolatov (2014)

Our main result is that the probability of chaos increaseswith the dimensionality d of the evolving system,approaching 1 for d ∼ 75. Moreover, our simulationsindicate that already for d ≳ 15, the majority of chaotictrajectories essentially ll out the available phenotypespace over evolutionary time. . . . (p. 1368)


-100 0 100

-100

0

100

x1

x2

Doebeli and Ispolatov (2014), g. 5


What’s the real-world timescale here?

How does it relate to the rate ofenvironmental change?


A surprising result at this level ofgenerality. In cases where it holds, whatkinds of tness-based predictions would

remain viable?


Charles H. Pence Ways Out? 43 / 53

Grant (1997)

e invasion is exponential, but nonlinear dynamics of theresident type produce uctuations around this trend.[Fitness] can therefore be most accurately estimated by theslope of the least squares regression of [daughterpopulation size] on t. (p. 305)


Two major problems:• Loses sight of the dynamics• Oers poor predictions


Move the goalposts:• Abandon all but short-term predictions• Abandon predictive content; predict simply‘chaos’

• Abandon prediction, focus on statisticalretrodiction


• Resuscitate central tendencies: poorpredictions that ignore (interesting)dynamics

• Move the goalposts: loses themedium-to-long-term predictions citedabove


The Moral

Charles H. Pence The Moral 48 / 53

Many uses of tness:

• Mathematical parameter in models• Causal property• Proxies for strength of selection inpopulations

• Statistical estimator for any of the above


Fitness concepts are far more complexthan a dichotomy between two simple

roles for tness.


What’s the relationship betweenshort-term and long-term evolutionary

processes?


Complete continuity, all the way to thelong run? Unlikely.

Medium-term continuity?reatenedby these results!


Questions?

[email protected]://charlespence.net

@pencechp



• Multi-generational life histories• Changing genotypes and environments overtime

• Disposition (propensity) dened over modalfacts about other possible lives of organisms

Charles H. Pence Bonus! 1 / 4



• Multi-generational life histories

• Changing genotypes and environments overtime





• Multi-generational life histories• Changing genotypes and environments overtime



State space of possible lives: Ω ∶ f ∶ R→ Rn

Cardinality, though, is too big! N(Ω) = 22ℵ0

Can still dene a σ-algebra F and a probability measurePr if we restrict our attention to:

• continuous functions ω,• functions ω with only point discontinuities, or• functions ω with only jump discontinuities

(Nelson 1959)


With that state space dened, we need three simplifyingassumptions:

1. Non-chaotic population dynamics2. Probabilities generated by a stationary randomprocess

3. Logarithmic moment of vital rates is boundede last two are trivial in our context.


en the following limit exists:

a = limt→∞

1tEw ln(ϕ(t)),

with Ew an expectation value (Tuljapurkar 1989). Fitness isthe exponential of this quantity a, and is equivalent (underfurther simplifying assumptions) to net reproductive rateand related to the Malthusian parameter.


fitness and prediction in evolutionary theory

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