What Role for Fitness?

Deep South Philosophy of Biology, 4/1/2017

Charles H. Pence

Department of Philosophy

Outline

1. Preliminaries2. Two Roles for Fitness3. e Claim4. Some New Arguments

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

5. Connections6. e Moral

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Charles H. Pence Preliminaries 3 / 47

Charles H. Pence Preliminaries 4 / 47

Charles H. Pence Preliminaries 4 / 47

Charles H. Pence Preliminaries 4 / 47

Why are philosophers of biologyinterested in tness?

What, in the philosophy of biology,is tness for?

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Charles H. Pence Preliminaries 6 / 47

Two Notions of

Fitness

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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)

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Matthen and Ariew (2002)

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)

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

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

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Matthen and Ariew (2002)

[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)

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The Claim

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ContraMatthen and Ariew, predictivetness is not a fruitful way to understandtness in the philosophy of biology.

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

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While oen unappreciated, a number ofrecent publications on tness also cast

doubt on the utility of thecausal-predictive dichotomy.

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Predictive Fitness

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

outcomes of interest

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Matthen and Ariew (2002)

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)

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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.)

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

in tness comparisons.

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Charles H. Pence Predictive Fitness 20 / 47

From Causal to

Predictive

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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.

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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

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

Ramsey model?

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F(G , E) = exp( limt→∞

1t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω)

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

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

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

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

with two features:

1. Density-dependent selectionpressures

2. High-dimensional phenotype space

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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)

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-100 0 100

-100

0

100

x1

x2

Doebeli and Ispolatov (2014), g. 5

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What’s the real-world timescale here?

How does it relate to the rate ofenvironmental change?

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

remain viable?

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Ways Out

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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)

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

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

• Abandon prediction, focus on statisticalretrodiction

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

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

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Connections

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Abrams (2012)

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One way to get these predictions:

Evolution as a process that maximizestness over time

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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)

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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. . . As for the bestway to compare probability distributions, I leave that tomathematicians and mathematical biologists. (pp. 615–6)

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The Moral

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Many uses of tness:

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

• Statistical estimator for any of the above

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Fitness concepts are far more complexthan a dichotomy between two simple

roles for tness.

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So what is mathematical tness for?

Of course, analyzing biological modelsis a great project, and worthwhile in its

own right.

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So what is mathematical tness for?

Of course, analyzing biological modelsis a great project, and worthwhile in its

own right.

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Derivingmathematicalmodels from ourcausal structures can give us condencethat the structure we are describing

really is a model of tness.

I think this is the way to interpret the results inPence and Ramsey (2013), as well as a number of

other propensity-interpretation papers.

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Derivingmathematicalmodels from ourcausal structures can give us condencethat the structure we are describing

really is a model of tness.

I think this is the way to interpret the results inPence and Ramsey (2013), as well as a number of

other propensity-interpretation papers.

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Questions?

charles@charlespence.nethttp://charlespence.net

@pencechp

F(G , E) = exp( limt→∞

1t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω)

• 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

F(G , E) = exp( limt→∞

1t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω)

• 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

F(G , E) = exp( limt→∞

1t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω)

• 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

F(G , E) = exp( limt→∞

1t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω)

• 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

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)

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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.

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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.

Charles H. Pence Bonus! 4 / 4