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The Matching Hypothesis Jeff Schank PSC 120

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Mating Mating is an evolutionary imperative Much of life is structured around securing and maintaining long-term partnerships

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Physical Attractiveness Focus on physical attractiveness may have basis in good genes hypothesis – Features associated with PA may be implicit signals of genetic fitness Social Psychology: How does physical attractiveness influence mate choice?

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The Matching Paradox Everybody wants the most attractive mate BUT, couples tend to be similar in attractiveness r =.4 to.6 (Feingold, 1988; Little et al., 2006)

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Matching Paradox How does this similarity between partners come about? How is the observed population-level regularity generated by the decentralized, localized interactions of heterogeneous autonomous individuals? (Thats a mouthful!)

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Kalick and Hamilton (1986) Previously, many researchers assumed people actively sought partners of equal attractiveness (the matching hypothesis) Repeated studies showed no indication of this, but rather a strong preference for the most attractive potential partners ABM showed that matching could occur with a preference for the most attractive potential partners

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The Model Male and female agents – Only distinguishing feature is attractiveness Randomly paired on dates Choose whether to accept date as mate Mutual acceptance coupling Attractiveness can represent any one- dimensional measure of mate quality

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The Model: Decision Rules Rule 1: Prefer the most attractive partner Rule 2: Prefer the most similar partner CT Rule: Agents become less choosy as they have more unsuccessful dates – Acceptance was certain after 50 dates.

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The Model: Decision Rules more Formally Rule 1: Prefer the most attractive partner Rule 2: Prefer the most similar partner CT Rule: Agents become less choosy as they have more unsuccessful dates – Acceptance was certain after 50 dates.

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Model Details Male and Female agents (1,000 of each) Each agent randomly assigned an attractiveness score, which is an integer between 1-10 Each time step, each unmated male was paired with a random unmated female for a date Each date accepted/rejected partner using probabilistic decision rule If mutual acceptance, the pair was mated and left the dating pool

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Problem: Model not Parameterized

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Model Parameterized Male and Female agent (1,000 of each) N m (males) and N f (females) Each agent randomly assigned an attractiveness score, which is an integer between 1 – 10 A random number between 1 – Max(A)

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What Can We Do? Replicate the model and check the original results – Are there any other interesting things to check out? Modify the model – Check robustness of findings – Increase realism and see what happens

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Replication Rule 1Rule 2 Kalick and Hamilton r.55.83 Mean r.61.83 95% Confidence Interval(.57-.65)(.78-.87) 95% confidence interval means 95% of simulations had results in this range.

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Mathematical Structure of Decision Rules Qualitative difference easy to explain: – Accept a mate with a probability that increases an agents objective maximizing: attractiveness (Rule 1) or similarity (Rule 2) There are many functions that could fit this description – Why a 3 rd -order power function? – What is the probability of finding a mate? – Is this the same for each rule?

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Mathematical Structure of Decision Rules AB

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Choice of Exponent n K & H used a 3 rd -order power function with no explanation The assumption is that the exact nature of the function, including the value of the exponent, is unimportant

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Choice of Exponent n

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Space and Movement Usually, agents are paired completely randomly each turn – Spatial structure can facilitate the evolution of cooperation (Nowak & May, 1992; Aktipis, 2004) – Foraging: Different movement strategies vary in search efficiency and behave differently in various environmental conditions (Bartumeus et al., 2005; Hills, 2006 ) Agents were placed on 200x200 grid (bounded) allowing them to move probabilistically Could interact with neighbors only within a radius of 5 spaces

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Space and Movement ZigzagBrownian

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Space and Movement

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Movement strategies and spatial structure influence mate choice dynamics Population density should influence speed of finding mates, as well as likelihood of finding an optimal mate Suggests the evolution of strategies to increase dating options (e.g., rise in Internet dating) Provides new opportunities for asking questions about individual behavior and population dynamics

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Conclusions By modifying any number of the parameters, either decision rule can generate almost any desired correlation The Matching Paradox remains unresolved by Kalick and Hamiltons (1986) ABM It is important to evaluate the effects of parameter values and environmental assumptions of a model

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