# Correlations and Evolutionary Responses

The effects of trait correlations on evolutionary responses

Ned Dochtermann1, Raphael Royaute1, Ann Hedrick2

1Department of Biological Sciences, North Dakota State University, Fargo, North Dakota

2Department of Neurobiology, Physiology and Behavior, University of California, Davis, Davis, California

Introduction

In preceding weeks you’ve learned how in many animals behaviors are correlated. For example, in looking at cricket calls, the frequency of an aggressive call was correlated with the number of chirps per aggressive call. However, what if females preferred high frequencies but low number of chirps? How would selection act on the population? In this exercise you’ll first examine how selection acts on single behaviors and then how it acts when behaviors are correlated.

Learning Goals

1. Understand how selection is predicted to act on single traits

2. Understand how covariances affect evolutionary responses

Learning Objectives

Part 1.

a. Apply the breeder’s equation: Given selection, predict composition of population after selection. Extend over multiple generations.

b. Infer long-term deterministic effects of selection on populations

i. Trait means

ii. Genetic variation

Part 2.

c. Use same single trait fitness relationships but vary strength of covariances; compare outcomes to those seen with univariate relationships

d. Introduce Lande-Arnold (1983) equation have them apply it numerically

e. Infer long-term deterministic effects of selection on population with varying covariance using graphical interface

i. Trait means

ii. Genetic variation

Part list

· Part I – Univariate selection responses 60 minutes

· Part II – Bivariate selection responses 60 minutes

Part I—Univariate selection responses

Humans have a long interest in understanding how populations will evolve in response to selection, not only for general evolutionary questions but also for the purposes of agriculture. Agriculture and domestication provide many of the clearest examples of evolution in action and many evolutionary biologists, including Charles Darwin, used domesticated species to better understand evolution. One very well studied mathematical approach to predicting evolutionary change is rooted in this framework: the Breeder’s Equation:

Δz=h2s

where is the change in a population’s mean for a trait after selection, is the “narrow-sense heritability” that we talked about in class, and s is the difference between the population’s mean for a trait before selection and the mean for those individuals able to reproduce. The Breeder’s Equation, and modifications of it have been used extensively by agronomists and animal scientists to increase agricultural yields for everything from corn yield to milk production.

Because this equation might initially be somewhat intimidating, let’s work through an example:

Scenario: You have a garden with twenty pepper plants. Each of the pepper plants produced a different number of peppers and for next year you want to increase the number your garden will produce. You know from some online searches that the heritability of the number of peppers produced is 0.4. Your pepper production was:

REVISED TABLE

Based on the above data, what is the average number of peppers produced:

If you only collect seeds from the top 25% of pepper plants and so only allow them to be the parents of next year’s pepper plants, what would the average of those peppers be:

What is the difference (this is “s”):

Based on the Breeder’s Equation, what will the average number of peppers your plants will produce be next year (note that is the change in population means):

Congratulations, you’ve now successfully evolved your population of peppers!