27 From population biology to fitness

27.1 Introduction

This practical is the bridge between the two halves of the course: it uses the matrix population models from the population-biology part to make the concept of fitness concrete in the evolution part. The key idea is that fitness is closely tied to population growth rate (\(\lambda\)): a genotype whose life history yields a higher \(\lambda\) will increase in frequency — it is fitter. Students then meet an evolutionary trade-off and test whether a benefit (higher juvenile survival) is worth its cost (lower adult survival). It uses the popdemo package and mirrors the earlier matrix-modelling exercise.

27.2 Key Concepts

  • Fitness ≈ population growth rate: the genotype with the higher \(\lambda\) spreads.
  • In silico selection: encode two genotypes as two matrices, compare their \(\lambda\), and infer which increases in frequency.
  • Trade-off: a beneficial change (↑ juvenile survival) that carries a cost (↓ old-adult survival); whether it is favoured depends on the net effect on \(\lambda\).

27.3 Learning Outcomes

By the end of this exercise, students will be able to: - Explain the relationship between population growth rate and fitness. - Explain the concept of an evolutionary trade-off. - Use a matrix model to compare the fitness of alternative genotypes.

27.4 Activity Overview

Suggested Timings: - 5 minutes: Recap MPMs and state the fitness–\(\lambda\) link. - 10 minutes: Build the baseline 3-stage matrix; project and get \(\lambda\) (≈1.166). - 10 minutes: “Caring” genotype — raise juvenile survival 0.10 → 0.11; recompute \(\lambda\) (≈1.192). - 10 minutes: Introduce the trade-off (↓ old-adult survival); decide if it is favoured.

27.5 Instructions for Facilitating

  1. Load popdemo (install.packages("popdemo") if needed) and build the baseline juvenile/adult/senescent matrix; read the entries aloud so students can map each to a biological statement (fecundities in the top row; survival/transition below).
  2. Project the population and show the transient period settling into steady exponential growth; extract \(\lambda \approx 1.166\) (~16.6%/yr).
  3. Introduce the “caring” genotype (juvenile survival 0.10 → 0.11) and show \(\lambda\) rises to ≈1.192 (~19.2%/yr); ask what happens to the frequency of the two genotypes over time.
  4. Add a trade-off genotype: keep the juvenile-survival benefit but cut old-adult survival (e.g. to 0.05); recompute \(\lambda\) and decide whether the benefit outweighs the cost.
  5. Have students probe prime-age adult survival: how far can it fall before the trade-off stops being worthwhile?

27.6 Questions & Model Answers

  1. Why will the “caring” genotype increase in frequency?
    • It gives a higher \(\lambda\) (≈1.192 vs ≈1.166), so its sub-population grows faster than the “ordinary” genotype’s. Higher \(\lambda\) = higher fitness = rising frequency.
  2. Is the trade-off genotype (↑ juvenile survival, ↓ old-adult survival) fitter than the original?
    • Compute its \(\lambda\) and compare to the baseline ≈1.166. If its \(\lambda\) is higher it spreads; if lower it is selected against. The answer depends on how large the old-adult-survival cost is relative to the juvenile-survival benefit — the whole point of the exercise.
  3. Why can a change that helps individual offspring still be selected against?
    • Because fitness is a whole-life-cycle property. A gain concentrated in one transition can be outweighed by a loss in another; only the net effect on \(\lambda\) determines whether the genotype is favoured.

27.7 Teaching Tips

  • \(\lambda\) is the fitness readout: keep returning to “which matrix gives the bigger \(\lambda\)?” as the operational definition of fitness here.
  • Elasticity intuition: the exercise is a natural moment to recall that \(\lambda\) is more sensitive to some transitions than others, which is why a small juvenile-survival change can matter and why the trade-off’s outcome is not obvious in advance.
  • Encourage experimentation: let students vary the cost to find the break-even point where the trade-off stops paying.

27.8 Common Pitfalls

  • popdemo not installed before running the projections.
  • Reading the matrix backwards: entries are “from column-stage to row-stage”; getting this wrong misplaces fecundity and survival.
  • Judging a genotype by one vital rate instead of by its overall \(\lambda\).
  • Assuming any benefit is favoured: without accounting for the cost, students may wrongly conclude the trade-off genotype must win.