Questions: Effective Population Size (Ne) and Its Estimation

Question 1

A population of 10,000 individuals crashes to 50 for a single generation due to a disease, then recovers to 10,000. What does the effective population size over this three-generation period most closely reflect?

• A. The arithmetic average census size, approximately 6,683
• B. The final recovered size, 10,000, since the crash was temporary
• C. The harmonic mean, dominated by the bottleneck of 50
• D. The initial size, 10,000, because the crash occurred after drift had already acted

Answer: (C)

Ne across multiple generations is the harmonic mean of per-generation sizes: 3 / (1/10,000 + 1/50 + 1/10,000) ≈ 3 / 0.0201 ≈ 149. The harmonic mean is dominated by the smallest value, so the bottleneck of 50 pulls Ne far below the arithmetic average. A single severe crash leaves a lasting genetic signature — the population loses alleles irreversibly during the bottleneck regardless of how quickly census size recovers afterward.

Question 2

A wildlife manager counts 1,010 individuals in a harem-based breeding species. Only 10 males and 1,000 females actually breed each generation. Using Ne ≈ 4·Nm·Nf / (Nm+Nf), what is the approximate effective population size?

• A. Approximately 1,010 — the same as census size, since all individuals are counted
• B. Approximately 505 — half the census size, by a standard correction factor
• C. Approximately 40 — dominated by the rare breeding sex
• D. Approximately 200 — applying the typical Ne/N ratio of 0.2

Answer: (C)

Ne = 4·10·1000/(10+1000) = 40,000/1,010 ≈ 40. The unequal sex ratio formula shows that Ne is largely determined by the rarer breeding sex. With only 10 males contributing genetically, the effective size is close to 4×10 = 40 regardless of the thousand females. Options A and B treat Ne as a simple fraction of N, missing the mechanism: genetic drift is governed by who passes genes to offspring, and when one sex is the bottleneck, that sex's count dominates.

Question 3

A species with a large census population size (N) is reliably protected against the genetic risks of inbreeding and loss of adaptive potential.

• T. True
• F. False

Answer: False

Census size N overestimates genetic size whenever sex ratios are unequal, reproductive success varies among individuals, or the population has passed through bottlenecks. A population of 5,000 counted individuals might have an Ne of only 200, placing it below the threshold for maintaining evolutionary potential (Ne > 500 by the 50/500 rule). Conservation decisions based on head counts alone can be dangerously misleading — Ne is the quantity that governs drift, inbreeding, and loss of genetic diversity.

Question 4

The linkage disequilibrium (LD) method for estimating Ne works because genetic drift in small populations creates non-random associations between alleles at different loci.

• T. True
• F. False

Answer: True

In an infinitely large population, alleles at separate loci assort independently (linkage equilibrium). In small populations, genetic drift randomly samples gametes, creating associations between alleles at unlinked loci by chance. These non-random associations — linkage disequilibrium — persist and accumulate when Ne is small. By measuring the extent of LD in a single contemporary sample, researchers can infer Ne without needing historical samples. Higher LD implies smaller Ne, giving a window into effective population size from a single time point.

Question 5

Explain why Ne is almost always smaller than census size N, and why this distinction matters for conservation biology.

Model answer: Ne is smaller than N because the idealized Wright-Fisher model assumes equal sex ratios, equal reproductive success, and constant size — conditions real populations violate. Unequal sex ratios (few breeding males), variance in reproductive success (some individuals produce many offspring), and population size fluctuations (harmonic mean is dominated by bottlenecks) all reduce Ne below N. Conservation matters because Ne governs genetic drift and inbreeding risk. A population with N=5,000 but Ne=200 may be genetically precarious despite appearing large by head count.

The Ne/N ratio commonly ranges from 0.1 to 0.3 in wildlife populations. The three main mechanisms are: (1) unequal sex ratio — Ne ≈ 4NmNf/(Nm+Nf), heavily influenced by the rarer breeding sex; (2) variance in reproductive success — when some individuals contribute many offspring and others none, drift is stronger than in equal-contribution populations; (3) bottlenecks — the harmonic mean formula means a single severe crash drives Ne toward that minimum. For conservation, the 50/500 rule uses Ne thresholds (not N) to assess inbreeding risk and evolutionary potential, making Ne estimation central to population viability analysis.