Questions: Population Viability Analysis and Predictive Modeling

Question 1

A PVA model for a population of 25 condors finds a 40% probability of extinction within 50 years, even though average birth rates exceed death rates. The most likely explanation is:

• A. The model contains an error — positive average growth rates preclude extinction by definition
• B. Demographic stochasticity — in small populations, random variation in individual outcomes can drive extinction despite favorable averages
• C. The model is too pessimistic because it omits density-dependent population recovery
• D. Environmental stochasticity is the only relevant factor; individual-level randomness is negligible at any population size

Answer: (B)

In small populations, demographic stochasticity (randomness in whether individual animals survive or reproduce) dominates. With only 25 birds, a run of bad luck — several females failing to breed, a disease killing a few individuals — can drive the population extinct even when average rates favor growth. In a population of 25,000, individual coin flips average out; in a population of 25, they don't. Option A is the key misconception: average growth rate > 1 does not guarantee persistence in stochastic small-population models.

Question 2

The primary output of a Population Viability Analysis is best described as:

• A. A single predicted population size at a specified future date
• B. The minimum viable population size for the species under current conditions
• C. A probability of extinction over a specified time horizon, estimated from many stochastic simulations
• D. The carrying capacity of the habitat given current resource levels

Answer: (C)

PVA runs hundreds or thousands of stochastic simulations incorporating random variation in survival, reproduction, and environmental conditions. The output is a probability — for example, '35% chance of extinction within 100 years under current conditions.' This framing is powerful because it lets managers compare scenarios quantitatively: adding individuals, protecting habitat, or assuming catastrophes each change the extinction probability curve. A single deterministic prediction (option A) would hide exactly the uncertainty that makes PVA valuable.

Question 3

A population with an average birth rate exceeding its death rate can seldom go extinct within 100 years, even if it is small.

• T. True
• F. False

Answer: False

This ignores stochasticity. In small populations, demographic stochasticity — the randomness inherent in individual survival and reproduction events — can drive extinction even when average rates favor growth. If only 10 individuals remain and several consecutive bad years occur, the population may hit zero before average rates can rescue it. PVA models quantify this risk precisely by running thousands of stochastic trials, not by extrapolating the average growth rate.

Question 4

PVA is more valuable for comparing the extinction probabilities of different management scenarios than for predicting exact extinction dates.

• T. True
• F. False

Answer: True

PVA cannot predict when extinction will occur with precision — its probabilistic estimates depend on data quality and model assumptions. Its real power is comparative: 'translocation of 10 individuals every 5 years reduces the 100-year extinction probability from 35% to 12%.' This makes trade-offs between management options explicit and quantitative. The absolute predictions carry wide uncertainty, but the relative ordering of scenarios is more reliable — which is exactly what conservation managers need to prioritize interventions.

Question 5

Why does demographic stochasticity pose a greater extinction risk to a population of 20 individuals than to a population of 20,000, even if both have identical average birth and death rates?

Model answer: Demographic stochasticity refers to randomness in individual-level outcomes — each animal independently has a probability of surviving or reproducing in a given year. In a large population, these individual coin flips average out to the mean rate: random variation in one individual's fate has negligible effect on the whole population trajectory. In a population of 20, individual outcomes dominate — if 3 of 20 breeding females happen to fail this year by chance, that is a 15% reduction in reproduction, potentially catastrophic. The law of large numbers protects large populations from demographic stochasticity but offers no protection to small ones.

This is why minimum viable population estimates typically run into the hundreds to thousands: below a critical size, stochastic extinction overwhelms even favorable average growth rates. Genetic deterioration (inbreeding, loss of heterozygosity) compounds the problem — small populations simultaneously face stochastic extinction risk and genetic erosion, a dynamic called the extinction vortex.