Which point corresponds to the Allee threshold in Fig. 4?

Fig. 4 Population Model

Question

Which point corresponds to the Allee threshold in Fig. 4?

Fig. 4 Population Model

BlackTom AI · Accepted Answer

An Allee threshold (critical depensation) is the unstable population size at which per-capita growth switches sign: populations below it have negative net growth and decline toward extinction, while populations above it have positive net growth and can increase toward a higher stable equilibrium. On a plot of growth versus stock size, the Allee threshold is therefore the zero-growth crossing that separates negative growth at lower biomass from positive growth at higher biomass.

Step-by-step reasoning applied to the figure:
1. Identify zero-growth intersections: the red growth curve crosses the horizontal zero-growth line at three places. From left to right these are A (leftmost), C (small positive biomass), and the rightmost crossing (nearwhere the curve later returns to zero).
2. Determine growth sign just below and above each crossing:
   - Left of A (very small biomass) the curve is at zero or slightly negative; between A and C the curve is below zero (negative growth — the trough at B).
   - Just to the right of C the curve rises above the zero line (positive growth), continues up through point D and reaches a peak at E (maximum growth).
3. The Allee threshold is the crossing where growth changes from negative (at lower stock) to positive (at higher stock) — that is the unstable equilibrium separating decline to the low equilibrium from recovery to larger stock.

Why C is correct:
- C is precisely the zero-growth point where growth changes sign from negative (for smaller stocks) to positive (for larger stocks). Populations below C experience net negative growth and will decline; populations above C experience net positive growth and can recover. That is the defining behavior of the Allee threshold.

Why the other points are incorrect:
- A corresponds to the low stable/extinction equilibrium or left boundary, not the unstable threshold.
- B is the local minimum of growth (most negative growth), not a zero-growth threshold.
- D and E are points with positive growth (E is near the maximum growth), not zero-growth thresholds.
- F is a point on the axis within the positive-growth region (not a zero crossing).

Therefore, the Allee threshold corresponds to point C, matching the provided answer.

Which point corresponds to the Allee threshold in Fig. 4? Fig. 4 Population Model单项选择题

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