Which of the following population growth models shown in Fig. 9 depicts a minimum viable population size that is greater than 0?

Fig. 9 Three Population Models

Question

Which of the following population growth models shown in Fig. 9 depicts a minimum viable population size that is greater than 0?

Fig. 9 Three Population Models

BlackTom AI · Accepted Answer

An Allee effect (strong depensation) produces a positive threshold: populations below that threshold decline (negative growth) and above it can increase. The minimum viable population (MVP) is the smallest stock level X* at which the net growth F(X) is zero and for any X > X* the growth is positive; for X < X* growth is negative and the population tends toward extinction. Relevant concepts: - F(X) is net population growth as a function of stock level X. - MVP is the positive root of F(X) where F switches from negative (below) to positive (above). - In a simple logistic model F(0) = 0 and F(X) ≥ 0 for small X, so there is no positive MVP (effective MVP = 0). - In a depensatory/Allee model F(X) < 0 at low X, crossing the axis at a positive K0 gives a positive MVP. Step-by-step reasoning applied to the three panels: 1. Panel (a): F(X) starts at zero at X = 0, rises to a peak (MSY), then returns to zero at carrying capacity K. For any small X > 0, F(X) > 0, so small populations grow. The only equilibrium causing extinction is X = 0, so MVP = 0. Thus (a) does not depict a positive MVP. 2. Panel (b): similarly shows F(X) ≥ 0 for small X (the curve does not go below the axis at low stock). There is no interval of negative growth at low X, so again MVP = 0. 3. Panel (c): the curve dips below the horizontal axis at small X (negative growth), crosses the axis at a positive stock level labeled K0, then becomes positive until it returns to zero at K. That positive root K0 is the MVP: any population below K0 declines toward extinction; any population above K0 can increase. This is the classic strong Allee effect. Why the other options are incorrect: - A and B: no negative growth at low abundance, so minimum viable population is zero. - “None of the above”: incorrect because (c) clearly shows a positive threshold. Therefore the correct choice is C, matching the provided answer.

Which of the following population growth models shown in Fig. 9 depicts a minimum viable population size that is greater than 0? Fig. 9 Three Population Models单项选择题

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