After leaving the Fish & Wildlife Service, you land a job as a botanist on islan

Question

After leaving the Fish & Wildlife Service, you land a job as a botanist on islands off the coast of California. You are studying an endangered plant species that only grows there and nowhere else in the world. You find these plants are outcompeted by an introduced species from Europe.

You study the populations and find the following conditions:

Species

Carrying capacity (K)

Growth rate (r)

native plant

200

0.5

invasive plant

500

0.5

One of the reasons that native plants are declining is that the invasive plants absorb nitrogen from the soil about twice as fast (? = 2). What value would you need to reduce this competition coefficient to in order to enable the native species to persist? Assume that the native species has no competitive effect of the invasive species (? = 0).

Species

Carrying capacity (K)

Growth rate (r)

native plant

200

0.5

invasive plant

500

0.5

Explanation / Answer

Ans

Plant growth is influenced by variation in time and resource size fluctuations which affects the biomass and reproduction of species. Resource fluctuations benefits invasive species more than the native species and this is predicted by “Fluctuating Resource Hypothesis”, as many of the invaders are highly effective to the rapid capturing resources.

Lotka-Volterra competition equations describes the competition between the native and invasive plant species and helps to study the competition coefficients, the community matrix, and diffuse competition.

In two competing (Native and invasive) species, N1 and N2, with carrying capacities K1 (200) and K2 (500) and growth rate r1 (0.5) and r2 (0.5).The simultaneous growth of these two competing species occurs together is explain by differential logistic equations:

Whereas, ?12 and ?21 are competition coefficients; ?12 is a characteristic of invasive Species which measures its competitive inhibition on the native Species population; and ?21 is a similar characteristic of native Species which measures per capita inhibitory effects on invasive Species. By putting the values in the equations and considering the situation when there is absence of interspecific competition in native species (?12 or N2= 0 in Equation (1); ?21 or N1 = 0 in Equation (2)), both native and invasive species grow sigmoidally according by Verhulst-Pearl logistic equation and they reaches an equilibrium population density with their own carrying capacity.

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