# Ecosystem

• Ans:3
Please explain how to solve this question. Why can't other options be the answer?

• @anag

S shaped curve is also called logistic growth curve

• @anag
Logistic population growth -- the plot shows population size (N) as a
function of time (t). At first, the population grows essentially exponentially.
At a population size of K/2 the growth rate begins to decline and eventually reaches an
asymptote at the carrying capacity, K. The "braking agent" is the additional term
(K-N)/K -- try various values of K and N to see what effect the term will have on exponential growth. Some of what the course will do is explore the factors that influence or determine K. Note that the form of the "solution" (to the right of the curve) is in a different form/rearrangement than in Eqn

The logistic equation (dN/dt) and its solution for Nt.
The logistic equation uses exponential growth as its base, but then adds a "braking force" as numbers increase toward the "carrying capacity", K. The equation is:

``````       dN/dt=rN(K-N/ K)
``````

dN/dt =rNis the exponential growth equation . The new term K-N/K discounts exponential growth by the difference from the carrying capacity. For a small population the term in K-N/K is near 1.0 and growth is essentially exponential. As the population, N, nears K, growth slows (and can be negative for N > K). This is a continuous, differential equation. Later in the course we will deal with a discrete (difference equation) form of the logistic (which can have very different dynamics). We will revisit continuous logistic growth when we consider models of competition and predation.
Estimating the r from real-world plots of N against time, when growth is logistic. The problem with equation 5.3 is that we have one equation with two unknowns (K and r). How can we find their values?

With an observed set of measurements of population size against time, we can estimate r by plotting the untransformed data (with X-axis, t and Y-axis, population sizes at various times t) and then:

1. eyeballing an estimate of K (the asymptote or place where the curve flattens out)

2. since we now have an estimate of K (and already knew NØ and Nt), we can solve Eqn for r

3. or, we can estimate r graphically, as (the negative of ) the slope of the plot of

• @sunitasaxena In any growth curve, the value of r<0 is not possible. Is that why opt 3 is incorrect?

Generally for logistic growth, 0<r<1 is seen.

Opt 4 should also be incorrect since N>K is impossible. Isn't it? Please explain. I am still confused.

• @anag
For N>K r is negative
means r<0
Statement 4 is incorrect

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