# Population Growth Rate Question?

A population of 600 birds faced a problem of biological magnification resulting in a large number of deaths reducing their population to 350. But 230 births also took place and 21 birds immigrated into the population while 13 birds migrated out. How many deaths took place in the population? What is the growth rate of this small population?

So I guess we need to use the PGR = (BIRTHS + IMMIGRATION) - (DEATH + EMIGRATION) / INITIAL POPULATION x 100%

So.. I keep getting -2% as my answer, but apparently the correct answer is -41.7%

Thanks!

• Tag as homework? Also, 350/600 -1 = -41.7% which is the alternative answer you are looking for. It all depends on whether the births, immigrations and emmigration are already included in the reduced population size at t+1. – fileunderwater Oct 21 '13 at 22:52
• You phrasing seems to imply that 350 remained after deaths, but that births etc also took place, making the population size at t+1 equal to 350+230+21-13=588. If so, the -2% would be correct. – fileunderwater Oct 21 '13 at 22:58
• @fileunderwater but how would I make it true so that it equals -41.7% using the full population growth equation? – Jesse Oct 21 '13 at 23:01
• Well, 250/600=41.7 – Amory Oct 22 '13 at 3:00

As you have phrased it, the question can be understood in two ways.

1. The population size at t+1 is 350, after births, deaths and migration have taken place.
2. The population size is 350 after deaths, but you also have to take births and migration into account to calculate population size at t+1

For alternative 1 the growth rate is:

$pgr = \frac{(230+21)-(488+13)}{600} = -0.417$,

with $\Delta N=-250 \Rightarrow -250 = 230+21-deaths-13$

For alternative 2 the growth rate is:

$pgr = \frac{(230+21)-(250+13)}{600} = -0.02$