The population can grow or shrink depending on the interaction of the two flows and the two rates.
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Birth and immigration both add individuals to a population, increasing the population size. Similarly, deaths and emigration remove individuals, reducing the population. So growth would be equal to the sum of immigration and births, minus the sum of emigration and deaths.
The birth rate and the Death rate are equal, providing there is no immigration/emigration of the population.
Emigration.
It achieves what used to be called "ZPG" - zero population growth. Births and deaths are essentially equal. The population sustains itself where it is, but does not grow or shrink.
A population with a death rate greater than a birth rate has a declining population.