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If the birth rate is higher than the death rate, the population increases. If the death rate is higher than the birth rate, the population decreases.
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 population can grow or shrink depending on the interaction of the two flows and the two rates.
The birth rate affects the size of population because of what its like. And the death rate is more than you can imagine.
births, death, immigration and emigration