This is a really weird article. It talks about how below replacement birth rates mean the population will decline. Which is true by definition.
Then about how some countries have lots of immigrants. Then it does nothing to link the two. So in spite of asking to talk about the link it doesn't.
I wanted to look first to see if there was a link. As the article does nothing to show there is.
I took a list of countries by their percentage of immigrants
And one of countries by their birthrate
I created this combined dataset of Country, Birthrate and Immigrant % and put it here
The correlation between birthrate and the percentage of immigrants in a country is weak.
> cor(data$FertilityRate, data$ImmigrantPer)  -0.3463663I am willing to bet you at odds that the correlation between wealth and birth rate and between wealth and % of immigrants is higher. That having money causes immigrants to come to your country and you to have less children. Not that people choose between having a child and a 25 year old Ethiopian.
So Irish Times please do talk about what is at best a weak link between immigration and low reproductive rates.