Selection pressure in declining populations?

"Furthermore evolution will push very hard not to get excluded of selection entirely. ". I heard this statement many times, yet i find no mathematical basis for it. For example - If for example mutation allows you to increase your successful offspring from 7 to 8, how come its inferior to mutation that increase it from 0 to 1?
Anyway if this is true, does it mean that in declining fertility rates - selection pressure increases , because for more and more members of the population it becomes matter of whether to have 0 or 1, not 7 or 8.

Does it differ in tournament and monogamous species?

Lastly i want to transfer humans. In countries and societies where the fertility rates are much below replaceable, does something differ in how reproductive success is redistributed in society(especially in males), compare to countries with high fertility?

Any references to any of the topics will be helpful, thanks!