Does a species change more through natural selection if the weaker, less favored individuals reproduce more, or if the stronger, more favored individuals reproduce more?
Either.
The problem is in the use of words like weaker and stronger, as they can be irrelevant to survival and sexual selection. That is why the oxymoron "fit" is used, where fitness is defined by the ability to survive and breed. Those that are "fit" breed more than those that are not fit (dead, sterile, etc).
For an individual of a species to be weaker than the other members of it's species, it must be genetically imperfect in some way, in other words, there is a variation in it's genetic code that is not in the stronger individuals.
Or it could be malnourished, but generally there are genetic differences between all individuals in a breeding population, and some variations may be better fit in some ecosystems while others are better fit in different ecosystems.
Pocket mice for example, the population is typically tan, living in a sandy desert ecology. Some however have a mutation that turns their fur black, these individuals are not as fit as the tan mice for the sandy desert ecology, but they are better fit for the neighboring lava bed ecology, where the tan mice are not as fit as the black mice.
Which is "weaker?" Which is "stronger?" Those terms do not adequately describe the situations, and thus give a false impression, one that leads people to these misinformed type questions.
If this is true, then according to evolution by 'survival of the fittest', ...
Another dubious phrase, as it can mean a range of fitness (all that survive) or it can mean the best most fittest (which is misleading). Better to say "survival of those able to survive and breed" as this includes those just barely able and those that are very able.
... if the stronger individuals succeed in reproducing more often than the weaker ones (as is claimed by evolutionists), ...
Actual evolutionary biologists would actually say "... if the
better adapted individuals succeed in reproducing more often than the
less adapted ones ... " which is observed as well nourished healthy individuals are generally more successful at breeding than poorly nourished sick individuals ...
... , then the genetic code {pool of the breeding population} would in fact vary less, as there would be less imperfections/ variations in the stronger {better adapted} individuals to pass on to their offspring.
Correct, the less advantageous traits are removed by selection.
Would natural selection then actually narrow the variation of species instead of broadening it, as is claimed?
Nobody claims that natural selection increases diversity, that role is taken by mutations, which occur in every individual in every generation, some altering traits in the phenotype (and thus subject to selection in the next round) and some biding their time (neutral). Some mutations of course are also deleterious and either cause death during development or make the individual susceptible to selection in the next round.
Mutations that survive selection add to the genetic diversity of the breeding population.
Evolution is a two-step feedback response system that is repeated in each generation:
Like walking on first one foot and then the next.
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