On the other hand, since it happens independently at many locus natural selection will also increase heterozygosity (or allele diversity), thereby increaing species-level variation of genes which in turn allows population to better adapt to the shifting envireonment.
How does natural selection enhance or reduce tha variability of a species?
Natural selection does both. As it favours certain allele, it reduces variability by causing that genes with those allele will out reproduce genes without.