It is not 100% true. We have to see other aspects such as socio-economic and biophysics. We have to analyse in more comprehensive way. We can refer to the IPCC climate risk assesement framework. Good luck.
Inbreeding, genetic drift, restricted gene flow, and small population size all contribute to a reduction in genetic diversity. Fragmented and threatened populations are typically exposed to these conditions, which is likely to increase their risk of extinction. Genetic drift is the reason why we worry about African cheetahs and other species that exist in small populations. Drift is more pronounced in such populations, because smaller populations have less variation and, therefore, a lower ability to respond favorably that is, adapt to changing conditions. Small population sizes put a species at extreme risk of extinction due to a lack of variation, and a consequent decrease in adaptability. This weakens the chances of survival under pressures such as climate change, competition from other species, or new diseases. To be more exact, genetic drift is change due to "sampling error" in selecting the alleles for the next generation from the gene pool of the current generation. Although genetic drift happens in populations of all sizes, its effects tend to be stronger in small populations. As populations decline in size, they become increasingly vulnerable to the combined impacts from the loss of genetic diversity, inbreeding depression, Allee effects, environmental stochasticity, and demographic stochasticity. Many rare and/or endemic species exhibit one or more of the attributes which make them especially prone to extinction: (1) narrow geographical range, (2) only one or a few populations, (3) small population size and little genetic variability, (4) over-exploitation by people, (5) declining in seed production and viability. It is well known that for an isolated population, the probability of extinction is positively related to population size variation: more variation is associated with more extinction. Small populations of animals, such as those typically found on islands, are prone to extinction because they are more vulnerable to unpredictable events. Small populations tend to lose genetic diversity more quickly than large populations due to stochastic sampling error. This is because some versions of a gene can be lost due to random chance, and this is more likely to occur when populations are small.