There are various grounds on which to question aspects of the current evolutionary model, and a lively debate persists today. Evolution is in principle hard to model precisely, since the changes it describes usually takes place over time periods that are inaccessible to human beings. Consider the related situation in astronomy. Changes in the movement of the stars are slow, and until very recently were too slow to be detected within the lifetime of an individual. However, with the help of a continuous series of observations dating back to the fifth century BC, Copernicus was able to formulate a detailed model that fit two thousand years of data. Unfortunately, in the case of biology, two thousand years of continuous observation would in most cases reveal very little. We must thus rely in indirect evidence, such as fossil remains and systematic structural similarities and differences in living forms. This evidence leaves room for a variety of possible interpretations of past events, and thus of the mechanisms of change that underlie them. I can examine only a few focal points of contention.
Gradualism. All the way back to Darwin, the notion that changes accrue gradually over long periods of time has been a central proposition of evolutionary theory. As Ernst Mayr put it in Animal Species and Evolution (1963), "all evolution is due to the accumulation of small genetic changes" (p. 586).
In contrast, the fossil record suggests long periods of stasis followed by brief periods of rapid change - what Niles Eldredge and Stephen J. Gould dubbed punctuated equilibrium. This data has sometimes been taken as evidence against the neo-Darwinian model by people who believe the order of nature is due to the intentional act or acts of a supernatural being. Within the scientific tradition, the relative lack of continuous change in the fossil record is interpreted as evidence that speciation events have typically taken place in small populations over relatively short periods of time.
In addition, gradualism should not be discounted. For instance, in the period from 300,000 to 100,000 year ago, fossil remains of the genus Homo show a wide range of forms. It is not unlikely that we have inherited alleles from individual mutations that took place over a wide geographical area during this period. As the best mutations spread throughout the existing populations, the range of functionally meaningful variation drops towards zero. Archeologists of the future may well see only our remains, appearing as if by the hand of God, while the gradual accumulation of alleles that made us possible leaves little or no trace.