For simplicity, we will assign the letter "a" for the gene of interest. Thus, the heterozygous genotype is Aa. You may sketch a punnet square of the cross: Aa x Aa to help illustrate that the combinations result in 50% chance of heterozygous offspring.

Arbitrarily, we may assign the letter "b" for the gene of interest. The cross then is as follows: Bb x Bb. Each parent has a 50% chance of donating a recessive (b) allele to the offspring. We must multiply these probabilities to get the chance of a homozygous recessive offspring. 

This question requires that we do a dihybrid cross. The cross in question is AaBb x AaBb, using A to represent dominant green color and B to represent dominant long shape. The parents are heterozygous for both traits, meaning they will carry one dominant color allele and one dominant shape allele.

The result of a punnet square for a dihybrid cross is: 1 AABB, 3 Aabb, 8 AaBb, 3 aaBb, 1 aabb.

This gives a total of sixteen different offspring. Two different genotypes carry dominant alleles for both traits: AABB and AaBb. There are a total of nine offspring between these two genotypes. The probability of an offspring being dominant for both traits is thus nine out of sixteen.

Genetic drift occurs as a result of chance events causing changes in the allele frequency of a population. It doesn't favor the most fit individuals, but occurs at random.

Mutations can contribute to genetic drift, however, genetic drift is a more specific answer and more relevant to the question at hand.

Genetic drift is the random process of alleles being passed from parents to offspring. Increasing genetic diversity in a population requires introducing a greater number of alleles, which can only occur through mutations or addition of unrelated members to the population. Genetic drift only affects how already-existing alleles are passed down.

If an allele has a high frequency at baseline, the chance of it being passed down to subsequent generations is higher than alleles of a lower frequency. Through random chance, a high-frequency allele can eventually have a frequency of 100%, becoming fixed in the population. Conversely, a low-frequency allele can eventually disappear from the population if none of the few parents who possess that allele happen to pass it onto their offspring.

Genetic drift describes the random selection of alleles that are passed from one generation to the next due to independent assortment in gametogenesis. Genetic drift cannot create new alleles, so it cannot increase genetic diversity (the number of alleles in a population). It can, however, decrease genetic diversity if an allele of a low frequency is not passed down to subsequent generations due to pure chance.

There is no hard and fast rule for whether genetic drift or natural selection have had a greater effect on shaping populations. Both have greatly shaped the populations present on Earth today, but their relative importance varies between species and has also varied over time. The conditions of Hardy-Weinberg equilibrium require that both natural selection and genetic drift be negligible. If genetic drift is occurring, then the population cannot be in Hardy-Weinberg equilibrium.

Small populations tend to have less genetic variation to begin with. Introducing a bottleneck effect further reduces variation and population size, amplifying the effect of genetic drift. This leaves them susceptible to changes in the environment that they may not be capable of adapting to due to limited differences among individuals.

A bottleneck effect is the term used to describe the loss of genetic variation that occurs after outside forces destroy most of a population. The few individuals left to reproduce pass their traits on to all of their offspring, which then may thrive without the competition of a large population. Eventually, there may be a large, very genetically similar population based on the traits of the few original survivors.

The founder effect describes the low genetic variation of a population derived from a small group of individuals in a new geographic location. Genetic drift is the random change of allele frequency in a population.

The bottleneck effect describes the phenomenon when a population has a sudden reduction in the gene pool due to natural environmental events, natural disasters, disease, or human involvement. This reduction in the gene pool will likely cause a bias that did not exist in the original population. For example, suppose a population of birds has a small number with a mutation making them unable to fly. If a disease reaches this population that kills all birds when they reach an altitude above 50m, then the gene pool of the population will suddenly shift to favor the flightless birds.

The bottleneck effect, after a long time, could potentially lead to speciation, but this is not a defining factor of the effect. Introducing a new species can increase the pressures of natural selection, but does not directly relate to the bottleneck effect. A decrease in genetic variety due to a small number of individuals from a larger population establishing a new population more aptly describes the founder effect.

The bottleneck effect describes the sudden, sharp decrease in the size of a population. After a bottleneck event, a population could either recover or go extinct depending on the fitness of the individuals remaining in the population.

Depending on the type of event that created the bottleneck, it is possible that the surviving members are the most fit, but this is not always the case. The new smaller population likely has less genetic diversity, which typically makes successful adaption more difficult and less likely, but if the surviving members of the population are highly fit, their ability to adapt may not be hindered.

While man-made events certainly are a source of bottleneck effects in the world today, there are still natural bottleneck events and no concrete evidence to say that man-made bottleneck events are more frequent or have more of an effect on genetic drift than natural events.