A recent paper called 'Genetic Influences in Sport and Physical Performance' states:
"Muscle fibre type determination is complex. Whilst initial composition is likely to be strongly influenced by genetic factors, training has significant effects on fibre shifts."
They also go onto say that:
"However, the role of genetic variation in determining psychological state and responses remains poorly understood; only recently have specific genes been implicated in motivational behaviour and maintenance of exercise."
"With the current state of knowledge, the field of genetic influences on sports performance remains in its infancy, despite over a decade of research."
An older paper which also examined fiber types stated that:
"These results reveal the existence of large interindividual variability and gender differences in the most common characteristics of the human skeletal muscle.".
Another study hypothesises that there may be racial differences in muscle fibre types.. It's also said that a large variation in fiber composition of skeletal muscle within subgroups of athletic ability. This suggests that factors other than fiber-type composition contribute to performance..
A small study carried out in the Croatian Navy found that ectomorphs had a better ability to sprint than endomorphs.. They also found a positive correlation between calf girth and sprinting ability.
The information is a bit disjointed and sparse. However, to finally come around to the question at hand, it seems that although there may be differences according to body type initially (which obviously also has a genetic basis), training and physical activity contributes significantly to what number and types of fibres individuals possess.
There are lots of sport-specific research papers examining individuals' performance and suitability on body types.
A note on somatotyping: I guess it might also be handy note that somatotyping (endomorph, ectomorph and mesomorph) is just one theory on measuring an individual and it does have critics. The theory was initially developed in an attempt to link body type to behaviour.
It's been suggested that measurements like BMI are much more objective and useful.. Another point made was that bodies change according to a number of environmental variables, nutrition etc.. For example, one study suggested that intense labour during adolescence may affect somatotype (there are a few similar studies).. So perhaps while using somatotypes to identify a person at one point in time is useful, it has limits in use as a long term classification.
This point probably has more relevance to the question at hand since with training and physical activity, a person can potentially change their somatotype at least to some extent; and also the number and types of muscle fibers (which evidence supports).
Puthucheary Z, et al. Genetic influences in sport and physical performance. Sports Med. 2011. 41:845-59.
Nielsen J. Glucose intolerance in the West African Diaspora: a skeletal muscle fibre type distribution hypothesis. Acta Physiol. 2011. 202(4):605-16.
DeLee: DeLee and Drez's Orthopaedic Sports Medicine. 3rd ed. Saunders.
Simoneau, et al. Human variation in skeletal muscle fiber-type proportion and enzyme activities. AJP - Endo. 1989. 257(4):567-572.
Sporis G. Impact of body composition on performance in fitness tests among personnel of the Croatian navy. Coll Antropol. 2011. 35(2):335-9.
Maddan, et al. The BMI as a somatotypic measure of physique: A rejoinder to Jeremy E.C. Genovese. The Social Science Journal. 2009. 46:394–401.
Parnell. Simplified somatotypes Original Research Article. Journal of Psychosomatic Research. 1964. 8(3):311-315.
Ozener, et al. The effect of labour on somatotype of males during the adolescent growth period. Homo. 2008. 59(2):161-72.