Sexual vs. Asexual
Like most other insects, wasp species tend to develop sexually; however, there are some wasp species that produce more than one way -- containing the ability to asexually reproduce as well. Although the science behind why two modes of reproduction still exist isn't understood, what is known is that species within a consistently changing environment tend to migrate toward sexual reproduction as it encourages genetic diversity. Asexual reproduction, although easier and more efficient, causes genetically identical individuals, which can more easily be wiped out by a similar threat should one be presented.
Females Stem from Fertilized Eggs
Through sexual reproduction, wasps extract sperm from the males, which will eventually be used to fertilize some of the eggs. Eggs are then laid in a safe location for larvae to develop; however, some species -- such as the parasitic Lysiphlebus fabarum -- evolved a system of laying eggs within aphid insects, using the insect to provide nutrients to the developing larvae. In all species, female wasps store sperm, systematically fertilizing eggs over time -- although not all eggs will be fertilized. The fertilized eggs will become females within a sexually reproducing wasp population.
Males Stem from Unfertilized Eggs
To match the females, unfertilized eggs will also be leftover -- these eggs will develop into males. Many wasp species live within social groups, while others have solitary lives, much different from their extremely social bee relatives. In wasp species, males take a secondary role to females, generally only taking on one task -- attempting to mate successfully when the time comes.
Genetic Determinants
One of the unusual factors in wasps that contain asexual reproduction is the methodology. According to ScienceDaily.com, the species that contain asexual reproducers do so because of a recessive trait that adheres to the common laws of Mendelian genetics, where a certain percentage of the offspring will be asexual reproducers.