Over the last several decades, the scientific community has gathered a large amount of information regarding genetics and genetic variation. what are two main sources that lead to increased genetic variation? . selective breeding . gamete mutations . recombination . genetic drift . i have looked all in my notes and can't find anything on this topic.

"Recombination" and "Genetic drift" are the two main sources among the following choices given in the question that lead to increased genetic variation. The correct options among all the options that are given in the question are the third and the fourth options. I hope the answer has helped you. 

The right answer is Recombination AND Genetic drift

Recombination is an exchange of genetic information (strand of DNA) between two different sectors of the genome. A frequent example is the meiosis between homologous chromosomes (crossing over).

Genetic drift is the evolution of a population or species caused by random phenomena, impossible to predict. From the genetic point of view, it is the modification of the frequency of an allele, or of a genotype, within a population, independently of the mutations, the natural selection and the migrations. Genetic drift is caused by random and unpredictable phenomena, such as the chance of sperm and egg encounters, in the case of sexual reproduction.

The answers are:
carrier proteins → charged amino acid     
Carrier proteins are transmembrane proteins for the facilitated diffusion of charged amino acids across plasma membranes.

osmosis → water molecule
A type of passive transport, osmosis is the diffusion of water molecules in and out of cells.

active transport → calcium moves from low concentration to high concentration
This is the movement of substances across membranes against concentration gradient.

simple diffusion → oxygen
Oxygen molecules enter through membrane by simple diffusion from an area of high to low concentration.

exocytosis → proteins from the Golgi apparatus 
This process of exocytosis is used by cells to release particles that has been packaged by the golgi bodies.