Jacob is speaking to his wives, Leah and Rachel, reminding them of how their father, Laban, had deceived him and changed his wages ten times. Yet, God had been with him, and whenever Laban had changed his wages, God had ensured that Jacob had been blessed in spite of his father-in-law's underhanded schemes. So when Laban had tried to undercut Jacob's wealth by assigning to him the sheep or goats with recessive coat patterns—speckled or streaked rather than the dominant solid colors—God blessed the production of the sheep that Jacob needed to prosper. What is clear is that Genesis 30-31 are describing divine intervention, a miracle, an event that would not occur naturally apart from God's involvement.
Many commentators have tried to explain how Jacob used "rods of green poplar and of the almond and chestnut trees, peeled white strips in them, and exposed the white which was in the rods" (Genesis 30:37) to entice the flocks to conceive and produce "streaked, speckled, and spotted" offspring (Genesis 30:39). But when all the evidence is presented, every theory of how this could be possible fails the test of known science. External objects like branches of trees with white strips in them cannot influence the markings of the next generation of sheep and goats. Even if Jacob was trying only to entice his flocks to mate, the use of these rods makes no scientific sense.
So what was the purpose of the rods? No one really knows. Some have suggested that Jacob's use of the rods was a superstitious practice he learned from other shepherds, something akin to Leah and Rachel's beliefs about the use of mandrakes. Certainly, there is no biblical evidence that God instructed Jacob to do this. Maybe the best supposition on the matter is that Jacob used this method to "help" God bring His promise to pass.
What is clear from Genesis 30:41-42 is that Jacob was controlling the breeding of the flocks, at least in terms of breeding the strong for himself and the more feeble for Laban. It would not take long for the two flocks to be significantly different in terms of both numbers and quality, as the stronger would produce more and healthier offspring, while the weaker animals' offspring would be fewer and inclined to frailty. Even without God's intervention, Jacob was using selective breeding to improve his livestock.
There is no doubt, however, that the credit for Jacob's breeding success story belongs to God. Jacob says this himself in Genesis 31:9: "So God has taken away the livestock of your father and given them to me" (emphasis mine). He goes on to relate a dream he had had in which God had assured him that the rams that impregnated his ewes "are streaked, speckled, and gray-spotted; for I have seen all that Laban is doing to you. I am the God of Bethel, where you anointed the pillar and where you made a vow to Me" (Genesis 31:12-13). This is the Bible's second-millennium BC way of saying that God Himself was manipulating the gene-pool of Jacob's flocks, causing the recessive coloring genes to dominate for Jacob's sake.
God's mention to Jacob of his vow at Bethel (Genesis 28:10-22)—and of the fact that He is the God with whom he made that promise—is a reminder that God was still with him and continuing to uphold His side of the agreement. In fact, He is essentially saying that He was willing to bend the laws of nature to ensure that Jacob prospered. God was building the man's faith toward his real conversion moment, wrestling with the Man at Peniel (Genesis 32:22-30).
Richard T. Ritenbaugh