Generations

The number of people in your family tree grows quickly, but there were only so many people alive at one time. You will eventually start finding the same ancestors in different branches of your tree. A child born in 2016 would have had about 16 million ancestors alive in 1556, but the entire population of Great Britain in 1600 was only 5.4 million.
Add to that the limited mobility of most people and you will understand why some degree of consanguinity is inevitable.

Year	Generation # (20 Years)		Ancestors in this Generation	Ancestors Alive This Year
2016	0	Child	1	7
1996	1	Parents	2	14
1976	2	Grandparents	4	28
1956	3	Great Grandparents	8	56
1936	4	2nd Great Grandparents	16	112
1916	5	3rd Great Grandparents	32	224
1896	6	4th Great Grandparents	64	448
1876	7	5th Great Grandparents	128	896
1856	8	6th Great Grandparents	256	1,792
1836	9	7th Great Grandparents	512	3,584
1816	10	8th Great Grandparents	1,024	7,168
1796	11	9th Great Grandparents	2,048	14,336
1776	12	10th Great Grandparents	4,096	28,672
1776	U.S. Population:     2.5 Million
1756	13	11th Great Grandparents	8,192	57,344
1736	14	12th Great Grandparents	16,384	114,688
1716	15	13th Great Grandparents	32,768	229,376
1696	16	14th Great Grandparents	65,536	458,752
1676	17	15th Great Grandparents	131,072	917,504
1656	18	16th Great Grandparents	262,144	1,835,008
1636	19	17th Great Grandparents	524,288	3,670,016
1616	20	18th Great Grandparents	1,048,576	7,340,032
1600	British Population:     5.4 Million
1596	21	19th Great Grandparents	2,097,152	14,680,064
1576	22	20th Great Grandparents	4,194,304	29,360,128
1556	23	21st Great Grandparents	8,388,608	58,720,256
1536	24	22nd Great Grandparents	16,777,216	117,440,512
1516	25	23rd Great Grandparents	33,554,432	234,881,024
1500	European Population:     90.7 Million

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^* This table was computed at 20 years per generation, both parents and all 4 grandparents alive at birth of next generation. This is all an approximation, as both generations and life spans were usually shorter.