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Complete the following problems using the equation:

Students are not required to memorize this formula but must know the meaning of the symbols:

D = diversity index

N = total number of organisms of all species found

Σ = the sum of

n = number of individuals of a particular species

D is a measure of species richness. A high value of D suggests a stable and ancient site, and a low value of D could suggest pollution, recent colonization or agricultural management. The index is normally used in studies of vegetation but can also be applied to comparisons of animal (or even all species) diversity.

Example:A lake contains 934 brown trout, 733 smallmouth bass, 34 catfish, 2003 carp,

234 steelheads, and 32 northern pikes.

Fish

Number (n)

n(n-1)

Brown Trout

934

934 x (934-1) = 871422

Smallmouth Bass

733

733 x (732) = 536556

Catfish

34

34 x (33) = 1122

Carp

2003

2003 x (2002)=4010006

Steelheads

234

234 x (233)=54522

Northern Pike

32

32 x (31)=992

Total (N)

3970

= 5 474 620

= 3970 x 3969 = 15 756 930

D = = 2.88

Simpson’s Diversity Index – Practice Problems

When comparing two or more samples, the location with the larger D has a greater amount of diversity. Note that a higher total population does not indicate higher diversity.

An area of the Black Forest in Germany contains 134 pitch pines, 24 douglas firs, and 53 red pines.

A meadow contains 1532 chestnut oaks, 342 black cherry trees, 12 white ash trees, and 1022 yellow birches.

Your backyard contains 12 fleas, 34 aphids, 84 ants, 93 beetles, and 1 butterfly.

An African National Park contains 15 lions, 94 giraffes, 1000 wildebeests, 50 elephants, and 5 hyenas.

Mindo (a city in Ecuador) has 832 toucans, 392 red headed barbets, 3 golden headed quetzals, 500 tanagers, 899 parrots, and 50 white capped dippers.

Answer the following questions in your workbook:

Calculate Simpson’s diversity index for each location. Include the table in your workbook.

Distinguish the differences in diversity between two locations listed above.

Explain what may lead to those differences.

Outline the significance of the Simpson’s Diversity Index. You may refer to the following online resource and your textbook to help outline your ideas - http://www.countrysideinfo.co.uk/simpsons.htm

americans began to notice growing differences between the northern and southern sections of the country. there were more people living in cities in the north, which made it more urban. more people lived on farms in the south, which made it more rural. while many people were farmers in the northern states, there were now other ways to make a living, such as working in mechanical cotton gins factories manufacturing cloth, tools and other goods. people in the north supported high tariffs on goods imported from europe because the extra cost encouraged people to “buy american” instead. in the southern states, planters did not like tariffs because they sold most of their production to europe and bought their tools from there as well. southerners believed the protective tariff was something that only northern factory owners keep their profits high. so the southern politicians came up with an idea. they would opt out. they would simply ignore the protective tariff. it was ‘null and void’ in south carolina. the state would not collect the taxes on goods imported into south carolina, no matter what the president said they had to do. this decision led to the nullification crisis.

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