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Calculating Diversity Class 3 Presentation 2 Outline • Lecture • Class room exercise to calculate diversity indices Why quantify biodiversity? • Initially thought that more diversity = more stable ecosystem* • Now used to measure and track changes *MacArthur, R. 1955. Fluctuations of animal populations and a measure of community stability. Ecology 35:533-536 How do we measure biodiversity? • Use functional categories – Ecosystem, species, genetic • Use theoretical categories* – Alpha – Beta – Gamma * Whittaker, R.H. 1960. Vegetation of the Siskiyou Mountains, Oregon and California. Ecol. Mono. 30:279-338. Alpha diversity • Diversity within a particular sample • E.g. the number of species surveyed Beta Diversity • Changes in sample composition along an environmental gradient • E.g. composition of forest stands on the slope of a mountain Gamma Diversity • Diversity due to differences in samples when all samples combined • E.g. diversity of a forest landscape Describing Communities • Two methods – Describe physical attributes (e.g. age class, size class) – Describe number of species and their abundance Biodiversity • • • • Diversity of living things Term often misused and overused Current focus in conservation studies Includes interest in genetic, species and ecosystem diversity • We will use species as our focus but concepts can be used for genetic and ecosystem diversity as well. Species Richness • • • • • Number of species in a community The simplest measure Can count all spp only is few simple ecosystems Does not consider number of individuals Difficulties – When is it a specie? • Aphids • Clonal plants – Cannot count all species with limited time Species Richness • • • • How? Identify organism groups of interest Identify boundaries of community Survey area for organisms of interest Species diversity • Species richness not very informative • Each community has 5 spp & 50 individuals Comm A Comm B Spp 1 Spp 2 Spp 3 Spp 4 Spp 5 10 10 10 10 10 46 1 1 1 1 Diversity indices • To get a better description of the community we need to get a measure of spp richness and evenness of their distribution • We usually use an index to represent several different measures – E.g. stock markets, air pollution, etc. Diversity indices • Over 60 indices used in ecology • Indices used to measure proportional abundance • Two major forms: – Dominance indices (e.g. Simpson index) – Information indices (e.g. Shannon Weiner index) Simpson Diversity Index (D) – Simpson’s index considered a dominance index because it weights towards the abundance of the most common species. – measures the probability two individuals randomly selected from a sample will belong to the same category – For example, the probability of two trees, picked at random from a tropical rainforest being of the same species would be relatively low , whereas in the boreal forest would be relatively high. Simpson Diversity Index (D) Ds = (n1(n1 -1)/N(N-1)) Where: Ds = Bias corrected form for Simpson Index n1 = number of individuals of spp 1 N = Total number of spp in community In this form as diversity increases index value gets smaller Simpson Diversity Index (D) • To make it easier to read the index is often read as: • Reciprocal i.e. 1/ Ds • Complimentary form: 1- Ds • Here as diversity increases Index value increases Simpson Diversity Index (D) Sugar Red Yellow Maple Maple Birch # Trees 56 48 12 Red Oak White Ash Total 6 3 125 See Excel ((56*55)/(125*124))+ Show how ((48*47)/(125*124)) + …………. index ….((3*2)/125*124)) = 0.35509 changes Simpson Diversity Index (D) • • • • Complimentary form = 1-D = 1-0.35509 = 0.6449 Reciprocal 1/D 1/0.35509 = 2.816 Shannon-Weiner Index (H') • The index measures the uncertainty of a category in a particular set • It is a measure of evenness • For example, very low uncertainty the letter y is the next letter in this string: yyyyyyy (H' = 0) Shannon-Weiner Index (H') • Assumptions: – All species represented – Sample randomized (equal probability of being selected in the sample) H' = - pilnpi pi= proportion of the ith species ln=natural logarithm Shannon-Weiner Index (H') Sugar Red Yellow Maple Maple Birch # Trees p 56 48 12 Red Oak White Ash Total 6 3 125 56/125 48/125 12/125 6/125 0.44 0.38 0.096 0.048 3/125 0.024 -plnp 0.359 0.367 0.224 0.146 0.089 1.187 Shannon-Weiner Index (H') • Index affected by both number of species and evenness of their population • Diversity increases as both increase • Diversity maximum when all species equally abundant Evenness • Can use Shannon Weiner index to get a measure of evenness • First calculate Hmax • Evenness = H‘/ Hmax • Evenness will vary between 1 and 0 Evenness • • • • • In the last example H‘= 1.1875 Hmax = 1.609 Therefore E = 1.1875/1.609 = 0.738 The closer to 1 the more even the populations that form the community Questions?