Practicing Diversity Indices - Final Document

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1 Species Richness and Diversity Exercise You may work in groups of up to 5 people/group. Reading Richness and Diversity Recall that biodiversity is one of the most important features of ecological research and often serves as a measure of the overall health of an ecosystem. Declining biodiversity may indicate that the ecosystem is undergoing some type of environmental stress. Species richness and diversity are two of the most widely used metrics of biodiversity. Species richness refers to the actual number of species present on a landscape, whereas diversity takes into account both the number of species and their relative abundances ( sometimes referred to as species evenness ). For example, species richness would estimate that there are 34 species of vertebrate species in a woodlot, whereas diversity would take into account that 12% of all vertebrate individuals are song sparrows. Unfortunately, in many instances species richness and diversity cannot be observed directly as, typically, some cryptic species are overlooked or the overall complexity of the system prohibits a complete census of all species present being conducted. Over the next few classes, we will be looking at several approaches to sample ecosystems and to estimate species richness, abundance, and site occupancy. Each method we will look at has advantages and drawbacks. Most estimates of diversity or richness are unit-less. This means that the estimates are essentially relativistic, or that they have little meaning by themselves. Rather, they become useful when we compare estimates of diversity and richness from one ecosystem to another similar ecosystem or the same ecosystem sampled at different times. In today’s exercise, we are going to work with a couple of the most basic estimates of species richness and diversity. 1) What is the most basic method you can think of to estimate ecosystem diversity? Count the number of species present in the ecosystem. 2) What might be some problems with using this estimate of ecosystem diversity? You won’t be able to reliably detect every single species. The number can be inflated by very few individuals of many different species. Additionally, if you are only focusing on the species level, you might miss out on measures of diversity at different taxonomic levels (i.e – many species, but all vertebrates). A slightly more refined method of estimating ecosystem diversity over raw richness is Margalef’s Diversity Index (Margalef 1958). 𝐷𝑖𝑣𝑒??𝑖?𝑦 = 𝑠−1 log 𝑁 Where s is the number of species observed and N is the number of individuals observed. Margalef was a limnologist (aquatic ecologist) which meant he typically worked with very complex ecosystems where both N and s were huge. His Names: James Shugart, John Morrow, Gavin Roberts, Alejandra Gage, Maya Madern (equation. 1)

2 diversity index works well when s and N are about the same for all ecosystems being assessed or they are both large values. However, when these assumptions are violated, as is true in many terrestrial ecosystems, the Margalef Diversity Index tends to be less useful due to a high bias. The bias exists because the Margalef Index does not account for species evenness (i.e. relative abundance of each species). The Shannon Diversity Index (Shannon 1948) adjusts for species evenness by using information theory. The Shannon Diversity Index measures the degree of uncertainty in the system. If diversity is low, then the certainty of picking a particular species at random is high. If diversity is high, then the certainty of predicating the identity of a randomly chosen individual from the population is low. Thus, high diversity = high uncertainty. The Shannon Index is calculated as: H ′ = − ∑ 𝑝𝑖(𝑙𝑛(𝑝𝑖)) 𝑆 𝑖=1 Where S is the total number of species and pi is the relative abundance of each species ( see equation 3 ). Notice the negative sign in front of the summation symbol; this means the index will almost always be positive. 𝑝𝑖 = 𝑛 𝑖 𝑁 Where n i is the number of individuals of species i and N is the total number of individuals for all species. Rarity Another attribute of ecosystems is the occurrence of rare species within them--Rarity. Rarity is the scarcity of a particular species across an ecosystem. In many cases species of high conservation value are species that occur rarely on a landscape. Consequently, if a particularly rare species of conservation concern, or a species of high conservation value occurs at a particular location , that location might have high conservation value, even if it doesn’t have high biodiversity or species richness. Rarity Weighted Richness (RWR) is an accounting method that gives sites a conservation value score based on having either 1) a large number of species presence or 2) the occurrence of a few rare or highly valuable species or 3) a combination of both factors. This can be an important metric for use in conservation planning, where a goal might be to identify a set of sites or the bounds of a reserve that represents all conservation targets in as efficient a manner as possible. Williams et al.(1996) proposed that the rarity value of a species can be characterized by the inverse of the number of sites or planning units in which it occurs. Thus if a species is found in only 1 site, the species would have the maximum rarity score of 1/1 = 1, and a species that occurs in 20 sites would have a rarity score of 1/20 = 0.05. Williams et al. also proposed that the rarity scores of all species in the site can be summed to yield a single RWR value for the site: ∑( 1 𝑐𝑖 ) 𝑛 1 where ci is the number of sites occupied by species i, and the values are summed for the n species that occur in that site. Thus, sites that have the only record of a particular species will receive higher scores as will sites that contain all detected (equation. 4) (equation. 2) (equation. 3)

3 species. Recently, Albuquerque and Gregory (2017) demonstrated that the use of RWR is a more efficient way of designing priority bird conservation reserve networks for Natura 2000 and IUCN sites throughout Europe. To calculate RWR you will need to keep track of the occurrence of each species at each site and the total number of sites at which a species occurs. Similarity Similarity of sites can be thought of as the antithesis of diversity and Rarity. Whereas both of the previous discussed sets of metrics look at differences within and among sample locations and biological communities, similarity evaluates how alike sites are. Similarity indices are frequently used to study the coexistence of species or the similarity of sampling sites. The main aim of this type of analysis is to discover distributional patterns common to different species and groups, or areas with similar biota (Birks 1987). There have been >60 different similarity indices proposed for use with ecological data. However, the Jaccard's index (Jaccard, 1908) is one of the simplest and most widely used . Jaccard’s index is used frequently in conservatio n because it may be applied to the power function of the relationship between species and areas to determine a measure for the optimum size for natural protection reserves (Higgs and Usher, 1980). Jaccard's index is independent of the number of operational taxonomic units OTUs studied. One of the simplest and most commonly used. Jaccard's index may be expressed in several ways. A common approach is the following: J= ? ?+?−? where A is the number of attributes present at site a, B is the number of attributes present at site b, and C is the number of attributes present in both sites a and b . In this case Jaccard’s index can be thought of as the proportion of species found at both sites compared to total species found at only one site or the other, but not both. Jaccard's index can also be expressed as: J= ? ?+?+? where A is the number of attributes present in a but absent in b, B is the number of attributes present in b but absent a, and C is the same as in Equation 5. In this case Jaccard’s index can be thought of as the proportion of species found at both sites compared to total species found at all sites. A third way of expressing Jaccard's index is as follows: J= ? 𝑵 in which C is the same as in Equations 5& 6 and N is the total number of species in the system. In this case Jaccard’s index is the proportion of shared species. The Jaccard’s index represented in equation 7 is the easiest and most accurate to use with a large number of sample sites. Whereas the other two indices are best used when comparing a few sites to each other. Regardless all three methods are equally valid and one really only needs define how the metric was calculated to justify its use. In this exercise, you may use any method you wish, but once you choose a method you must maintain fidelity to it throughout the analysis. I suggest using equation 7 as it will be the easiest to calculate and has the most straightforward interpretation. (equation. 5) (equation. 7) (equation. 6)

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4 Similarly to RWR, to calculate a Jaccard index, you will need to collect data on the identity of each species present at each site. Thus, in Tables 1&2 the most important data that you will collect are the data in column 1 (species ID) and column 2 (number of occurrences of that species/site). In-class Exercise In today’s class, we are going to calculate each of the above metrics of richness , diversity and similarity using some data that I have provided on bird species richness at three sites in Texas. Objective #1: Students will be able to use the Shannon diversity estimator, Jaccard indices and a Rarity weighted richness index to estimate and compare species diversity of a complex ecological system. Objective #2: Students will be able to identify and correct for common sources of error in field data collection. Table 1 . Sample Bellevue Study Site diversity calculation data. Table 2 . Sample Crescent Creek Study Site diversity calculation data.

5 species ni pi ln(pi) pi(ln(pi)) Rarity American Crow 3 0.073171 -2.61496 -0.19134 0.333333 Brown-headed Cowbird 1 0.02439 -3.71357 -0.09057 0.333333 Canada Goose 1 0.02439 -3.71357 -0.09057 1 Carolina Chickadee 1 0.02439 -3.71357 -0.09057 0.333333 Carolina Wren 2 0.04878 -3.02042 -0.14734 0.333333 Dickcissel 4 0.097561 -2.32728 -0.22705 0.333333 Eastern Meadowlark 5 0.121951 -2.10413 -0.2566 0.333333 Eastern Phoebe 1 0.02439 -3.71357 -0.09057 0.333333 Grasshopper Sparrow 2 0.04878 -3.02042 -0.14734 0.333333 Great-tailed Grackle 1 0.02439 -3.71357 -0.09057 1 Northern Cardinal 3 0.073171 -2.61496 -0.19134 0.333333 Northern Mockingbird 2 0.04878 -3.02042 -0.14734 0.5 Painted Bunting 4 0.097561 -2.32728 -0.22705 0.333333 Purple Martin 4 0.097561 -2.32728 -0.22705 1 Red-bellied Woodpecker 1 0.02439 -3.71357 -0.09057 0.333333 Red-tailed Hawk 3 0.073171 -2.61496 -0.19134 1 Red-winged Blackbird 1 0.02439 -3.71357 -0.09057 0.333333 Tufted Titmouse 1 0.02439 -3.71357 -0.09057 0.333333 Upland Sandpiper 1 0.02439 -3.71357 -0.09057 1 Species Richness 19 Margalef Diversity Index 11.16083 Shannon Diversity Index 2.768959 Rarity Weighted Richness 9.833333

6 Table 3 . Sample Grandview Study Site diversity calculation data. Jaccard Similarity among all pairwise sites and each sit to the whole [use eq. 7]: Bellevue to Crescent Creek: 0.37 Bellevue to All: 0.57 Bellevue to Grandview: 0.61 Grandview to All: 0.52 Grandview to Crescent Creek: 0.32 Crescent Creek to All: 0.32 species ni pi ln(pi) pi(ln(pi)) Rarity American Crow 15 0.072816 -2.61983 -0.190764027 0.333333333 Barn Swallow 7 0.033981 -3.38197 -0.114921175 0.5 Black Vulture 1 0.004854 -5.32788 -0.025863477 1 Blue Grosbeak 2 0.009709 -4.63473 -0.044997369 1 Blue-gray Gnatcatcher 4 0.019417 -3.94158 -0.076535569 0.5 Brown-headed Cowbird 5 0.024272 -3.71844 -0.090253356 0.333333333 Carolina Chickadee 13 0.063107 -2.76293 -0.174359459 0.333333333 Carolina Wren 15 0.072816 -2.61983 -0.190764027 0.333333333 Cliff Swallow 4 0.019417 -3.94158 -0.076535569 0.5 Common Nighthawk 3 0.014563 -4.22926 -0.061591222 0.5 Crested Caracara 1 0.004854 -5.32788 -0.025863477 1 DickcisselDickcissel 16 0.07767 -2.55529 -0.198468928 0.333333333 Eastern Meadowlark 2 0.009709 -4.63473 -0.044997369 0.333333333 Eastern Phoebe 1 0.004854 -5.32788 -0.025863477 0.333333333 Grasshopper Sparrow 3 0.014563 -4.22926 -0.061591222 0.333333333 Great Blue Heron 1 0.004854 -5.32788 -0.025863477 0.5 Great EgretGreat Egret 1 0.004854 -5.32788 -0.025863477 1 Indigo Bunting 3 0.014563 -4.22926 -0.061591222 1 Lark Sparrow 1 0.004854 -5.32788 -0.025863477 1 Mourning Dove 16 0.07767 -2.55529 -0.198468928 0.5 Northern Cardinal 14 0.067961 -2.68882 -0.182735261 0.333333333 Painted Bunting 31 0.150485 -1.89389 -0.285002708 0.333333333 Red-bellied Woodpecke 6 0.029126 -3.53612 -0.10299369 0.333333333 Red-winged Blackbird 4 0.019417 -3.94158 -0.076535569 0.333333333 Scissor-tailed Flycatcher 2 0.009709 -4.63473 -0.044997369 0.5 SwallowSwallow 2 0.009709 -4.63473 -0.044997369 1 Tufted Titmouse 12 0.058252 -2.84297 -0.165609875 0.333333333 Turkey Vulture 3 0.014563 -4.22926 -0.061591222 0.5 White-eyed Vireo 5 0.024272 -3.71844 -0.090253356 0.5 Yellow-billed Cuckoo 13 0.063107 -2.76293 -0.174359459 0.5 Species Richness 30 Margalef Diversity Index 12.53313 Shannon Diversity Index 2.970096 Rarity Weighted Richnes 16.33333

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7 Post-lab Questions 1) Across all sites, was diversity high or low? We can see that Bellevue has not only the most amount of species richness, but also the highest number of total individuals sampled. Some species did dominate more (Dickcissel, Eastern Meadowlark, Grasshopper Sparrow), and the Shannon and Margalef indices are the second highest compared to the other sites. Grandview shows the highest diversity index, while also having the second highest species richness and second most individuals. Crescent Creek shows the lowest diversity index values, indicating that diversity is lower compared to the other 2 sites. 2) Interpret the diversity data relative to the Jaccard Index. Does any one site have greater diversity than any other? Use your richness, rarity, diversity and Jaccard similarity indices to support your answer. Relative to the Jaccard Index, Crescent Creek would seem to have the least amount of similarity to other sites. This is most likely due to the lower quantity of species individuals and richness. Since there is less species in total in Crescent Creek, there is lower similarity due to excluding species found at Bellevue and Grandview that are not found at Crescent Creek. The site with the greatest number of species and species richness would be Bellevue, as well as having the most unique species and species with a rarity value of 1. Grandview, however, has higher diversity according to the Shannon and Margalef values, most likely due to the presence of less domineering species than Grandview, who’s populations of Dickcissels and Grasshopper Sparrows take up a large majority of the individua ls in the population. Grandview’s species are more evenly populated. 3) For each site, what is the rarity weighted richness value and which species(s) drives rarity? RWR Values were calculated for each site, returning the following 3 values- Site ID RWR Bellevue 18.83333 Crescent Creek 8.83333 Grandview 16.33333 Species with an individual Rarity Score of 1 drive rarity the most – these are species that only occur at one site, and nowhere else. All other species contain either a score of 0.5 or 0.333~, thus contributing less to the overall score. Species found at only one site are listed below- Bellevue – Bewick’s Wren, Chuck - will’s -widow, Common Grackle, Downy Woodpecker, Great Crested Flycatcher, Great Horned Owl, Northern Bobwhite, Red-shouldered Hawk, White-winged Dove Crescent Creek – Canada Goose, Great-tailed Grackle, Purple Martin, Red-tailed Hawk, Upland Sandpiper Grandview – Black Vulture, Blue Grosbeak, Crested Caracara, Great Egret, Indigo Bunting, Lark Sparrow, Swallow (unspecified) These rare species account for 27.273% of the total species at Bellevue, 26.316% of the total species at Crescent Creek, and 23.333% of the total species at Grandview.

8 4) What is the difference between species richness and diversity? Why is this an important distinction? Species richness simply describes the quantitative amount of distinctive species within an area. Diversity takes into account this quantitative amount, but also the amount of individuals of each of the distinctive species present within said area, taking into account their abundance, or lack thereof. While a certain ecosystem may be rich in species, if there is a lack of abundance, then one might not consider the ecosystem diverse. This distinction is important, especially when considering where to focus conservation efforts, as high species richness but low diversity may indicate an area to be a high priority area for conservation efforts. This is assuming that it would be more beneficial (depending on the types of species present) to focus said efforts on an area declining in abundance/diversity that also has more species richness than it would be to focus those efforts on an area declining in abundance/diversity with less species richness. 5) Why are all three metrics (richness, diversity and rarity) important determinants to describe local species conditions at a particular place and time? All three metrics are important because they serve not only to define species over one period of place and time, but instead in many areas over great lengths of time. These can be measured daily, month-to-month, year-to- year and more – this allows researchers to view and identify trends related to migration, climate, and overall conditions at any site. If any metric fluctuates seasonally or due to outside pressures, then conservation efforts can be applied if there is a loss, or sustained if species data remains the same. Furthermore, identifying data on individual species may also allow us to understand relationships within populations and communities. On their own, these data are useful to know, yet all three of these are interrelated. If we have multiple sites with differing environmental parameters, and first identify species richness, we can draw conclusions about how diverse each site is, which sites rare species thrive in, and more. In conjunction they answer the most questions and help to identify the best methods of wildlife and environmental conservation. 6) What might be some sources of error when estimate alpha and beta diversity as you did in this exercise? Which of these calculations were alpha diversity comparisons and which were beta diversity comparisons? Choose one source of error that you listed above and propose a method to try to control that type of error and resultant bias. Alpha and beta diversity can both be affected by cryptic species skewing quantitative results, improper data sampling (maybe one sight was oversampled, and another undersampled), inconsistencies in defining distinct species for each site sampled, and improper retrieval of quantitative species data simply due to human error on account of the fact that ecosystems are complex and constantly changing. Margalef’s diversity index and the Shannon index are measures of alpha diversity. The rarity weighted richness equation and the Jaccard Similarity index are measures of beta diversity. In order to limit inconsistencies in defining distinct species for sampling sites, one should use tools like the Merlin app, field guides and ensure that everyone collecting species data is using the same taxonomic references and/or defining species by using the same base species concepts. There should also be some sort of training for data collectors to establish a good foundational knowledge, and experts should also be involved in the species identification process, especially when conducting peer review on the species data collected. One should also keep documentation of the methodology used to identify species in any publications created while performing said field work.

9 Signatures of all group members certifying that the work was an equal partnership and collaboration (unsigned documents will not be graded): James Shugart John Morrow Gavin Roberts Alejandra Gage

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10 Maya Madern

Practicing Diversity Indices - Final Document

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