Patterns of diversity across space
Mid-semester survey results
- Positive attitudes towards reflections & activities
- Some uncertainty about semester project – to be clarified in coming week
- Desire for more activities in class to solidify understanding
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Diversity of vertebrate species, from Mannion et al. 2014
- Negative slope between diversity and absolute latitude
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Meta-analysis of diversity, from Kinlock et al. 2018
But, nature holds surprises
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Diversity of Saccharomycotina yeasts, from David et al. 2024
But, nature holds surprises
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Diversity and speciation rates of marine fish species, from Rabosky et al. 2018
To accurately define patterns of diversity, we need accurate measures of diversity.
Note: there are many dimensions to diversity that we won’t cover in depth.
- Phylogenetic diversity
- Two communities with 10 species each – in the first, all species from the same genus; in the second, 8 genera represented
- Functional diversity
- Two communities with 10 species each – in the first, each of the 10 is a herbivore; in the second, an even mix of herbivores, omnivores, carnivores
To accurately define patterns of diversity, we need accurate measures of diversity.
Today, we will focus on measuring “evenness” as a dimension of quantifying diversity
- Using local birds as a case study
Consider two locations where the same set of twelves species can be found.
In the first location, the bird community is dominated by just a few species:
In second location, individuals from each species are fairly common:
Comparing abundance patterns between the communities
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Do the two communities have equal amounts of “biodiversity”?
Quantifying biodiversity
- Ecologists measure biodiversity through a variety of metrics
- One common metric is the Shannon diversity index
Shannon diversity index
Intuition behind the Shannon index
- If I were randomly finding birds in Location 1 and had to guess which species I would find next, which should I guess?
Shannon diversity index
- Location 1 is more “predictable”
- Higher degree of “surprise” in Location 2
- This is also called “Information entropy”
- Commonly used across science, e.g. in computers, to optimize information storage and transfer
Shannon diversity index
A quantitative measure of biodiversity and community “evenness”
\[\overbrace{H'}^{\substack{\text{Shannon}\\{\text{index}}}} = -\sum_{i = 1}^{n} \overbrace{p_i}^{\substack{\text{proportional}\\ \text{abundance}}}*\overbrace{\text{ ln}(p_i)}^{\log\big(\substack{\text{proportional}\\ \text{abundance}}\big)}\]
Calculating Shannon diversity
| Cardinal |
32 |
|
|
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| Blue jay |
29 |
|
|
|
| Mockingbird |
20 |
|
|
|
| House sparrow |
7 |
|
|
|
| Carolina wren |
3 |
|
|
|
| Carolina chickadee |
2 |
|
|
|
| Red-bellied woodpecker |
2 |
|
|
|
| Downy woodpecker |
1 |
|
|
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| Magnolia warbler |
1 |
|
|
|
| Yellow-rumped warbler |
1 |
|
|
|
| Prothonotory warbler |
1 |
|
|
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| Red-tailed hawk |
1 |
|
|
|
Calculating Shannon diversity
| Cardinal |
32 |
0.32 |
|
|
| Blue jay |
29 |
0.29 |
|
|
| Mockingbird |
20 |
0.20 |
|
|
| House sparrow |
7 |
0.07 |
|
|
| Carolina wren |
3 |
0.03 |
|
|
| Carolina chickadee |
2 |
0.02 |
|
|
| Red-bellied woodpecker |
2 |
0.02 |
|
|
| Downy woodpecker |
1 |
0.01 |
|
|
| Magnolia warbler |
1 |
0.01 |
|
|
| Yellow-rumped warbler |
1 |
0.01 |
|
|
| Prothonotory warbler |
1 |
0.01 |
|
|
| Red-tailed hawk |
1 |
0.01 |
|
|
Calculating Shannon diversity
| Cardinal |
32 |
0.32 |
-1.139 |
|
| Blue jay |
29 |
0.29 |
-1.238 |
|
| Mockingbird |
20 |
0.20 |
-1.609 |
|
| House sparrow |
7 |
0.07 |
-2.659 |
|
| Carolina wren |
3 |
0.03 |
-3.507 |
|
| Carolina chickadee |
2 |
0.02 |
-3.912 |
|
| Red-bellied woodpecker |
2 |
0.02 |
-3.912 |
|
| Downy woodpecker |
1 |
0.01 |
-4.605 |
|
| Magnolia warbler |
1 |
0.01 |
-4.605 |
|
| Yellow-rumped warbler |
1 |
0.01 |
-4.605 |
|
| Prothonotory warbler |
1 |
0.01 |
-4.605 |
|
| Red-tailed hawk |
1 |
0.01 |
-4.605 |
|
Calculating Shannon diversity
| Cardinal |
32 |
0.32 |
-1.139 |
-0.364 |
| Blue jay |
29 |
0.29 |
-1.238 |
-0.359 |
| Mockingbird |
20 |
0.20 |
-1.609 |
-0.322 |
| House sparrow |
7 |
0.07 |
-2.659 |
-0.186 |
| Carolina wren |
3 |
0.03 |
-3.507 |
-0.105 |
| Carolina chickadee |
2 |
0.02 |
-3.912 |
-0.078 |
| Red-bellied woodpecker |
2 |
0.02 |
-3.912 |
-0.078 |
| Downy woodpecker |
1 |
0.01 |
-4.605 |
-0.046 |
| Magnolia warbler |
1 |
0.01 |
-4.605 |
-0.046 |
| Yellow-rumped warbler |
1 |
0.01 |
-4.605 |
-0.046 |
| Prothonotory warbler |
1 |
0.01 |
-4.605 |
-0.046 |
| Red-tailed hawk |
1 |
0.01 |
-4.605 |
-0.046 |
Exercise: calculating the Shannon index
- Two species lists from eBird, both from BREC Bluebonnet Swamp
- Splitting into groups of 2–3, quantify Shannon diversity
- If time, share something interesting about one of the birds on your list.
Patterns of biodiversity across space
Recap
- At the global scale, the latitudinal diversity gradient is a robust pattern (with exceptions)
- But, quantifying biodiversity isn’t just a matter of counting up species
- Phylogenetic diversity, Functional diversity, Species abundance (and more) dimensions
Recap
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If we are sampling individuals from Community 2, there is more uncertainty of which species to expect
We can quantify this uncertainty as the Shannon diversity (\(H'\))
\[H' = -\sum_{i = 1}^n p_i~*~ \text{ln}(p_i)\]
Think back: what does this equation mean (in words)?
. . . Bottomland Hardwood Forests and Swamps
Prominent Physical Features: Forested wetlands that occupy broad floodplains and depressions bordering large river systems. The soil, hydrology and plant community vary based on river influence and landscape position. Floodplain soils are fertile and desired for agriculture, so most of the original forests have been converted to agriculture. Flood control efforts have also degraded the forests of this plant region.
Prominent Vegetation: Oaks, cottonwood, sycamores, elms, maples and ashes in bottomland hardwood forests. Bald cypress, water tupelo and swamp tupelo occur in the swamps
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Coastal Prairies
Prominent Physical Features: Coastal Prairies Prominent Physical Features: Extension of Midwestern tall-grass prairie, with a subtropical influence. Once covered approximately 2.5 million acres in Louisiana. Modern agriculture has reduced Louisiana’s coastal prairie to less than 1 percent of its former extent. Today, coastal prairie is limited to small remnants on grazing land, along railroads and a few small patches in urban areas. Fire, along with harsh soil conditions, restrict woody species to forests along streams dissecting the plant region
Prominent Vegetation: A diverse mix of lush grasses (little bluestem, big bluestem, eastern gamma grass, switchgrass, and Indian grass), sedges, rushes, and many wildflowers.
There is clearly lots of turnover between regions
Bottomland Hardwood Forests and Swamps
Prominent Vegetation: Oaks, cottonwood, sycamores, elms, maples and ashes in bottomland hardwood forests. Bald cypress, water tupelo and swamp tupelo occur in the swamps
Coastal Prairies
Prominent Vegetation: A diverse mix of lush grasses (little bluestem, big bluestem, eastern gamma grass, switchgrass, and Indian grass), sedges, rushes, and many wildflowers.
Biodiversity patterns in action
In the following communities, each species is represented by a different letter.
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Let’s calculate \(\alpha\), \(\beta\), and \(\gamma\) diversity.
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\(\alpha_{\text{community }1} = 7 \text{ species}\)
\(\alpha_{\text{community }2} = 6 \text{ species}\)
\(\gamma = 8 \text{ species}\) (A,B,C,D,E,F,G,H)
\(\beta\) is the number of species unique to one community
- Species \(A\) and \(F\) only in Community 1
- Species \(H\) only in Community 2
- \(\beta = 3\) unique species
Your turn: calculate \(\alpha\), \(\beta\), and \(\gamma\) diversity for the following
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- \(\beta\) diversity is an important and complicated concept
Back to understanding patterns of diversity
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Why does this pattern exist?
As we often do, let’s simplify the complexity
As we often do, let’s simplify the complexity
Processes that govern species richness:
\(\uparrow\) by immigration of new species
\(\downarrow\) by local extinction (‘extirpation’) of existing species
\(\uparrow\) by local speciation
Let’s assume speciation is very slow and not relevant to our dynamics
Processes that govern species richness:
- \(\uparrow\) by immigration of new species
- \(\downarrow\) by local extinction (‘extirpation’) of existing species
- What determines rate of immigration of new species and local extinction?
Actual islands are not the only “islands” out there
Urban forests
Lake systems
Application of island biogeography to conservation
