3. Species Richness and Diversity

.title[
# 3. Species Richness and Diversity
]
.subtitle[
## Beta Diversity
]
.author[
### Jasper Slingsby, BIO3018F
]
.date[
### 2025-01-28
]

---

## How do we compare diversity between sites?

These 3 sites could easily have the same `$\alpha$`-diversity measure. Would that mean they're the same?
]

<img src="images/forestyoung.jpg" width="75%" style="display: block; margin: auto;" />
]

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## Are these two fynbos sites the same?

]

<img src="images/fynbos.png" width="90%" style="display: block; margin: auto;" />
]

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Alpha `$(\alpha)$` = mean species diversity/richness within local-scale sites, habitats or communities (often termed "point diversity")

Beta `$(\beta)$` = diversity/richness differences between sites or habitats (attributable to species "turnover" or "nestedness")

Gamma `$(\gamma)$` = total landscape species diversity/richness

.pull-right[
<img src="images/diversitycomponents.png" width="110%" style="display: block; margin: auto 0 auto auto;" />

]

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class: center, middle

## WARNING!
** `$\beta$` diversity can get a little complicated... **

There's lots of methods, and opinions often differ among experts...1

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There are two major approaches:

* *"Classical" diversity metrics*, calculated directly from measures of regional `$(\gamma)$` and local `$(\alpha)$` diversity through additive or multiplicative decomposition

* *Multivariate measures* that calculate distances (or dissimilarities) that represent the compositional resemblance between pairs of samples

.footnote[The two are related, and can even be the same thing in certain scenarios, but I'm not going to go there in this course...]

]

.pull-right[
<img src="images/diversitycomponents.png" width="110%" style="display: block; margin: auto 0 auto auto;" />
]

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## The decomposition of "classical" diversity metrics...

Consider this in the context of the species-area relationship. 
]

If `$\gamma$` is constant (32) across sites, then

- S1 = higher `$\alpha$`, lower `$\beta$` (i.e. more homogeneous)
- S2 = intermediate `$\alpha$` and `$\beta$`
- S3 = lower `$\alpha$`, higher `$\beta$` (i.e. more heterogeneous)
]

---

Fynbos has moderate to high `$\alpha$` and very high `$\beta$`, resulting in high `$\gamma$`
- ~9500 vascular plant species in the Cape Flora
- ~2200 native species on the Cape Peninsula alone

]

English meadows have very high `$\alpha$`, but very low `$\beta$`, resulting in moderate to low `$\gamma$`
- only 1390 native species in the entire Great Britain and Ireland (~3 x the size of the CFR)

]

---

We often compare the diversity of different regions using species-area curves (usually on log-log axes so the curves are linear) - e.g. Cowling et al. 2015

]

]

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## The decomposition of "classical" diversity metrics...

The components of biodiversity are interrelated and, depending on your preference or application, can be expressed:

**Multiplicatively** (*sensu* Whittaker 1972):

`$$\beta = \gamma/\alpha$$`

**Additively** (*sensu* MacArthur et al. 1966, Lande 1996):

`$$\beta = \gamma - \alpha$$`
.footnote[1For reviews see Veech et al. 2002 and Anderson et al. 2011.]
]

.pull-right[
<img src="images/diversitycomponents.png" width="90%" style="display: block; margin: auto 0 auto auto;" />
]

---

## Multiplicative "classical" diversity

`$\beta = \gamma/\alpha$` (*sensu* Whittaker 1972)

...expresses `$\beta$` diversity as the ratio of landscape `$(\gamma)$` to local `$(\alpha)$` diversity (usually the mean of multiple local samples, i.e. `$\bar{\alpha}$`).

If most local `$(\alpha)$` samples capture most of the landscape `$(\gamma)$` diversity, then `$\beta$` diversity (i.e. differences between sites or habitats) must be low, and vice versa.

Disadvantages: 
* the ratio is unitless
* usually need to know landscape diversity `$(\gamma)$`

]

.pull-right[
<img src="images/betadiversity_mult.png" width="90%" style="display: block; margin: auto 0 auto auto;" />
]

---

## Additive "classical" diversity

`$\beta = \gamma - \alpha$` (*sensu* MacArthur et al. 1966, Lande 1996)

...expresses `$\beta$` diversity as the difference between landscape `$(\gamma)$` and local `$(\alpha)$` diversity (again, usually the mean of multiple local samples, i.e. `$\bar{\alpha}$`).

If local `$(\alpha)$` samples capture most of the landscape `$(\gamma)$` diversity, then `$\beta$` diversity (i.e. differences between sites or habitats) must be low, and vice versa.

Advantage:
* the difference is expressed as species (i.e. the average number of species missing from each local site)

Disadvantage: still usually need to know `$(\gamma)$`

]

.pull-right[
<img src="images/betadiversity_add.png" width="90%" style="display: block; margin: auto 0 auto auto;" />
]

---

## Multivariate measures of `$\beta$` diversity

There are a large number of metrics that calculate the dissimilarity of pairs of samples based on the number of species that are shared between them or unique to each.

The metrics typically differ in whether they:

* are based on species presence/absence only, or also include abundance information

* include/exclude joint absence information

* account for differences in the `$\alpha$` diversity of samples
]

.pull-right[
<img src="images/diversitycomponents.png" width="90%" style="display: block; margin: auto 0 auto auto;" />
]

---
layout: false

## Multivariate measures of `$\beta$` diversity

e.g. the same equation, `$(A+B-2*J)/(A+B)$`

*where J is the shared quantity, and A and B are totals for each community*

can be...
]

when based on species presence/absence only

### Bray-Curtis distance

when it includes abundance information

Values range from 0 (identical communities) to 1 (complete turnover).

.footnote[Be careful. The indices are often inverted (i.e. similarity metrics) depending on the goals of the study.]

]

---

.pull-left[
<img src="images/anderson_fig2.png" width="110%" style="display: block; margin: auto 0 auto auto;" />

]

The application of `$\beta$` diversity can be largely split into: 
* directional analyses, that explore *turnover* along spatial, temporal or environmental gradients, and

* non-directional analyses, that explore *variation* within or among groups.

---

.pull-left[
<img src="images/anderson_fig3.gif" width="85%" style="display: block; margin: auto 0 auto auto;" />

]

Typically explores change in community composition of one or more groups (e.g. taxa) along one or more gradients (e.g. distance, time, elevation, rainfall).

`$\Delta$`y = change in community composition

`$\Delta$`x = change in gradient

`$\delta y/\delta x$` = rate of turnover along a gradient

---

<img src="images/baetic.JPG" width="72%" style="display: block; margin: auto;" />
]

.pull-right[
E.g. Floristic _**turnover**_ with change in elevation vs between mountains (Molina‐Venegas et al. 2015)

Eudicots of the Baetic mountains of Andalusia, Spain 
]

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<img src="images/molina_belts.jpg" width="72%" style="display: block; margin: auto;" />
]

.pull-right[
E.g. Floristic _**turnover**_ with change in elevation vs between mountains (Molina‐Venegas et al. 2015)

]

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.pull-left[
<img src="images/anderson_fig4.gif" width="85%" style="display: block; margin: auto 0 auto auto;" />

]

Typically explores the amount of variation in community composition among sample units across one or more groups (e.g. taxa), sometimes trying to partition the drivers of variation among factors (e.g. experimental treatments), spatial scales or environmental variables.

`$\Delta$`y = change in community composition

`$\hat{\sigma}$`2 = variation in community structure among sample units

`$\bar{d}$`cen = average distance-to-centroid of all sample units

---

## "Variation" examples

Exploring variation among samples from one or more surveys or datasets

.pull-left[
<img src="images/taylor_resurvey_1966_96.png" width="100%" style="display: block; margin: auto auto auto 0;" />
]

.pull-right[
<img src="images/beta_variation_CP.png" width="100%" style="display: block; margin: auto 0 auto auto;" />
]
.footnote[Average turnover between plots: 1966 = 0.784; 1996 = 0.780]

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## "Variation" examples

Variation among communities in relation to an environmental variable

]

.pull-right[
<img src="images/NMDS.png" width="90%" style="display: block; margin: auto 0 auto auto;" />

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Grouping samples by compositional similarity

e.g. used to identify distinct vegetation communities

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## Take-home

There are many ways of measuring and analysing `$\beta$` diversity.

>*"Plurality in the concept of `$\beta$` diversity can yield important ecological insights when navigated well. By knowing the properties of the measures being used and applying more than one, the underlying ecological structures in the data generating patterns in `$\beta$` diversity can be revealed..."* - Anderson et al. 2011

>*"This applies to most measures of diversity..."* - Slingsby 2023

---

## References

.small[
Anderson, M. J., T. O. Crist, J. M. Chase, et al. (2011). "Navigating
the multiple meanings of beta-diversity: a roadmap for the practicing
ecologist". En. In: _Ecology letters_ 14.1, pp. 19-28. ISSN: 1461-023X,
1461-0248. DOI:
[10.1111/j.1461-0248.2010.01552.x](https://doi.org/10.1111%2Fj.1461-0248.2010.01552.x).

Gotelli, N. J. and R. K. Colwell (2001). "Quantifying biodiversity:
procedures and pitfalls in the measurement and comparison of species
richness". In: _Ecology letters_ 4.4, pp. 379-391. ISSN: 1461-023X,
1461-0248. DOI:
[10.1046/j.1461-0248.2001.00230.x](https://doi.org/10.1046%2Fj.1461-0248.2001.00230.x).

Lande, R. (1996). "Statistics and Partitioning of Species Diversity,
and Similarity among Multiple Communities". In: _Oikos_ 76.1, pp. 5-13.
ISSN: 0030-1299, 1600-0706. DOI:
[10.2307/3545743](https://doi.org/10.2307%2F3545743).

MacArthur, R., H. Recher, and M. Cody (1966). "On the Relation between
Habitat Selection and Species Diversity". In: _The American naturalist_
100.913, pp. 319-332. ISSN: 0003-0147. DOI:
[10.1086/282425](https://doi.org/10.1086%2F282425).

Slingsby, J. A., C. Merow, M. Aiello-Lammens, et al. (2017).
"Intensifying postfire weather and biological invasion drive species
loss in a Mediterranean-type biodiversity hotspot". En. In:
_Proceedings of the National Academy of Sciences of the United States
of America_ 114.18, pp. 4697-4702. ISSN: 0027-8424, 1091-6490. DOI:
[10.1073/pnas.1619014114](https://doi.org/10.1073%2Fpnas.1619014114).

Veech, J. A., K. S. Summerville, T. O. Crist, et al. (2002). "The
additive partitioning of species diversity: recent revival of an old
idea". En. In: _Oikos_ 99.1, pp. 3-9. ISSN: 0030-1299, 1600-0706. DOI:
[10.1034/j.1600-0706.2002.990101.x](https://doi.org/10.1034%2Fj.1600-0706.2002.990101.x).

Whittaker, R. H. (1972). "Evolution and measurement of species
diversity". En. In: _Taxon_ 21.2-3, pp. 213-251. ISSN: 0040-0262,
1996-8175. DOI: [10.2307/1218190](https://doi.org/10.2307%2F1218190).
]

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# Thanks!

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