FishDiversityEcology.Rmd

---
title: "Fish Diversity Ecology Assessment"
author: "James Tsalah"
output:
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    highlight: tango
---

# Diversity Metrics Background

Types of Diversity

-   Gamma Diversity encompasses the diversity of an entire region.
-   Alpha Diversity encompasses the diversity at a sampling site (richness).
-   Beta Diversity encompasses the difference in diversity between samples.
    -   Typically calculated through space, but can also be calculated through time.
    -   We are thinking about two communities, and how they are different frome each other.

Dissimilarities among communities arises from two different processes:

-   Species Replacement (Turnover): Species tend to replace each other along ecological gradients.
-   Richness differences (Nestedness): One comunity might have more species present than the other. For example, one community may be a nested subset of another community-meaning that with five species at a location, three of those same five might be present at another location.

Beta Diversity Indices: Jaccard vs. Sorensen

-   Jaccard calculates the unique species as a proportion of the total number of species recorded in the two communities.
-   Sorensen does the same, but double weights the shared species.
-   Sorensen therefore always has a lower value than Jaccard.

# Two Families of Beta Diversity

#### Table 1: Podani & Baslega Family Calculations

|              | **Podani**                                     | **Baslega**                                                                                                 |
|------------------|------------------------|------------------------------|
| **Jaccard**  | $$Repl_J = \frac{2 \min(b, c)}{(a + b + c)}$$  | $$Repl_{BJ} = \beta_{Jtu} = \frac{2 \min(b, c)}{a + 2 \min(b, c)}$$                                         |
|              | $$Rich_J = \frac{|b - c|}{(a + b + c)}$$       | $$Nes_{BJ} = \beta_{jne} = DJ - \beta_{Jtu} = \frac{|b - c|}{a + b + c} \times \frac{a}{a + 2 \min(b, c)}$$ |
| **Sorensen** | $$Repl_S = \frac{2 \min(b, c)}{(2a + b + c)}$$ | $$Repl_{BS} = \beta_{Sim} = \frac{\min(b, c)}{a + \min(b, c)}$$                                             |
|              | $$Rich_S = \frac{|b - c|}{(2a + b + c)}$$      | $$Nes_{BS} = \beta_{nes} = DS - \beta_{Sim} = \frac{|b - c|}{2a + b + c} \times \frac{a}{a + \min(b, c)}$$  |

Key:

-   a is the shared species.
-   b & c the number of sapecies that are unique to either the first (b) or second (c) community.

# The Doubs Fish Dataset - Verneaux, J. (1973)

```{r, echo=FALSE, warning=FALSE, message=FALSE}
suppressPackageStartupMessages({
  require(adespatial)
  require(ade4)
  require(vegan)
})
```

Let's view the dataset! The Doubs Fish dataset contains fish taxa as columns, each of the 30 rows is a site, and the row value represents the amount of observations at that site.

```{r}
data(doubs)
fish = doubs$fish
fish = fish[-8,] # Remove site 8 which has no observations for any fish.
head(fish[,1:14])
```

Each column is a species of fish, while each row is a site with the number of each species observed at that site.

# Assessing Fish Gamma Diversity

Gamma diversity is essentially the total number of unique species across all sites.

```{r}
# Calculate gamma diversity (total species richness across all sites)
gamma_diversity <- specnumber(colSums(fish))

# Display gamma diversity result
cat("Gamma Diversity (Total Species Richness):", gamma_diversity, "\n")
```

# Assessing Fish Alpha Diversity

Alpha diversity refers to the diversity within a particular area or ecosystem, and is typically expressed by the number of species (species richness) in that ecosystem.

```{r}
# Calculate species richness (alpha diversity) for each site
alpha_diversity <- specnumber(fish)

# Calculate Shannon diversity index for each site
shannon_diversity <- diversity(fish, index = "shannon")

# Calculate Simpson diversity index for each site
simpson_diversity <- diversity(fish, index = "simpson")

# Display results
alpha_results <- data.frame(Site = rownames(fish), 
                            Species_Richness = alpha_diversity,
                            Shannon_Index = shannon_diversity,
                            Simpson_Index = simpson_diversity)
print(alpha_results)
```

# Assessing Fish Beta Diversity

## Calculate Beta Diversity Components

We can utilize the beta.div.comp() function from the adespatial package in order to calculate fish replacement and richness difference components. This utilizes our fish species presence-absence data, and for this analysis we will be focusing on the Podani family of indices which includes the Jaccard and Sorensen dissimilarity coefficients and their quantitative forms.

### Jaccard's Component Beta Diversity

```{r}
# Calculate Beta Diversity Components for Jaccard
fish.bd.j = beta.div.comp(fish, coef = "J", quant = T)

# View Jaccard's Beta Diversity Components
fish.bd.j$part
```

Jaccard's Component Beta Diversity Interpretation

-   BDtotal = Total Beta Diversity = 37.7%: Suggests that about 37.7% of the species composition is different among the sites. This means that the sites share some species, but there are also species that are unique to each site.
-   Repl = Replacement: 14.15% of Beta Diversity is accounted for by Replacement
-   RichDif = Richness Difference: 23.55% of Beta Diversity is accounted for by Richness Differences
-   Proportions of influence are calculated with Repl/BDtotal and RichDif/BDtotal, which tell us that 37.53% of Beta Diversity is proportionally influenced by Replacement and 62.47% is by Richness Differences (sums to 1).

### Sorensen's Component Beta Diversity

```{r}
# Calculate Beta Diversity Components for Sorensen
fish.bd.s = beta.div.comp(fish, coef = "S", quant = T)

# View Sorensen's Beta Diversity Components
fish.bd.s$part
```

Sorensen's Component Beta Diversity Interpretation

-   BDtotal = Total Beta Diversity = 32.38%: Suggests that about 32.38% of the species composition is different among the sites. This means that the sites share some species, but there are also species that are unique to each site.
-   Repl = Replacement: 12.03% of Beta Diversity is accounted for by Replacement
-   RichDif = Richness Difference: 20.03% of Beta Diversity is accounted for by Richness Differences
-   Proportions of influence are calculated with Repl/BDtotal and RichDif/BDtotal, which tell us that 37.17% of Beta Diversity is proportionally influenced by Replacement and 62.83% is by Richness Differences (sums to 1).

## Calculate Local Contributions to Beta Diversity

Local Contributions to Beta Diversity narrows the scope from all sites, like in the previous calculation of Beta Diversity Components, to site specific contributions.

### Jaccard's Local Contributions to Beta Diversity

#### Jaccard's Local Replacement Contributions to Beta Diversity

```{r}
# Calculate Local Contribution to Beta Diversity for Jaccard
local.repl.j = LCBD.comp(fish.bd.j$repl, sqrt.D = T)

# View Jaccard's Local Replacement Contributions
local.repl.j
```

#### Jaccard's Local Richness Difference Contributions to Beta Diversity

```{r}
# Calculate Jaccard's Local Richness Difference / Turnover Contributions
local.rich.j = LCBD.comp(fish.bd.j$rich, sqrt.D = T)

# View Jaccard's Local Richness Difference / Turnover Contributions
local.rich.j
```

### Sorensen's Local Contributions to Beta Diversity

#### Sorensen's Local Replacement Contributions to Beta Diversity

```{r}
# Calculate Sorensen's Local Replacement Contributions
local.repl.s = LCBD.comp(fish.bd.s$repl, sqrt.D = T)

# View Sorensen's Local Replacement Contributions
local.repl.s
```

#### Sorensen's Local Richness Difference Contributions to Beta Diversity

```{r}
# Calculate Sorensen's Local Richness Difference / Turnover Contributions
local.rich.s = LCBD.comp(fish.bd.s$rich, sqrt.D = T)

# View Sorensen's Local Richness Difference / Turnover Contributions
local.rich.s
```

### Local Contributions to Beta Diversity

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#### Table 2: Jaccard's Local Contributions to Beta Diversity

| Site | Repl. LCBD   | Repl. Impact  | RD LCBD    | RD Impact     |
|------|--------------|---------------|------------|---------------|
| 1    | -0.006412591 | Low Impact    | 0.08471002 | High Impact   |
| 2    | 0.031057500  | Medium Impact | 0.03689583 | Medium Impact |
| 3    | 0.045826744  | Medium Impact | 0.02564589 | Medium Impact |
| 4    | 0.041488590  | Medium Impact | 0.02430854 | Medium Impact |
| 5    | 0.050099738  | High Impact   | 0.02430643 | Medium Impact |
| 6    | 0.033288092  | Medium Impact | 0.02590333 | Medium Impact |
| 7    | 0.038157146  | Medium Impact | 0.02669263 | Medium Impact |
| 8    | 0.062190531  | High Impact   | 0.02994095 | Medium Impact |
| 9    | 0.036298246  | Medium Impact | 0.03192175 | Medium Impact |
| 10   | 0.029138579  | Medium Impact | 0.04130865 | High Impact   |
| 11   | 0.045281708  | Medium Impact | 0.02413163 | Medium Impact |
| 12   | 0.062168779  | High Impact   | 0.02188155 | Medium Impact |
| 13   | 0.049345906  | Medium Impact | 0.02361610 | Medium Impact |
| 14   | 0.042641201  | Medium Impact | 0.02475546 | Medium Impact |
| 15   | 0.042421271  | Medium Impact | 0.02535543 | Medium Impact |
| 16   | 0.032310835  | Medium Impact | 0.02748067 | Medium Impact |
| 17   | 0.034572053  | Medium Impact | 0.02614698 | Medium Impact |
| 18   | 0.032215076  | Medium Impact | 0.02769883 | Medium Impact |
| 19   | 0.024644628  | Medium Impact | 0.03182826 | Medium Impact |
| 20   | 0.022357400  | Medium Impact | 0.03395379 | Medium Impact |
| 21   | 0.017866032  | Low Impact    | 0.03931829 | High Impact   |
| 22   | 0.006678116  | Low Impact    | 0.07649302 | High Impact   |
| 23   | 0.068538661  | High Impact   | 0.02911869 | Medium Impact |
| 24   | 0.049834767  | Medium Impact | 0.04087927 | High Impact   |
| 25   | 0.044771438  | Medium Impact | 0.02497104 | Medium Impact |
| 26   | 0.027217645  | Medium Impact | 0.03370123 | Medium Impact |
| 27   | 0.022237378  | Medium Impact | 0.03776519 | Medium Impact |
| 28   | 0.001319271  | Low Impact    | 0.05017985 | High Impact   |
| 29   | 0.012445261  | Low Impact    | 0.04909067 | Medium Impact |

#### Table 3: Sorensen's Local Contributions to Beta Diversity

| Site | Repl. LCBD   | Repl. Impact  | RD LCBD    | RD Impact     |
|------|--------------|---------------|------------|---------------|
| 1    | -0.001714649 | Low Impact    | 0.09507352 | High Impact   |
| 2    | 0.035404519  | Medium Impact | 0.03703022 | Medium Impact |
| 3    | 0.047725546  | Medium Impact | 0.02624392 | Medium Impact |
| 4    | 0.038258992  | Medium Impact | 0.02225857 | Medium Impact |
| 5    | 0.044715682  | Medium Impact | 0.02151469 | Medium Impact |
| 6    | 0.028114225  | Medium Impact | 0.02225857 | Medium Impact |
| 7    | 0.038277136  | Medium Impact | 0.02624392 | Medium Impact |
| 8    | 0.063242693  | High Impact   | 0.03040469 | Medium Impact |
| 9    | 0.033338279  | Medium Impact | 0.03040469 | Medium Impact |
| 10   | 0.030989795  | Medium Impact | 0.04105238 | High Impact   |
| 11   | 0.046741511  | Medium Impact | 0.02404728 | Medium Impact |
| 12   | 0.065791821  | High Impact   | 0.02326592 | Medium Impact |
| 13   | 0.050770890  | High Impact   | 0.02162119 | Medium Impact |
| 14   | 0.040029554  | Medium Impact | 0.02143146 | Medium Impact |
| 15   | 0.036657017  | Medium Impact | 0.02261790 | Medium Impact |
| 16   | 0.024921859  | Medium Impact | 0.02400430 | Medium Impact |
| 17   | 0.027294303  | Medium Impact | 0.02313578 | Medium Impact |
| 18   | 0.025612533  | Medium Impact | 0.02519746 | Medium Impact |
| 19   | 0.022755535  | Medium Impact | 0.03116836 | Medium Impact |
| 20   | 0.021960902  | Medium Impact | 0.03454923 | High Impact   |
| 21   | 0.018499105  | Low Impact    | 0.04099183 | High Impact   |
| 22   | 0.012371688  | Low Impact    | 0.08552391 | High Impact   |
| 23   | 0.078778104  | High Impact   | 0.02810169 | Medium Impact |
| 24   | 0.057510394  | High Impact   | 0.04105238 | High Impact   |
| 25   | 0.046333699  | Medium Impact | 0.02351030 | Medium Impact |
| 26   | 0.027675386  | Medium Impact | 0.03515723 | High Impact   |
| 27   | 0.022676147  | Medium Impact | 0.03965913 | High Impact   |
| 28   | 0.001344199  | Low Impact    | 0.05062086 | High Impact   |
| 29   | 0.013923136  | Low Impact    | 0.05185863 | High Impact   |

## Calculate Species Contribution to Beta Diversity

```{r}
# Calculate Species Contribution to Beta Diversity
SCBD = beta.div(fish, method = "hellinger")

# View Species Contribution to Beta Diversity
SCBD
```

#### Table 4: Species Contributions to Beta Diversity

| Species | SCBD       | Impact        |
|---------|------------|---------------|
| Cogo    | 0.03179477 | Medium Impact |
| Satr    | 0.14229130 | High Impact   |
| Phph    | 0.09491247 | High Impact   |
| Neba    | 0.07129053 | High Impact   |
| Thth    | 0.03367740 | Medium Impact |
| Teso    | 0.03031386 | Medium Impact |
| Chna    | 0.01535243 | Low Impact    |
| Chto    | 0.02335210 | Medium Impact |
| Lele    | 0.03448797 | Medium Impact |
| Lece    | 0.03534994 | Medium Impact |
| Baba    | 0.02901233 | Medium Impact |
| Spbi    | 0.02093510 | Low Impact    |
| Gogo    | 0.03134639 | Medium Impact |
| Eslu    | 0.02722712 | Medium Impact |
| Pefl    | 0.02705394 | Medium Impact |
| Rham    | 0.02321227 | Medium Impact |
| Legi    | 0.02060750 | Low Impact    |
| Scer    | 0.01900080 | Low Impact    |
| Cyca    | 0.01654732 | Low Impact    |
| Titi    | 0.02923874 | Medium Impact |
| Abbr    | 0.01899880 | Low Impact    |
| Icme    | 0.01330308 | Low Impact    |
| Acce    | 0.03326809 | Medium Impact |
| Ruru    | 0.05494183 | High Impact   |
| Blbj    | 0.02410392 | Medium Impact |
| Alal    | 0.07964366 | High Impact   |
| Anan    | 0.01873634 | Low Impact    |