# Spatial Association and Diversity of Dominant Tree Species in Tropical Rainforest, Vietnam

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1.Study Site and Data Collection

#### 2.2. Data Analysis

#### 2.2.1. Uni- and Bivariate Pair Correlation Functions

_{11}(r) for the univariate pattern of species 1 can be defined based on the neighborhood density, which is the mean density of trees of species 1 within rings with radius r and width dr centered on the trees of species 1 [23] where λ

_{1}is the density of species 1 trees in the plot. Therefore, the pair correlation function is the ratio of the observed mean density of trees in the rings to the expected mean density of trees. The univariate pair correlation function g

_{11}(r) can be used to find out whether the distribution of a species is random (g

_{11}(r) = 1), aggregated (g

_{11}(r) > 1), or segregated (g

_{11}(r) < 1), and at which distances r these patterns occur. The pair correlation function for bivariate patterns (i.e., species 1 and species 2) follows intuitively: the value of g

_{12}(r) is the ratio of the observed mean density of species 2 trees in the rings around species 1 trees to the expected mean density of species 2 trees in these rings [23]. The association of a species pair is that of independence if g

_{12}(r) = 1, attraction if g

_{12}(r) > 1, or repulsion if g

_{12}(r) < 1 at distances r.

_{12}(r) and g

_{21}(r) for each species association due to the asymmetric interactions of species.

#### 2.2.2. Individual Species—Area Relationship

^{2}, around an arbitrarily chosen individual of a target species t [7]. ISAR is used to analyze the spatial diversity structure in forest ecosystems and combine the species–area relationship with the individual perspective of point pattern analysis [21]. For a species, the ISAR can be estimated as:

_{tj}(0, r) is the emptiness probability that species j is not present in the circle with radius r around individuals of the target species t. If a = πr

^{2}, the ISAR function can be expressed in terms of circular area a to resemble the common species area relationship [7].

#### 2.2.3. Used Software Package

_{11}(r) was above the simulation envelopes and regularity if it was below. Conversely, the bivariate analysis indicated a positive interaction if the observed g

_{12}(r) was above the simulation envelopes, and a negative interaction if it was below.

## 3. Results

#### 3.1. Species Distribution Patterns

#### 3.2. Species Associations

#### 3.3. Individual Species Area Relationship

## 4. Discussion

#### 4.1. Species Distribution Patterns

#### 4.2. Species Associations

#### 4.3. Individual Species—Area Relationship

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix

**Table A1.**Characteristics of common species in both study plots. N—number of individuals, IVI—Important Value Index, (relative abundance + relative basal area)/2, expressed as percentage proportion. DBH—Diameter at Breast Height (mean ± Standard deviation).

No | Tree Species | P1 | P2 | Shade Tolerance | ||||
---|---|---|---|---|---|---|---|---|

N | DBH (cm) | IVI (%) | N | DBH (cm) | IVI (%) | |||

1 | Garuga pierrei Guillaumin | 282 | 10.08 ± 10.89 | 8.985 | 232 | 11.30 ± 13.26 | 7.72 | Tolerant |

2 | Tarrietia javanica Blume | 383 | 5.62 ± 6.39 | 7.285 | 330 | 4.52 ± 3.58 | 5.14 | Intolerant |

3 | Ormosia balansae Drake | 138 | 17.05 ± 12.97 | 7.26 | 187 | 14.75 ± 10.81 | 6.605 | Intolerant |

4 | Bursera tonkinensis Guillaumin | 384 | 6.15 ± 4.16 | 6.72 | 253 | 6.67 ± 4.12 | 4.41 | Medium |

5 | Paviesia annamensis Pierre. | 240 | 9.18 ± 7.64 | 6.025 | 239 | 6.94 ± 4.86 | 4.325 | Intolerant |

6 | Litsea glutinosa (Loureiro) C.B. Rob. | 229 | 8.06 ± 6.21 | 4.965 | 264 | 8.26 ± 6.70 | 5.495 | Intolerant |

7 | Castanopsis indica (Rox. ex Lin.) A. | 168 | 10.21 ± 8.27 | 4.65 | - | - | Intolerant | |

8 | Polyalthia nemoralis Aug.DC. | 303 | 5.02 ± 1.77 | 4.58 | 244 | 5.53 ± 1.88 | 3.78 | Intolerant |

9 | Syzygium wightianum Wall. ex Wig. & Arn. | 179 | 9.36 ± 7.04 | 4.405 | 81 | 11.56 ± 8.17 | 1.545 | Intolerant |

10 | Erythrophloeum fordii Oliver | 63 | 18.52 ± 15.35 | 3.96 | 36 | 19.33 ± 21.97 | 2.475 | Medium |

11 | Mallotus kurzii Hook.f. | 265 | 4.01 ± 0.98 | 3.76 | 114 | 3.71 ± 0.73 | 1.63 | Intolerant |

12 | Amoora dasyclada C.Y. Wu | 148 | 7.99 ± 6.73 | 3.285 | 96 | 8.89 ± 6.93 | 2.08 | Medium |

13 | Cinnamomun obtusifolium Nees | 100 | 10.71 ± 9.25 | 3.005 | 267 | 13.01 ± 10.59 | 8.51 | Intolerant |

14 | Vatica odorata (Griff.) Symington | 48 | 17.67 ± 15.90 | 2.945 | 48 | 23.46 ± 16.73 | 3.24 | Intolerant |

15 | Gironniera Subaequalis Planch | 92 | 9.71 ± 6.65 | 2.27 | 137 | 11.19 ± 9.28 | 3.73 | Medium |

16 | Endospermun sinensis Benth. | 54 | 11.77 ± 13.18 | 2.14 | 83 | 21.67 ± 13.33 | 4.63 | Intolerant |

17 | Sindora cochinchinensis auct. non Baill. | 41 | 16.52 ± 13.44 | 2.125 | 33 | 15.77 ± 14.19 | 2.77 | Intolerant |

18 | Garcinia oblongifolia Chanp. ex Benth. | 121 | 6.23 ± 4.08 | 2.115 | 67 | 6.22 ± 3.48 | 1.115 | Tolerant |

19 | Canarium album (Lour.) DC. | 46 | 15.01 ± 8.88 | 1.79 | 155 | 11.03 ± 6.04 | 3.685 | Intolerant |

20 | Koilodepas hainanense (Merr.) Croizat | 104 | 5.83 ± 2.61 | 1.685 | 80 | 8.41 ± 4.52 | 1.545 | Tolerant |

21 | Cassine glauca (Rottb.) Kuntze | 74 | 8.41 ± 5.51 | 1.59 | 89 | 8.69 ± 7.66 | 1.97 | Tolerant |

22 | Vitex trifolia L. | 33 | 14.83 ± 9.63 | 1.305 | - | - | Intolerant | |

23 | Litsea vang Lecomte | 71 | 6.54 ± 3.30 | 1.27 | 76 | 8.72 ± 4.67 | 1.5 | Intolerant |

24 | Symplocos laurina (Retz.) Wall. ex G. | 55 | 9.31 ± 5.61 | 1.255 | 145 | 11.81 ± 6.86 | 3.715 | Intolerant |

25 | Alangium ridleyi King | 40 | 7.89 ± 5.19 | 0.81 | 49 | 9.10 ± 6.27 | 1.045 | Tolerant |

26 | Engelhardtia roxburghiana Lindl. | - | - | 63 | 28.78 ± 11.91 | 4.845 | Tolerant | |

27 | Antheroporum pierrei Gagnep | - | - | 47 | 19.81 ± 7.39 | 2 | Intolerant | |

28 | Knema pierrei Warb. | - | - | 46 | 10.05 ± 4.86 | 0.99 | Tolerant | |

29 | Polyalthia cerasoides (Roxb.) Bedd. | - | - | 33 | 25.59 ± 20.80 | 1.4 | Intolerant | |

30 | Madhuca pasquieri (Dubard) H.J. Lam | - | - | 32 | 14.69 ± 9.76 | 1.07 | Medium |

**Figure A1.**Spatial patterns of all trees with DBH ≥10 cm in two plots P1 and P2 using univariate pair-correlation g-function (

**a**,

**c**,

**e**,

**g**) and L-function (

**b**,

**d**,

**f**,

**h**). Null models were CSR (

**a**–

**b**,

**e**–

**f**) and IPP (

**c**–

**d**,

**g**–

**h**) with R = 50 m. In the P1, the g-function and L-function showed no large scale departure from the null model of CSR (

**a**,

**b**) indicating environmental homogeneity. In the P2, the g-function was significant (>1) for scales larger than 10 m (

**e**), the L-function showed a clear departure from scales r > 25 m and did not approach value 0 (

**f**) under the null model of CSR. Moreover, the spatial arrangement of trees >10 cm fitted very well under the null model of IPP with R = 50 m (

**c**–

**d**,

**g**–

**h**) when analyzed by the g- and L-functions. These evidences significantly exhibited large scale homogeneity at P1 and heterogeneity at P2. Note: L-function is a transformation of Ripley’s K-function, L(r) = (K(r)/π)

^{0.5}− r. The g pair-correlation function is the derivative of the K function, g(r) = K’(r)/(2πr) and r is radius of the circle from a randomly chosen tree (please see more details about K function in [23]).

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**Figure 1.**Distribution maps of investigated trees on the two 2-ha plots P1 (

**a**) and P2 (

**b**) with 10 m contour lines of altitude.

**Figure 2.**Significant conspecific associations analyzed by the univariate pair-correlation function g

_{11}(r) from 199 Monte Carlo simulations under the null models of CSR at P1 (

**a**) and IPP at P2 (

**b**) at p values ≤ 0.05. Black lines indicate aggregation, grey lines indicate regularity.

**Figure 3.**Significant heterospecific associations analyzed by the bivariate pair-correlation function g

_{12}(r) from 199 Monte Carlo simulations at p values ≤ 0.05. The null models were independence at P1 (

**a**), and pattern 1 fixed and pattern 2 randomized by inhomogeneous Poisson process at P2 (

**b**). Black lines indicate attraction, grey lines indicate repulsion.

**Figure 4.**Results of ISAR analyses from 199 Monte Carlo simulations under null models of CSR in P1 (

**a**–

**b**) and IPP in P2 (

**c**–

**d**); significant at p ≤ 0.05.

Characteristic | Plot P1 | Plot P2 |
---|---|---|

Elevation (m): mean ± standard deviation (min–max) | 134 ± 6.3 (119–148) | 160 ± 11.1 (137–184) |

Slope (degree):mean ± standard deviation (min–max) | 20 ± 6.6 (5–40) | 26 ± 7.5 (5–45) |

Number of individuals | 3936 | 3731 |

Total basal area (m^{2}) | 48.4 | 64.6 |

DBH (cm) (mean, min–max) | 8.6 (2.5–79.6) | 10.3 (2.5–95.5) |

Number of species | 61 | 52 |

Number of species with one individual | 13 | 7 |

Number of species with ≥30 individuals | 25 | 28 |

Number of shared species | 47 | 47 |

Number of individuals from shared species | 3732 | 3698 |

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## Share and Cite

**MDPI and ACS Style**

Nguyen, H.H.; Erfanifard, Y.; Pham, V.D.; Le, X.T.; Bui, T.D.; Petritan, I.C. Spatial Association and Diversity of Dominant Tree Species in Tropical Rainforest, Vietnam. *Forests* **2018**, *9*, 615.
https://doi.org/10.3390/f9100615

**AMA Style**

Nguyen HH, Erfanifard Y, Pham VD, Le XT, Bui TD, Petritan IC. Spatial Association and Diversity of Dominant Tree Species in Tropical Rainforest, Vietnam. *Forests*. 2018; 9(10):615.
https://doi.org/10.3390/f9100615

**Chicago/Turabian Style**

Nguyen, Hong Hai, Yousef Erfanifard, Van Dien Pham, Xuan Truong Le, The Doi Bui, and Ion Catalin Petritan. 2018. "Spatial Association and Diversity of Dominant Tree Species in Tropical Rainforest, Vietnam" *Forests* 9, no. 10: 615.
https://doi.org/10.3390/f9100615