# 植物群落物种多样性功能多样性群落稳定性等指标计算公式

Shannon多样性指数(Shannon’s diversity index, H')

Shannon多样性指数H' was determined by the following equation (Shannon and Weaver 1949 Shannon C.E., Weaver W. 1949. The Mathematical Theory of Communication. University of Illinois Press, Urbana, Illinois, pp. 1‒117.):

where Pi represents the relative abundance of plant species i in one particular quadrat. Pi was calculated as follows: Pi=ni/N, where ni represents the number of individuals of plant species i and N represents the total number of individuals of all plant species in one particular quadrat, respectively.

Simpson优势度指数(Simpson’s dominance index, D)

Simpson优势度指数D was calculated as (Simpson 1949 Simpson, E.H. 1949. Measurement of diversity. Nature 163, 688.):

OR

where ni represents the number of individuals of plant species i and N represents the total number of individuals of all plant species in one particular quadrat, respectively.

Pielou均匀度指数(Pielou’s evenness index, EH)

Pielou均匀度指数EH was calculated as follows (Pielou 1966 Pielou E.C. 1966. The measurement of diversity in different types of biological collections. Journal of Theoretical Biology 13: 131‒144.):

where S represents the number of plant species in one particular quadrat.

Margalef丰富度指数(Margalef’s richness index, F)

Margalef丰富度指数F was calculated as follows (Margalef 1951 Margalef R. 1951. Diversidad de especies en las comunidades naturales (Vol. 6, pp. 59‒72). Barcelona: Publicaciones del Instituto de Biologia Aplicada.):

where S represents the number of plant species and N represents the total number of individuals of all plant species in one particular quadrat, respectively.

CWM was calculated as follows (Garnier et al. 2004 Garnier E, Cortez J, Billès G, Navas M, Roumet C, Debussche M, Laurent G, Blanchard A, Aubry D, Bellmann A, Neill C, Toussaint JP (2004). Plant functional markers capture ecosystem properties during secondary succession. Ecology 85: 2630‒2637.; Lavorel et al. 2008 Lavorel S, Grigulis K, McIntyre S, Williams NS, Garden D, Dorrough J, Berman S, Quétier F, Thébault A, Bonis A. 2008. Assessing functional diversity in the field‒methodology matters!. Functional Ecology 22: 134‒147.; Ricotta and Moretti 2011 Ricotta C, Moretti M. 2011. CWM and Rao’s quadratic diversity: a unified framework for functional ecology. Oecologia 167: 181‒188.):

where Pi represents the relative abundance of plant species i in one particular quadrat, and Xi represents one functional trait of plant species i in one particular quadrat.

Mason’s a功能多样性指数(Mason’s a functional diversity index, Fa)

Fa was calculated as follows (Mason et al. 2003 Mason NW, MacGillivray K, Steel JB, Wilson JB. 2003. An index of functional diversity. Journal of Vegetation Science 14: 571‒578.):

where Xi represents the merged community-weighted mean trait value (calculated as the mean of all functional traits) of plant species i in one particular quadrat, and X represents the merged community-weighted mean trait value (calculated as the mean of all functional traits) of all plant species in the same quadrat (Mason et al. 2003 Mason NW, MacGillivray K, Steel JB, Wilson JB. 2003. An index of functional diversity. Journal of Vegetation Science 14: 571‒578.).

Mason’s β功能多样性指数(Mason’s β functional diversity index, Fβ)

Fβ was calculated as follows (Mason et al. 2005 Mason NWH, Mouillot D, Lee WG, Wilson JB. Functional richness, functional evenness and functional divergence: the primary components of functional diversity. Oikos 2005, 111: 112‒118):

where Xk represents the merged community‒weighted mean trait value (calculated as the mean of the ten functional traits) of all plant species in one particular quadrat, X represents the merged community‒weighted mean trait value (calculated as the mean of the ten functional traits) of all plant species in all quadrat, and n represents the number of quadrats, respectively.

FDQ was calculated as follows (Rao 1982 Rao CR. 1982. Diversity and dissimilarity coefficients: An unified approach. Theoretical Population Biology 21: 24‒43.; Botta-Dukat 2005 Botta-Dukat Z. 2005. Rao’s quadratic entropy as a measure of functional diversity based on multiple traits. Journal of Vegetation Science 16: 533‒540.; Weigelt et al. 2008 Weigelt A, Schumacher J, Roscher C, Schmid B. 2008. Does biodiversity increase spatial stability in plant community biomass? Ecology Letters 11: 338–347.; Ricotta and Moretti 2011 Ricotta C, Moretti M. 2011. CWM and Rao’s quadratic diversity: a unified framework for functional ecology. Oecologia 167: 181‒188.; Fu et al. 2014 Fu H, Zhong J, Yuan G, Ni L, Xie P, Cao T. 2014. Functional traits composition predict macrophytes community productivity along a water depth gradient in a freshwater lake. Ecology and Evolution 4: 1516‒1523.):

where Pi and Pj are the relative abundances of plant species i and j in one particular quadrat, respectively, and dij represents the interspecific distance.

dij was calculated as follows:

where Xik and Xjk represent functional trait k of plant species i and j in one particular quadrat, respectively, and n represents the number of functional traits, respectively.

The niche breadth of each species was evaluated using the Levins’ standardized niche breadth index (Levins, 1968 Levins, R. (1968) Evolution In Changing Environments: Some Theoretical Explorations. Princeton: Princeton University Press.; Hurlbert, 1978 Hurlbert, S. H. (1978) The measurement of niche overlap and some relatives. Ecology, 59, 67–77.; Granot ET AL. 2017 Granot I, Shenkar N, Belmaker J. Habitat niche breadth predicts invasiveness in solitary ascidians. Ecology and Evolution.7: 7838–7847.):

where s is the focal species, pi,s is the proportion of individuals of species S found on niche i, and n is the number of niches available. This index is a modification of the basic Levins’ niche breadth index, with the advantage of scores scaled between zero to one, where zero is an extreme specialist and one an extreme generalist.

To evaluate the degree of niche overlap of two plant species, niche overlap index (Oij) was calculated as follows (Pianka ER. 1973. The structure of lizard communities. Annual Review of Ecology and Systematics, 4, 53–74.):

where Oij represents the niche overlap index between plant species i and j; Pik and Pjk represent the relative abundances of plant species i and j in in one particular quadrat k, respectively, and r represents the number of quadrats, respectively. If the value of this index is 1, it means that the ecological niches of the two plant species i and j overlap completely. If the value of this index is 0, it means that the ecological niches of the two plant species i and j do not overlap at all.

Plant community stability was assessed by calculating the inverse of coefficient of variation (ICV) as

where μ represents the mean of relative abundance of all plant species in one particular quadrat and σ represents the standard deviation for the mean of relative abundance of all plant species in one particular quadrat, respectively (Tilman 1999 Tilman D (1999) The ecological consequences of biodiversity: a search for general principles. Ecology 80:1455–1474; Valone and Hoffman 2003 van Ruijven, J., Berendse, F. (2007) Contrasting effects of diversity on the temporal stability of plant populations. Oikos 116, 1323–1330.; Tilman et al. 2006 Tilman D, Reich PB, Knops JMH (2006) Biodiversity and ecosystem stability in a decade-long grassland experiment. Nature 441:629–632; Sasaki and Lauenroth, 2011 Sasaki T, Lauenroth WK. Dominant species, rather than diversity, regulates temporal stability of plant communities. Oecologia 2011, 166: 761‒768.; Yang et al., 2011 Yang ZL, van Ruijven J, Du GZ. The effects of long-term fertilization on the temporal stability of alpine meadow communities. Plant and Soil 2011, 345: 315‒324.; Yao et al., 2016 Yao TH, Zhu ZH, Li YN, Pan SY, Kong BB, Wei XH, Du JL. 2016. Effects of functional diversity and functional redundancy on the community stability of an alpine meadow. Acta Ecologica Sinica 36:1547‒1558.; Wang et al., 2017 Wang HF, Lü GH, Zhou YZ, Cao J. 2017. Effects of functional diversity and functional redundancy on the stability of desert plant communities under different water and salt gradients. Acta Ecologica Sinica 37: 79286‒7937.; Valone and Balaban-Feld 2018 Valone TJ, Balaban-Feld J. 2018. Impact of exotic invasion on the temporal stability of natural annual plant communities. Oikos 127: 56‒62.). In particular, plant communities with higher values of ICV possess greater stability compared with those with lower values of ICV.

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