Package BioFTF. February 18, 2016

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1 Version Date Package BioFTF February 18, 2016 Title Biodiversity Assessment Using Functional Tools Author Fabrizio Maturo [aut, cre], Francesca Fortuna [aut], Tonio Di Battista [aut] Maintainer Fabrizio Maturo Depends R (>= 3.1.0) Suggests MASS The main drawback of the most common biodiversity indices is that different measures may lead to different rankings among communities. This instrument overcomes this limit using some functional tools with the diversity profiles. In particular, the derivatives, the curvature, the radius of curvature, the arc length, and the surface area are proposed. The goal of this method is to interpret in detail the diversity profiles and obtain an ordering between different ecological communities on the basis of diversity. In contrast to the typical indices of diversity, the proposed method is able to capture the multidimensional aspect of biodiversity, because it takes into account both the evenness and the richness of the species present in an ecological community. License GPL (>= 2) URL BugReports f.maturo@unich.it NeedsCompilation no Repository CRAN Date/Publication :51:26 R topics documented: alltools arc area beta

2 2 alltools betaprime betaprime_plot betasecond betasecond_plot beta_plot curvature curvature_plot datirel radius radius_plot ranking summary_species summary_species_relative Inde 17 alltools Apply the whole analysis to the dataset. This function provides the derivatives, the curvature, the radius of curvature and the arc length of diversity profiles. Morever, it computes the surface area under the beta profile and ranks the communities. alltools() A data matri with the abundance of the species (the rows are the communities

3 arc 3 Eamples #eample 1 =matri(c(3,5,5,2,1,2,6,8,5,1),2,5) alltools() #Some eamples espressed by relative abundance: #eample 2 =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) alltools() #eample 3 =matri(runif(1000),10,100) #let s consider some missing species [1,1:20]=0 [2,1:40]=0 [3,1:60]=0 [4,1:19]=0 alltools() #eample 4 =matri(runif(100),20,5) [1,1:2]=0 [2,1:3]=0 alltools() #eample 5 a=c(0.35,0.35,0.27,0.01,0.02) b=c(0.54,0.20,0.17,0.06,0.03) c=c(0.35,0.35,0.30,0,0) d=c(0.51,0.31,0.07,0.10,0.01) e=c(0.40,0.20,0.10,0.30,0) =matri(rbind(a,b,c,d,e),5,5) alltools() arc Compute the arc length of beta profile for each community. This function provides the arc length of beta profile for each community. In an ecological framework, the arc length can be used to assess biodiversity because it can rank communities, given the number of species. Indeed, in a case of maimum dominance, the profile length is etremely high; while in a case of evenness, it decreases. The main advantage of using profile length is that the ordering among communities can be investigated without the analysis of a graph. It provides a scalar

4 4 area measure of diversity preserving its multidimensional aspect. This is not possible with the classical indices. arc() A data matri with the abundance of the species (the rows are the communities Eamples =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) arc() area Compute the area under the beta profile for each community. This function provides the area under the beta profile for each community. In an ecological framework, the area under the profiles can be used to assess biodiversity because it can rank communities, even if they have different number of species. Indeed, in a case of maimum dominance, the area is etremely low; while in a case of evenness, it increase. The main advantage of using area is that the ordering among communities can be investigated without the analysis of a graph. It provides a scalar measure of biodiversity preserving its multidimensional aspect. This is not possible with the classical indices. area()

5 beta 5 A data matri with the abundance of the species (the rows are the communities Eamples =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) area() beta Compute the values of beta profile for each community in every part of the beta domain. The matri obtained with "beta" contains the values of diversity computed for each community for each point of the domain. This matri provides the values of diversity profile; it displays a complete picture of diversity. Indeed, the most frequently used indices of biodiversity are special cases of this function. beta() A data matri with the abundance of the species (the rows are the communities Eamples =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) beta()

6 6 betaprime betaprime Compute the values of the first derivative of beta profile for each community in every part of the beta domain. This function provides the values of the first derivative of beta profile. This is an essential component of functional data analysis (Ramsay and Silverman, 2005), and in an ecological framework, is useful for highlighting the characteristics of the profiles and eplaining some of the variation from curve to curve. For "beta" close to???1, high absolute values for the first derivative correspond to a strong decrease of the profile; thus, a sudden decrease suggests the presence of few prevalent species in a community (dominance). On the contrary, low absolute values indicate that living organisms tend to be equally distributed among the species (evenness). betaprime() A data matri with the abundance of the species (the rows are the communities Eamples a=c(0.35,0.35,0.27,0.01,0.02) b=c(0.54,0.20,0.17,0.06,0.03) c=c(0.35,0.35,0.30,0,0) d=c(0.51,0.31,0.07,0.10,0.01) e=c(0.40,0.20,0.10,0.30,0) =matri(rbind(a,b,c,d,e),5,5) betaprime()

7 betaprime_plot 7 betaprime_plot Plot the first derivative of the beta profile for each community. This function provides the plot of the first derivative of the beta profile. The domain "beta" represents the sensibility to changes in the presence of rare species. This is an essential component of functional data analysis (Ramsay and Silverman, 2005), and in an ecological framework, is useful for highlighting the characteristics of the profiles and eplaining some of the variation from curve to curve. For "beta" close to???1, high absolute values for the first derivative correspond to a strong decrease of the profile; thus, a sudden decrease suggests the presence of few prevalent species in a community (dominance). On the contrary, low absolute values indicate that living organisms tend to be equally distributed among the species (evenness). betaprime_plot() A data matri with the abundance of the species (the rows are the communities Eamples a=c(0.35,0.35,0.27,0.01,0.02) b=c(0.54,0.20,0.17,0.06,0.03) c=c(0.35,0.35,0.30,0,0) d=c(0.51,0.31,0.07,0.10,0.01) e=c(0.40,0.20,0.10,0.30,0) =matri(rbind(a,b,c,d,e),5,5) betaprime_plot()

8 8 betasecond betasecond Compute the values of the second derivative of beta profile for each community in every part of the beta domain. This function provides the values of the second derivative of the beta profile. The second derivative represents the deceleration of the profile for any given value of "beta". The second derivative represents the deceleration of the profile for any given value of "beta". For "beta" close to???1, high values of the second derivative denote high dominance because the profile tends to be etremely curved when some prevalent species are present in a community. For the interval [0,1] the second derivative tends always towards zero. betasecond() A data matri with the abundance of the species (the rows are the communities Eamples a=c(0.35,0.35,0.27,0.01,0.02) b=c(0.54,0.20,0.17,0.06,0.03) c=c(0.35,0.35,0.30,0,0) d=c(0.51,0.31,0.07,0.10,0.01) e=c(0.40,0.20,0.10,0.30,0) =matri(rbind(a,b,c,d,e),5,5) betasecond()

9 betasecond_plot 9 betasecond_plot Plot the second derivative of the beta profile for each community. This function provides the plot of the second derivative of the beta profile. The domain "beta" represents the sensibility to changes in the presence of rare species. The second derivative represents the deceleration of the profile for any given value of "beta". For "beta" close to???1, high values of the second derivative denote high dominance because the profile tends to be etremely curved when some prevalent species are present in a community. For the interval [0,1] the second derivative tends always towards zero. betasecond_plot() A data matri with the abundance of the species (the rows are the communities Eamples a=c(0.35,0.35,0.27,0.01,0.02) b=c(0.54,0.20,0.17,0.06,0.03) c=c(0.35,0.35,0.30,0,0) d=c(0.51,0.31,0.07,0.10,0.01) e=c(0.40,0.20,0.10,0.30,0) =matri(rbind(a,b,c,d,e),5,5) betasecond_plot()

10 10 beta_plot beta_plot Plot the beta profile for each community. This function provides a plot of the diversity profiles of the considered communities. The domain "beta" represents the sensibility to changes in the presence of rare species. It is a decreasing and concave upward curve showing different values of biodiversity for each value of beta. The most frequently used indices of biodiversity are special cases of this function. The diversity profile displays a complete picture of diversity. Its plot allows the analyst to rank different communities. Indeed, the higher curve highlights biological populations with higher diversity and vice versa. The plot tends towards a straight line, decreasing from???1 to 1, in the case of maimum equitability with few species, and it becomes more curved with the prevalence of a few species over the others. Difficulties arise if we compare communities with intersecting profiles. In this case, it is impossible to determine which curve is the highest only using the diversity profile. beta_plot() A data matri with the abundance of the species (the rows are the communities Eamples a=c(0.35,0.35,0.27,0.01,0.02) b=c(0.54,0.20,0.17,0.06,0.03) c=c(0.35,0.35,0.30,0,0) d=c(0.51,0.31,0.07,0.10,0.01) e=c(0.40,0.20,0.10,0.30,0) =matri(rbind(a,b,c,d,e),5,5) beta_plot()

11 curvature 11 curvature Compute the values of the curvature of the beta profile function for each community in every part of the beta domain. This function provides the values of the curvature of the beta profile for each part of the domain. The curvature reflects the community composition; in particular, if we consider communities with different numbers of species, the curvature is a good indicator of the lack of balance among species. Great levels of curvature highlights high imbalance among different species and vice-versa. curvature() A data matri with the abundance of the species (the rows are the communities Eamples =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) curvature()

12 12 curvature_plot curvature_plot Plot the curvature of the beta profiles for each community. This function provides a plot of the curvature functions of the diversity profiles for the considered communities. The domain "beta" represents the sensibility to changes in the presence of rare species. The graph of the curvature reflects the community composition; in particular, if we consider communities with different numbers of species, the curvature is a good indicator of the lack of balance among species. Great levels of curvature highlights high imbalance among different species and vice-versa. curvature_plot() A data matri with the abundance of the species (the rows are the communities Eamples =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) curvature_plot()

13 datirel 13 datirel Create a matri with the relative frequencies for each community. Create a matri with the relative frequencies for each community. datirel() A data matri with the absolute abundance of the species. Eamples =matri(c(3,5,5,2,1,2,6,8,5,1),2,5) datirel() radius Compute the values for the radius of curvature of the beta profile for each community in every part of the beta domain. This function provides the values of radius of the curvature for each part of the domain. The radius of curvature reflects the community composition; in particular, if we consider communities with different numbers of species, the radius of curvature is a good indicator of the lack of balance among species. This tool is alternative to the curvature because it is its inverse. Low levels of radius of curvature highlights high imbalance among different species and vice-versa. radius() A data matri with the abundance of the species (the rows are the communities

14 14 radius_plot Eamples =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) radius() radius_plot Plot the radius of curvature of the beta profiles for each community. This function provides a plot of the radius of curvature of the diversity profiles for the considered communities. The domain "beta" represents the sensibility to changes in the presence of rare species. The graph of the radius of curvature reflects the community composition; in particular, if we consider communities with different numbers of species, the radius of curvature is a good indicator of the lack of balance among species. This graph is alternative to the curvature. Low levels of radius of curvature highlights high imbalance among different species and vice-versa. radius_plot() A data matri with the abundance of the species (the rows are the communities

15 ranking 15 Eamples =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) radius_plot() ranking Compute the communities ranking according to the biodiversity computed using the functional tools. This function provides the communities ranking according to the biodiversity computed using the functional tools. ranking() A data matri with the abundance of the species (the rows are the communities Eamples =matri(c(0.3,0.5,0.1,0.05,0.05,0.25,0.25,0.25,0.25,0,0.35,0.3,0.35,0,0),3,5) ranking()

16 16 summary_species_relative summary_species Create a species summary for each community. Based on the dataset with absolute abundance Create the species summary for each community (absolute abundance). summary_species() A data matri with the absolute abundance of the species. Eamples =matri(c(3,5,5,2,1,2,6,8,5,1),2,5) summary_species() summary_species_relative Create a species summary for each community. Based on the dataset with relative abundance. Create a species summary for each community (relative abundance). summary_species_relative() A data matri with the absolute abundance of the species. Eamples =matri(c(3,5,5,2,1,2,6,8,5,1),2,5) summary_species_relative()

17 Inde alltools, 2 arc, 3 area, 4 beta, 5 beta_plot, 10 betaprime, 6 betaprime_plot, 7 betasecond, 8 betasecond_plot, 9 curvature, 11 curvature_plot, 12 datirel, 13 radius, 13 radius_plot, 14 ranking, 15 summary_species, 16 summary_species_relative, 16 17