Ecology Lab Report 2 Finished

“Application of Basic Statistical Tools in Ecology using Correlations of Ficus nana (Moraceae) Leaf Length-Width Ratio and Human Height-Weight-Age Relation”

Camaño, ErlJohn C., De Guzman, Patricia Mae C., Dupla, Allan R., Miñano, Lyndie Pearl M., Seroma, Amira Shiekah Biology Students, Department of Biology, College of Science, Polytechnic University of the Philippines, Sta. Mesa, Manila

Abstract In Ecology, gathering data from the environment is important. Statistical approach gives us better understanding in the relationship of the data to other data in correlation. Statistical tools help us to accomplish the collection and interpretation of data. We collected 100 leaves of Ficus nana and measured the length and width. We also conducted a survey from 100 students within the College of Science. Age, Height and Weight were the information gathered from them. Frequency distribution of Ficus nana shows that there are more leaves that have 53-55 cm length (30%) and 35-36 cm width (32%) while in College of Science, there are more students under 18 years old (31%), weights 45-49 kg (27%) and has a height of 158-164 cm (39%). 18.31 is the average value in the set of data for age, 162.06 is the average value for the set of data for height. 53.25 is the average value for the weight. All variances obtained are Positive, data points are very spread out from the mean and from each other. For the standard Deviation, data points tend to be far from the mean or expected value. . Both the length and the width of the leaves are insignificant having correlation is significant at the 0.01 level The affinity of LWR to length is directly proportional while the connection between width and LWR is reversely proportional. The scatter diagram show can be considered as weak positive correlation because the value of (y) width increases slightly as the value of (x) length increases. In using statistical tools, the data we have gathered were organized using tables and graphs. The resulting regression is Y=0.412888494x+14.06673946. Through this we can easily understand and relate the results to draw logical conclusions. Statistical analysis makes research papers more reliable reference for a study.

Keywords: basic statistical tools, frequency distribution, scatter diagram, length-width ratio, correlation, regression

Introduction Ecology is undergoing some major changes in response to changing times of societal concerns coupled with remote sensing information and computer technology. Both theoretical and applied ecology are using more of statistical thought processes and procedures with advancing software and hardware to satisfy public policy and scientific research, variously incorporating sample survey data, intensive site-specific data, and remote sensing image data. Ecology and Statics are disciplines that belong to two (2) different branch of Science. Ecology belongs to life science studying and dealing with the total relations of the animal to both its organic and inorganic environment while Statistics is a branch of Mathematics that’s described as a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data. Even though Ecology and Statistics came from different branches of Science they have been fused together to help and solve one another. Statistical methods were initially developed for use in basic and applied sciences, and later in engineering and management. While basic statistical science is common to all areas, there are specific techniques developed to answer specific questions in each area. Statistical ecology and environmental statistics are relatively new and need some of its own special methodologies. Statistical thinking is an aid to the collection and interpretation of data. It may help confuse seeming clarity. The statistical approach is expected to contribute to the overall balance, insight and perspective of the substantive issue and its resolution in the light of the evidence on hand, be it in the nature of empirical data, literature-assembled data, expert opinion data or a combination thereof. Statistics will be more a way of thinking or reasoning rather than a tool for beating data to yield answers (Patil, 1995). This paper aims review some statistical tools useful in ecological studies, to determine the relationship of the data to other data in correlation and to apply it in practical use: relationship of height and width ratio of Ficus nana and age, height and weight relationship in humans.

Methodology In this activity 100 leaves of Ficus nana were collected. The general morphology and laminar shape were described. The length of the leaves, from tip of the apex to its base was measured. The greatest width of the leaves was measured to the nearest millimeter. Then, a scatter diagram was made to show the relationship between length and width. The standard deviate was computed and the mean, minimum, and maximum value of the leaf. Next, the slope and Y-intercept was computed using the equation of linear regression line. Data was summarized by presenting the number of leaves with such length and width in a frequency distribution table (FDT). Length width ratio (lwr) was computed and correlated using the leaf length and width. Finally, diagram was made to show the relationship of lwr and leaf length and width. Also in this activity were survey 100 students in Polytechnic University of the Philippines Sta. mesa Manila, 50 male and 50 female students were ask knowing their age, height

and

weight.

Then

solve

for

the

mean

of

age,

height

and

weight.

Next is the standard deviation and variance of height and weight. Data was summarized using frequency distribution table presenting the age, height and weight. The ratio of height and weight was obtained. Computed and the correlation of height and weight. Finally, diagram was made to show the relationship of height and weight.

Figure 1. Ficus nana leaves

Discussions Leaf samples of Ficus Sp. gathered from a single tree located near the PUP Chapel was obtained randomly on the different parts of the tree to prevent any form of bias to observe the correlation of the length and width of the leaf. . The thick, shiny, two to five-inch-long, evergreen leaves generously clothe the long branches, and the tiny figs eventually turn a deep red. Branches will weep toward the ground forming a canopy so dense that nothing grows beneath it. (Caine and Zane). Leaves are important organs for photosynthesis and play an important role in survival and growth of a plant. Many previous studies have revealed that variations in leaf traits are the result of adapting to growth habits (Pandey Nagur, 200). Quantification and visualization of morphological variation of of leaves, flowers and other structures are essential for an overview of evolutionary and ecological processes of phenotypic diversification and is the fundamental basis from which to develop more complex studies to achieve new perspective on the interaction of phenotype, genotype and environment (Jensen,2003). Leaf traits are globally repeated despite large variations in the values of the traits across individual species with very diverse phylogenetic, biogeographical and environmental affinities. The best indicator of species differences is the average length/width ratio, where averaging has smoothed out the overlapping range extremes. Leaf size serves as a reflection of the environment in dry, hot, sunny environments; water is often a limiting factor. So leaves from these environments may exhibit special adaptations that retard water loss. For example, the leaves may be covered with a thick waxy layer that keeps moisture inside the leaf. Small leaves have less total surface area than large

leaves, and they lose less water than large leaves. Overheating can also be a problem for large leaved plants in dry, hot environments. Studies have shown that wide leaves heat up more than narrow leaves of the same length. An evaluation of the length to width ratio of plants from different habitats can yield interesting results. In general, leaves with higher length-to-width ratios are relatively elongate and narrow and dissipate heat faster than leaves with smaller length to width ratios. Leaves with higher length-to-width ratios have more surface area per volume for heat loss than leaves with lower length to width ratios. In general, small, narrow leaves are well adapted to hot, dry, sunny environments. Leaves may also be arranged vertically to reduce exposure to the hot drying sun when the sun is at its zenith. In moist, shady environments light may be a limiting factor. Leaves from these environments may exhibit adaptations that enhance their ability to absorb the sunlight that penetrates to the forest floor. Where radiant energy is scarce, overheating is not a problem and leaves may have a low length to width ratio (EdScope, 2005). As well, leaf traits can thus provide a link between various environmental factors and leaf functions and they have been widely used in functional structural plant models (Roche et al.,2004 Price and Equist, 2007). Shape, size and leaf morphology, whose interest in studies of biomass, and organic and mineral nutrition is well established. This knowledge are currently a component of increasing importance in studies of morphological and genetic diversity of many species, In order to improve their conservation and to base management efforts on sound scientific information of their biology (Dupouey et al., 1991; Harrison et al., 1997, Wu et al. 1997, Leite, 2002, Lutz Eckstein et al., 2006, Xu et al., 2009) One of the reasons for measuring the length and width of the leaf is because it serves as a reflection of the environment the plant lives in. In dry, hot environments, water is often a limiting factor. So leaves from these environments may exhibit special adaptations that retard water loss. Small leaves have less total surface area than large leaves, so they lose less water than large leaves. In general, leaves with higher length-to width ratios are relatively longer and narrower and these leaves dissipate heat faster than leaves with smaller length to width ratios. In addition, leaves with higher length-to-width ratios have more surface area per volume for heat loss than leaves with lower length to width ratios. In moist, shady environments light may be a limiting factor. Leaves from these environments may exhibit adaptations that enhance their ability to absorb the sunlight that penetrates to the forest floor. Where radiant energy is scarce, overheating is not a problem and leaves may have a low length to width ratio (EdScope, 2005). Leaf size and shape may covary with each other and with other physical or physiological characteristics of the tree (Brown et al., 1991) – this may be especially true of very small leaves where biomechanical tradeoffs relating to the production of support structures become less relevant. Furthermore, it has already been shown (Malhado et al., 2009) that the proportion of largeleaved species in the RAINFOR database decreases with some metrics of water availability. Thus, in order to control for the potential covariance between leaf size and leaf shape a sub-set of the data that included only trees with large leaves (those in mesophyll, macrophyll, and megaphyll categories – sensu Webb, 1959)

Table 1. Measure of Central Tendency and Dispersion for Human Data

MEAN STDEV VAR

AGE 18.31 1.276794 1.630202

HEIGHT 162.06 8.59389 73.85495

Mean value: 18.31 is the average value in the set of data for age. 162.06 is the average value for the set of data for height. 53.25 is the average value for the weight

WEIGHT 53.25 8.83562 78.06818

Variance: All variances obtained are Positive, data points are very spread out from the mean and from each other. Standard Deviation: Data points tend to be far from the mean or expected value. Table 2. Standard error of the mean ( age, weight and height).

Standard error of Mean Age

Weight

Height

0.1276794

0.859389

0. 883562

Table 3. Measure of Central Tendency and Dispersion for Leaf Data

LENGTH 54.95 4.461677 19.90657

MEAN STDEV VAR

WIDTH 36.74 2.769312 7.669091

Mean value: 54.95 is the average value in the set of data for length. 36.74 is the average value for the set of data for width. Variance: All variances obtained are Positive, data points are very spread out from the mean and from each other. Standard Deviation: Data points tend to be far from the mean or expected value.

Table 4. Standard error of the mean (length and width)

Standard error of Mean Length

Width

0.4461677

0.2769312

The values of Mean, Variance, Standard deviation and minimum and maximum value were obtained using standard error. These values are also significant in statistics because aside from the relationship of variables it can also show the behaviors.

The mean of any distribution is the average of all the values added together. This is computed by taking all the values and adding them together, and dividing by the number of values. The Variance is the average of the squared differences from the Mean .It is a determinant of measure of how far a set of numbers is spread out. It is typically a raw material of statistics and it is important since it helps and allows you to compute the dispersion of a set of variables around their mean likewise they are useful because it can tell the accuracy of the data. Meanwhile, the Standard deviation measures the amount of variation or dispersion from the average or how spread out numbers are. (Altman and Bland, 1996) It helps in measuring the variability of a mean. It used in evaluating values in records set to the mean and measuring of dispersion. So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small. To sum up the values for the length and width of the leaves obtained, Tables 3.1-3.5 were provided to show the different figures and the implication of the values of thee other factors to be solved in this activity. Frequency Distribution Table (FDT) for X and Y was made to summarize all the values and to present it in a systematic manner. Moreover, Frequency Distribution Table (FDT) was used in the activity in order to know the number of leaf/leaves that were similar, close or different from one another in terms of their length and width. in this way, the table summarizes the distribution of values in the sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, Frequency is an important element in Statistical analysis because it shows the relationship of different variables hence it also show how far or how near the variables are from each other. It is a particular observation is the number of times the observation occurs in the data. The distribution of a variable is the pattern of frequencies of the observation (Viljoen et al., 2000). Table 5. Frequency Distribution Table for Height

Human height Class Interval 121-128 129-136 137-143 144-150 151-157 158-164 165-171 172-178 179-185

Class Boundaries 120.5-128.5 128.5-136.5 136.5-143.5 143.5-150.5 150.5-157.5 157.5-164.5 164.5-171.5 171.5-178.5 178.5-185.5

f 1 0 0 6 14 39 32 4 4 n=100

Class Mark 124.5 132.5 140 147 154 161 168 175 182

rf(%) 1 0 0 6 14 39 32 4 4

Table 6. Frequency Distribution Table for Weight

Human weight Class Interval 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84

Class Boundaries 39.5-44.5 44.5-49.5 49.5-54.5 54.5-59.5 59.5-64.5 64.5-69.5 69.5-74.5 74.5-79.5 79.5-84.5

f 10 27 25 10 12 10 3 2 1 n=100

Class Mark 42 47 52 57 62 67 72 77 82

rf(%) 10 27 25 10 12 10 3 2 1

Table 7. Frequency Distribution Table for Age

Class Interval 15 16 17 18 19 20 21

Class Boundaries 14.5-15.5 15.5-16.5 16.5-17.5 17.5-18.5 18.5-19.5 19.5-20.5 20.5-21.5

Human age f 1 7 17 31 28 11 5 n=100

Class Mark 15 16 17 18 19 20 21

rf(%) 1 7 17 31 28 11 5

Table 8. Frequency Distribution Table for (X) Length

Leaf length Class Interval

Class Boundaries

f

Class Mark

rf%

47-49 50-52 53-55 56-58 59-61 62-64 65-67

46.5-49.5 49.5-52.5 52.5-55.5 55.5-58.5 58.5-61.5 61.5-64.5 64.5-67.5

11 19 30 19 15 4 0

48 51 54 57 60 63 66

11 19 30 19 15 4 0

68-70

67.5-70.5

2 n=100

69

2

Furthermore, the y-values or the width was also represented with a frequency distribution table. In Table 3, Frequency distribution of Ficus nana shows that there are more leaves that have 53-55 cm length (30%) and 35-36 cm width (32%) while in College of Science, there are more students under 18 years old (31%), weights 45-49 kg (27%) and has a height of 158-164 cm (39%). The tables were made by first assigning a desired number of class. We have also determined the relationship between length (x) and width (y) which possesses the values for x and y acquired through direct measurement using a ruler. Regression, on the other hand, is used to describe the linear association between quantitative variables. It is used to assess the contribution of one or more “explanatory” variables (called independent variables) to one “response” (or dependent) variable. Regression takes a group of random variables, thought to be predicting the value of one variable based on the values of others, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points. Regression is often used to determine how many specific factors influence the other. When there is only one independent variable and when the relationship can be expressed as a straight line, the procedure is called simple linear regression (Yan et al., 2009).Regression analysis was used in the activity so that we could predict the value of the length based on the value of the width. In this case, the width is the independent variable or the predictor variable, and the length is the dependent variable or sometimes known as the outcome variable. It attempts to determine the strength of the relationship between one dependent variable (usually denoted by Y) and a series of other changing variables (known as independent variables).

Table 9. Frequency Distribution Table for (Y) Width

Leaf width Class Interval

Class Boundaries

f

Class Mark

rf%

31-32 33-34 35-36 37-38 39-40 41-42 43-44 45-46

30.5-32.5 32.5-34.5 34.5-36.5 36.5-38.5 38.5-40.5 40.5-42.5 42.5-44.5 44.5-46.5

7 13 32 23 18 3 2 2 n=100

31.5 33.5 35.5 37.5 39.5 41.5 43.5 45.5

7 13 32 23 18 3 2 2

Regression Equation (y) = a + bx Slope (b) = (NΣxy - (Σx)(Σy)) / (NΣx2 - (Σx)2) Intercept (a) = (Σy - b(Σx)) / N Where: x and y are the variables. b = the slope of the regression line a = the intercept point of the regression line and the y axis. N = number of values or elements x = first score y = second score Σxy = sum of the product of first and second scores Σx = sum of first scores Σy = sum of second scores Σx2 = sum of the square of first scores The values are shown in the appendix A

Likewise we have also computed the slope, y-intercept and the regression line for us to show, understand and graph the relationship of the data that we have gathered. The LWR or Length-Width ratio was also done; a diagram that shows the relationship of Leaf Length, Width and LWR was made. The resulting regression is Y=0.412888494x+14.06673946 Table 10. Leaf Length-Width Ratio

# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Length x 56 47 50 50 49 50 51 61 54 55 54 70 56 55 47 58 64 55 49 57 53 68 58 52 55 52 63 51 57 53 48 53 55

Width y 39 36 31 31 34 36 35 36 35 34 38 45 39 36 35 43 41 37 37 39 35 46 38 34 35 36 41 36 32 34 33 35 37

xy ratio 1.435897 1.305556 1.612903 1.612903 1.441176 1.388889 1.457143 1.694444 1.542857 1.617647 1.421053 1.794872 1.435897 1.527778 1.342857 1.348837 1.560976 1.486486 1.324324 1.461538 1.514286 1.478261 1.526316 1.529412 1.571429 1.444444 1.536585 1.416667 1.78125 1.558824 1.454545 1.514286 1.486486

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

56 52 55 53 49 47 53 53 60 61 54 58 56 59 59 59 50 60 55 61 48 52 51 60 55 58 58 61 50 55 56 55 59 51 59 64 60 52 55 56

39 35 34 32 35 33 32 32 40 39 36 36 35 38 38 41 38 39 39 38 36 38 38 40 39 37 40 39 38 37 36 38 40 37 38 43 39 37 36 36

1.435897 1.485714 1.617647 1.65625 1.4 1.424242 1.65625 1.65625 1.5 1.564103 1.5 1.611111 1.6 1.552632 1.552632 1.439024 1.315789 1.538462 1.410256 1.605263 1.333333 1.368421 1.342105 1.5 1.410256 1.567568 1.45 1.564103 1.315789 1.486486 1.555556 1.447368 1.475 1.378378 1.552632 1.488372 1.538462 1.405405 1.527778 1.555556

74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

52 49 53 57 52 49 53 50 51 55 53 55 62 55 55 54 53 56 56 49 54 51 57 56 60 54 60

36 33 34 40 36 35 32 34 33 36 37 35 36 37 37 39 36 36 38 34 39 36 36 39 36 38 34

1.444444 1.484848 1.558824 1.425 1.444444 1.4 1.65625 1.470588 1.545455 1.527778 1.432432 1.571429 1.722222 1.486486 1.486486 1.384615 1.472222 1.555556 1.473684 1.441176 1.459459 1.416667 1.583333 1.435897 1.666667 1.421053 1.764706

A scatter diagram is a tool for analyzing relationships between two variables. One variable is plotted on the horizontal axis and the other is plotted on the vertical axis. The pattern of their intersecting points can graphically show relationship patterns. Most often a scatter diagram is used to prove or disprove cause-and-effect relationships. While the diagram shows relationships, it does not by itself prove that one variable causes the other. In addition to showing possible cause and-effect relationships, a scatter diagram can show that two variables are from a common cause that is unknown or that one variable can be used as a surrogate for the other.

Line regression

Figure.1 Scatter plot diagram of L and W Scatter diagrams will generally show one of six possible correlations between the variables: Strong Positive

Correlation The value of Y clearly increases as the value of X increases. Strong Negative Correlation The value of Y clearly decreases as the value of X increases. Weak Positive Correlation The value of Y increases slightly as the value of X increases. Weak Negative Correlation The value of Y decreases slightly as the value of X increases. Complex Correlation The value of Y seems to be related to the value of X, but the relationship is not easily determined. No Correlation There is no demonstrated connection between the two variables. (Concordia, 2014) In this case, the scatter diagram show can be considered as weak positive correlation because the value of (y) width increases slightly as the value of (x) length increases. The Relationship of L,W and L,W,R

70 60 50

Series1

40

Series2

30

Series3

20 10 0 1

3

5

7

9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

Figure.2 Length, Width and LWR relationship

Table 11. The relationship of LWR to Length and Width of the Leaves of Ficus nana using Pearson Correlation Correlations Width LWR

**

Pearson Correlation

-.339

Sig. (2-tailed)

.001

N

100

LWR

Length

1

.472

**

.000 100

100

**. Correlation is significant at the 0.01 level (2-tailed).

The relationship of the length of leaves (Ficus nana) to its LWR with a coefficient of 0.472 and a significance value of 0 and the relationship of width to LWR having a coefficient of -0.339 having significance value of 0.001. Both the length and the width of the leaves are insignificant having correlation is significant at the 0.01 level as shown in table 5.

Figure 3. Graph showing the relationship of LWR to Length and Width of the Leaves of Ficus nana.

Figure 3 , shows the relationship of LWR to width and length: having length and width as the independent variable and LWR ratio as the dependent variable. The affinity of LWR to length is directly proportional while the connection between width and LWR is reversely proportional. Table 12. The 12 Factors affection Regression

1. n

12 Factor 100

2. ∑x 3. ∑y

5495 3674

4. ∑x2 5. ∑y2

303921 135742

6. ∑xy 7. (∑x)2

202700 30195025

8. 9. 10. 11. 12.

(∑y)2 (∑x) (∑y) Ctx Cty Ctxy

13498276 20188630 3039.21 134982.76 201886.3

Conclusion In using statistical tools, the data we have gathered were organized using tables and graphs. Through this we can easily understand and relate the results to draw logical conclusions. Statistical analysis makes research papers more reliable reference for a study.

Appendix A x 56 47 50 50 49 50 51 61 54 55 54

y 39 36 31 31 34 36 35 36 35 34 38

Xy

x2 2184 1692 1550 1550 1666 1800 1785 2196 1890 1870 2052

3136 1521 2500 2500 2401 2500 2601 3721 2916 3025 2916

70 56 55 47 58 64 55 49 57 53 68 58 52 55 52 63 51 57 53 48 53 55 56 52 55 53 49 47 53 60 61 54 58 56 59 59 59 50 60 55

45 39 36 35 43 41 37 37 39 35 46 38 34 35 36 41 36 32 34 33 35 37 39 35 34 32 35 33 32 40 39 36 36 35 38 38 41 38 39 39

3150 2184 1980 1645 2497 2694 5335 1813 2223 1855 3128 2204 1768 1925 1872 2583 1836 1824 1802 1584 1855 2035 2184 1820 1870 1696 1715 1551 1696 2400 2379 1944 2088 1960 2242 2242 2419 1900 2340 2145

4900 3136 3025 2209 3364 4096 3025 2401 3249 2809 4624 3364 2704 3025 2704 3969 2601 3249 2809 2304 2809 3025 3139 2704 3025 2809 2401 2209 2809 3600 3721 2916 3364 3136 3481 3481 3481 2500 3600 3025

61 48 52 51 60 55 58 58 61 50 55 56 55 59 51 59 64 60 52 55 56 52 49 53 57 52 49 53 50 51 55 53 55 62 55 55 54 53 56 56

38 36 38 38 40 39 37 40 39 38 37 36 38 40 37 38 43 39 37 36 36 36 33 34 40 36 35 32 34 33 36 37 35 36 37 37 39 36 36 38

2318 1728 1976 1938 2400 2145 2146 2320 2379 1900 2035 2016 2090 2360 1887 2242 2752 2340 1924 1980 2016 1872 1617 1802 2280 1872 1715 1696 1700 1683 1980 1961 1925 2232 2035 2035 2106 1908 2016 2128

3721 2304 2704 2601 3600 3025 3364 3364 3721 2500 2025 3136 3025 3481 2601 3481 4096 3600 2704 3025 3136 2704 2401 2809 3249 2704 2401 2809 2500 2601 3025 2809 3025 3844 3025 3025 2916 2809 3136 3136

49 54 51 57 56 60 54 60 56 ∑x=5495

34 39 36 36 39 36 38 34 34 ∑y=3674

1666 2106 1836 2052 2184 2160 2052 2040 1904 ∑xy= 202700

2401 2916 2601 3249 3136 3600 2916 3600 3136 ∑x2= 303921

REFERENCES Dale, M. R. T. et al. 2002. Conceptual and mathematical relationships among methods for spatial analysis. – Ecography 25: 558–577 EdScope, L.C.C. November 2005. Learning from leaves: A look at leaf. Botanical Garden Programs: Reading Plants. pp. 3 - 4. Gilman, Patil, G. P. 1991. Encountered data, statistical ecology, environmental statistics, and weighted distribution methods. Environmetrics 2:377-423 Viljoen, C.S., and L Van der Merwe. 2000. Applied Elementary Statistics. Pearson Education South Africa. The HigherEducation Division of Maskew Miller Longman. Vol.2. p25. Yan, X., X. Gang Su.2009. Linear regression Analysis. World Scientific Publishing Co. Pte.Ltd. Singapore. pp.9-10 Brown, V. K., Lawton, J. H., and Grubb, P. J.: Herbivory and the evolution of leaf size and shape, Philos. T. Roy. Soc. B, 333, 265–272, 1991. Caine, S. and Zane, T.L. UADA Fact Sheet ST-251, Ficus sp. Jensen , R.J 2003 The conundrom of morphometics. Taxon 52: 663-671. Malhado, A. C. M., Malhi, Y., Whittaker, R. J., Ladle, R. J., ter Steege, H., Phillips, O. L., Butt, N., Aragao, L. E. O. C., Quesada, C. A., Araujo-Murakami, A., Arroyo, L., Peacock, J.,Lopez-Gonzalez, G., Baker, T. R., Anderson, L. O., Almeida,S., Higuchi, N., Killeen, T. J., Monteagudo, A., Neill, D., Pitman, N., Prieto, A., Salomao, R. P., V ˜ asquez-Mart ´ ´ınez, R., and Laurance, W. F.: Spatial trends in leaf size of Amazonian rainforest trees, Biogeosciences, 6, 1563–1576, 2009, http://www.biogeosciences.net/6/1563/2009/

Pandey S., Nagar P.K , 2002 . Leaf surface wetness and morphological characteristics of Valeriana jatamansi grown under open and shade habitats. Biol Plant.45: 291-294 Dupouey L.L. , Daval L., Prat D., 1991. Foursier analysis of leaf shape. L arbre. Biologie at developpement- C. Edelin ed.- Naturalia Monspeliensia n h s. 598-599. Roche P., Díaz-Burlinso N., Gachet S., 20 4. Congruency analysis of species ranking based on leaf traits: are the more reliable? Plant Ecol, 174.37-48