Events (eg., agricultural pest) can have different magnitudes (numerical measurements), frequencies, and distributions (aggregate, random, or regular) of occurrence. In general, higher magnitude and frequency, with aggregated distribution, greater will be the problem or the solution (eg., natural enemies versus pests) on system (Da Silva et al. 2017). Hence, indices are used to help on decision-making in certain questions and, many of them, determine key-factors in an event, on some knowledge areas, such as in agrarian and biological: Crop and Ecological Life Tables (Henderson and Southwood 2016 and Da Silva et al. 2017), among others. In general, these tools use abundance (magnitude), constancy and/or frequency of the events, which can be analyzed by correlation, factor analysis, frequency distribution, matrices, mean or t-tests, multiple or simple regression analysis (Henderson and Southwood 2016 and Da Silva et al. 2017). The objective of this study was to develop an indice, which can determine the loss and solution sources, classifying them according to their importance in terms of loss or income gain on system (eg. natural system = cerrado).
The data used were adapted (Leite et al. 2006, 2012, 2016, 2017) and classified as loss source (L.S.) or solution source (S.S.) are not mentioned, and production, in 48 samples. Scientific names of herbivorous insects (L.S.) and natural enemies (S.S.) due to the importance indice can be used in other areas such as exotic mammals, plant diseases, weeds, versus production.
The type of distribution (aggregated, random, or regular) of L.S. or S.S. was defined by the Chi-square test using the BioDiversity Professional program, version 2 (Krebs 1989). The data were subjected to simple regression analysis and theirs parameters were all significant (P< 0.05) using the statistical program System for Analysis Statistics and Genetics (SAEG 2007), version 9.1 (table 1). Simple equations were selected by observing the criteria: i) distribution of data in the figures (linear or quadratic response), ii) the parameters used in these regressions were the most significant ones (P <0.05), iii) P < 0.05 and F of the Analysis of Variance of these regressions, and iv) the coefficient of determination of these equations (R2). Only loss sources and solution sources with P < 0.05 were showed in the table 1. It is necessary knowledge of the system to select the possible loss sources and solution sources.
Source | Qui-square test | |||||
---|---|---|---|---|---|---|
Loss | Variance | Mean | Chi-square | d.f. | P | Distribution |
1 | 177.45 | 16.5 | 505.45 | 47 | 0.000 | Aggregated |
2 | 93.45 | 20.54 | 213.81 | 47 | 0.000 | Aggregated |
3 | 0.25 | 0.46 | 26.00 | 47 | 0.994 | Regular |
4 | 0.33 | 0.58 | 26.86 | 47 | 0.992 | Regular |
5 | 1050.97 | 37.08 | 1332.02 | 47 | 0.000 | Aggregated |
6 | 19.38 | 1.67 | 546.40 | 47 | 0.000 | Aggregated |
7 | 4936.34 | 29.00 | 8000.28 | 47 | 0.000 | Aggregated |
Solution | ||||||
1 | 57.66 | 11.71 | 231.45 | 47 | 0.000 | Aggregated |
2 | 1.53 | 1.50 | 48.00 | 47 | 0.432 | Random |
3 | 50.21 | 7.50 | 314.67 | 47 | 0.000 | Aggregated |
4 | 0.55 | 0.71 | 36.59 | 47 | 0.863 | Random |
5 | 1.57 | 1.04 | 70.96 | 47 | 0.014 | Aggregated |
6 | 3.77 | 0.75 | 236.00 | 47 | 0.000 | Aggregated |
7 | 0.20 | 0.13 | 74.00 | 47 | 0.007 | Aggregated |
8 | 140.50 | 7.58 | 870.81 | 47 | 0.000 | Aggregated |
9 | 193.33 | 6.83 | 1329.76 | 47 | 0.000 | Aggregated |
Simple regression analysis | ANOVA | |||||
R2 | P | F | ||||
R.P. = - 39.43 + 33.26 x L.S.1 - 0.80 x L.S.1 2 | 0.61 | 0.0000 | 35.25 | |||
R.P. = 50.85 + 1404.77 x L.S.7 - 2242.16 x L.S.7 2 | 0.20 | 0.0060 | 5.75 | |||
R.L.S.1 = - 0.46 + 5.13 x S.S.3 - 0.21 x S.S.3 2 | 0.99 | 0.0000 | 7312.19 | |||
R.L.S.7 = 0.13 + 0.46 x S.S.4 - 0.18 x S.S.4 2 | 0.39 | 0.0000 | 14.15 | |||
R.L.S.7 = 0.11 + 0.26 x S.S.5 - 0.04S.S.5 2 | 0.53 | 0.0000 | 25.63 | |||
R.L.S.7 = 0.21 + 0.16 x S.S.6 - 0.01 x S.S.6 2 | 0.27 | 0.0007 | 8.50 | |||
R.L.S.7 = 0.10 + 0.04 x S.S.8 - 0.0006 x S.S.8 2 | 0.71 | 0.0000 | 55.10 | |||
R.L.S.7 = 0.15 + 2.94 x S.S.9 - 3.71 x S.S.9 2 | 0.44 | 0.0000 | 17.89 |
The developed indice was:
where,
i) key source (ks) is:
where,
R2 = determination coefficient and P = significance of ANOVA, of the simple regression equation of the loss source (L.S.) or solution source (S.S.).
In the case of L.S. is:
where,
R.P. = [R 2 x (1 - P)]/total n of the L.S. on the samples,
In the case of S.S. is:
where,
E.S. = [R 2 x (1 - P)]/total n of the S.S. on the samples.
When a S.S. acts on more than one L.S., theirs E.S. are summed. E.S. or R.P. = 0 when E.S. or R.P. is non-significative on the L.S. or R.P., respectively, and
ii) constancy (c) is:
where,
absence = 0 or presence = 1, and
iii) distribution source (ds) is:
Percentage of loss of production per loss source (% L.P.L.S.) is:
where,
P. = total production on the system,
and
where,
R.P.L.S. = {R 2 x (1 - P)]/total n of L.S. on the samples.
Percentagem of loss of production per loss source (% L.P.L.S.) per soluction source (S.S.) is:
where,
I.G. = {total production (P.) x reduction of the L.S. by S.S. (R.L.S.)] x total n of the S.S on the samples,
and
The ks of the S.S. are separeted per L.S..
Interaction between two or more sources of loss or solution may be added as a treatment to be tested together with the other sources. If not, the interaction, as a treatment, may apply the following:
ks of the interaction = [(R 2 x (1 - P)]/total n on the samples, R 2 = determination coefficient and P = significance of ANOVA of the interaction, of the simple regression equation of the loss source (L.S.) or solution source (S.S.) of the interaction. But the new n of the interaction will be obtained from the means of this parameter isolated from the two or more sources of loss or solution,
c and ds of the interaction will be obtained from the means of these parameters isolated from the two or more sources of loss or solution, and
all calculations are made separately for the interaction and at the end it is compared with the other sources of loss or solution.
The loss source (L.S.) L.S.1 and L.S.7 showed, among the seven L.S., the % I.I. (85.06 and 14.94%, respectively) significatives on production reduction (5.89 and 3.37%, respectively), on system (tables 2, 3).
Loss source | ||||||||
---|---|---|---|---|---|---|---|---|
L.S. | ||||||||
1 | 792 | 0.6100 | 0.000770202 | 38 | 1.000 | 0.029267677 | 0.034409056 | 85.058 |
2 | 986 | 0.0000 | 0.000000000 | 48 | 1.000 | 0.000000000 | 0.034409056 | 0.000 |
3 | 22 | 0.0000 | 0.000000000 | 22 | 0.006 | 0.000000000 | 0.034409056 | 0.000 |
4 | 28 | 0.0000 | 0.000000000 | 26 | 0.008 | 0.000000000 | 0.034409056 | 0.000 |
5 | 1780 | 0.0000 | 0.000000000 | 46 | 1.000 | 0.000000000 | 0.034409056 | 0.000 |
6 | 80 | 0.0000 | 0.000000000 | 10 | 1.000 | 0.000000000 | 0.034409056 | 0.000 |
7 | 1392 | 0.1988 | 0.000142816 | 36 | 1.000 | 0.005141379 | 0.034409056 | 14.942 |
Solution source | ||||||||
S.S. not associated with any L.S. or associated with L.S.2-6 | ||||||||
S.S. | Σ |
|||||||
1 | 562 | 0.000 | 0.000000000 | 48 | 1.000 | 0.000000000 | 0.000000000 | 0.000 |
2 | 72 | 0.000 | 0.000000000 | 38 | 0.568 | 0.000000000 | 0.000000000 | 0.000 |
7 | 7 | 0.000 | 0.000000000 | 8 | 0.993 | 0.000000000 | 0.000000000 | 0.000 |
L.S.1 | ||||||||
3 | 360 | 0.990 | 0.002750000 | 38 | 1.000 | 0.104500000 | 0.104500000 | 100.00 |
L.S.7 | ||||||||
4 | 34 | 0.39 | 0.011470588 | 26 | 0.134 | 0.040726564 | 0.529809273 | 7.687 |
5 | 51 | 0.53 | 0.010392157 | 28 | 0.986 | 0.287031585 | 0.529809273 | 54.176 |
6 | 36 | 0.270 | 0.007494750 | 14 | 1.000 | 0.104926500 | 0.529809273 | 19.805 |
8 | 365 | 0.710 | 0.001945205 | 32 | 1.000 | 0.062246575 | 0.529809273 | 11.749 |
9 | 328 | 0.440 | 0.001341463 | 26 | 1.000 | 0.034878049 | 0.529809273 | 6.583 |
I.I. = ks x c x ds. ks = R.P./n or E.S./n. R.P. or E.S. = R 2 x (1 - P), R 2 = determination coefficient and P = significance of ANOVA, of the simple regression equation. c = Σ of occurrence of L.S. or S.S. on each sample, 0 = absence or 1 = presence. ds = 1 - P of Chi-square test of the L.S. or S.S.. When a S.S. operates in more than one L.S., its E.S. are summed. R.P. or E.S. = 0 when R.P. or S.S. non-significant with reduction on production or of the L.S.
Loss of production by loss source | |||||||||
---|---|---|---|---|---|---|---|---|---|
L.S. | |||||||||
1 | 792 | 0.61 | 48 | 10.07 | 171 | 5.89 | |||
7 | 1392 | 0.1988 | 48 | 5.77 | 171 | 3.37 | |||
Reduction on production per loss source and total | |||||||||
L.S.1 | |||||||||
S.S. | |||||||||
3 | 360 | 0.99 | 48 | 7.425 | 10.07 | 171 | 0.208 | 0.122 | 2.063 |
Σa | --- | --- | --- | --- | --- | --- | --- | 0.122 | 2.063 |
L.S.7 | |||||||||
4 | 34 | 0.39 | 48 | 0.276 | 5.77 | 171 | 0.047 | 0.027 | 0.813 |
5 | 51 | 0.53 | 48 | 0.563 | 5.77 | 171 | 0.064 | 0.037 | 1.104 |
6 | 36 | 0.27 | 48 | 0.202 | 5.77 | 171 | 0.032 | 0.019 | 0.562 |
8 | 365 | 0.71 | 48 | 5.399 | 5.77 | 171 | 0.085 | 0.050 | 1.479 |
9 | 328 | 0.44 | 48 | 3.007 | 5.77 | 171 | 0.053 | 0.031 | 0.917 |
Σb | --- | --- | --- | --- | --- | --- | --- | 0.165 | 4.875 |
Σa+b | --- | --- | --- | --- | --- | --- | --- | 0.287 | 6.934 |
L.P.L.S. = (n x R.P.L.S.)/Sa. % L.P.L.S. = (L.P.L.S./P.) x 100. R.L.S. = (n x ks)/Sa.. I.G. = (P. x R.L.S.) x n. S.S.. % I.G. = (I.G. x 100)/P.. % R.P.L.S. = (I.G. x 100)/L.P. Ks of S.S. are separated by L.S.
Solution source (S.S.) S.S.3 (% I.I. = 100) reduced the loss per L.S.1; and S.S.5 (% I.I. = 54.18), S.S.6 (% I.I. = 19.81), S.S.8 (% I.I. = 11.75), S.S.4 (% I.I. = 7.69), and S.S.9 (% I.I. = 6.58) that of L.S.7 on system production. The possible solution sources S.S.1, S.S.2, and S.S.7 showed % I.I. = 0.00% due to non-significative effect on the reduction of losses by important L.S. or due to reduced the L.S. which did not correlate with production loss on system. The S.S.3 reduced production loss (2.06%) per L.S.1 increasing in income gain (0.12%) on system production. The loss of production per L.S.7 was reduced by the S.S.8 (1.48%), S.S.5 (1.10%), S.S.9 (0.92%), S.S.4 (0.81%), and S.S.5 (0.56%), totaling 4.88%. The loss reduction per L.S.7 due to the soluction factors S.S.8, S.S.5, S.S.4, S.S.9, and S.S.6, increasing in income gain (0.05, 0.04, 0.03, 0.03, and 0.02%, respectively), totaling 0.17%. The total reduction in production loss due to loss sources (L.S.1 and L.S.7) was 6.93%, with an increase on system productivity of 0.29% due to solution sources cited above (tables 2, 3).
The percentage of importance indice (% I.I.) was effective in identifying of loss sources on system (eg., reduction on production), being simpler than a Crop Life Table (Da Silva et al. 2017), but this indice does not replace a Crop Life Table. The use of % I.I. is for cases (eg. natural system, cerrado) in which it is not possible to evaluate all flowers and fruits of all plants in the experimental useful plot, identifying the factors of plant loss, as done by Crop Life Table (Da Silva et al. 2017). Parameters of Life Table supply reliable information, eg. reproductive potential and mortality factors of species (Henderson and Southwood 2016). Fruit production and arthropods (leaves, flowers, and fruits) data, used to test % I.I., were obtained on Caryocar brasiliense Camb. (Caryocaraceae) trees, over 3 m high, randomly, in cerrado areas, in three years, monthly (Leite et al. 2006, 2012, 2016, 2017). Flowers and fruits were evaluated on some tree branches and then estimated the total per tree (Leite et al. 2006), thus, the use of this indice is for cases where it is not possible to use a Crop Life Table.
The % I.I. was, also, effective in identifying solution sources on system (eg., increasing production), similar to an Ecological Life Table (Henderson and Southwood 2016). The % I.I. does not replace an Ecological Life Table (Henderson and Southwood 2016). The use of % I.I. is for cases (eg. natural system, cerrado) in which it is not able to mark and monitor the animal (eg., pest insects), identifying the cause of its mortality, as done by Ecological Life Table (Henderson and Southwood 2016). Insect pest rearing, detailed field studies, time and researchers trained to identify and quantify the control of natural factors daily until the insect pest life cycle is complete, are the major steps to determine the parameters of a Life Table of pest insects (Da Silva et al. 2017). The evaluation of herbivorous insects and their natural enemies, including spiders, on C. brasiliense trees, was not individually during their lives (Leite et al. 2012, 2016, 2017), nor would it be possible due to the height of these plants in cerrado areas. But, with the application of this indice, it was possible to determine the effects of these natural enemies on herbivores and fruit production per tree on natural system.
The % I.I. separated the loss sources (eg., L.S.1 = 85.06%) on production reduction (eg., 5.89%) and the solution sources (eg., S.S.5 = 54.18%) with total income gain (eg., 0.29%) on system, with the possibility to calculate, monetarily, these losses or effectiveness of the solutions. The % I.I. can help, as example, to determine which pests, eg. exotic mammals, insects, plant diseases, and weeds, cause the biggest problems in plant production and the best control methods (eg., biological control) are more harmful or effective on system (eg., crops) and how much money is lost or saved. Here it is shown the percentage of I.I. is an indice to detect the loss or solution key-sources on a system, doing it possible to obtain of loss and income gain on some knowledge areas.