Hybrid Method for Fitting Nonlinear Height–Diameter Functions
, Rafael Menali Oliveira 2, Joseph Peter Roise 1, Henrique Ferraço Scolforo 2 and Lucas Rezende Gomide 2
Round 1
Reviewer 1 Report
The paper presents an interesting concept of the approach to solving nonlinear regression problems. The paper was prepared very carefully in terms of content and editing. I did not notice any serious errors and have only a few remarks that I think may facilitate understanding of the content.
I list my observations below.
L. 109. Order of values: 5, 7, 8
L.138-140. The description of the silviculture system is short and therefore unclear.
L. 162. In the description under the table, the "1" before h(d) is unnecessary in my opinion.
L. 221. Please consider the direct reference to table 2 instead of ":"
L. 310-311. Unlike other parts of the paper, the symbols used in the formulas are not described.
Figure 4. There are outliers in the charts that have not been removed. What is the rationale behind this? The symbols “ρ” and “p” are graphically very similar. Please consider other designations.
Section 3.1 including Table 3 and Figure 4 presents the characteristics of the datasets. These are not results related to the aim of the paper. In my opinion, that part should be included in chapter 2: “Material and methods”.
Figure 5: The description of the graph ("Error of best average" and "Dynamic range") is not well explained in the text.
L.324-325. Unnecessary repetitions of "... h-d date".
Table 4. Information about the variability of the results would also be useful. For example, sd values could be added in parentheses.
Figure 6. This chart is unnecessary. The same information can be presented in a few sentences.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this manuscript, the authors proposed a new hybrid method to fit the nonlinear regression models (namely the biological height-diameter function), actually, obtaining more appropriate initial values for model parameter through an improved genetic algorithm. From a point of view of the proposed new method, I recognized the interest of this work. Thanks to the precise initial value of model parameters provided by genetic algorithm, it was showed that the new method has the excellent fitting ability and stability regardless of database variability and complexity of mathematical model. Nevertheless, in the present version, I think that the wider applicability of the new method should be proved.
Over the past few decades, we have many other methods to fit the nonlinear models and some of these methods were widely recognized because they worked well. Hence, it was necessary to showed the advantages of the new hybrid method when compared to the present commonly used methods. On the other hand, the height-diameter model was one of the basic models in forestry, and it can be fitted well in most cases usually. Why don't the authors test some more complex models, such as the classical taper equation. Besides, I noticed that the maximum of time consumption of fitting process is nearly 59 seconds whereas the largest data include only 1, 975 observations, which seemed to be inefficient in my opinion. A larger data may be necessary to test the efficiency of the hybrid method.
Overall, I recommend a revision of more testing for the new method.
Detailed comments follow:
Title: the present title seemed to be too broad, as only 12 height-diameter models were fitted, which was a class of models in many forestry models.
Line 153: diameter at breast height (d) was used to predict total tree height (h) in all height-diameter studies, the relationship between h and d should not be “weak”
Lines 180-185: I am considering that whether the authors could provide the R codes, or packed the codes as a R package. Actually, this new method can be better promoted and used by others if the detailed codes were given.
Line 224: what criteria were used to determine whether g is the elitist strategy
Figure 5: “2pg”, “3pg”,…should be explained. Besides, it would be better to change the axis scale of y-axis in right panel, for clearer knowing of parameter range.
Lines 442-445: this explanation was incorrect as the data had not changed in each fitting process, the variation on b1 and b2 seemed to be more likely caused by different initial values of parameters in the repetition
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Thank you for considering the comments. The revised manuscript has taken into consideration the raised points and the authors also had answered or discuss all points in great detail. To my mind, I think that it can be accepted at the present form.
