Journal of Biosystems Engineering. December 2018. 410-419
https://doi.org/10.5307/JBE.2018.43.4.410


ABSTRACT


MAIN

  • Introduction

  • Materials and Methods

  •   Target species

  •   Data required for CLIMEX simulation

  •   Parameters in CLIMEX and its estimation

  •   Sensitivity analysis

  •   Software

  • Results and Discussion

  •   Responses to changes in 12 parameters

  •   Sensitivity analysis for three significant parameters

  • Conclusions

  • Conflict of Interest

Introduction

Biological invasion by alien pests has caused severe damage globally to human society and biodiversity (Gurevitch and Padilla, 2004). This problem, along with the need for the evaluation of a specific pest’s potential invasion risk owing to climate change, increases the application of species distribution modeling (SDM) for predicting a species’ distribution (Mainali et al., 2015). SDM is useful for identifying the suitability of a species’ introduction and its survival, and consequently provides fundamental data applicable for establishing a strategy for pest management (Shabani and Kumar, 2014). Several tools therefore implement the SDM algorithm (Busby, 1991; Kriticos et al., 2015; Phillips and Dudík, 2008). CLIMEX is one of such SDM tool, which predicts potential distribution by relating climatic variables to biological characteristics and actual species occurrence (Jung et al., 2016; Kriticos et al., 2015).

An important and time-consuming process for modeling biological systems is parameter estimation. Because model accuracy is highly dependent on parameter values, a reliable method for parameter estimation is essential (Elith and Leathwick, 2009). The intensive study of previous publications and the collection of empirical data are necessary for this process. The source of uncertainty in the SDM is often parameter uncertainties (Van Klinken et al., 2009). When constructing a niche model, a possible habitat range is determined by the environmental suitability of a species in a location, which is defined by parameters representing the maximal and minimal tolerance of the species (Barry and Elith et al., 2006; Sabani and Kumar, 2014). This implies that the potential distribution predicted by the SDM varies with the parameter values, and the impact of some parameters on the results is significantly large (Taylor and Kumar, 2012). Hence, parameter estimation is considered to be important to generate reliable predictions (Hallgren and Pitman, 2000; Van Klinken et al., 2009; Zaehle et al., 2005).

Because a model cannot include all aspects of a system, it is necessary to appropriately select the primary variables governing species distribution. Previous studies of the CLIMEX parameter sensitivity indicated that modelers should focus on the detailed data collection for sensitive parameters, while other insensitive parameters only require small investments for data collection (Taylor and Kumar, 2012). Climate has been considered to be the primary determinant of the potential distribution of a species (Andrewartha and Birch, 1954; Shabina and Kumar, 2014) and the dominant controller of its natural distribution (Van Klinken et al., 2009). Hence, climate could be considered the most critical variable for modeling, and the parameters related to climatic conditions must be established correctly. As previously mentioned, CLIMEX uses climatic conditions as the primary variables, and it can produce a better predictive distribution of a species than other SDM tools under future climate scenarios (Sutherst and Boume, 2009; Taylor and Kumar, 2012; Webber et al., 2011,). For example, Jung et al. (2017a) reported that the effect of parametric change in implementing a climate change scenario is observable in the modeling response, resulting in different distributions of yellow crazy ants under various climate change scenarios. Therefore, it is necessary to investigate the effect of climatic parameters to appropriately select the primary parameters that affect the potential distribution of a species substantially, to ensure an effective modeling with the least investment in relatively unimportant parameter estimation (Taylor and Kumar, 2012).

The sensitivity analysis of the parameters tests the effect of parametric changes on the modeling outcome, which indicates the parameters considered to be important. Various studies have suggested that model inaccuracies associated with model parameterization can be understood using sensitivity analysis (Burgman et al., 2005; Hanspach et al., 2011; Taylor and Kumar, 2012), because it provides insight into the model parameters by identifying those most influential to model the results, and helps eliminate the effects of inaccuracy and error on the output (Barry and Elith, 2006; Burgman et al., 2005; Hamby, 1994). Because of the advantages above, sensitivity analysis has been applied for the identification of parameters significantly influencing the CLIMEX results for the distribution of Lantana camara L. (Taylor and Kumar, 2012) and Phoenix dactylifera L. (Shabani and Kumar, 2014), and to select sensitive parameters in the Global Biome Model (BIOME3) for the simulated distribution of different plant functional types (Hallgren and Pitman, 2000). It was suggested that the most cost-effective management strategies for estimating parameters and collecting data could be determined via the identification of parameters important in the SDM (Shabani and Kumar, 2014; Taylor and Kumar, 2012).

In general, the SDM is more suitable for large areas than small areas. This is because the climatic variation in a large area is significant to generate sufficient data regarding the effect of climatic variables on the species distribution, whereas small areas, having fewer stations, may not provide a representative view of the climate in that region (Bennett et al., 1998; Poutsma et al., 2007). Hence, more precise parameter estimation, along with a high-resolution climate database, is required to use the SDM in a small area. Therefore, this study investigates the effect of parametric changes on a species’ distribution using CLIMEX to assess the distribution of Metcalfa pruinosa in South Korea. Because sensitivity analysis has not been applied to predict pest distribution using CLIMEX, and South Korea contains a small national area suffering from significant climate change, we expect that this study can provide fundamental information for the application of CLIMEX to predict insect distributions.

Materials and Methods

Target species

We targeted Metcalfa pruinosa to simulate the effect of changes in CLIMEX parameters on its distribution on South Korea. This species is a North American native pest globally distributed from Europe to Asia (Byeon et al., 2018), and is known to be extremely harmful to both agricultural and sanitary systems owing to its high density in nature and variety of host plants (Kim and Kil, 2014). In particular, it is reported that M. pruinosa is distributed in 28 sites in South Korea, and can attack 145 plant species at roadsides, and in forests and orchards (Kim and Kil, 2014). Most studies regarding M. pruinosa in South Korea focus on its control and current damage (Ahn et al., 2011; Kim et al., 2011); however, its potential distribution according to climate change has been studied, suggesting that CLIMEX parameters suitable for South Korea are available (Byeon et al., 2017).

Data required for CLIMEX simulation

Two types of pre-requisite datasets exist for CLIMEX simulation in addition to the biological information for M. pruinosa: 1) distribution data; and 2) climate data for target areas (Kriticos et al., 2015). The actual worldwide distribution record was obtained from the Global Biodiversity Information Facility website (GBIF), while the detailed distribution data in South Korea were generated in a previous study (Kim and Kil, 2014). The distribution data were used to determine the optimal parameter values, resulting in the best simulation with the least discrepancy with actual records. The reason for using both global and domestic distribution datasets was such that model accuracy could be improved by the global datasets (Mainali et al., 2015). For climate data, the same database used for predicting the potential distribution of pests in South Korea was used (Byeon et al., 2017; Jung et al., 2017a, 2017b). The climate database was constructed by averaging the historical data of temperature, precipitation, and relative humidity from 1981 to 2010, provided by the Korean Meteorological Administration, in 74 major cities in South Korea. Details regarding the 74 cities in South Korea are described elsewhere (Byeon at al., 2017).

Parameters in CLIMEX and its estimation

The parameters in CLIMEX were required to address population growth under favorable seasons and the limitations of unfavorable conditions, and were finally integrated to calculate the ecoclimatic index (EI) measuring favorableness of the location of a target species based on conditions for growing and the limiting population (Kriticos et al., 2015; Jung et al., 2016). The primary CLIMEX parameters are those for temperature and soil moisture (lower limit, lower optimal, upper optimal, and upper limit for each variable), and are related to stress accumulation, including the stress accumulation threshold and rate of stress accumulation. Moreover, growing degree days, represented by PDD, is another important parameter for the completion of at least one cycle by a species under the given climatic conditions. Most parameters in CLIMEX were determined either based on actual rearing experimentation that records population changes in response to temperature and humidity, based on previously published data, or based on a previous CLIMEX study performed on similar species. To achieve a reliable prediction, more observations and species parameter values are necessary (Poutsma et al., 2007). The definitions and background theory of the parameters have been described previously by Jung et al. (2016) and. Kriticos et al. (2015).

The basic procedure to determine the parameter values have been described elsewhere (Poutsma et al., 2007). The recommended strategy to determine the parameter values in CLIMEX for a species is to use the native distribution as a basis for estimating the model parameters, and to use the distribution outside the native areas to verify the parameter values. Moreover, the more observations and biological information necessary for parameter estimation are introduced, the more reliable is the outcome obtained.

In this study, we utilized parameter values for M. pruinosa from a previous study by Byeon et al. (2017). Based on the data reported by Kim and Kil (2014), it appears that M. pruinosa is adapted to the climate of South Korea, suggesting that parameter estimation must consider adaption using the actual distribution in South Korea, the primary target region in this study. The study by Byeon et al. (2017) employed the CLIMEX model parameters published by Strauss (2010) and modified them to fit the actual distribution in South Korea. This is consistent with the recommended process of parameter estimation, and the determined optimal parameters values for South Korea. Hence, we used these for the reference prediction to be compared with the other simulation using sensitivity analysis. All the parameter values are summarized in Table 1, while Figure 1 shows the predicted and actual distributions of M. pruinosa in South Korea.

Table 1. Parameter values used for M. pruinosa simulation1

Parameters Parameter definitions Values
Temperature parameters
DV0 Lower temperature threshold 13℃
DV1 Lower optimal temperature 22℃
DV2 Upper optimal temperature 28℃
DV3 Upper temperature threshold 31℃
PDD Degree-days to complete one generation 500
Moisture parameters
SM0 Lower soil moisture threshold 0.25
SM1 Lower optimal soil moisture 0.5
SM2 Upper optimal soil moisture 1.0
SM3 Upper soil moisture threshold 1.5
Heat stress
TTHS Heat stress temperature threshold 31℃
THHS Heat stress temperature rate 0.002 week-1
Cold stress
TTCS Cold stress temperature threshold -1℃
THCS Cold stress temperature rate -0.0001 week-1
Dry stress
SMDS Dry stress threshold 0.25
HDS Dry stress rate -0.005 week-1
Wet stress
SMWS Wet stress threshold 1.5
HWS Wet stress rate 0.002 week-1
Diapause parameters
DPD0 Diapause induction day length 9h
DPT0 Diapause induction temperature 0℃
DPSW Diapause summer or winter indicator 0
1The table, parameters and their values were from Byeon et al. (2017).

http://static.apub.kr/journalsite/sites/ksam/2018-043-04/N0770430418/images/ksam_43_04_18_F1.jpg
Figure 1.

Potential distribution of M. pruinosa. (a) Potential (circles) and actual (hatched region) distribution of M. pruinosa, (b) EI distribution by administrative districts

Sensitivity analysis

Sensitivity analysis is a tool for a systematic analysis exploring the effects of perturbing parameters on the model responses (Lee and Okos, 2016; Tortorelli and Michaleris, 1994). In CLIMEX, many parameters affect the potential distribution, and one of these factors may act as the limiting factor (Poutsma et al., 2007). Hence, sensitivity analysis facilitates us in obtaining a factor that is the most important in model prediction and consequently, species distribution. Based on previous studies on sensitivity analysis in CLIMEX modeling (Shabina and Kumar, 2014; Taylor and Kumar, 2012), we designed two steps for sensitivity analysis on the M. pruinosa distribution.

To reduce the intensive computational time (Tortorelli and Michaleris, 1994), a small number of perturbation levels were first applied for 12 parameters: DV0, DV1, DV2, DV3, SM0, SM1, SM2, SM3, THCS, THHS, HDS, and HWS. The amount of perturbation was selected arbitrarily to reduce the number of parameters for further sensitivity analysis. For DVs and SMs, ±2°C and ±50% were applied, respectively, while the stress rates were changed by ±50%. The responses to changing parameter values were estimated by the changes in the EI in 74 primary cities in South Korea. We categorized the EI values into five groups: 0-2, 2-10, 10-20, 20-30, and 30-, assigned for unsuitable (U), marginally suitable (MS), suitable (S), very suitable (VS), and optimally suitable (OS), respectively. Subsequently, we counted the number of cities in the groups and recorded the change by parametric change.

From the first step, we selected three parameters from each parameter type, which produced the most significant changes in the distribution of EI values. Subsequently, the selected parameters were further analyzed with a larger range of their changes and a narrow increment according to the type of parameters. Many methods can be used for testing the sensitivity of the model parameters; it has been suggested that the simplest method is to vary one parameter at a time, while maintaining the others as constant (Hamby, 1994). In this study, the units and increments of parameters were different; thus, we used a sensitivity index calculated using the output difference (Equation 1) (Hoffman and Gardner, 1983),

$$\mathrm{SI}=\frac{D_\max\mathit-D_\mathit{min}}{D_\max}$$ (1)

where Dmax and Dmin are the max and min output values, respectively, resulting from changing the input over its entire range (Hoffman and Gardner, 1983).

Software

Species distribution modeling and sensitivity analysis were performed using CLIMEX (version 4.0, Hearne software, Melbourne, Australia).

Results and Discussion

Responses to changes in 12 parameters

For the first analysis using 12 parameters, we calculated the root of the sum of squares for the changed EI values (Table 2). In general, alterations in temperature- related parameters (DV0, DV1, DV2, and DV3) indicated the most significant change in the EI value distribution compared to those with original parameter values. Particularly, the EI distribution was most sensitive to DV2, which is the upper optimum temperature. For soil moisture, SM0 resulted in the largest change while SM1 demonstrated a comparable change to SM0, which is consistent with a previous study that reported that SM1, SM2, and SM3 demonstrated little or no effect on lantana distribution (Taylor and Kumar, 2012). The stress-related parameters did not affect the potential distribution of M. pruinosa, except the cold stress accumulation rate (THCS). The result was consistent with a previous study by Shabani and Kumar (2014), who reported that the parameters related to population growth were more sensitive than the stress-related parameters. However, the detailed parameters with the highest sensitivity differed slightly between this study and our study. This is because the previous study targeted a plant while the current target is an insect. Specifically, the temperature suitable for the development of M. pruinosa was shown to be the most important in this analysis. Compared to the parameter of soil moisture, temperature demonstrated a relatively larger effect on the potential distribution of M. pruinosa. No studies have directly examined the simultaneous effect of temperature and humidity on M. pruinosa development and distribution. However, the higher sensitivity to temperature than to soil moisture can be supported by an insect study, demonstrating that changes in soil moisture did not vary the Diaprepes abbreviatus (Coleoptera: Curculionidae) larvae population compared to temperatures indicating proportionality to larvae populations within optimal ranges (Lapointe and Shapiro, 1999). In addition, temperature has been proposed as the dominant factor influencing herbivorous insects by directly affecting the development, survival, range, and abundance (Bale et al., 2002). Nevertheless, the sensitivity of parameters related to soil moisture was not small, suggesting that one of the factors determining soil moisture was rainfall, which might be attributed to an increased mortality factor (Dixon, 1998; Thacker et al., 1997). Moreover, M. pruinosa may be indirectly influenced by soil moisture, which determines the growth of its hosts (Kriticos et al., 2015). For instance, we could deduce that a higher sensitivity to a lower soil moisture threshold than to other soil moisture-related parameters might indicate that drought, causing the death of a hosting plant, can limit the distribution of a species living on it. Based on the CLIMEX manual (Kriticos et al., 2015), it is effective to first control stress-related parameters prior to changing other parameters. However, the results indicated that the cold stress accumulation rate had a relatively low sensitivity, and other stress parameters did not affect the distribution at all. As aforementioned, this was consistent with a previous study (Shabani and Kumar, 2014), although such results may occur due to the degree of the changing parameters of stress being not as large as that of the population growth. Therefore, further analysis using a wide range with small intervals is necessary.

Table 2. Result of changes in climatic suitability by altering 12 parameters

Parameters related to temperature (DV)
EI value Category Reference number2 No. changed by DV0 No. changed by DV1 No. changed by DV2 No. changed by DV3
-2℃ +2℃ -2℃ +2℃ -2℃ +2℃ -2℃ +2℃
0~2 U 1 1 0 1 0 1 1 0 0
3~10 MS 3 0 -3 0 -4 11 3 -8 0
11~20 S 35 3 -4 7 -8 43 26 -4 6
21~30 VS 29 -2 4 -4 7 17 32 9 -3
31~ OS 6 -2 3 -4 5 2 12 3 -3
RSS1 4.24 7.07 9.06 12.41 16.97 11.22 13.04 7.3
Total 11.31 21.47 28.20 20.39
Parameters related to soil moisture (SM)
EI value Category Reference number2 No. changed by SM0 No. changed by SM1 No. changed by SM2 No. changed by SM3
-0.05 +0.05 -0.05 +0.05 -0.05 +0.05 -0.05 +0.05
0~2 U 1 0 -1 0 0 0 0 0 0
3~10 MS 3 0 -1 0 -2 -1 0 -2 1
11~20 S 35 5 -5 5 -4 -2 2 1 1
21~30 VS 29 -3 7 -2 3 3 -1 1 -1
31~ OS 6 -2 0 -3 3 0 -1 0 -1
RSS1 6.16 8.72 6.16 6.16 3.74 2.45 2.45 2.00
Total 14.88 12.33 6.19 4.45
Parameters related to stress accumulation rate
EI value Category Reference number2 No. changed by THCS No. changed by THHS No. changed by HDS No. changed by HWS
-0.05 +0.05 -0.05 +0.05 -0.05 +0.05 -0.05 +0.05
0~2 U 1 0 0 0 0 0 0 0 0
3~10 MS 3 0 -2 0 0 0 0 0 0
11~20 S 35 2 -3 0 0 0 0 0 0
21~30 VS 29 -2 5 0 0 0 0 0 0
31~ OS 6 0 0 0 0 0 0 0 0
RSS1 2.83 6.16 0 0 0 0 0 0
Total 8.99 0 0 0
1RSS: Root sum of square calculated by taking the root of value obtained by summing square of numbers of locations changed by parameters.
2Reference number means that EI distribution obtained from original parameters values in Table 1.

Sensitivity analysis for three significant parameters

Further sensitivity analysis was performed by selecting significant factors from each type of parameter based on the root of sum of squares: DV2, SM0, and THCS. For this analysis, we expanded a range of parametric changes with smaller intervals than those in the first analyses. Consequently, DV2 (originally) 28°C was changed from 23°C to 30°C by 1°C because the lower and upper limits could not pass DV1 (23°C) and DV3 (31°C). For SM0, it was changed to 0.1 to 0.45 at 0.05 intervals. THCS was altered by multiplying 0.1, 0.2, 0.5, 2, 5, 10, and 15, resulting in the range used for sensitivity analysis being -0.00001 to -0.0015. Hence, we conceived that each parameter contained eight simulations.

The sensitivity index indicated that the response of parametric changes differed by the parameters as well as by categories (Table 3). Specifically, DV2 and SM0 did not affect the number of unsuitable habitats. This might be due to the parametric characteristics of DV2, which defines the optimal lower limit, and DV0, which demonstrates a significant impact on limiting the unsuitable areas in CLIMEX modeling (Jung et al., 2016; Kriticos et al., 2015). The lower soil moisture threshold (SM0) was expected to affect the numbers for category U; however, it did not. Based on a previous study investigating the effect of soil moisture on the development of Diaprepes abbreviatus (Coleoptera: Curculionidae), its larvae could not survive in extreme moisture conditions (Lapointe and Shapiro, 1999). In addition, M. pruinosa moves by flying, suggesting that soil moisture is not the limiting factor for insect distribution, but indirectly affects it via rainfall (Dixon, 1998; Thacker et al., 1997). In contrast, a large increase in U was observed when increasing THCS to -0.0015. Because THCS defines the cold stress accumulation rate, its significant increase limits the survival of M. pruinosa, resulting in the increasing the number of U. Specifically, cold parts of South Korea, such as Gyunggi-do, and Gangwon-do, indicated a large decrease in EI with increasing THCS, because its cold weather accelerated the high stress accumulation rate. In contrast, relatively warm parts, such as Jeju Island and south coastal regions, indicated a lower degree of changes in EI. Interestingly, Ulleungdo was not affected by changes in THCS. This is because this island experiences relatively high winter temperatures than cities at the same latitude (Lee and Kim, 2007).

Table 3. Result of sensitivity analysis for three selected parameters (DV2, SM0 and THCS)

DV2
Category 23 24 25 26 27 28 29 30 Sensitivity index
0~2 U 1 1 1 1 1 1 1 1 0.000
3~10 MS 31 19 16 11 6 3 3 3 0.903
11~20 S 39 45 42 43 40 35 28 26 0.422
21~30 VS 3 8 14 17 24 29 31 32 0.906
31~ OS 0 1 1 2 3 6 11 12 1.000
Total 74 74 74 74 74 74 74 74
SM0
Category 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Sensitivity index
0~2 U 1 1 1 1 1 1 1 1 0.000
3~10 MS 3 3 3 3 5 14 17 20 0.850
11~20 S 26 29 30 35 40 34 34 34 0.350
21~30 VS 32 33 32 29 22 22 19 16 0.515
31~ OS 12 8 8 6 6 3 3 3 0.750
Total 74 74 74 74 74 74 74 74
THCS
Category -0.00001 -0.00002 -0.00005 -0.0001 -0.0002 -0.0005 -0.001 -0.0015 Sensitivity index
0~2 U 1 1 1 1 1 1 8 21 0.952
3~10 MS 3 3 3 3 5 15 19 15 0.842
11~20 S 32 33 33 35 39 32 25 19 0.513
21~30 VS 31 30 31 29 23 21 17 14 0.548
31~ OS 7 7 6 6 6 5 5 5 0.286
Total 74 74 74 74 74 74 74 74
*Shaded parameter values were original values used for M. pruinosa simulation.

For suitable areas, including MS, S, VS, and OS, the variation in their numbers was dependent on the parameter characteristics. In contrast to category U, the value of MS indicated the overall highest sensitivity index. Increasing DV2 reduced the value of MS significantly, while an increasing trend appears when increasing SM0 and THCS. This is because the large number of cities assigning S, VS, and OS was changed to MS with decreasing EI value. The suitable regions (S) indicated a lower sensitivity index than category U, but it was still high: 0.422, 0350, and 0.513 for DV2, SM0, and THCS, respectively. Very suitable regions were increased by DV2 but decreased by increasing SM0 and THCS. The number of OS indicated a high sensitivity index for DV2 and SM0, but not for THCS. Because DV2 is related to the determination of the optimal growth conditions of a target species, it is typical that DV2 exhibits a high sensitivity index for all the categories having an EI larger than 2. Moreover, an increase in DV2 indicates that the range in temperature for optimal growth is expanded, suggesting a high possibility for rapid growth. In contrast, increasing SM0 causes a reduced suitable soil moisture range, resulting in a decrease in the overall EI value. Because THCS participates in limiting the population growth, its increase causes a large reduction in the number of suitable areas and a high sensitivity index for all categories. Hence, THCS is considered to be the first parameter that must be tuned for fitting the simulation to the actual distribution of a target species (Kriticos et al., 2015). Overall, the sum of the sensitivity index was influenced by the order of DV2, THCS, and SM0, suggesting that temperature exhibits a higher impact on M. pruinosa distribution than soil moisture. As aforementioned, this is consistent with a previous study indicating that temperature was a dominant factor for insect distribution (Bale et al., 2002; Lapointe and Shapiro, 1999), while soil moisture was as important as temperature when simulating plant distribution (Shabina and Kumar, 2014; Taylor and Kumar, 2012).

Finally, it is noteworthy that an optimal parameter value exists that maximizes the number for each category. Highly sensitive parameters demonstrate a more significant impact on the model response than insensitive parameters; thus, sensitivity analysis evaluates the importance of parameters to be used for improving model accuracy (Merow et al., 2011; Taylor and Kumar, 2012). Hence, we can effectively select parameters that require more extensive research and data collection methods (Shabina and Kumar, 2014). To visually present the sensitivity index, we have developed a map to visualize the effect of parametric changes on the potential distribution of M. pruinosa (Fig. 2). Via this figure, we can confirm that DV2 and THCS led to greater changes in EI distribution than SM0.

http://static.apub.kr/journalsite/sites/ksam/2018-043-04/N0770430418/images/ksam_43_04_18_F2.jpg
Figure 2.

Effect of parametric changes on potential distribution of M. pruinosa. (a) original parameter value (b) change in DV2 from 28°C to 23°C , (c) change in SM0 from 0.25 to 0.45, and (d) change in THCS from -0.0001 to –0.0015.

Conclusions

Because species distribution modeling evaluates the possibility of an invasive species inhabiting a specific area, it has been considered to be a useful tool for providing the fundamentals for the control and management of alien species. In this study, we analyzed the sensitivity of parameters in CLIMEX, a popular species distribution modeling software, and reported the most important parameters affecting M. pruinosa distribution in South Korea. Even though climate is the most critical factor determining the distribution of plants and insects, CLIMEX does not consider other environmental factors, implying that its accuracy is limited (Pattison and Mack, 2008). Hence, parameter estimation must be as precise as possible, and field data, which requires money and labor, is necessary. In this context, sensitivity analysis can provide insight into which parameter is necessary for emphasis thus allowing for limited experimental investments. Moreover, sensitivity analysis has been used to identify the optimal values for unknown parameters whose information is limited

Conflict of Interest

The authors have no conflicting financial or other interests.

Acknowledgements

This study was supported by research funds provided by the Chungnam National University in 2017.

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