# Seasonal Changes and the Interaction between the Horse Chestnut Leaf Miner Cameraria ohridella and Horse Chestnut Leaf Blotch Disease Caused by Guignardia aesculi

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site

^{2}, and the total green public open space is 260 ha inside the town. České Budějovice is the largest city in South Bohemia, with almost 100,000 inhabitants. The town is surrounded by forests and agricultural fields. The total number of horse chestnut trees in the town was estimated as 534 (Kopačka 2011). For the purpose of the present study, the city area was divided into eight semi-isolated sites (Table 1). All parameters and the map of the study sites are the same as those in a previous study [54], with the exception that two additional study sites, “Stromovka Park” and “Třebotovice and Kaliště village” were included in the survey. The area of green public open space at both study sites was one ha. The range of tree age was 23–37 years in Třebotovice and Kaliště village and 31–56 years in Stromovka Park. Only the Stromovka Park site is situated near a wetland, providing suitable conditions for the development of G. aesculi. All horse chestnut trees grow within 12–29 m of the wetland borders. Two rivers and some streams flow through České Budějovice, as seen from the map. Previous studies [28,54] have demonstrated higher damage to leaves attacked by G. aesculi in the city center than in other areas. At the Nádražní Street site, leaf litter is not removed; therefore, A. hippocastanum leaves are severely infested with C. ohridella every year [54]. The average cadastral area per site was 107.25 ha (SEM = 35.44, n = 8), and the average of green public open space was 21.55 ha (SEM = 7.43, n = 8). The average number of horse chestnut trees was 50.13 (SEM = 20.58, n = 8), and the average age of the studied trees was 52.13 years (SEM = 7.60, n = 8) at the study sites.

#### 2.2. Sampling of Horse Chestnut Leaves

#### 2.3. Measurement of Proportion of Leaf Area Damaged by Leaf Miner and Fungus

^{TM}model 3DX-700028 (3Dconnexion, Boston, Massachusetts, USA) and standard tools in Adobe Photoshop. Each sampled leaf thus resulted in three images amounting to 1200 threshold images during the entire study. These images were subsequently processed by our custom-made software written in Java™ programming language [57], which saved the values of the areas (number of black pixels in an image) in CSV files (comma-separated values). The damages attributed to C. ohridella and G. aesculi were finally calculated as percentages of the total leaf area.

#### 2.4. Data Presentation and Statistical Analysis

#### 2.5. Modeling Dynamics of Leaf Damage Caused by Cameraria ohridella and Guignardia aesculi

#### 2.5.1. The Model

_{C}(t) and p

_{G}(t), respectively, where 0 ≤ p

_{C}(t) ≤ 1 and 0 ≤ p

_{G}(t) ≤ 1. Furthermore, as the total damaged leaf area at time t, found as p

_{total}(t) = p

_{C}(t) +p

_{G}(t), cannot exceed 1, we also have the constraint that 0 ≤ p

_{total}(t) ≤ 1.

^{γ}gradually declines from being close to 1 to approaching 0 when p approaches 1. How fast this occurs depends on the parameter γ. Thus, if γ = 0, the species will grow exponentially until p becomes 1, whereas growth will level off at lower values of p, the higher the value of γ. In other words, γ expresses how sensitive the growth of a species is to damage.

_{i}is the proportion of damage caused by species i, while α

_{i}, $\beta $

_{i}and γ

_{i}are species-specific values of α, β and γ.

_{i}(t) is the damage caused by species i when it coexists with its competitor, while ${p}_{i}^{\prime}\left(t\right)$ is the predicted damage when it occurs alone, i.e., by setting p

_{total}= p

_{i}in Equation (3).

#### 2.5.2. Estimation of Model Parameter Values

_{i}/dt with Δp

_{i}/Δt, using a time step (Δt) of a half day starting from time t = 0. Thus, the predicted damage attributed to species i at time t + Δt was calculated as ${\widehat{p}}_{i}\left(t+\Delta t\right)={\widehat{p}}_{i}\left(t\right)+\Delta {\widehat{p}}_{i}$. t was calculated as the number of days since the first sampling. As sampling was conducted over several days, we used the midpoints of each sampling period to calculate t, implying that t = 0 corresponds to May 20. Thus, for the following four sampling periods, t was set to 28, 56, 85.5, and 117 days, respectively.

_{i}(0), which were estimated for each site and species. In total, this yielded 22 unknown constants that had to be estimated from 80 data points (two assessments of damage obtained at eight sampling sites on five sampling occasions). For this purpose, we used the Solver tool in Excel

^{®}. The method is based on iterating the model’s constants until the sum of squared deviations (SSD) between the observed and estimated values of p

_{i}(t) is minimized. Ideally, the values of the constants should gradually converge from their initial values (chosen by the researcher) towards a final set of values, which represents the best estimates of the model’s constants (i.e., the values that minimize SSD). However, in order to reduce the risk of ending up in a local minimum, it is recommended to start the iteration procedure with different combinations of initial values and then check whether the procedure converges to the same set of values, irrespective of their initial values.

^{2}), while the significance of the R

^{2}was assessed by an F-test as the ratio between the mean square (MS) of the model divided by the mean square error (MSE) with p − 1 degrees of freedom (df) in the numerator and n − p df in the denominator. p is the number of estimated values (22) and n the number of data points (80).

#### 2.5.3. Evaluating the Model as a Predictive Tool

_{i}(0) (denoted ${\overline{p}}_{i}$) should be close to the a posteriori values (denoted ${\widehat{p}}_{i})$, obtained retrospectively by fitting the model to data spanning over the entire season; and (ii) the biological system should basically be predictable with relatively little noise obscuring the underlying dynamics described by the model.

## 3. Results

#### 3.1. Damage to A. hippocastanum Leaves during the Vegetation Period

_{14,2318}= 87.532, p < 0.0001) and sampling period (Wilk’s λ = 0.199, F

_{8,2318}= 359.882, p < 0.0001) on leaf damage. The interaction between the site and period was also highly significant (Wilk’s λ = 0.629, F

_{56,2318}= 10.813, p < 0.0001).

_{7,1160}= 156.853, p < 0.0001 and F

_{4,1160}= 556.997, p < 0.0001, respectively). The interaction between these two factors was also highly significant (F

_{28,1160}=13.604, p < 0.0001). A highly significant effect of both site and sampling date was also confirmed for G. aesculi damage (F

_{7,1160}= 33.618, p < 0.0001 and F

_{4,1160}= 466.230, p < 0.0001, respectively). The interaction between these two factors was also highly significant (F

_{28,1160}= 8.082, p < 0.0001).

#### 3.2. Modeling Leaf Damage Caused by Cameraria ohridella and Guignardia aesculi

^{2}= 0.972; F

_{21,58}= 94.4; p < 0.0001). The estimated parameter values and the initial damages due to C. ohridella and G. aesculi are shown in Table 3.

^{−5}(0.0055%) and 5.278·10

^{−4}(0.0528%) for C. ohridella and G. aesculi, respectively. The fit was highly significant (R

^{2}= 0.983; F

_{1,8}= 469.7; p < 0.0001).

^{−1}for C. ohridella and $0.0478\times {p}^{1.0096}$d

^{−1}for G. aesculi. Thus, for a given value of p, the growth rate of C. ohridella will exceed that of G. aesculi, provided p > 0.00023.

#### 3.3. The Model as a Predictive Tool

_{1,6}= 0.460; p = 0.523; G. aesculi: ${\overline{p}}_{i}=-0.0896;{\widehat{p}}_{i}+0.0363;$ r = −0.3487; F

_{1,6}= 0.830; p = 0.3973). In other words, if the estimates of p

_{i}obtained by leaf sampling in mid-May had been used to initialize the model, the predicted dynamics would differ significantly from what was actually observed.

## 4. Discussion

#### 4.1. Damage to the Leaf Area of A. hippocastanum during the Vegetation Period

#### 4.2. Interaction between C. ohridella and G. aesculi on the Leaves of Horse Chestnut Trees

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The observed (points) and model predicted (lines) damages during one season at the eight sampling sites (Table 1). First sampling took place around May 20. Each point represents the average damage of 30 leaves attributed to C. ohridella (

**blue**) and G. aesculi (

**red**) or in combination (

**green**).

**Figure 2.**Damage caused by C. ohridella (

**blue**) and G. aesculi (

**red**) or combined (

**green**) averaged over the eight sampling sites so that each dot represents the average (±2SEM) of 240 leaves. Full lines show the damage when both species are present, while the dashed lines show the expected damage of a species in absence of the other. The lines were calculated by means of Equation (3) using the values of α, β and γ given in Table 3, and with p(0) equal to 5.489 × 10

^{−5}for C. ohridella and 5.278·10

^{-4}for G. aesculi.

**Figure 3.**Relative impact of the two species on each other based on Figure 2. Blue line: impact of C. ohridella on G. aesculi. Red line: impact of G. aesculi on C. ohridella.

Study Site | Cadastral Area | Green Public Open Space | Horse Chestnut Trees | Avg. Age ± SEM ^{&} of Horse Chestnut Tree | |
---|---|---|---|---|---|

Label | Name | (Hectares) | (Hectares) | (Number) | (Year) |

A | City centre | 133 | 12 | 186 | 74.99 ± 1.86 |

B | Šumava and Máj estate | 183 | 58 | 40 | 39.02 ± 3.19 |

C | Vltava estate | 92 | 34 | 40 | 41.79 ± 3.49 |

D | Třebotovice and Kaliště village | 30 | 2 | 5 | 17. 82 ± 6.86 |

E | Rožnov estate | 294 | 29 | 57 | 70.49 ± 4.43 |

F | Pražské předměstí estate | 124 | 37 | 49 | 49.74 ± 2.75 |

G | Stromovka Park | 1 | 1 | 6 | 43.53 ± 4.13 |

H | Nádražní Street | 1 | 1 | 18 | 77.74 ± 3.02 |

^{&}SEM = standard error of the mean.

**Table 2.**The average percentage of horse chestnut leaf area damaged by Cameraria ohridella and Guignardia aesculi during vegetation season. Pooled data from all sampling sites across city (average ± SEM, n = 240).

Sampling Date | Leaf Area Damaged by Cameraria ohridella | Leaf Area Damaged by Guinardia aesculi | ||
---|---|---|---|---|

Avg. ± SEM | Range | Avg. ± SEM | Range | |

from 16 to 24 May | 0.018 ± 0.002 | 0.000–0.329 | 0.031 ± 0.005 | 0.000–0.591 |

from 13 to 21 June | 0.214 ± 0.117 | 0.000–28.071 | 0.448 ± 0.126 | 0.000–27.612 |

from 11 to 19 July | 2.594 ± 0.402 | 0.003–37.582 | 0.924 ± 0.095 | 0.000–14.882 |

from 11 to 22 August | 5.058 ± 0.756 | 0.000–78.790 | 2.726 ± 0.255 | 0.022–22.636 |

from 9 to 19 September | 7.416 ± 0.666 | 0.006–60.686 | 9.612 ± 0.891 | 0.000–78.864 |

**Table 3.**Estimated parameter values and site-specific initial damages (proportions). α has dimension d

^{−1}, while β and γ are dimensionless.

Species | |||
---|---|---|---|

C. ohridella | G. aesculi | ||

Parameters | α | 3.0066 | 0.0478 |

β | 1.5023 | 1.0096 | |

γ | 14.611 | 0.6732 | |

Initial damage | Site A | 5.42 × 10^{−5} | 6.54 × 10^{−4} |

(p(0)) | Site B | 4.35 × 10^{−5} | 2.11 × 10^{−4} |

Site C | 4.30 × 10^{−5} | 3.25 × 10^{−4} | |

Site D | 3.96 × 10^{−5} | 1.73 × 10^{−4} | |

Site E | 4.82 × 10^{−5} | 3.44 × 10^{−4} | |

Site F | 4.84 × 10^{−5} | 3.51 × 10^{−4} | |

Site G | 8.96 × 10^{−5} | 1.538 × 10^{−3} | |

Site H | 2.29 × 10^{−4} | 1.453 × 10^{−3} |

**Table 4.**Correlations between damages caused by C. ohridella and G. aesculi assessed at two different sampling occasions.

Periods | C. ohridella | G. aesculi | ||||
---|---|---|---|---|---|---|

r | F_{1,6} | p | r | F_{1,6} | p | |

Period 1 vs. Period 5 | 0.3975 | 1.126 | 0.3295 | −0.1823 | 0.206 | 0.6657 |

Period 2 vs. Period 5 | −0.2950 | 0.572 | 0.4781 | −0.1429 | 0.125 | 0.7358 |

Period 3 vs. Period 5 | 0.9698 | 95.02 | <0.0001 | 0.6848 | 5.299 | 0.0609 |

Period 4 vs. Period 5 | 0.9715 | 100.7 | <0.0001 | 0.9555 | 62.96 | 0.0002 |

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## Share and Cite

**MDPI and ACS Style**

Kopačka, M.; Nachman, G.; Zemek, R.
Seasonal Changes and the Interaction between the Horse Chestnut Leaf Miner *Cameraria ohridella* and Horse Chestnut Leaf Blotch Disease Caused by *Guignardia aesculi*. *Forests* **2021**, *12*, 952.
https://doi.org/10.3390/f12070952

**AMA Style**

Kopačka M, Nachman G, Zemek R.
Seasonal Changes and the Interaction between the Horse Chestnut Leaf Miner *Cameraria ohridella* and Horse Chestnut Leaf Blotch Disease Caused by *Guignardia aesculi*. *Forests*. 2021; 12(7):952.
https://doi.org/10.3390/f12070952

**Chicago/Turabian Style**

Kopačka, Michal, Gösta Nachman, and Rostislav Zemek.
2021. "Seasonal Changes and the Interaction between the Horse Chestnut Leaf Miner *Cameraria ohridella* and Horse Chestnut Leaf Blotch Disease Caused by *Guignardia aesculi*" *Forests* 12, no. 7: 952.
https://doi.org/10.3390/f12070952