# Differentiation of Forest Stands by Susceptibility to Folivores: A Retrospective Analysis of Time Series of Annual Tree Rings with Application of the Fluctuation-Dissipation Theorem

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

^{−1}, the average height is 26 m, and the average diameter is 33 cm.

^{−1}, the age 100–120 years, the average height 20 m, and the average diameter 20 cm.

_{max}was chosen as a characteristic of the spectrum. The software allows the computation of characteristics of spectra of all trees on a sample plot in batch mode.

## 3. Results

_{max}had the maximum possible value (Nyquist frequency f = 0.5), while for the trees at the outbreak location, f

_{max}was much lower. Figure 5 shows the s and f

_{max}values of the trees on sample plots pp04D and pp04K in the {s, f

_{max}} plane.

_{max}.

_{max}will be linear. With increasing s, f

_{max}will also go up, while in the control, no relation between s and f

_{max}is discernable; for all control sample plots, at f

_{max}values between 0.4 and 0.5, s values varied from 30 to 60. It can be theorized that the outlier plots pp08K and pp09K, whose characteristics deviated from the patterns observed for control plots, are located in areas with relatively severe damage, and these “control” plots should actually be regarded as small sites attacked by the spongy moth. As proof of this statement, we present a view of sample plot pp09K from an unmanned aerial vehicle, which clearly indicates damage to some tree crowns (the lower part of the photo in Figure 7).

_{max}(Figure 9) was assessed using Wilks’ λ distribution. For the tree groups being analyzed, λ was 0.602, with F

_{2,47}= 15.50 and p < 0.00001. Table 2 is a classification matrix of linear discriminant analysis for trees in the outbreak region of the pine looper and in the control undamaged stand.

_{max}values normalized to the control stands were calculated next (Figure 10).

_{i}and f

_{max,i}are the same between outbreak locations and control stands, then the normalized values are 1.0. As follows from Figure 10, some outbreak locations of the spongy moth and of the Siberian silk moth had slightly lower f

_{max}as compared to controls. For several spongy moth outbreak locations, s turned out to be greater than that in the control, whereas f

_{max}was slightly lower relative to the control. The greater s values than in the control for pine looper outbreak locations may be due to the fact that the core samples from trees at these outbreak locations were taken decades after the outbreak period (in 2015, whereas the outbreak happened in the mid-1970s), i.e., when trees heavily damaged at outbreak locations had already died and it became impossible to collect core samples from them. Only trees with minor damage survived, in which the crown recovered after the damage.

## 4. Discussion

_{max}and s; tree group 2 with small s and large f

_{max}; tree group 3 with large s and f

_{max}; and finally, tree group 4 with large s and small f

_{max}.

_{max}close to f = 0.5 at the outbreak locations).

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Kovalev, A.V.; Soukhovolsky, V.G. Analysis of Forest Stand Resistance to Insect Attack According to Remote Sensing Data. Forests
**2021**, 12, 1188–1201. [Google Scholar] [CrossRef] - Esper, J.; Schweingruber, F.H.; Winiger, M. 1300 years of climatic history for Western Central Asia inferred from tree-rings. Holocene
**2002**, 12, 267–277. [Google Scholar] [CrossRef] [Green Version] - Büntgen, U.; Frank, D.; Grudd, H.; Esper, J. Long-term summer temperature variations in the Pyrenees. Clim. Dyn.
**2008**, 31, 615–631. [Google Scholar] [CrossRef] [Green Version] - Wilson, R.; Anchukaitis, K.; Briffa, K.R.; Büntgen, U.; Cook, E.; D’Arrigo, R.; Davi, N.; Esper, J.; Frank, D.; Gunnarson, B.; et al. Last millennium northern hemisphere summer temperatures from tree rings: Part I: The long term context. Quat. Sci. Rev.
**2016**, 134, 1–18. [Google Scholar] [CrossRef] [Green Version] - Fritts, H.C. Dendroclimatology and dendroecology. Quat. Res.
**1971**, 1, 419–449. [Google Scholar] [CrossRef] - Morrow, P.A.; Lamarche, V.C. Tree ring evidence for chronic insect suppression of productivity in subalpine eucalyptus. Science
**1978**, 201, 1244–1246. [Google Scholar] [CrossRef] - Jardon, Y.; Filion, L.; Cloutier, C. Tree-ring evidence for endemicity of the larch sawfly in North America. Can. J. For. Res.
**1994**, 24, 742–747. [Google Scholar] [CrossRef] - Ryerson, D.E.; Swetnam, T.W.; Lynch, A.M. A tree-ring reconstruction of western spruce budworm outbreaks in the San Juan Mountains, Colorado, USA. Can. J. For. Res.
**2003**, 33, 1010–1028. [Google Scholar] [CrossRef] - Pohl, K.A.; Hadley, K.S.; Arabas, K.B. Decoupling Tree-Ring Signatures of Climate Variation, Fire, and Insect Outbreaks in Central Oregon. Tree Ring Res.
**2006**, 62, 37–50. [Google Scholar] [CrossRef] [Green Version] - Fan, Z.X.; Bräuning, A. Tree-ring evidence for the historical cyclic defoliator outbreaks on Larix potaninii in the central Hengduan Mountains, SW China. Ecol. Indic.
**2017**, 74, 160–171. [Google Scholar] [CrossRef] - Campbell, R.; Smith, D.J.; Arsenault, A. Multicentury history of western spruce budworm outbreaks in interior Douglas-fir forests near Kamloops. British Columbia. Can. J. For. Res.
**2006**, 36, 1758–1769. [Google Scholar] [CrossRef] [Green Version] - Fraver, S.; Seymour, R.S.; Speer, J.H.; White, A.S. Dendrochronological reconstruction of spruce budworm outbreaks in northern Maine, USA. Can. J. For. Res.
**2007**, 37, 523–529. [Google Scholar] [CrossRef] - Hogg, E.H.; Brandt, J.P.; Kochtubajda, B. Growth and dieback of aspen forests in northwestern Alberta, Canada, in relation to climate and insects. Can. J. For. Res.
**2002**, 32, 823–832. [Google Scholar] [CrossRef] - Girardin, M.P.; Tardif, J.; Bergeron, Y. Radial growth analysis of Larix laricina from the Lake Duparquet area, Québec, in relation to climate and larch sawfly outbreaks. Écoscience
**2001**, 8, 127–138. [Google Scholar] [CrossRef] - Büntgen, U.; Liebhold, A.; Nievergelt, D.; Wermelinger, B.; Roques, A.; Reinig, F.; Krusic, P.J.; Piermattei, A.; Egli, S.; Cherubini, P.; et al. Return of the moth: Rethinking the effect of climate on insect outbreaks. Oecologia
**2020**, 192, 543–552. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Castagneri, D.; Vacchiano, G.; Hacket-Pain, A.; DeRose, R.J.; Klein, T.; Bottero, A. Meta-analysis Reveals Different Competition Effects on Tree Growth Resistance and Resilience to Drought. Ecosystems
**2022**, 25, 30–43. [Google Scholar] [CrossRef] - Dorf, R.C.; Bishop, R.H. Modern Control Systems; Prentice Hall: Hoboken, NJ, USA, 2008; 1018p. [Google Scholar]
- Kogan, S.M. Electronic Noise and Fluctuation in Solid; Cambridge University Press: Cambridge, UK, 1996; 354p. [Google Scholar]
- Bellon, L.; Ciliberto, S. Experimental Study of the Fluctuation Dissipation Relation during an Aging Process. Phys. D Nonlinear
**2002**, 27, 325–335. [Google Scholar] [CrossRef] [Green Version] - Kubo, R.; Toda, M.; Hashitsume, N. Statistical Physics II: Nonequilibrium Statistical Mechanics; Springer Science & Business Media: Berlin, Germany, 2012; Volume 31, 279p. [Google Scholar]
- Rodríguez, M.A.; Wio, H.S. Stochastic Entropies and Fluctuation Theorems for a Discrete One-Dimensional Kardar-Parisi-Zhang System. Phys. Rev. E
**2019**, 100, 032111. [Google Scholar] [CrossRef] - Gudowska-Nowak, E.; Oliveira, F.A.; Wio, H.S. Editorial: The Fluctuation-Dissipation Theorem Today. Front. Phys.
**2022**, 10, 859799. [Google Scholar] [CrossRef] - Koltunov, E.V.; Ponomarev, V.I.; Fedorenko, S.I. Ecology of Gypsy Moth under Anthropogenic Impact; Publishing House of the Ural Branch of the RussianAcademy of Sciences: Ekaterinburg, Russia, 1998; 212p, ISBN 5-7691-0796-0. (In Russian) [Google Scholar]
- Palnikova, E.N.; Sviderskaya, I.V.; Soukhovolsky, V.G. Pine Looper in Siberian Forests; Nauka Publisher: Novosibirsk, Russia, 2002; 232p. (In Russian) [Google Scholar]
- Isaev, A.S.; Khlebopros, R.G.; Kiselev, V.V.; Kondakov, Y.P.; Nedorezov, L.V.; Soukhovolsky, V.G. Forest Insects Population Dynamics; Publishing House of the Eurasian Entomological Journal: Novosibirsk, Russia, 2009; 115p. [Google Scholar]
- Isaev, A.S.; Soukhovolsky, V.G.; Tarasova, O.V.; Palnikova, E.N.; Kovalev, A.V. Forest Insect Population Dynamics, Outbreaks and Global Warming Effects; Wiley: Hoboken, NJ, USA, 2017; 298p. [Google Scholar]
- Cybis Dendrochronology. Home of CDendro & CooRecorder. Available online: https://cybis.se/forfun/dendro/index.htm (accessed on 15 May 2023).
- Wei, W.W.S. Time Series Analysis. In Univariate and Multivariative Methods; Addison Wesley: Boston, MA, USA, 2006; 614p. [Google Scholar]
- Stock, J.H.; Watson, M.W. Introduction to Econometrics; Addison-Wasly: Boston, MA, USA, 2011; 832p. [Google Scholar]
- Blahut, R. FastAlgorithms for Digital Signal Processing; Addison-Wesley: Boston, MA, USA, 1985; 441p. [Google Scholar]
- Wigley, T.M.L.; Briffa, K.R.; Jones, P.D. On the average value of correlated time series, with applications in dendrochronology and hydrometeorology. J. Clim. Appl. Meteorol.
**1984**, 23, 201–213. [Google Scholar] [CrossRef] - Briffa, K.R.; Jones, P.D. Measuring the statistical quality of a chronology. In Methods of Dendrochronology: Applicationsin the Environmental Sciences; Cook, E.R., Kairiukstis, L.A., Eds.; Kluwer Academic Publishers: Boston, MA, USA, 1990; pp. 137–152. [Google Scholar]
- Martemyanov, V.V.; Dubovskiy, I.M.; Belousova, I.A.; Pavlushin, S.V.; Domrachev, D.V.; Rantala, M.J.; Salminen, J.P.; Bakhvalov, S.A.; Glupov, V.V. Rapid induced resistance of silver birch affects both innate immunity and performance of gypsy moths: The role of plant chemical defenses. Arthropod–Plant Interact.
**2012**, 6, 507–518. [Google Scholar] [CrossRef] - Martemyanov, V.V.; Dubovskiy, I.M.; Belousova, I.A.; Shokorova, N.S.; Pavlushin, S.V.; Glupov, V.V. Sex-specific variations in gypsy moth fitness, immune function, and parasite resistance mediated by background defoliation of the host plant. Ecol. Parasitol. Immunol.
**2013**, 2, 7. [Google Scholar] [CrossRef] [Green Version] - Pogue, M.; Schaefer, P.W. A Review of Selected Species of Lymantria Hübner (1819) (Lepidoptera: Noctuidae: Lymantriinae) from Subtropical and Temperate Regions of Asia, Including the Descriptions of Three New Species, Some Potentially Invasive to North America; Forest Health Technology Enterprise Team: Washington, DC, USA, 2007. [Google Scholar]
- Martemyanov, V.V.; Bykov, R.A.; Demenkova, M.; Gninenko, Y.; Romancev, S.; Bolonin, I.; Mazunin, I.; Belousova, I.A.; Akhanaev, Y.B.; Pavlushin, S.V.; et al. Genetic evidence of broad spreading of Lymantria dispar in the West Siberian Plain. PLoS ONE
**2019**, 14, e0220954. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ghimire, R.; Markkanen, J.M.; Kivimäenpää, M.; Lyytikäinen-Saarenmaa, P.; Holopainen, J.K. Needle removal by pine sawfly larvae increases branch-level VOC emissions and reduces below-ground emissions of Scots pine. Environ. Sci. Technol.
**2013**, 47, 4325–4332. [Google Scholar] [CrossRef] [PubMed] - Caron, L.; Deslauriers, A.; Mshvildadze, V.; Pichette, A. Volatile compounds in the foliage of balsam fir analyzed by static headspace gas chromatography (HS-GC): An example of the spruce budworm defoliation effect in the boreal forest of Quebec, Canada. Microchem. J.
**2013**, 110, 587–590. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Locations of insect attack outbreaks (“D” at the end of a label) and of control intact forest stands (“K” at the end of a label) in the studied regions.

**Figure 2.**Series of TRWs L (1) and first differences ΔL of TRWs (2) of drooping birch for tree “d03” on sample plot pp03D.

**Figure 3.**Average TRWs <L> and their average standard deviations <s> for drooping birch trees in outbreak locations (1) and control stands (2).

**Figure 4.**Spectra of series of first differences in birch TRWs. 1: tree d01 on sample plot pp03D (f

_{max}= 0.16) at a location of an outbreak of gypsy moth mass reproduction; 2: tree k02 on sample plot pp03K (f

_{max}= 0.40) in a control undamaged stand.

**Figure 5.**Characteristics of birch trees on plots pp04D (1) and pp04K (2) in forest stands of the Novosibirsk region.

**Figure 6.**Average standard deviations of first-difference series and mean frequencies of spectrum maxima for sample plots pp04–pp11 D and K. 1: Outbreak locations, 2: control, 3: sample plots pp08K and pp09K, and 4: sample plot pp09D.

**Figure 8.**Parameters s and f

_{max}for trees in a control intact forest stand (1) and at a location of a Siberian silk moth outbreak (2).

**Figure 9.**Parameters s and f

_{max}of trees in the region of pine looper outbreaks. 1: Control, 2: outbreaks of the pest.

**Figure 10.**Values of s

_{i}and f

_{max,i}at outbreak locations, respectively, divided by s

_{c}and f

_{max,c}of control intact forest stands. 1: Spongy moth outbreak locations, 2: Siberian silk moth outbreak locations, 3: pine looper outbreak locations, and 4: control.

**Table 1.**Average standard deviations ± standard error of first-difference series and mean frequencies of spectrum maxima ± standard error for sample plots at locations of outbreaks of pest mass reproduction (spongy moth, Siberian silk moth, and pine looper).

Insect Species | Sample Plots | Outbreak Locations | Control Stands | ||
---|---|---|---|---|---|

StandardDeviation | Frequency | StandardDeviation | Frequency | ||

Spongy moth | pp04D, pp04K | 38.79 ± 2.70 | 0.33 ± 0.05 | 62.39 ± 9.56 | 0.46 ± 0.028 |

pp05D, pp05K | 41.60 ± 8.14 | 0.33 ± 0.06 | 42.87 ± 4.68 | 0.40 ± 0.046 | |

pp06D, pp06K | 55.92 ± 5.15 | 0.36 ± 0.45 | 42.25 ± 4.57 | 0.39 ± 0.041 | |

pp07D, pp07K | 81.43 ± 17.39 | 0.41 ± 0.03 | 35.28 ± 5.77 | 0.46 ± 0.036 | |

pp08D, pp08K | 85.47 ± 7.46 | 0.44 ± 0.04 | 102.14 ± 13.70 | 0.44 ± 0.044 | |

pp09D, pp09K | 111.31 ± 21.77 | 0.31 ± 0.04 | 102.16 ± 12.88 | 0.39 ± 0.058 | |

pp10D, pp10K | 55.59 ± 8.34 | 0.35 ± 0.05 | 59.61 ± 12.55 | 0.42 ± 0.037 | |

pp11D, pp11K | 51.92 ± 7.87 | 0.35 ± 0.06 | 31.96 ± 5.66 | 0.43 ± 0.040 | |

Siberian silk moth | ip1D, ip1K | 44.50 ± 7.09 | 0.39 ± 0.035 | 64.54 ± 4.84 | 0.43 ± 0.033 |

Pine looper | kp1D, kp1K | 22.11 ± 1.67 | 0.40 ± 0.03 | 14.80 ± 1.62 | 0.42 ± 0.016 |

kp2D | 29.08 ± 6.65 | 0.39 ± 0.03 |

Trees on Sample Plots | % of Correctly Classified Trees | Classified Trees | |
---|---|---|---|

Control | Damaged | ||

Control | 76.5 | 13 | 4 |

Damaged | 87.9 | 4 | 29 |

Total | 84.0 | 17 | 33 |

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**MDPI and ACS Style**

Soukhovolsky, V.; Krasnoperova, P.; Kovalev, A.; Sviderskaya, I.; Tarasova, O.; Ivanova, Y.; Akhanaev, Y.; Martemyanov, V.
Differentiation of Forest Stands by Susceptibility to Folivores: A Retrospective Analysis of Time Series of Annual Tree Rings with Application of the Fluctuation-Dissipation Theorem. *Forests* **2023**, *14*, 1385.
https://doi.org/10.3390/f14071385

**AMA Style**

Soukhovolsky V, Krasnoperova P, Kovalev A, Sviderskaya I, Tarasova O, Ivanova Y, Akhanaev Y, Martemyanov V.
Differentiation of Forest Stands by Susceptibility to Folivores: A Retrospective Analysis of Time Series of Annual Tree Rings with Application of the Fluctuation-Dissipation Theorem. *Forests*. 2023; 14(7):1385.
https://doi.org/10.3390/f14071385

**Chicago/Turabian Style**

Soukhovolsky, Vladislav, Polina Krasnoperova, Anton Kovalev, Irina Sviderskaya, Olga Tarasova, Yulia Ivanova, Yuriy Akhanaev, and Vyacheslav Martemyanov.
2023. "Differentiation of Forest Stands by Susceptibility to Folivores: A Retrospective Analysis of Time Series of Annual Tree Rings with Application of the Fluctuation-Dissipation Theorem" *Forests* 14, no. 7: 1385.
https://doi.org/10.3390/f14071385