It was previously shown that the width of earlywood and latewood respond differently to defoliation [6,20]. It can therefore be expected that if the damage caused by these species of phyllophagous insects is confined to a particular season, then: (a) the growth of early- and latewood will change in different ways, and (b) these differences will be the same for any of this species outbreaks. The reconstruction technique proposed here is limited to the late-summer and autumn phenological group of pest insects.

It follows from the scheme (Figure 2) that past defoliation by B. piniaria can be detected when searching for pointer years [31] in tree-ring series built for early- and latewood simultaneously. Here we propose a method of past outbreaks detection based on this approach. As a criterion for identifying pointer years, we used the relative growth change (RGC) [32], calculated (for early-, latewood, or ring width) as the ratio between current year absolute radial growth Rt and growth of the previous one Rt−1:

Conceptual scheme of late-summer and fall defoliation impact on assimilates distribution and seasonal wood increment [1,4,6,21,22,23,24]. The sources are green-colored, and the sinks are orange-colored; early season sinks/sources are lighter than the late season’s. The diameter of the circle indicates the volume of synthesized, stored, or consumed assimilates. The principal scheme of carbohydrates flows is located in the right extra section of the figure; the arrows indicate the direction of assimilates relocation.

The year t was considered a defoliation year if: (a) the year t + 1 latewood RGC value was less than the threshold change.l (%) for the proportion of trees equal to or greater than sync.l (%) and (b) the year t + 2 earlywood RGC value was less than the threshold change.e (%) for a proportion of trees equal to or greater than sync.e (%) (Figure 2). The method for recognizing past outbreaks based on this approach will be referred to as the pointer year method (PYM).

A more common approach to reconstructing outbreaks history is based on the annual ring width patterns of affected trees. It is a well-known fact that a more or less prolonged recovery follows the drastic decline in radial growth caused by defoliation. The history of insect outbreaks reconstructions based on the detection of such patterns in the series of annual ring width measurements is implemented in the OUTBREAK algorithm [9] (hereinafter, this approach is referred to as the OUTBREAK). A version of this algorithm for cases when it is impossible to use an unaffected tree species’ radial growth as control is described by James H. Speer and colleagues [6].

The algorithm’s initial data included the detrended by cubic smoothed spline ring width series for each tree in the studied area [9,28,29]. The assumed defoliation was recorded by the algorithm for an individual tree in year t if: (a) t and following years in the number ≥ lng have got radial growth indexes ≤ (std × standard deviation of series) and (b) RGC (Equation (1)) for the year tabrupt. We would consider the year t as the first year of defoliation if the proportion of trees meeting both of these criteria was ≥10%.

Several studies considered the ring width’s local minimum values as an additional sign of defoliation [16,33,34]. This method implies comparing absolute ring width in t year with ones on the interval from twidth to t + width years. If the proportion of trees with the local minimum in t year is ≥perc (a unit fraction), this serves as evidence in favor of probable defoliation in the year t [16,34]. From now on, this approach is referred to as the moving window method (MWM).

The method of outbreak reconstruction based on multivariate statistics is known [18]. The tree-ring series studied using the method are preliminarily reduced to the same length by removing their early sections, which is necessary for the method to work correctly. Next, the series of measured annual ring width values are standardized so that the arithmetic mean of each of them becomes equal to zero, and the standard deviation becomes equal to one.

The resulting matrix of the annual ring width indexed values is decomposed by the method of independent components fast analysis into separate components using the ica package [35] in the R environment. Evidence of defoliation (or other unfavorable effects) is recorded preliminary if values of any identified component decrease below a certain value lim (threshold value of deviation from the mean) for lng (length of such series) years in a row.

On the next step, the ring-width series for each tree were detrended using cubic splines [28,29], and the resulting radial growth indexes record was averaged for the site. If year t has been selected on the previous step and its radial growth index declined below some quantile q, this coincidence was interpreted as a consequence of defoliation [18]. From now on, the method is called MICA (method of independent component analysis).

Besides, some artifacts might appear during the preceding calculations. It is possible that by these artifacts, the minima in detrended chronology will not coincide with low values in the independent components. However, we assumed that such an offset should not exceed the rng value.

In the protocols we used [6,9,18,34], there are no justifications for specific values of arguments. Nevertheless, it is not obvious that values that had been used previously are optimal for our case. Therefore, we try to found optimal values of the arguments using PYM, MWM, MICA, and OUTBREAK methods for each investigated sample plot. For the first three methods, values were considered optimal if they had indicated outbreaks of 1996–1999 and 2003–2008, known from the Altai Forest Protection Center’s departmental materials, with a minimum (ideally in the absence) of false-positive results. The OUTBREAK method’s optimality was assessed by maximizing the proportion of trees indicated as defoliated during the B. piniaria outbreaks mentioned above.

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