Science, Irving K. Barber Faculty of (Okanagan)
Non UBC
Biology, Department of (Okanagan)
DSpace
Li, Chao
Roitberg, Bernard
Huang, Shongming
Lalonde, Robert G.
Most experiments on thinning effects are based upon short-term outcomes, which has led to a common conclusion that stand gross volume will be reduced after various thinning operations. However, contrary results are emerging from more recent long-term thinning experiments. The well-known biological concept of compensatory growth was introduced to reconcile these opposing results. This synthetic article describes a systematic investigation on overcompensation under the conceptual framework of compensatory growth and consists of the following: (1) empirical evidence of overcompensation in forests; (2) a theoretical proof of the possibility of emerging overcompensation using a life-history-theory based analytical tree adaptive growth (TAG) model; and (3) an empirical data-based tree compensatory growth (TreeCG) model that resembles the growth relationships from natural stands. Our results indicate that (1) overcompensation is an expected common phenomenon across different tree species and geographical regions, and (2) overcompensation can be predicted from at least two different mechanisms: optimal allocation of available energy to growth, reproduction, maintenance and reserves, and redistribution of freed resources from dead trees. Therefore, overcompensation is a predictable phenomenon, and forest managers can make SFM (Sustainable Forest Management) decisions based on their specific management goals. Research recommendations are suggested for next steps.
Academic Editor: Byung Bae ParkReceived: 14 February 2025Revised: 15 March 2025Accepted: 17 March 2025Published: 21 March 2025Citation: Li, C.; Roitberg, B.; Huang,S.; Lalonde, R. PredictableOvercompensation in Post-ThinningStand Dynamics of Canadian Forests:A Synthesis. Plants 2025, 14, 982.https://doi.org/10.3390/plants14070982Copyright: © 2025 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/).ArticlePredictable Overcompensation in Post-Thinning StandDynamics of Canadian Forests: A SynthesisChao Li 1,*, Bernard Roitberg 1,2,*, Shongming Huang 3 and Robert Lalonde 41 Canadian Wood Fibre Centre, Canadian Forest Service, Edmonton, AB T6H 3S5, Canada2 Department of Biological Sciences, Simon Fraser University, Burnaby, BC V5A 1S6, Canada3 Alberta Forestry and Park, Edmonton, AB T5M 3V9, Canada; shongming.huang@gov.ab.ca4 Department of Biology, University of British Columbia, Okanagan, BC V1V 1V7, Canada;robert.lalonde@ubc.ca* Correspondence: chao.li@nrcan-rncan.gc.ca (C.L.); roitberg@sfu.ca (B.R.)Abstract: Most experiments on thinning effects are based upon short-term outcomes, whichhas led to a common conclusion that stand gross volume will be reduced after variousthinning operations. However, contrary results are emerging from more recent long-termthinning experiments. The well-known biological concept of compensatory growth wasintroduced to reconcile these opposing results. This synthetic article describes a systematicinvestigation on overcompensation under the conceptual framework of compensatorygrowth and consists of the following: (1) empirical evidence of overcompensation in forests;(2) a theoretical proof of the possibility of emerging overcompensation using a life-history-theory based analytical tree adaptive growth (TAG) model; and (3) an empirical data-basedtree compensatory growth (TreeCG) model that resembles the growth relationships fromnatural stands. Our results indicate that (1) overcompensation is an expected common phe-nomenon across different tree species and geographical regions, and (2) overcompensationcan be predicted from at least two different mechanisms: optimal allocation of availableenergy to growth, reproduction, maintenance and reserves, and redistribution of freedresources from dead trees. Therefore, overcompensation is a predictable phenomenon, andforest managers can make SFM (Sustainable Forest Management) decisions based on theirspecific management goals. Research recommendations are suggested for next steps.Keywords: compensatory growth; forest productivity; growth and yield; overcompensation;pre-commercial thinning; TAG; TreeCG; thinning theory1. IntroductionEnhancing productivity is a primary goal for applied plant and animal scientists inmany different research fields. In forestry and silviculture, in particular, it is crucial toelucidate efficient ways of enhancing stand productivity to mitigate disturbance-inducedreduction in stand volume (including harvest) to ensure sustainable wood supply andsatisfy the increasing demands from human society. Thinning is a common silviculturaltool which has been extensively studied in the past for more-than-two centuries for itsimpact on post-thinning stand dynamics, and the diverse results has led to some consen-sus [1,2]; however, some associated phenomena such as increased stand gross volume orovercompensation are still unexplainable by conventional thinning theory. As a result,these phenomena have usually been ignored as “out-of-the-ordinary” or treated as statisti-cal outliers. Nevertheless, such simple conclusions might result in missing opportunitiesof reaching the goal of productivity enhancement. In this article, we describe a researchPlants 2025, 14, 982 https://doi.org/10.3390/plants14070982Plants 2025, 14, 982 2 of 18framework for resolving one such silvicultural puzzle, overcompensation, which providesa pathway for reaching the goal of enhancing stand productivity.1.1. A Silviculture PuzzleThinning immediately reduces the stand density and thus its gross volume, andsuch reduction is unlikely to recover in a short period of time due to the slow growthrate of trees. Therefore, any enhanced stand gross volume in the short-term cannot beexpected. These results have been well summarized in the literature (e.g., [1,2]). Severalkey conclusions reached on thinning include enhanced growth in diameter and height,basal area, and merchantable volume; however, gross volume is usually lower than thatfrom the unthinned sites. These conclusions have been confirmed by numerous short-termthinning experiments worldwide [3] and have driven conventional thinning theory andguided decisions in forestry practices [4]. The drawback of reduced gross volume has beenseen as a serious concern by forest managers and practitioners in their implementation ofthinning in forestry practice.Exceptions, however, have also been reported in the literature from time to time. Forexample, seven decades ago, Steel [5] reported that the gross volume in a pre-commerciallythinned Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco) stand on the Wind River Ex-perimental Forest in Skamania County, Washington, exceeded that of its unthinned coun-terparts after 20 years. More than two decades later, Warrack [6] summarized 50-yearpre-commercial thinning (PCT) research results from the famous Schenstrom ThinningPlots in BC, Canada [7], showing that after seven major thinnings, there was no differencein growth volumes for whatever treatment was compared with the unthinned control whenconsidering all the site differences. The original Tree and Stand Simulator (TASS) [8] alsopredicted the stand basal area could be enhanced by PCT and fertilization.These observations were apparently inconsistent with conventional thinning theoryand formed a silviculture ‘puzzle’, i.e., forest productivity cannot be enhanced in theshort-term in general, but might be possible from a long-term perspective, despite it beingdifficult to explain using existing thinning theory. As pointed out by Zeide [2] “in all ofthe [PCT] trials, the basal area and total volume of the thinned plots is well below thatof the unthinned plots, but sufficient time has yet to elapse since treatment to indicatewhether the thinned plots will ever catch up to their unthinned counterparts”, and so,revisiting historical PCT sites could provide a fuller picture of the post-thinning standdynamics. With this approach, Pitt and Lanteigne [9] revisited the historical balsam fir(Abies balsamea (L.) Mill.) PCT experimental site in the Green River, New Brunswick, Canada,42 years after the initial treatments, and found that the stand volumes in treatment siteswere about 15% higher than those from untreated sites. Nevertheless, the issue remaineduncertain due to insufficient evidence and difficulties in explanations and predictions inpractical applications.1.2. A Research FrameworkIn analyzing a 40-year PCT and fertilization experimental dataset from ShawniganLake, BC, Canada, Li et al. [10] introduced the concept of compensatory growth (CG) fromgeneral biology to explain the diverse patterns in post-thinning stand dynamics. CG isa common phenomenon widely observed in animals and plants [11] but not previouslyreported in forests. Li et al. [12] defined CG in forestry as “a change in growth rate, usuallypositive, in a forest stand following a disturbance that reduces biomass and/or individ-uals from the population” and provided a number of examples and research progress indifferent fields. CG is a process that consists of a spectrum of states ranging from under-compensation (stand gross volume from a thinned site is lower than that of an unthinnedPlants 2025, 14, 982 3 of 18counterpart site), exact compensation (stand gross volume from a thinned site is equalto that of an unthinned counterpart site, and can also be called compensatory-induced-equality, CIE), and overcompensation (stand gross volume from a thinned site is higherthan that of an unthinned counterpart site) over time. Conventional thinning theory hasdescribed under-compensation short-term post-thinning stand dynamics across species andgeographical regions well, in addition to how increased stand productivity in long-termpost-thinning stand dynamics falls in terms of overcompensation, this being the other endof CG spectrum. The work described below focuses on overcompensation that representsenhanced stand gross volume. CG is a special case of growth response that indicates howtrees respond to a disturbance in their environment, i.e., CG needs to be triggered by adisturbance of reduced biomass. A possible way of inducing expected post-thinning standdynamics, such as overcompensation, could be manipulated by altering the disturbance interms of its timing and intensity, as well as the rules of thinning [11].To examine whether overcompensation is possible in forest stand productivity en-hancement in post-thinning stand dynamics, a combined empirical data analysis andmodeling approach is employed. The empirical data analysis is employed to compilehistorical long-term silvicultural datasets and identify the stand growth patterns afterthinning treatments. This work determines whether the reported overcompensation issingular/unique or a common case. Thus, we compiled five published long-term thinningdatasets for different major commercial tree species across Canada and concluded thatovercompensation is a common phenomenon that appeared in all five datasets. If over-compensation can be seen as a common phenomenon in Canadian forests, there is a needto identify the possible underlying mechanisms for predicting its occurrence to supportdecisions in forestry practices.Since any field experiments in forests will take a long period to complete, it makessense to apply a modeling approach to enhance the exploration of logical consequencesof possible mechanisms of overcompensation. In this regard, we aimed to determine ifany existing theory in biology/ecology could be applied to our conceptual framework.Any positive answer would confirm that overcompensation is an expected outcome underspecific conditions. We also address the question as to whether existing stand growthrelationships obtained from natural stands can be employed to predict the occurrence ofovercompensation and thus support the decisions in sustainable forest management (SFM).1.3. Objectives and Presentation ArrangementThis article presents a systematic investigation on whether overcompensation is apredictable phenomenon in post-thinning stand dynamics, with the specific objectivesof (1) summarizing the empirical evidence of overcompensation in Canadian forests;(2) explaining a theoretical proof that overcompensation can be expected in long-term post-thinning stand dynamics; (3) providing an example of published stand growth relationshipsthat can be used to predict the occurrence of overcompensation; and (4) discussing the prosand cons of overcompensation and recommending the next steps in research. We describethe results associated with these objectives next.2. Empirical Evidence2.1. Long-Term PCT DataThe research took place under the premise that should overcompensation be atruly common phenomenon in forests, there should be considerable empirical evidencedemonstrating its occurrence. In searching the empirical evidence, we started by ana-lyzing a Douglas-fir PCT and fertilization experimental dataset from the west coast ofCanada that spans 40 years, near Shawnigan Lake, British Columbia (lat. 48◦38′13′′ N;Plants 2025, 14, 982 4 of 18long. 123◦43′16′′ W). Douglas-fir is a major commercial tree species with a long lifespan ofat least 500 years, sometimes exceeding 1000 years in BC and the Pacific Northwest Region.It has also been a major plantation species for more than half a century with an extensivehistory of research activities. The Shawnigan Lake trial was established with a 24-year-oldstand, with a unique factorial experimental design that enables researchers to understandthe effect of various combinations of PCT and fertilization treatments on stand dynam-ics [13]. The treatments included three levels of PCT (0, 1/3, and 2/3 removals named asT0, T1, and T2) and three levels of fertilization (0, 224 kg/ha, and 448 kg/ha fertilizersnamed as F0, F1, and F2), with all stands equally managed otherwise. Four plots were runfor each of the nine treatments of combined PCT and fertilization. The other feature of thisexperiment is the multiple remeasurements over time, which allow for the display of afull picture of the stand dynamics, before and right after initial treatments, 3, 6, 9, 12, 15,18, 24, 32, 40, and 50 years after initial treatments. The most recent remeasurement wasconducted in 2022. Figure 1a shows the estimated stand volumes from different treatmentsover time. As estimated, absolute stand volumes may vary when using different volumeequations, even with same measured DBH and H [14]; these volumes are transformedinto relative values against the volumes of control plots using the following equation toreduce/eliminate such differences, and are presented in Figure 1b:RG(%) = VolTreat/VolControl × 100% (1)Figure 1a shows that stand volumes are significantly reduced as a result of thinning op-erations, but they gradually catch-up with unthinned (T0F0) sites over time and eventuallyexceeded that of the unthinned, unfertilized controls (T0F0) in the long run. This clearlydemonstrated how the concept of compensatory growth can characterize diverse growthpattens, i.e., compensatory growth is a gradual process, from under compensation rightafter thinning (stand volume of thinned stands is lower than that of control) to gradualcatch-up growth to exact compensation (stand volume of thinned stands becomes equal tothat of control), and eventually to overcompensation after that (stand volume of thinnedstands becomes higher than that of control).As stand volume is represented by relative growth in Figure 1b, different states ofcompensatory growth can be seen more clearly: a stand volume of 100% for T0F0 is rep-resented as a horizontal line, and any stand volume under the 100% line indicates undercompensation; any stand volume that intercepts with 100% represents exact compensation,and any stand volume above 100% line denotes overcompensation. In T0F1 (light fertiliza-tion without thinning), for example, a greater performance than the control can be seenstarting at 5 years after the treatment. In T2F0 (heavy thinning without fertilization), asanother example, overcompensation can only be seen at nearly 50 years after the treatment.Figure 2a shows the post-thinning stand dynamics of lodgepole pine (Pinus contortaDouglas) from a long-term experiment of stand density management through PCT, ex-pressed as relative growth. Lodgepole pine is a common tree in western North America,and the provincial tree for AB. The experiment was established in 1954 and located at theMacKey, on the eastern slopes of the Canadian Rocky Mountains, Alberta (lat. 53◦32.7′′ N;long. 115◦32.3′′ W). The original purpose of the experiment was to determine whether thePCT of lodgepole pine could improve merchantable volume and quality at a young ageand, in turn, shorten rotation and increase annual allowable cuts [15,16]. The experimentwas implemented on plot sizes of 0.08 ha each in block A, B, and C, and 0.30 ha in block D,measured for DBH at 1.3 m for all living trees, with PCT treatments that reduced initialstand densities ranging from 9762 to 11,887 stems per ha, to 4330, 2990, 1680, and 750 stemsper ha, on 22-year-old stands. The stand conditions were measured in 1954, 1960, 1969,1979, 1989, 1996, 2003, 2008, 2013, 2018, and 2023. However, only the data collected beforePlants 2025, 14, 982 5 of 182018 were used in the current analysis. The relationship between thinning intensity andcompensatory response is inconsistent; however, it appears that too severe thinning mayprevent stands from ever catching up or surpassing control plots. We will return to thispoint in the modeling section below (Section 3).Plants 2025, 14, x FOR PEER REVIEW 5 of 18 1969, 1979, 1989, 1996, 2003, 2008, 2013, 2018, and 2023. However, only the data collected before 2018 were used in the current analysis. The relationship between thinning intensity and compensatory response is inconsistent; however, it appears that too severe thinning may prevent stands from ever catching up or surpassing control plots. We will return to this point in the modeling section below (Section 3). Figure 1. Observed 50-year post-thinning stand dynamics from Shawnigan Lake trial represented in (a) stand gross volume over time, and (b) growth of stand gross volume, relative to unthinned control, over time under different treatments compared to no thinning, no fertilizer treatments (T0F0). Figure 2b shows the cumulated stand gross volume of red pine (Pinus resinosa Aiton) from a commercial thinning experiment, established in 1953 and located in the Petawawa Research Forest in central Canada, Chalk River, Ontario (lat. 46°00′0″ N; long. 77°26′0″ W) [16,17], expressed in relative growth. The spacing experiment was established on aban-doned farmland, with a factorial design of six initial spacings of 1.2, 1.5, 1.8, 2.1, 2.4, and 3.0 m randomly allocated to 10 stands. In 1962, two 0.08–0.101 ha permanent sampling plots were established for each spacing and measured periodically, and the DBH and H before each of the thinning entries were measured for these permanent sampling plots. DBH was measured for every tree in each sample plot, but H was only measured for a subsample of trees (19–76% of live stems). The commercial thinning was performed Figure 1. Observed 50-year post-thinning stand dyna ics fro Sha nigan Lake trial representedin (a) stand gros volu e over ti , ( ) r t f t r ss olu e, relative to unthi nedcontrol, over time under differ nt treatments compared to n thinn g, no fertilizer trea ments (T0F0).Figure 2b shows the cumulated stand gross volume of red pine (Pinus resinosaAiton) from a commercial thinning experiment, established in 1953 and located in thePetawawa Research Forest in central Canada, Chalk River, Ontario (lat. 46◦00′0′′ N;long. 77◦26′0′′ W) [16,17], expressed in relative growth. The spacing experiment was estab-lished on abandoned farmland, with a factorial design of six initial spacings of 1.2, 1.5, 1.8,2.1, 2.4, and 3.0 m randomly allocated to 10 stands. In 1962, two 0.08–0.101 ha permanentsampling plots were established for each spacing and measured periodically, and the DBHand H before each of the thinning entries were measured for these permanent samplingplots. DBH was measured for every tree in each sample plot, but H was only measuredfor a subsa ple of trees (19–76% of live stems). The commercial thinning was performedPlants 2025, 14, 982 6 of 18repeatedly in 1992, 2002, and 2013 to bring BA down to the same original residual BA targetvalue of 37.9 m2/ha.Plants 2025, 14, x FOR PEER REVIEW 6 of 18 repeatedly in 1992, 2002, and 2013 to bring BA down to the same original residual BA target value of 37.9 m2/ha. Figure 2. Diverse overcompensation patterns from four long-term thinning datasets across Can-ada. Values exceeding 100 (the control line) are overcompensation; (a) Lodgepole pine in Rocky Mountain foothills, Alberta; (b) red pine in Petawawa, Ontario; (c) balsam fir in Green River, New Brunswick; and (d) hardwood species in Flat Top, New Brunswick. Figure 2c shows the post-thinning stand dynamics of balsam fir from the Green River watershed, located in eastern Canada, in the extreme northwestern corner of New Bruns-wick (lat. 47°46′ N; long. 68°17′ W), expressed as relative growth. The area contains ap-proximately 100 000 ha of balsam fir-dominated forests, and the experiment was aimed at studying the effects of PCT and vegetation management on the growth, yield, and value [18–21]. The experiment included three nominal spacings of 4 ft (1.2 m), 6 ft (1.8 m), and 8 ft (2.4 m) compared to an unthinned control in six replicate blocks. Forty-eight permanent sample plots were measured every five years between thinning and 30 years post thin-ning. The study site was revisited in 2004 and measured at 43 years post thinning and with PSPs reevaluated in 2008 and 2013. Figure 2d shows the results from a spacing experiment at Flat Top Mountain near Pokiok, New Brunswick (lat. 45°54′04.7″ N; long. 67°16′39.6″ W), established in 1979 for determining the proper spacing to shorten the pulpwood rotation that meets hardwood kraft mill requirements, by the Valley Forest Products Ltd. (Langley, BC, Canada), Wood-lands Division of the Ste. Anne Nackawic Pulp Co. Ltd. (Nackawic, NB, Canada) [22]. The main hardwood species include beech (Fagus grandifolia Ehrh.), white birch (Betula pa-pyrifera March.), yellow birch (Betula alleghaniensis Britt.), red maple (Acer rubrum L.), sugar maple (Acer saccharum L.), and ironwood (Ostrya virginiana (Mill.) K. Koch). Three spac-ings, 5 × 5 ft (1.5 m), 7 × 7 ft (2.1 m), and 9 × 9 ft (2.7 m), were compared with an untreated control in 0.2-acre (0.08-ha) plots in a 4 × 4 Latin square design. Within each plot, a 1/10-acre (0.04-ha) measurement plot was established, and all trees were tagged for remeasure-ment in 1980, 1985, 1990, 1995, 2000, and 2009. Figure 2. iverse overco pensation patterns fro four long-ter thinning datasets across Canada.V lues exc eding 100 (the control line) are ove compensatio ; (a) Lodgep le pine in Rocky Mountainfoothills, Alberta; (b) red pine in Petawawa, Ontario; (c) balsam fir in Green River, New Brunswick;and (d) hardwood species in Flat Top, New Brunswick.Figure 2c sho s the post-thinning stand dynamics of balsam fir from the GreenRiver watershed, located in eastern Canada, in the extreme northwestern corner of NewBrunswick (lat. 47◦46′ N; long. 68◦17′ W), expressed as relative growth. The area containsa proximately 10 , 00 ha of balsam fir-dominated forests, and the experiment was aimedat studying the ffects of PCT and vegetation management on the growth, yield, andvalue [18–21]. Th experiment includ d three nominal spacings of 4 ft (1.2 m), 6 ft (1.8 m),and 8 ft (2.4 m) comp red to an unthinned cont ol in six replicate blocks. Forty-eightper anent sampl plots w re m asured every five y ars between thinning and 30 yearspost thinning. The study it was revisited in 2004 and measured at 43 years post thinningand with PSPs reevaluated in 2008 and 2013.Figure 2d sho s t r l i e t at Flat Top ountain nearPokiok, New Brunswick (lat. 45◦ ′ ′′ ◦ 6′39.6′′ W), established in 1979 fordetermining the pro er s i t ti n t at eets hardwoodkraft mil require e t , cts Ltd. (Langley, BC, Canada), W od-lands i isi t Ste. A ne Nackawic Pulp Co. Ltd. (Nackawic NB, C nada) [22].The main hardwood species includ beech (Fa us grandifolia Ehrh.), wh te birch (Betulapapyrifera March.), yellow birch (Betula alleghaniensis Britt.), red maple (Acer rubrum L.),sugar maple (Acer saccharum L.), a d ir nwood (Ostrya virginiana (Mill.) K. Koch). Threespacings, 5 × 5 ft (1.5 m), 7 × 7 ft (2.1 m), and 9 × 9 ft (2.7 m), were comp red with anuntreated control in 0.2-acre (0.08-ha) plots in a 4 × 4 Latin square design. Within eachplot, a 1/10-acre (0.04-ha) measurement plot was established, and all trees were tagged forremeasurement in 1980, 1985, 1990, 1995, 2000, and 2009.Plants 2025, 14, 982 7 of 182.2. Diverse PatternsA common feature of the above five empirical datasets is that overcompensationoccurred at certain periods after the thinning treatments. However, the dynamics ofovercompensation are diverse in terms of timing and amplitude.In the Douglas-fir case (Figure 1), the slow speed of CG resulted in a gradual tran-sition in status from under compensation right after the thinning operations, to exactcompensation, and eventually to overcompensation (up to ~130%). With increasing thin-ning intensity, the timing to reaching exact compensation can be significantly delayed(ranging from 15 to over 45 years). On the other hand, increased fertilization level canreduce the period required to reach exact compensation.In the case of lodgepole pine (Figure 2a), it took more than 40 years to reach exactcompensation, and some plots remained in an under-compensation state without reachingtransition status. An interesting point is that two plots with same target stand density of2990 stems per ha displayed different patterns: one reached overcompensation and theother did not. This suggests that individual difference in response to thinning might behighly variable.For balsam fir (Figure 2c), a faster transition from under compensation to exact andovercompensation was observed, but then compensation declined to a lower level (stillhigher than that of unthinned sites), followed by maintenance at that level over time.The 6 ft spacing treatment generated the highest overcompensation of ~150% at 10 yearsafter thinning treatments.For the hardwood species (Figure 2d), a pattern similar to balsam fir appeared; how-ever, it is still uncertain as to whether this lower level of overcompensation will be main-tained, which will be confirmed when the most recent remeasurment data become available.The 1.5 m spacing treatment generated the highest overcompensation at 15 years afterinitial treatments.For the case of red pine (Figure 2b), it appears that overcompensation can be observedat the spacings of 1.2, 1.8, and 2.1 m, but not at the larger spacings of 2.1, 2.4, and 3.0 m.2.3. Possible Influencing FactorsFrom a perspective of forestry practices, identification of possible influencing factorsfor diverse overcompensation patterns is important for assisting managerial decision mak-ing. The following is a preliminary summary from the above datasets (see Figures 1 and 2):• Tree species: The lifespans for different species might be the first notable factor. Specieswith a long lifespan tend to require longer periods to reach the CG transition status,such as with Douglas-fir, which has a longevity of over 800 years. Species with a shortlongevity (e.g., 150-year lifespan for balsam fir and hardwoods) might be expected toreach overcompensation in a shorter period.• Site quality: Plots with a poor site quality (e.g., Douglas-fir experimental site with apoor site index) tend to require long periods to reach overcompensation. On the otherhand, plots with a high site quality tend to have a fast CG status transition, like withthe balsam fir experimental site, which has a very high site index. Compared with thesame species and Acadian Forest region in Maine, US, but which has a low site quality,complete overcompensation was not observed 32 years after thinning operations [23].• Physical environmental conditions: Sites with poor climatic conditions could delaytree growth and thus require long periods to reach overcompensation, such as withlodgepole pine growing at Rocky foothills, where the winter tends to be longer thanthat for Douglas-fir growing near the Pacific coast, with warm winters.The stand structure, the mixing regime, and the species’ light demands are potentialinfluencing factors for stand dynamics. Therefore, they could also be considered potentialPlants 2025, 14, 982 8 of 18influencing factors for diverse overcompensation patterns. But since they are primarilydriven by species composition, site quality, and physical environmental conditions, theyare embedded in the aforementioned factors and not separately addressed further.Given the clear yet highly variable evidence for stand response to thinning, there is aclear need for a general theory that can account for the aforementioned phenomenon ofcompensatory dynamics, i.e., simply reducing stand density is not sufficient to generateovercompensation. We expect that the inherent differences in life history [24] and resourceacquisition are required for such a unified theory. In the next section, we present such atheory based on life-history.3. A Theoretical Proof of ConceptDespite the fact that the concept of compensatory growth can explain overcompen-sation in the long-term and post-thinning stand dynamics well, and thus reconcile thecontroversial observations from both short- and long-term silviculture datasets, it is criticalto identify the underlying mechanisms that lead to overcompensation. We explored a pos-sible mechanism from the life-history theory (LHT), the most cited ecological theory in theliterature [25], which is a framework in evolutionary biology that elucidates how naturalselection influences patterns of growth, reproduction, and survival across an organism’slifespan. The LHT is based on the premise that organisms generally face trade-offs duringtheir life, arising from various causes, including energetic, physiological, developmental,environmental, and genetic constraints, which determine the patterns of survivorship andreproduction we observe in nature [26]. When applied to trees, LHT can help explain howdifferent species adapt their growth and reproductive strategies to their environments.LHT is applicable to organisms with either short or long lifespans. Compensatorygrowth (CG) is a special case of growth response, triggered by some sudden and catas-trophic events such as thinning. The CG process in short-lifespan species can happen fast orvery fast, and experiments that generate CG are usually easy to implement, with outcomeswhich are consistent for a single status (either under, exact, or overcompensation) at thetime of measurement (see [12] for a summary of examples). However, it is generally difficultto elucidate how the process plays out over time because the short time scale can obfuscategrowth dynamics. For long-living species such as trees, despite the technical difficulties ofworking with such slow-growing organisms, these species are excellent model species fordocumenting the CG process over time, providing a fuller picture for investigating the CGprocess because their ontogeny unfolds slowly, and so it is easy to characterize the processfor these organisms.3.1. The TAG ModelRoitberg et al. [27] described a simple, theory-driven simulation model called TreeAdaptive Growth (TAG), which explores the thinning-driven stand dynamics based on theprinciple of LHT for individual trees, in the sense that individual trees allocate mobilizedenergy to (1) vegetative growth, leading to morphological structure build-up, (2) seedproduction for reproduction, reflecting the evolutionary fitness to be maximized, (3) main-tenance of the morphological structure that is often assumed as default, and (4) storage inreserve for meeting future allocations that is important for multi-growing-season species.The trade-off facing an individual tree is how to optimize the allocation to these processesto achieve maximized lifetime fitness under various environmental conditions.The key to implementing this LHT-based approach is state-dependence, which isdifferentiated from the conventional age-dependent growth prediction [11] in the sensethat tree growth is determined by yearly changes in internal and external/environmentalconditions/states, such as the internal states of tree size (S), age (A), and the energyPlants 2025, 14, 982 9 of 18reserve (R), and the external states of the available level of nutrients or competitive ability(ψ), and fluctuations in weather variables (W). This approach assumes that changing annualgrowth is an adaptive response of trees to their environmental conditions and also impliesthat simulated tree growth curves may not be as smooth as predicted by age-dependentrelationships.The TAG model employs the following four basic assumptions:1. Innate tree growth follows a sigmoidal pattern [28];2. Tree growth strategies have evolved to maximize lifetime reproductive success ac-cording to the principles of evolutionary ecology [29];3. Individual trees will acquire resources and modify their investment in growth in astate-dependent manner, according to (S), (R), and (A);4. There are no genetic constraints on the above, i.e., it is assumed that selectiononphenotypic variation translates directly into selection on heritable variationin the population [30].The model uses a modified logistic submodel to characterize the potential growthincrement for a tree of size (s) as follows:γ = (ρ− 1)(1− (s/smax)θ(e−ζy) (2)where γ is energy harvesting, ρ is the intrinsic growth rate, Smax is the maximum massthat an individual tree can realize, θ is a shape parameter, and ζ is a senescence term thatdescribes decreasing energy harvesting with age. For any given year, a resource allocationstrategy is determined according to the combination of the current three state values (s,r, a) of individual trees. In each year, a focal tree will mobilize reserves for growth andreproduction, at a rate of alpha (α).α = (r− Rmin)/(1+ e−(w1s+w2a)) (3)where Rmin is the minimum reserve value for a tree of size (s), and w values are weightconstants for the state variables. The α is expected to increase with size, reserves, and ageup to some maximum that is not to exceed its critical reserve state value (Rcrit), which is theminimal level required to maintain metabolic function. Then, the proportion of mobilizedreserves that go to reproduction versus growth is calculated as (β):β(s, r, a) ={1− e−(w3s+w4a) if r > π0 otherwise(4)where π is the start-up cost for initiating reproduction and the w values are weight con-stants for size and age states. Two effects of size are assumed: (i) small trees have smallreserves such that r will rarely exceed π, meeting the β = 0 condition, and (ii) small treesare inefficient at producing seeds; thus, the size weight (w3) is set low. Furthermore, oldertrees should strongly bias their mobilized reserves toward reproduction because future dis-counting will offset small gains from growth, particularly if older trees are large; therefore,a small value for (w4) is employed.Finally, the allocation of harvested energy to growth versus reserves is defined as (φ):ϕ =[1/(ϕs + ϕr)]ϕs if r′ < s′Rmax and r′ < s′Rmin1− [(r− α+ γ− sRmax)/γ] if r′ < s′Rmax1− {[(s + γ)Rmin − r′]/γ} if r′ < s′Rmin(5)Plants 2025, 14, 982 10 of 18where ϕs = 1− (s− smin)/s, ϕr = 1− [r− (Rmin)]r, s′ = s+ γ[1/(ϕs + ϕr)]ϕs + α(1− β)ξ,and r′ = r + γ[1/(ϕs + ϕr)]ϕs − α are potential updated values for size and reserves,respectively, and ξ is the efficiency in mobilizing reserves to the structure.The trade-off between growth and reproduction is based on the satisfaction of threeconditions: (i) sufficient reserves remain after metabolic costs; (ii) reproduction start-upcost is paid; and (iii) allocation to reserves does not exceed the maximum reserve levelafter adjusting for γ. Otherwise, φ is adjusted to meet those minimum and maximumreserve levels, respectively. The rationale for the φ decision is that as trees increase insize, their growth rate decelerates; thus, there is little gain from further investment ingrowth vs. the buildup of reserves for reproduction [31]. The above three state-dependentstrategies can then be summarized as follows: (i) investment in growth when that leads toaccelerated returns, but only when reserves are sufficiently high to avoid starvation (i.e.,metabolic reserves fall below critical level), and (ii) investment in reproduction when treesare large and growth is constrained, when it is safe to do so because of the greater return oninvestment for the latter. Also, note that future discounting means that future reproductivereturns from current investment in growth will be constrained for older and larger trees.The LHT logic that provides a mechanism of explaining overcompensation is that treesin thinned stands acquire more energy due to reduced competition and that they invest agreater proportion of this greater acquisition than control trees because they will not riskdeath through starvation during bad years. Control trees are forced to invest conservativelyin growth, whereas thinned trees are no longer constrained by LH parameters.Detailed implementation methods are documented in [27]; below, we summarize themain results from the model simulations in the next section.3.2. Overcompensation PredictionPredictable overcompensation is represented by the two series of simulations inthinned versus unthinned stands. In each series, 10 replications (plots), with 100 trees ineach plot, are performed for a hypothetical plantation stand, and the mean stand grossvolume is plotted as a representative. In the unthinned stand, trees are allowed to freelygrow until the end of simulation (200 years in this case). For the thinned stand, a pre-commercial thinning (PCT) is conducted at year 10 with 30% of the smallest trees removed.The basic pattern of stand dynamics is shown in Figure 3.Plants 2025, 14, x FOR PEER REVIEW 11 of 18 Figure 3. Mean stand volume over time from 10 stochastically simulated TAG stands that initially comprised 100 trees each that were either subjected to pre-commercial thinning of 30% at year 10 (red line) or left unthinned (black line). Simulations were run using C++. Growth of individual trees was based upon stochastically determined weather conditions, relative competitive value of individual trees, and investment by those trees in growth. See [27] for details. This result supports the notion that overcompensation should be a common outcome in post-thinning forest stands when the stand growth over time is sigmoid shaped. The exact growth curve could vary under different environmental conditions such as compe-tition pressures [27]. This theoretical proof should also be generally applicable to other plant and animal species. The TAG model allowed theoretical exploration of how different thinning operations (a combination of timing, intensity, and rules of thinning) could affect post-thinning stand dynamics. These theoretical explorative investigations indicated that (1) overcompensa-tion in post-thinning stand dynamics is an expected outcome according to LHT, rather than being a statistical outlier, and (2) diverse patterns of overcompensation could be ex-pected, depending on how the thinning operations are implemented. Therefore, to take advantage of overcompensation, forest managers and practitioners need to calibrate the model to their own area under management, and the optimal thinning strategy needs to be determined based on tree species, geographical regions, and physical site conditions. With the above theoretical demonstration of expected overcompensation in post-thinning stand dynamics, overcompensation should be predictable through assembling available growth relationships. In the next section, we describe a model as an example that employed published growth relationships from natural stands. 4. Growth Relationship-Based Overcompensation Prediction As mentioned previously, CG is a special case of growth response, triggered by a disturbance that causes biomass reduction. Therefore, we examined the premise that if overcompensation is an expected outcome in post-thinning stand dynamics, it should be predictable from the quantitative growth relationships obtained from natural stands. Li et al. [32] described one such model called Tree Compensatory Growth (TreeCG), and the underlying mechanism is that a forest will redistribute the freed resources such as space and nutrients from dead trees to the remaining survived trees to reach a full utilization of the available resources. 4.1. The TreeCG Model Different from the conventional increment of stand volume over time directly, the focus of TreeCG is to take into account the state of the mean resources available for Figure 3. ea st l i l t t s t t i itia lycomprised 10 tre s each that were ither subjected to pre-com ercial thinning of 30% at year 10 (redline) or left unthinned (black line). Simulations were run using C++. Growth of individual trees wasbased upon stochastically determined weather conditions, relative competitive value of individualtrees, and investment by those trees in growth. See [27] for details.Plants 2025, 14, 982 11 of 18This result supports the notion that overcompensation should be a common outcome inpost-thinning forest stands when the stand growth over time is sigmoid shaped. The exactgrowth curve could vary under different environmental conditions such as competitionpressures [27]. This theoretical proof should also be generally applicable to other plant andanimal species.The TAG model allowed theoretical exploration of how different thinning operations(a combination of timing, intensity, and rules of thinning) could affect post-thinning standdynamics. These theoretical explorative investigations indicated that (1) overcompensationin post-thinning stand dynamics is an expected outcome according to LHT, rather thanbeing a statistical outlier, and (2) diverse patterns of overcompensation could be expected,depending on how the thinning operations are implemented. Therefore, to take advantageof overcompensation, forest managers and practitioners need to calibrate the model to theirown area under management, and the optimal thinning strategy needs to be determinedbased on tree species, geographical regions, and physical site conditions.With the above theoretical demonstration of expected overcompensation in post-thinning stand dynamics, overcompensation should be predictable through assemblingavailable growth relationships. In the next section, we describe a model as an example thatemployed published growth relationships from natural stands.4. Growth Relationship-Based Overcompensation PredictionAs mentioned previously, CG is a special case of growth response, triggered by adisturbance that causes biomass reduction. Therefore, we examined the premise that ifovercompensation is an expected outcome in post-thinning stand dynamics, it should bepredictable from the quantitative growth relationships obtained from natural stands. Liet al. [32] described one such model called Tree Compensatory Growth (TreeCG), and theunderlying mechanism is that a forest will redistribute the freed resources such as spaceand nutrients from dead trees to the remaining survived trees to reach a full utilization ofthe available resources.4.1. The TreeCG ModelDifferent from the conventional increment of stand volume over time directly, the focusof TreeCG is to take into account the state of the mean resources available for individualtrees, which changes with the changing stand density, and simulates the annual incrementsof DBH and H that facilitate the calculation of gross and merchantable volumes, as wellas the estimation of various forest products and values [14]. In other words, TreeCG goesa step deeper, looking into the published growth relationships and assembling them in anon-traditional way.TreeCG simulates how major mortalities affect stand density for yearly time steps.In addition to the natural mortality of trees each year, stand density is also influenced bythinning operations. Correspondingly, increased annual growth increments of DBH andH can usually be displayed following the thinning year, as released growth that will bedamped over time. Therefore, the total annual growth increments can be split into the sumof normal growth (without thinning) and released growth (after thinning). As a result, thekey relationships required for simulating the dynamic annual increments are the normalgrowth increments and the released growth increments. If overcompensation took place innature, one should be able to predict its occurrence through the growth relationships fromnatural stands.As common sense tells us that trees generally grow taller in high-density stands thanin low-density stands, and thinning is a common forestry operational tool for reducingstand density to achieve the goals of stand density management, the relationship betweenPlants 2025, 14, 982 12 of 18stand density and H is essential for investigating the thinning effect on stand dynamics.Such information could generally be derived from the variable-density yield tables, andthe one published [33] for natural stands of lodgepole pine in Alberta, Canada, was used indeveloping the TreeCG model:log10 H = 1.0688− 0.00276672× Age + 0.717927 log10 Age−0.0000371084× Stems− 0.132622 log10 Stems(6)where Stems is the number of stems with a DBH larger than 0.6 inches of outside barkper acre. By converting the units in the formula from the British system into metricsystem, we were able to calculate the H of each tree at a given stand density and hence thecorresponding DBH through the softwood equation [34] with species-specific parametersfor lodgepole pine in Alberta:DBH ={b1/b2 × [1− exp(−b1 × b2 × (H − 1.3)]}1/b3 (7)As such, the annual increment of DBH, DBHInc, can be calculated as below:DBHInct = DBHt+1 − DBHt (8)where the subscript t and t + 1 indicate the measured variables at the year t and t + 1,respectively; a response surface of how the DBHInc decreases with increasing tree age andstand density was constructed (Figure 4), which is consistent with the common observationsof faster growth of trees in young stands.Plants 2025, 14, x FOR PEER REVIEW 13 of 18 Figure 4. Response surface of annual increments of DBH, DBHInc, at different stand ages and stand densities based on variable density yield table [33] (redraw from [32]). Applying the surface smoothing techniques, the DBHInc at any given age and den-sity without thinning can be estimated as below: )ln())(ln()))(ln(ln())(ln()ln()ln())(ln())(ln()ln()ln(22322yxjyxiyhyxfyexdycxbaz+++++++++=(9) where x is tree age (year), y is stand density (stems/ha), z is DBHInc (cm), and a, b, c, d, e, f, g, h, i, and j are parameters. For tree growth with thinning at the year of thinning, the altered tree DBHIncactual can be decomposed as the sum of DBHInc of stand density before thinning, DBHIncnatural, and the released growth, DBHIncnatural-new, of stand density after thinning: ( ) ( ) ( )acturl natural natural newDBHInc cm DBHInc cm DBHInc cm−= + (10) where the subscripts natural and new indicate the stand density before and after the thin-ning operation. To calculate DBHIncactual (cm), we need to have both DBHIncnatural (cm) and DBHIncnatural-new (cm). DBHIncnatural-new (cm) is the released growth of DBH induced by the thinning operation. To simplify the DBHIncnatural-new (cm) calculation, DBHIncnatural (cm) and DBHIncnew (cm) are presented in a relative sense (with regard to an assumed maximal stand density of 20,000 stems/ha for lodgepole pine), and in this case, as RDBHIncnatural (%) and RDBHIncnew (%), respectively: 20,000(%) ( ) / ( ) 100natural naturalDBHInc DBHInc cm DBHInc cm= × (11) 20,000(%) ( ) / ( ) 100new newDBHInc DBHInc cm DBHInc cm= × (12) where ( ) ( ) [1 (%)]actual natural natural newDBHInc cm DBHInc cm RDBHInc −= × + , and (%) (%)(%) 100(%)new naturalnatural newnaturalRDBHInc RDBHIncRDBHIncRDBHInc−−= × . These equations allowed the estimation of DBHIncactual (cm) directly from the stand densities before and after thinning. The same surface smoothing Equation (9) is applied, Figure 4. Response surface of annual increments of DBH, DBHInc, at different stand ages and standdensities based on variable density yield table [33] (redraw from [32]).pplying the surface smo thing techniques, the DBHInc at any given age and densitywithout thinning ca be estimated as below:z = a + b ln(x) + c ln(y) + d(ln(x))2 + e(ln(y))2 + f ln(x) ln(y) + g(ln(x))3+h(ln(y))3 + i ln(x)(ln(y))2 + j(ln(x))2 ln(y)(9)where x is tree age (year), y is stand density (stems/ha), z is DBHInc (cm), and a, b, c, d, e,f, g, h, i, and j are parameters.Plants 2025, 14, 982 13 of 18For tree growth with thinning at the year of thinning, the altered tree DBHIncactual canbe decomposed as the sum of DBHInc of stand density before thinning, DBHIncnatural, andthe released growth, DBHIncnatural-new, of stand density after thinning:DBHIncacturl(cm) = DBHIncnatural(cm) + DBHIncnatural−new(cm) (10)where the subscripts natural and new indicate the stand density before and after the thin-ning operation. To calculate DBHIncactual (cm), we need to have both DBHIncnatural (cm)and DBHIncnatural-new (cm). DBHIncnatural-new (cm) is the released growth of DBH in-duced by the thinning operation. To simplify the DBHIncnatural-new (cm) calculation,DBHIncnatural (cm) and DBHIncnew (cm) are presented in a relative sense (with regardto an assumed maximal stand density of 20,000 stems/ha for lodgepole pine), and in thiscase, as RDBHIncnatural (%) and RDBHIncnew (%), respectively:DBHIncnatural(%) = DBHIncnatural(cm)/DBHInc20,000(cm)× 100 (11)DBHIncnew(%) = DBHIncnew(cm)/DBHInc20,000(cm)× 100 (12)where DBHIncactual(cm) = DBHIncnatural(cm) × [1 + RDBHIncnatural−new(%)], andRDBHIncnatural−new(%) =RDBHIncnew(%)−RDBHIncnatural(%)RDBHIncnatural(%)× 100.These equations allowed the estimation of DBHIncactual (cm) directly from the standdensities before and after thinning. The same surface smoothing Equation (9) is ap-plied, where x is tree age, y is stand density, and z is DBHIncactual (cm). In other words,RDBHIncnatural-new (%) can be obtained by calculating two stand densities, before andafter thinning.The response surface of H after the released growth, corresponding to DBHIncactual (cm),can then be obtained using the provincial equation for lodgepole pine [35]:H = 1.3+ 35.7547/{1+ exp[3.8234− 1.2824 ln(DBH)]} (13)The above adjustments allow for a much simplified calculation of the annual in-crements of DBH and H, and easy implementation in the TreeCG model. See [32] forparameters and other details.4.2. Model ValidationIf the way of assembling growth relationships is reasonable, the logical consequencesof the model simulations should reflect the observations from the field experiments, i.e.,the model will be able to be validated against empirical observations. A qualitative modelvalidation was conducted accordingly through comparing the simulated forest growthpatterns to a long-term silvicultural experiment, the Shawnigan Lake PCT and fertilizationdataset described in the above empirical evidence. The focus of the comparison is not thematching of absolute values, because the relationships employed in the TreeCG simulationwere not specifically from the Douglas-fir forests.The initial stand density was set as 7500 stems/ha, and the simulation results wereevaluated for the total gain over a planning horizon of 100 years, which accounted for thesum of the immediate gain from the thinning operation and the gain from the remainingtrees at the year 100. Thinning operations were implemented at two different stand ages, of30 (representing an early partial mortality) and 60 (representing a late partial mortality)years old. A control without thinning was also implemented. The partial mortality wasrepresented by the intensity of thinning, which was set as a reduction of 33% (as a lightmortality) and 66% (as a heavy mortality) of the total number of trees. If this premise werePlants 2025, 14, 982 14 of 18true, the simulated CG capacity could differ under early and late partial mortality, as wellas light and heavy mortality.The model output includes the stand conditions (DBH and H of each living tree) atinitialization and every 5-year interval until 100 years, and harvested wood at the yearof thinning. The simulation results are presented in relative growth terms to reflect thepatterns in post-thinning stand dynamics, as in Figure 5.Plants 2025, 14, x FOR PEER REVIEW 14 of 18 where x is tree age, y is stand density, and z is DBHIncactual (cm). In other words, RDBHInc-natural-new (%) can be obtained by calculating two stand densities, before and after thinning. The response surface of H after the released growth, corresponding to DBHIncactual (cm), can then be obtained using the provincial equation for lodgepole pine [35]: 1.3 35.7547 /{1 exp[3.8234 1.2824ln( )]}H DBH= + + − (13) The above adjustments allow for a much simplified calculation of the annual incre-ments of DBH and H, and easy implementation in the TreeCG model. See [32] for param-eters and other details. 4.2. Model Validation If the way of assembling growth relationships is reasonable, the logical consequences of the model simulations should reflect the observations from the field experiments, i.e., the model will be able to be validated against empirical observations. A qualitative model validation was conducted accordingly through comparing the simulated forest growth patterns to a long-term silvicultural experiment, the Shawnigan Lake PCT and fertiliza-tion dataset described in the above empirical evidence. The focus of the comparison is not the matching of absolute values, because the relationships employed in the TreeCG sim-ulation were not specifically from the Douglas-fir forests. The initial stand density was set as 7500 stems/ha, and the simulation results were evaluated for the total gain over a planning horizon of 100 years, which accounted for the sum of the immediate gain from the thinning operation and the gain from the remaining trees at the year 100. Thinning operations were implemented at two different stand ages, of 30 (representing an early partial mortality) and 60 (representing a late partial mortality) years old. A control without thinning was also implemented. The partial mortality was represented by the intensity of thinning, which was set as a reduction of 33% (as a light mortality) and 66% (as a heavy mortality) of the total number of trees. If this premise were true, the simulated CG capacity could differ under early and late partial mortality, as well as light and heavy mortality. The model output includes the stand conditions (DBH and H of each living tree) at initialization and every 5-year interval until 100 years, and harvested wood at the year of thinning. The simulation results are presented in relative growth terms to reflect the pat-terns in post-thinning stand dynamics, as in Figure 5. Figure 5. TreeCG model validation: (a) simulated and (b) observed relative growth in stand gross volume under different pre-commercial thinning (PCT) treatments. Figure 5a shows the gross stand volume after experiencing an early thinning at year 30 under three levels of intensity (i.e., 0, 33%, and 66% removal for the initial stand density of 3950 stems/ha, indicated by PCT00, PCT33, and PCT66, respectively), in which partial mortality first reduced stand gross volume and then the stand gross volume gradually Figure 5. Tree odel validation: (a) simulated and (b) observed relative growth in stand grossvolume under different pre-c i l t i i ( ) t t t .Figure 5a s t r eriencing an early thi ning at year30 under t ree l ls , 66 re oval for the initial stand densityof 3950 ste s/ , i t 00, T33, and PCT66, respectively), in which partialortalit fir t r t e t e stand gro s volume graduallycatches up with the gross volume of the control stand, and eventually exceeds the controland results in overcompensation. The heavier thinning (PCT66) resulted in higher over-compensation than that of the lighter thinning (PCT33). The trends displayed in this seriesof simulations appeared consistent with those observed in the measurements from theShawnigan Lake trial (Figure 5b). This indicates that our simulation results are validatedqualitatively by the observations from this long-term PCT and fertilization experiment, andthe overcompensation is a predictable phenomenon.5. DiscussionForests are invaluable resources for human society in the commercial (productivitysuch as biomass and wood products) and associated non-commercial (ecosystem servicessuch as for carbon, biodiversity, habitat, hydrology, and air quality) senses. As such, akey focus of forest management is ensuring the sustainable use and conservation of forestresources [36]. Here, we evaluated the potential for enhancing overcompensation viapre-commercial thinning, an approach that is supported by empirical studies and modelingexercises. Further, we showed that such overcompensation can vary dramatically amongtree species based upon inherent growth rates and site characteristics. Regardless, over-compensation can have a positive impact in reaching the goals of SFM, through providinga new way of enhancing forest productivity by manipulating thinning regimes [11].5.1. Modeling Approach for Predicting OvercompensationPredicting overcompensation could be based on analytical results using empiricaldata. However, the time required to obtain field experimental results could be very long,usually well beyond the average professional career. Therefore, research on predictingovercompensation can only be based on available historical datasets (e.g., Figures 1 and 2).As pointed out in [37], “what makes the science of forestry necessary are the lim-itations of the traditional empirical approach and recent modeling efforts”. Modelingis a complementary tool of speeding up research for predicting overcompensation. WePlants 2025, 14, 982 15 of 18demonstrated two different approaches that are based on two different mechanisms underthe CG conceptual framework. In the TAG model, a top-down approach based on LHTwas employed to simulate how individual trees allocate available energy to growth, repro-duction, maintenance, and reserves to maximize their inclusive fitness for reproductivesuccess. In the TreeCG model, a bottom-up approach based on actual growth relationshipsobserved from natural stands was used to simulate the consequences of forest redistributingfreed resources like space and nutrients from dead trees to survived trees to maximizethe utilization of available resources on site. Both models indicated that similar patternsof post-thinning stand dynamics could be expected, including the transition from undercompensation to exact compensation and to the overcompensation of a full CG process.However, the TreeCG model explains how overcompensation is generated, whereas theTAG model explains why.The TAG and TreeCG models were both developed using the concept of CG that wasintroduced to explain the observed overcompensation phenomenon from the ShawniganLake trial that was unable to be explained by conventional thinning theory. The predic-tion from the two models successfully confirmed the CG concept and the possibility ofovercompensation occurring in post-thinning stand dynamics and thus further verifiedthe reconciliation of overcompensation with conventional thinning theory. In other words,the CG concept can expand existing thinning theory to explain both short- and long-termobservations and thus resolve the silviculture puzzle.To make the model practical in operation, in addition to model validation with fieldobservations like TreeCG, methods of calibration to given species/forest types, geograph-ical regions, and site conditions must be developed, as have also been described in theTreeCG paper [32].5.2. Pros and Cons of OvercompensationThinning is the practice of selectively removing trees from a forest stand to reducecompetition for resources such as light, water, and nutrients. Some key benefits have beenidentified through enhanced growth rates due to increased access to the essential resourcesfor surviving trees [38], improved tree quality through allowing surviving trees to developlarger crowns and stronger trunks [39], increased stand economic value by promoting thegrowth of high-value species and improving overall health [40], enhanced carbon storagein biomass [10] and soil [41], a reduced risk of pests and diseases spread in overcrowdedconditions, and enhanced wildlife habitats through the creation of a more diverse and openhabitat for supporting a wider range of species.In addition, overcompensation has been widely observed in many species of plantsand animals, and different industries have benefitted from this phenomenon tremendouslyin two aspects: enhanced productivity and reduced costs for production, typically in agri-culture (e.g., cotton, beans, and fruit vegetables) and farm animal production or husbandry(e.g., livestock and fisheries) (see a summary from [12]). In forestry, however, overcompen-sation was not considered as the norm and was often ignored as an “out-ot-the-ordinary”phenomenon due to it being incongruent with the conventional understanding of thethinning effect. The introduction of the CG concept reconciled overcompensation withconventional thinning theory and allowed the development of a model for predicting theoccurrence of overcompensation.Despite the fact that all the mechanisms of overcompensation have still not been fullyuncovered, the confirmation of the phenomenon of overcompensation in post-thinningstand dynamics appears to be good news for reaching the goal of enhanced productivityand biomass carbon pooling through sustainable forest management; however, it may alterthe temporal pattern of fuel accumulation.Plants 2025, 14, 982 16 of 186. Conclusions and RecommendationsThe take-home messages from this systematic investigation are as follows: (1) five long-term PCT datasets confirmed that overcompensation is common in Canadian forests; (2)the conceptual framework of CG can reconcile different observations from both short- andlong-term PCT experiments; (3) the TAG model theoretically proved that overcompensationis an expected phenomenon in long-term post-thinning stand dynamics; and (4) the TreeCGmodel confirmed that overcompensation can be predicted from growth relationships fromnatural stands.As a result, further refinement of the models for regional major tree species or foresttypes could enable forest managers and researchers to explore the optimal thinning strate-gies and optimal plantation densities for areas under management, and support decisionsin forestry practice, with a view to reaching the goals of maximizing forest productivityand utilization while maintaining resource sustainability for the next generations.Author Contributions: Conceptualization, C.L., B.R., S.H., and R.L.; methodology, C.L., B.R., S.H.,and R.L; software, C.L. and B.R.; validation C.L. and S.H.; formal analysis, C.L. and B.R.; investi-gation, C.L., B.R., S.H., and R.L.; writing—original draft preparation, C.L.; writing—review andediting, C.L., B.R., S.H., and R.L.; visualization, C.L., B.R., and R.L.; supervision, C.L.; project ad-ministration, C.L.; funding acquisition, C.L. All authors have read and agreed to the publishedversion of the manuscript.Funding: This research was financially supported by Natural Resources Canada—Canadian ForestService’s Developing Sustainable Fibre Solutions Research Program.Data Availability Statement: Permission to use the empirical datasets in this study was obtainedfrom the data providers; further inquiries can be directed to the corresponding authors.Acknowledgments: This study benefited from extensive discussions with the late Hugh Barclay, whopointed out the Shawnigan Lake dataset for the initial investigation. The authors thank the datasupport provided by Cosmin Filipescu, Shared Baral, Dick Adam, Derek Sattler, Jim Steward, NelsonThiffault, Michael Hoepting, and James Farrell of the Canadian Forest Service, in addition to WenliXu and Dea Cameron of the BC Ministry of Forests, Lands, Natural Resource Operations and RuralDevelopment. The authors also thank Marc Mangel for helpful discussions on compensatory growth.Conflicts of Interest: The authors declare no conflicts of interest.References1. Johnstone, W.D. Thinning lodgepole pine. In Lodgepole Pine: The Species and Its Management. Symposium Proceedings; Baumgartner,D.M., Krebill, R.G., Arnott, J.T., Weetman, G.F., Eds.; Washington State University: Pullman, WA, USA, 1985; pp. 253–262.2. Zeide, B. Thinning and growth: A full turnaround. J. Forest. 2002, 99, 20–25. [CrossRef]3. Reukema, D.L. Guidelines for precommercial thinning of Douglas-fir. In General Technical Report PNW-GTR-030; Department ofAgriculture, Forest Service, Pacific Northwest Research Station: Portland, OR, USA, 1975; 10p.4. Bose, A.K.; Weiskittel, A.; Kuehne, C.; Wagner, R.G.; Turnblom, E.; Burkhart, H.E. Tree-level growth and survival followingcommercial thinning of four major softwood species in North America. For. Ecol. Manag. 2018, 427, 355–364. [CrossRef]5. Steele, R.W. Growth After Precommercial Thinning in Two Stands of Douglas-Fir; Forest Service, U.S. Department of Agriculture:Washington, DC, USA, 1955; pp. 1–4.6. Warrack, G.C. Successive Thinnings in a Natural Stand of Douglas-Fir Over a Fifty Year Period; Ministry of Forests: Victoria, BC,Canada, 1979; p. 87.7. Schenstrom, S.R. Thinning Experiments in Douglas Fir Forests of British Columbia (Unpubl. M.S); Ministry of Forests Library: Victoria,BC, Canada, 1931; p. 67.8. Mitchell, K. Dynamics and simulated yield of Douglas-fir. For. Sci. Monogr. 1975, 17, 39.9. Pitt, D.G.; Lanteigne, L. Long-term outcome of precommercial thinning in northwestern New Brunswick: Growth and yield ofbalsam fir and red spruce. Can. J. For. Res. 2008, 38, 592–610. [CrossRef]10. Li, C.; Huang, S.; Barclay, H.; Filipescu, C.N. Estimation of compensatory growth of coastal Douglas-fir following pre-commercialthinning across a site quality gradient. For. Ecol. Manag. 2018, 429, 308–316. [CrossRef]Plants 2025, 14, 982 17 of 1811. Li, C.; Barclay, H.; Roitberg, B.; Lalonde, R. Forest productivity enhancement and compensatory growth: A review and synthesis.Front. Plant Sci. 2020, 11, 575211. [CrossRef]12. Li, C.; Barclay, H.; Roitberg, B.; Lalonde, R. Ecology and prediction of compensatory growth: From theory to application inforestry. Front. Plant Sci. 2021, 12, 655417. [CrossRef]13. Crown, M.; Brett, C.P. (Eds.) Fertilization and Thinning Effect on a Douglas-Fir Ecosystem at Shawnigan Lake: An Establishment Report;Information Report BC-X-110; Environment Canada, Canadian Forest Service, Pacific Forest Research Centre: Victoria, BC,Canada, 1975.14. Li, C.; Barclay, H.; Huang, S.; Sidders, D. Wood fibre value simulation model: A new tool to assist measuring changes in forestlandscapes by evaluating forest inventory. Landsc. Ecol. 2017, 32, 1517–1530. [CrossRef]15. Stewart, J.D.; Jones, T.N.; Noble, R.C. Long-Term Lodgepole Pine Silviculture Trials in Alberta: History and Current Results; NaturalResources Canada, Canadian Forest Services, Northwest Forestry Center: Edmonton, AB, Canada; Foothills Model Forest: Hinton,AB, Canada, 2006.16. Li, C.; Barclay, H.; Huang, S.; Roitberg, B.; Lalonde, R.; Thiffault, N. Detecting compensatory growth in silviculture trials:Empirical evidence from three case studies across Canada. Front. Plant Sci. 2022, 13, 907508. [CrossRef]17. Thiffault, N.; Hoepting, M.K.; Fera, J.; Lussier, J.M.; Larocque, G.R. Managing plantation density through initial spacing andcommercial thinning: Yield results from a 60-year-old red pine spacing trial experiment. Can. J. For. Res. 2021, 51, 181–189.[CrossRef]18. Baskerville, G.L. Establishment Report—Cleaning and Thinning Young Fir, 1959; Project M-443-59. Internal Report; Department ofNorthern Affairs and National Resources, Forestry Branch, Maritimes District: Fredericton, NB, Canada, 1959; 28p.19. Baskerville, G.L. Establishment Report—Cleaning and Thinning Young Fir, 1960; Project M-443-59. Internal Report; Department ofNorthern Affairs and National Resources, Forestry Branch, Maritimes District: Fredericton, NB, Canada, 1960; 5p.20. Akerley, B.J. Establishment Report—Cleaning and Thinning Young Fir, 1961; Project M-443-59. Internal Report; Department ofNorthern Affairs and National Resources, Forestry Branch, Maritimes District: Fredericton, NB, Canada, 1961; 29p.21. Pitt, D.G. Valuing long-term research—The Green River Legacy. For. Chron. 2013, 89, 419–422. [CrossRef]22. Lees, J.C. The Growth, Branchiness, and Resprouting of Sapling Northern Hardwoods After Spacing; Information Report M-X-193E;Canadian Forest Service—Maritimes Region, Natural Resources Canada: Fredericton, NB, Canada, 1995; 15p.23. Weiskittel, A.R.; Kenefic, L.S.; Li, R.; Brissette, J. Stand structure and composition 32 years after precommercial thinning trestmentsin a mixed northern conifer stand in central Maine. North J. Appl. For. 2011, 28, 92–96. [CrossRef]24. Stearns, S.C. Life history evolution: Successes, limitations, and prospects. Naturwiss 2000, 87, 476–486. [CrossRef] [PubMed]25. Marque, P.Q.; Allen, A.P.; Brown, J.H.; Dunne, J.A.; Enquist, B.J.; Gillooly, J.F.; Gowaty, P.A.; Greem, J.L.; Harte, J.; Hubbell, S.P.;et al. On theory in ecology. BioScience 2014, 64, 701–710. [CrossRef]26. Mangel, M.; Munch, S.B. A life-history perspective on short- and long-term consequences of compensatory growth. Am. Nat.2005, 166, E155–E176. [CrossRef] [PubMed]27. Roitberg, B.; Li, C.; Lalonde, R. Tree adaptive growth (TAG) model: A life-history theory-based analytical model for post thinningforest stand dynamics. Front. Plant Sci. 2024, 15, 1344883. [CrossRef]28. Weiner, J.; Thomas, S.C. The nature of tree growth and the “Age-related decline in forest productivity”. Oikos 2001, 94, 374–376.[CrossRef]29. Davies, N.B.; Krebs, J.R. An Introduction To Behavioural Ecology; Wiley-Blackwell Scientific Publications: Cambridge, UK, 1993.30. Grafen, A. Behavioural Ecology: An Evolutionary Approach, 2nd ed.; Krebs, J.R., Davies, N.B., Eds.; Blackwell Scientific Publications:Oxford, UK, 1984; pp. 62–84.31. Lalonde, R.; Roitberg, B. On the evolution of masting behaviour in trees:Predation or weather? Am. Nat. 1992, 139, 1293–1304.[CrossRef]32. Li, C.; Barclay, H.; Huang, S.; Roitberg, B.; Lalonde, R.; Xu, W.; Chen, Y. Modelling the stand dynamics after a thinning inducedpartial mortality: A compensatory growth perspective. Front. Plant Sci. 2022, 13, 1044637. [CrossRef]33. Johnstone, W.D. Variable-Density Yield Tables for Natural Stands of Lodgepole Pine in Alberta; Department of Fisheries and theEnvironment, Canadian Forestry Service: Ottawa, ON, Canada, 1976; p. 20.34. Huang, S. Individual Tree Diameter Prediction Models from Tree Height; Technical Report Pub. No. T/606; Forest Management Branch,Alberta Agriculture and Forestry: Edmonton, AB, Canada, 2016; 59p.35. Huang, S.; Yang, Y.; Aitkin, D. Population and Plot-Specific Individual Tree Height-Diameter Models for Major Alberta Tree Species;Technical Report Pub. No. T/600; Forestry and Emergency Response Division, Alberta Ministry of Environment and SustainableResource Development: Edmonton, AB, Canada, 2013; 81p.36. US Forest Service. A Historical Perspective. Available online: https://www.fs.usda.gov/forestmanagement/aboutus/histperspective.shtml (accessed on 15 December 2024).37. Zeide, B. The Science of Forestry. J. Sustain. For. 2008, 27, 345–473. [CrossRef]Plants 2025, 14, 982 18 of 1838. Cartner, T. Thinning Pine for Profit, Health, and Wildlife. Timberland Advisors 2018. Available online: https://www.forestryandland.com/post/thinning-pine-for-profit-health-and-wildlife (accessed on 15 December 2024).39. Cunningham, K.; Walkingstick, T.; Guffey, C. Improve Your Pine Stand by Thinning. University of Arkansas, CooperativeExtension Service. FSA5001-PD-10-04RV. Available online: https://www.uaex.uada.edu (accessed on 15 December 2024).40. Albert, R. The Benefits of Forest Thinning. Albert Land Management 2021. Available online: https://www.albertlandmanagement.com/2021/11/17/forest-thinning/ (accessed on 15 December 2024).41. Zhang, H.; Liu, S.; Yu, J.; Li, J.; Shangguan, Z.; Deng, L. Thinning increases forest ecosystem carbon stocks. For. Ecol. Manag. 2024,555, 121702.Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individualauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury topeople or property resulting from any ideas, methods, instructions or products referred to in the content.
Article
eng
Reviewed
Vancouver : University of British Columbia Library
Multidisciplinary Digital Publishing Institute
CC BY 4.0
Faculty
Researcher
compensatory growth
forest productivity
growth and yield
overcompensation
pre-commercial thinning
TAG
TreeCG
thinning theory
Predictable Overcompensation in Post-Thinning Stand Dynamics of Canadian Forests : A Synthesis
Text