Density Effects on Giant Sequoia (Sequoiadendron giganteum) Growth Through 22 Years: Implications for Restoration and Plantation Management

Abstract

vary distinctly between species and growth parameters, providing specific insights for predictions of competitive effects and corresponding management implications. We, therefore, focus on measuring the nature of the development of the density-growth relationships over time, an approach possible in this case because of the frequency and precision of measurements at regular intervals during stand development. Methods Study Site Blodgett Forest Research Station (BFRS) is located on the western slope of the Sierra Nevada mountain range in California (38°52 N; 120°40 W). The study is within BFRS at an elevation of 1,320 m. The climate is Mediterranean with dry, warm summers (14–17° C) and mild winters (0–9° C). Annual precipitation averages 166 cm, most of it coming from rainfall during fall and spring months, while snowfall ( 35% of total precipitation) typically occurs between December and March. Before fire suppression (ca. 1890), the median point fire interval in the area was 9–15 years (Stephens and Collins 2004). The soil developed from andesitic lahar parent material. Soils are productive, with heights of mature codominant trees at BFRS typically reaching 31 m in 50 years. Vegetation at BFRS is dominated by a mixed conifer forest type, composed of variable proportions of five coniferous and one hardwood tree species (Tappeiner 1980). Giant sequoia is not among the five native conifer species present. BFRS is, however, approximately 16 km south of the northernmost native grove. The topography, soils, and climate of the study area are similar to the conditions found in native groves, although total precipitation at BFRS tends to be greater than in the southern Sierra Nevada where the majority of native groves occur. As within native groves, giant sequoia grows well in the study area, outgrowing all associated species through at least year 7 in planted canopy openings (Peracca and O’Hara 2008, York et al. 2004, 2011). In plantation settings throughout the Sierra Nevada, giant sequoias outgrow other conifer species through 3 decades after planting where soil productivity is high (Kitzmiller and Lunak 2012). Where it has been planted in Europe, it also typically outgrows other conifers (Knigge 1992). Study Design and Analysis for Height and Stem Diameter Seedlings were planted in 1989 at nine levels of density ranging from 2.1to 6.1-m hexagonal spacing between seedlings. To ensure that a tree was growing at each planting location, seedlings were initially double-planted, with the less vigorous seedling of the pair removed after 2 years. Treatments were applied across 0.08to 0.2-ha plots, depending on planting density (i.e., wider spacings required larger plots). Competing vegetation was removed periodically to control for any variation in resource availability not due to gradients in giant sequoia density (e.g., West and Osler 1995). Treatments were installed with a randomized block design (Figure 1), with each treatment randomly assigned once within three adjacent blocks (i.e., n 3 plot replications for each level of density). Measurements of height and dbh (1.37 m) for all trees following the 4th, 10th, 16th, and 22nd growing seasons are reported. For analysis, trees along the edges of the treated areas (i.e., “guard trees”) were removed to avoid interactions between treatments. Trees that had a dead or missing neighbor on any side after 22 years were also removed from the analysis (32 planting spots had dead or missing trees). The final dataset was made up of 2,303 trees. Results through the 7th year were presented by Heald and Barrett (1999). Here, detailed analysis of density effects is done for the most recent measurement (year 22), and all of the diameter and height measurements from 6-year intervals are used to reconstruct the trend in density-related competitive effects over time. Measurements are analyzed with the plot as the experimental unit and density as a continuous variable (n 3 replicates for each of 9 density levels 27 total sample units). The first step in the analysis of height and diameter growth was to fit the 22nd-year measurements with an appropriate equation that best described the relationship between density and tree size. We then used the selected 22nd-year equation to fit data from previous measurement years to reconstruct how the density effect developed. This approach has the drawback of assuming that the density-tree size relationship is similar over time because separate fits are not selected for each measurement period. It has the advantage, however, of providing the same slope parameter over time so that the trend of the density-size relationship can be quantified. Tracking the change in slope allowed us to profile the changing nature of competitive effects on the given growth parameter over time. For each level of planting density, the amount of horizontal growing space partitioned equally between each tree (m) was used as the predictor variable. Growing space was calculated by dividing the total space of each treatment area by the number of trees planted in the area with hexagonal spacing. The boundaries of the growing space for each treatment were defined to extend out beyond the stems of the perimeter trees, halfway to adjacent neighbor trees. Hence, growing space is here defined simply as the amount of horizontal space partitioned to each seedling at the time of planting and is related to linear distance between trees and inversely to tree density. From this point on, we use the term growing space to indicate stem density, but note that growing space is inversely related to density. The treatment gradient ranged from a minimum growing space of 3.7 m/stem (2,702 stems/ha) to a maximum of 28.4 m/stem (353 stems/ha). We used the 22nd-year measurements to select the best model from a set of bona fide candidate models (sensu Johnson and Omland 2004) to describe the effect of growing space on average individual tree growth in terms of height and stem diameter. We then used the selected model to fit measurements from previous years, comparing the models’ slope parameters and corresponding 95%-confidence intervals between years to track the change in competitive effects over time. Candidate models had to be simple (i.e., Figure 1. Overhead view of randomized block design from the giant sequoia density study at Blodgett Forest, CA. WEST. J. APPL. FOR. 28(1) 2013 31 few parameters) quantifications of plausible growing space-size relationships that each represented separate biological mechanisms at work. The candidate set included four relationships. The first was a simple linear equation, reflecting an additive relationship between growing space and tree size (i.e., more space equals more growth without any diminishing or increasing returns): Tree size a b*growing space where a is the y-intercept and b is linear coefficient (i.e., the slope). The management application of such a relationship is that individual tree growth is maximized at the widest spacing. The second model was a log-linear fit, reflecting a multiplicative effect of growing space on tree size: Tree size a b(log*growing space) A log-linear fit occurs when tree size increases monotonically across the range of growing space considered. Growth is maximized at the widest spacing, but unlike with a linear fit, the returns in terms of tree size diminish with the widest spacings. The third model was a quadratic fit, reflecting an eventual negative effect of growing space on tree size: Tree size a b*growing space c*growing space where c is the quadratic coefficient. A quadratic fit occurs when there is an eventual negative effect of increased growing space on tree size. This has been known to occur when, for example, trees grow taller as a response to near-neighbor shading (Gilbert et al. 2001). The final model was a Michaelis–Menten fit, which is an asymptotic curve reflecting a saturating effect: Tree size d*growing space / e growing space where d is the asymptote of the curve (the maximum tree size predicted) and e is the growing space at which tree size is half of maximum. This relationship implies a maximum growing space where further increases cause neither greater nor less in terms of tree size. It is worth noting that these mathematical relationships, when expressed in graphical form and when used for making inferences to management, are constricted by the limits of the data. For example, if a quadratic form were to be chosen, we obviously do not expect tree size to trend to zero. Nor would we expect a linear relationship to continue indefinitely. While differences between these curves can be subtle when correlations are variable, the high precision of this particular data set allowed us to distinguish between them. Akaike’s information criteria weights (AICw), with a small sample correction (Sugiura 1978), were used to rank and choose the best models. AIC weights are likelihood transformations of raw AIC values, and are, therefore, more meaningful than raw values when comparing how well each model performed. An AICw of 0.80, for example, implies an 80% likelihood of that model being the best model when compared with the other candidate models and given the data (Burnham and Anderson 2002). While raw AIC values are typically interpreted as the lowest value being the best model, AIC weights are the opposite. We also report the evidence ratio, which is the ratio between the best model’s AICw and each other model. The evidence ratio essentially measures how much better the best model was. Measurements and Analysis for Branch Diameter, Branch Density, and Stem Volume Branch diameter and branch density data were collected following the 16th year only (timed to coincide with a logical age for conducting artificial pruning). The branch closest to 1.37-m stem height on the west side of each tree was measured with digital calipers where the branch attached to the stem (while avoiding the swollen branch collar). To measure br