Power Laws in Cone Production of Longleaf Pine across Its Native Range in the United States

Abstract

Longleaf pine (Pinus palustris Mill.) forests in the southeastern United States are considered endangered ecosystems, because of their dramatic decrease in area since European colonization and poor rates of recovery related to episodic natural regeneration. Sporadic seed production constrains restoration efforts and complicates sustainable management of this species. Previous studies of other tree species found invariant scaling properties in seed output. Here, using long-term monitoring data for cone production at seven sites across the native range of longleaf pine, we tested the possible presence of two types of power laws. Findings indicate that (i) the frequency distribution of cone production at seven sites, from 1958 to 2014, follows power law relationships with high level of significance; (ii) although there is no general trend in the dynamics of scaling exponents among all sites, there are dynamics of scaling exponents at each site, with sudden changes in scaling exponents generally corresponding to the years of higher or lower cone production; and (iii) Taylor"s power laws explain cone production at different locations, but the scaling exponents vary among these. Results from this computational approach provide new insight into the irregular cone production of longleaf pine at spatial and temporal scales. Integrated ecosystem monitoring will be necessary to more fully understand future changes in cone production.

The Percentage of Trees Bearing Cones as a Predictor for Annual Longleaf Pine Cone Production

“…Longleaf pine cone crops have entered their seventh decade of observation, beginning in Escambia County, Alabama in 1958 (Connor et al, 2014) and currently monitored by the United States Forest Service (hereafter USFS) and collaborators at 11 locations throughout the species' range (Brockway, 2019). Data from these stands have supported numerous studies that have examined annual cone production as it relates to climate (Pederson et al, 1999;Guo et al, 2016;Leduc et al, 2016), fire (Haymes and Fox, 2012), stand dynamics (Loudermilk et al, 2016), basal ring growth (Patterson andKnapp, 2016, 2018), and its inherit complexity as a masting species (Chen et al, 2016(Chen et al, , 2017(Chen et al, , 2018(Chen et al, , 2020. The robustness of the multi-decadal dataset lies in the repeated measures of cone counts, which are outlined each year in the annual USFS cone report (e.g., Brockway, 2019).…”

Temporal patterns of pollen shedding for longleaf pine (Pinus palustris) at the Escambia Experimental Forest in Alabama, USA

“…This scaling relationship has been expanded from population density and widely observed in ecology (e.g., Cohen et al, 2013;Taylor, 2019), such as pollination success in a shrub species at Mexico's Yucatan Peninsula (Arceo-Gómez et al, 2016). Our recent studies indicated that some plants followed Taylor's law in their growth traits (Chen et al, 2017;Chen, 2020;Chen & Chen, 2020), but it was not tested in pollen shedding. In this study, Taylor's power-law can be expressed in the following equation:…”

“…Where Variance stands for the variance of pollen shedding time (TPPS or TAPD) at different years, Mean as the average time, r is the slope of the fitting line, and log(a) is the intercept. With the time increase of one year from 1958 to 2013, the average and variance of pollen shedding time at different periods (such as from 1958 to 1959, 1960… and 2013, respectively) was estimated (Chen et al, 2017). r was estimated from the correlation between log (mean) and log (variance).…”

Variation of Fruit Size and Its Frequency Distribution in Chinese Torreya

“…After sorting the fruit volumes (or lengths or widths) from the smallest to the largest for each tree, the linear relationship between the log(average) and log(variance) of fruit volume (or the length or width of fruits) was estimated for each tree by correlation with the increase of fruit quantity from 2, 3 to 100. Any deviations may indicate disturbance or regime shift (Chen et al, 2017). The same method was also used to study fruit length and width.…”