Discussion
Point-pattern analyses represent a snapshot view into the processes that actively shape the distribution of trees over time. Analyses of many sites in the Midwestern and Oklahoma datasets initially reflected a random distribution, but closer examination provided insight into the factors that have shaped them in the past and will further shape them in the future. The point-pattern analyses of redcedar in the Midwest indicate varied point-processes influence the structure of stands at different stages of stand development. Sites representing the earliest stage of redcedar encroachment, comprised of seedlings and saplings, had inhomogeneous point-patterns. This irregular distribution of trees is most likely the result of small-scale environmental heterogeneity in resource patches and the non-uniform dispersal of seeds by birds (Nathanet al. 2000; Escribano-Avila et al. 2012; Fogarty et al. 2022) and, perhaps, mammals (Horncastle et al. 2004; Horncastle et al. 2005). Consequently, the distribution of redcedars in the early stages of encroachment depend largely on proximity to source populations, the dispersal habits of frugivores, and the microsite conditions in the encroached area. The phenomenon of clumping of individuals that could result from frugivorous birds using a predominant perch was not detected. Conversely, several sites comprised of small trees showed signs of regular spacing between individuals. Negative density dependence among seedlings of the same species has been attributed to proximity to larger trees due to shading and the increase in density of predators (Marchand et al. 2020; Barry and Schnitzer 2021). Alternatively, this may be a relic of the scale of investigation being too large to properly evaluate the relationships between neighboring redcedar seedlings or saplings. For example, if the sampling window were smaller and centered around a homogeneous patch of redcedars, the findings may have changed and resulted in observation of a random distribution or clumping.
The signal of density-dependent thinning is detectable in relatively young- to mature-redcedar stands. Redcedar stand density increases rapidly during the first ~10 years of establishment and is then followed by a period of increasing height and cover (Fogartyet al. 2021). In the Midwestern dataset, the highest intensities of redcedar are found in young stands averaging < 6 m in height. All sites in the Midwestern dataset over an average of 6 m in height had a defined signal of overdispersion in the K-function envelopes or DCLF tests weighted by tree diameter or both.
The analysis of the unmarked Midwestern dataset comprised of living and dead redcedars found clumping in > 25% of sites. Removal of dead trees from this dataset resulted in the signal of clustering being completely erased. Similarly, the analysis of point-patterns representing all living and dead Quercus and redcedar trees in the Oklahoma dataset found indications of clustering in about half the 13 study sites. However, after excluding dead trees, the signal of clumping was largely dampened. Both these examples indicate non-random mortality of trees consistent with density-dependent thinning. If the likelihood of death of each tree is independent of neighboring trees, then mortality events should occur randomly. In an independent point-pattern, random deletions of a few points should not change the overall characteristics of the pattern (Wiegand et al. 2013; Baddeley et al. 2015). However, in the case of the Midwestern and Oklahoma data, relatively few mortality events shifted the pattern from a clumped distribution to a random distribution. This is a strong indication the trees are not independent and the processes leading to their mortality is related to neighboring trees.
Many of the Midwestern and Oklahoma sites with larger trees showed signs of overdispersion when pairs of trees were evaluated for dependence while considering their diameter at breast height. Regular spacing between large trees is a common phenomenon and is often the result of partitioning canopy space for light (Gendreau-Berthiaume et al.2016). This pattern has been documented to occur more frequently between conspecifics and closely related trees (Chen et al. 2018). Further evidence of density-dependent effects playing out in larger redcedar stands come from the segregation tests in the Midwestern and Oklahoma datasets. The segregation tests alone do not suggest a mechanism that promotes the separation between redcedar, Quercus , and other deciduous trees (Dixon 2002). However, when considering the segregation between species in combination with the separation in space between large and small trees, one can assume competition for light, space, and other resources likely drive the observed patterns. Limitation of understory species in redcedar stands is well documented, with proposed mechanisms including litter accumulation, shading, and negative plant-soil feedbacks (Gehring and Bragg 1992; Van Els et al. 2010; Bennion and Ward 2022).
The widespread clearing of the eastern deciduous forest (including populations of redcedar) in the Midwest and the flatland tracts of the Cross Timbers of Oklahoma indicate that even the oldest of these stands are all relatively young (Keddy and Drummond 1996; Therrell and Stahle 1998). The interactions between redcedars and long-lived neighbors such as Quercus stellata are likely to continue to change over time (Hoff et al. 2018; Joshi et al. 2019). Understanding the ongoing processes that influence the structure of these stands is important to planning appropriate management for the future. Future studies that further clarify interactions between redcedar and dominant trees in forested portions of its encroaching range will enable timely and appropriate action.