Ecological and Physiological Implications of Vascular Structure and Function in Oaks

Ecological and physiological implications of vascular structure and function in oaks

A DISSERTATION SUBMITTED TO THE FACULTY OF THE UNIVERSITY OF MINNESOTA BY

Jennifer Teshera-Levye

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

Advisor: Dr. Jeannine Cavender-Bares

December 2019 ©2019. Jennifer Teshera-Levye “Drivers of habitat partitioning among three Quercus species along a hydrologic gradient” accepted for publication November 15, 2019 in Tree Physiology. DOI: 10.1093/treep- hys/tpz112 Acknowledgements

I am grateful to the support, advice, guidence, and feedback I recieved from countless people over the years. My advisor, Dr. Jeannine Cavender-Bares, has been tremendously supportive of all my ideas and goals. My committee, Dr. Arindam Banarjee, Dr. Rebecca Montgomery, and Dr. Daniel Stanton, as well as former members Dr. Peter Reich and Dr. Emma Goldberg, have helped shape the direction of the work through their questions and insights. My first chapter, “Drivers of habitat partitioning among three Quercus species along a hydrologic gradient” was written with several co-authors: Brianna Miles, Catherine Love- lock, Valery Terwilliger, and Dr. Cavender-Bares. Their feedback and suggestions were invaluable during the submission and revision process for that manuscript. The data used in that chapter was collected by a group lead by Dr. Cavender-Bares at the Smithsonian Environmental Research Center from 2001-2003. I also need to thank the Smithsonian En- vironmental Research Center for logistical support, William Brinley and Nathan Phillips for technical assistance in construction of the sapflow sensors and Geoffrey Parker for providing access to the 50-ha plot and for other support. We thank Marilyn Fogel for allowing us to use her former facilities the Geophysical Lab at the Carnegie Institution in Washington, D.C. for isotopic analyses, Lauren Urgenson, George Raspberry (posthumously), Roxane Bowden, Kati Dawson, Andrea Krystan, and Patrick Neale for technical and other assistance. The water table and soil moisture data provided in the appendix were gathered as part of an NSF funded project to Sean McMahon (NSF Grant 1137366) and is curated by Rutuja Chitra-Tarak. The data collected for my second and third chapter was made possible by the greenhouse common garden projects maintained by Dr. Matthew Kaproth and Dr. Beth Fallon, along with a team of undergraduate students. Lab work was assisted by several students, most critically Philip Johnson, Hilary Major, and Alejandra Villasenõr. Cory Teshera-Levye contributed code that was used in the LeafGrapher software. My labmates in the Cavender-Bares lab over the years have provided countless suggestions and improvements to my work, and this dissertation would not have been possible without them. Finally, my family and friends offered support in myriad ways. My parents, Marc and Judy Levye, instilled in me from an early age the value of perseverance and dilligence. Cory Teshera-Levye is my partner in life, the universe, and everything.

i Dedication

“Life needs things to live”1 and graduate students need things to keep them sane. This work dedicated to the people who helped me stay connected, grounded, and who let me escape into fantasy worlds when the real one was overwhelming. Also dedicated to Rosemary, Bernie, and Bean Sprout, for keeping me warm through many cold winters.

1Jaﬀe, T. (2016) ”Critical Role Ep. 63: The Echo Tree.” www.youtube.com/watch?v=1cUx2oLUGqI

ii Contents

List of Figures iv

List of Tables vi

Introduction 1

1 Drivers of habitat partitioning among three Quercus species along a hydrologic gradient 3

2 LeafGrapher: A software tool for network analysis of leaf venation 28

3 Network-derived traits help demonstrate resource-allocation trade-oﬀs in oaks 44

Bibliography 59

Appendix 72

iii List of Figures

1.1 Broad and local distributions of Q. alba,Q. falcata, and Q. palustris . . . . 14 1.2 Weather conditions at SERC ...... 15 1.3 Average daily sap ﬂux patterns ...... 16 1.4 Water-use traits in mature trees ...... 20 1.5 Hydraulic conductance in mature trees and seedlings ...... 21 1.6 Growth rates in mature tree species with elevation ...... 22 1.7 Physiological traits measured in seedlings ...... 27

2.1 An illustration of network terminology ...... 31 2.2 Illustration of graph spectra...... 32 2.3 Estimating vessel diameter ...... 34 2.4 Example leaf venations ...... 38 2.5 Four core graph metrics ...... 39 2.6 Eﬃciency versus hydraulic conductance ...... 40 2.7 Fault tolerance comparison between ginkgo and oak ...... 41 2.8 Eigenvalues of the graph Laplacian ...... 42

3.1 Theoretical “return on investment” ...... 46 3.2 Correlations between graph traits and leaf functional traits...... 50 3.3 Principle component analysis of venation and functional traits ...... 51 3.4 Hydraulic performance return on investment in vasculature ...... 52 3.5 Resistance to damage return on investment in vasculature ...... 52 3.6 Mean trait values in leaves diﬀerentiated by venation performance . . . . . 53 3.7 Correlations among venation traits and climate variables ...... 54 3.8 Graph traits vary with mean species aridity index ...... 55 3.9 Fault tolerence in red versus white deciduous oaks ...... 56 S1 Appendix: Hypothesis schematic ...... 74 S2 Appendix: Soil types at SERC ...... 75 S3 Appendix: Water table depth at SERC ...... 76 S4 Appendix: Soil water content at SERC ...... 77 S5 Appendix: Within-tree sap velocity comparison ...... 78

iv S6 Appendix: Sap ﬂow sensor comparisons ...... 79 S7 Appendix: Sap ﬂux velocity ...... 80 S8 Appendix: predawn and midday water potential ...... 81

v List of Tables

1.1 Soil moisture in mature tree and common garden sites ...... 6 1.2 Soil charactistics at SERC by elevation ...... 7 1.3 Mean climatic conditions of species ranges ...... 13 1.4 Trait means in mature trees ...... 17 1.5 Trait means in common garden seedlings ...... 18

3.1 Specimens included in analysis ...... 47 3.2 Major graph traits, with units and notes. * = unitless ...... 49 S1 Appendix: Mature tree sampling ...... 72 S2 Appendix: Weather conditions at SERC ...... 72 S3 Appendix: Species distributions by elevation ...... 73 S4 Appendix: Tree wood characteristics ...... 73

vi Introduction

Water plays a critical role in the survival of all life, and access to sufficient water to support physiological needs has been a primary driver in the evolution of plant form and function since they moved onto land. Among other innovations, plants developed a rigid vascular system that offers both mechanical support and transport of water and nutrients (Tyree 2003). Indeed, plant vasculature has been described as the “backbone” supporting the productivity of terrestrial ecosystems (Brodribb 2009). This system is also vulnerable: function can be lost due to air embolism introduced through drought or freezing, as well as through physical damage or blockages introduced by pests or pathogens (Rockwell et al. 2014, Pratt et al. 2008). Despite its importance, there is still much that is unknown about the physiological ecology of the plant vascular system. In this dissertation I investigate connections between plant hydraulics and ecological function at at two scales. First, I consider the implications of differing performance in whole-plant water transport traits for the habitat partitioning of several closely related tree species along a hydrologic gradient. Second, I consider the vascular architecture of leaves by demonstrating a novel methodology for quantifying venation structure and by applying this methodology to consider resource-allocation trade-offs. In this work, I primarily use the oaks (genus Quercus in family Fagaceae) to consider these questions. The oaks are diverse and cosmopolitan; they are a dominant clade in North American forests, and are found across the Americas, Europe, and Asia (Cavender-Bares 2016). The genus includes both evergreen and deciduous species, and can be found in a wide range of habitats. In the United States, the oaks are economically valuable, providing over $22 billion per year in ecosystem services, but are also increasingly vulnerable to climate change and pathogens (Cavender-Bares et al. 2019). The first chapter, “Drivers of habitat partitioning among three Quercus species along a hydrologic gradient”, I and my co-authors considered how differences in water-use traits might permit three oak species to co-exist in a small geographic area (the Big Tree Plot at the Smithsonian Environmental Research Center). We compare the performance of both mature trees and and seedlings of these oak species when grown under different hydrologic conditions. In addition to differences in physiological and functional traits, we consider the ability of the climate of broad geographic ranges to predict local habitat partitioning. For my second and third chapters, I shift from a consideration of whole-plant hydraulics

1 to leaf hydraulics. Leaves are a critical bottleneck in the overall water transport system of plants (Sack and Frole 2006), but our understanding of how the structure of leaf vascular systems influences plant function remains incomplete (Roth-Nebelsick et al. 2001). Here, I attempt to apply tools developed from the mathematical field of network theory to better understand vascular architecture. I present “LeafGrapher,” a software tool developed to represent a leaf vein system abstractly as a graph, and then calculate a set of metrics drawn from the network theory literature (Barthélemy 2011). I illustrate the use of this software tool with a sample data set capturing the diversity of plant vascular and show a tentative assoication of one of these metrics with empirically measured leaf hydraulic conductance. I follow this with an analysis of the leaf venation architecture of 16 oak species, testing for associations between known plant functional traits and my new network-informed vascular traits, as well as the potential influence of climate on these venation traits. A central theme running through these chapters is an attempt to understand the trade- offs plants make in allocating resources. Given a limited set of available resources, plants must “choose” between using these resources for growth, productivity, reproduction, pro- tection, or any number of other functions (Obeso 2002, Chapin III 1989, Coley et al. 1985). Plants may opt for a strategy involving rapid growth and high productivity, or one involving slow growth and long-living tissues (Wright et al. 2004). Even within the vascular tissue, there is a potential trade-off between efficient water transport and safety from embolism (Sperry et al. 2008a). I consider trade-off schemes on a number of scales: how plants may trade faster growth in ideal conditions for more consistent performance under variable ones, or how they may invest in vascular tissue instead of photosynthetic tissue to be more resistant to damage. It is my aim in these three chapters to offer both additional data and potentially novel frameworks for considering resource trade-offs in vascular plants. At the scale of whole trees and plant communities, we found that Quercus palustris has specialized to quickly take advantage of water when it is readily available, exhibiting rapid growth where other trees decline by sacrificing some ability to resist droughts or grow in drier sites. At the scale of individual leaves, I found that leaves with traits that situate them on the “slow” end of the leaf economic spectrum (Wright et al. 2004), like longer leaf lifespan and lower specific leaf area, are better able to gain a performance benefit from an increased investment in vascular tissue. It is my hope that these empirical observations and the underlying tools and theory enable future work that continues to uncover the ecophysiology of plant vasculature.

2 Chapter 1

Drivers of habitat partitioning among three Quercus species along a hydrologic gradient

Introduction

Understanding the mechanisms that permit the coexistence of multiple closely related species in a community has been fundamental to ecological research for over a century (Volterra 1926, Connell 1961, May and MacArthur 1972). Local-scale abiotic heterogeneity in factors like water, nutrients, light, or physical space affects the biotic community com- position because performance differences among species provide competitive advantages in different parts of the gradient (Hutchinson 1959, Silvertown et al. 1999, Silvertown 2004). Variation in a small number of abiotic factors can allow a large number of closely related species to coexist within a landscape (Cavender-Bares et al. 2004a). Temporal variation or intermittent stressors can provide an additional “axis” on which species can partition local environments (Levins 1966, 1969, May and MacArthur 1972, Tilman 1994). The broad question of coexistence thus narrows: how do similar species exploit temporal and spatial variability to coexist sympatrically? Trait-based approaches (e.g. Shipley et al. 2017) have focused on the ways that physiological differences between species affect community assembly processes or predict habitat preferences. Wei et al. (2017) identified several key traits in Salicaceae species that showed variation along a hydraulic gradient associated with fitness that predicted species distribution. The traits that support local diversity may operate at different timescales: plants can adjust solute concentration or stomatal opening within minutes and alter wood vascular growth or phenology along growing seasons or lifetimes (Munns 2002, Chenu et al. 2008). The magnitude of these responses may be very sensitive to changes in water availability, or may be coordinated to allow plants to maintain a relatively constant water status despite

3 environmental changes (Meinzer et al. 2016), and different combinations of traits may affect similar fitness responses in an environment (Reich et al. 2003). Biogeographic history may offer a macro-scale explanation for how species sort into local niches; species whose lineages stem from different climate regimes may sort into different local habitats where their ranges overlap (Cavender-Bares et al. 2016, Ackerly 2003). For example, Sedio et al. (2013) found that a plant’s microhabitat on Barro Colorado Island, Panama, is associated with the climate of the region where it originated. This pattern is also seen in communities which sort along elevation gradients, reflecting the water availability and temperatures of climates of origin (Harrison et al. 2010). Close relatives, which may be ecologically similar due to shared ancestry (Webb et al. 2002, Wiens and Graham 2005) are often expected to exhibit functional differences in resource use and/or stress tolerance that promote niche differentiation (Donoghue 2008). Re- search has shown that niche differentiation can occur directly through competition to meet similar resource requirements, or indirectly via density-dependent mortality (Violle et al. 2011, Gilbert and Webb 2007, Parker et al. 2015). Experimental tests in plants (e.g. Cahill et al. 2008) are equivocal, however, and there are many instances of plant communities without this pattern (e.g. Kluge and Kessler 2011), especially in cases where changing environments or stressors can drive similar species to cluster (Burns and Strauss 2011, Mayfield and Levine 2010). In this study, we examined whether the local distribution patterns of three oak species showed evidence for differences in physiological and growth responses to gradients of water availability and stress that promote habitat (and thus niche) partitioning. We further considered these factors in relation to their biogeographic history and phylogenetic relatedness.Quercus alba L., Quercus falcata Michx., and Quercus palustris Münchh. are three forest canopy species at the Smithsonian Ecological Research Center near coastal Maryland. Red (Q. falcata and Q. palustris, Quercus section Lobatae) and white (Q. alba, Quercus section Quercus) oaks have been shown to have a long history of parallel and sympatric diversification in eastern North America (Hipp et al. 2018), and the two lineages therefore coexist across the continent (Cavender-Bares et al. 2018). While these three species coexist broadly, they have been qualitatively described as being found in contrasting hydrologic niches (Gleason and Cronquist 1991, le Hardy de Beaulieu and Lamant 2006). We hypothesized that the apparent habitat partitioning along a hydrologic gradient shown among these three species could be demonstrated quantitatively. If large-scale patterns predicted local- scale partitioning, we hypothesized that partitioning can be explained by some combination of the following factors (Figure S1):

1. Climatic envelopes of the full ranges of each species, especially considering moisture, are predictive of the distribution of species across the local elevation gradient in our study site

4 2. Species more able to tolerate water stress induced by temporal variation (i.e. a drought versus wet year) will occupy a more varied environmental range than less tolerant species

3. Trade-oﬀs in growth and physiological (e.g. transpiration and water use) performance will emerge among species across the gradient, consistent with an interpretation of contrasting adaptive advantages at either end of the elevation gradient.

We further expected to see more habitat separation between Q. falcata and Q. palustris than between either of those species and Q. alba, as both are red oaks and thus more closely related to each other than either is to Q. alba (Cavender-Bares et al. 2004b), though with only three species we could not meaningfully quantify phylogenetic niche partitioning in this study system. We focused on a set of traits, centered around sap flow measurements in mature trees and gas exchange measurements in seedlings, to understand the trait differences that might explain differences in distribution driven by water availability. In mature trees heat-dissipation measurement of xylem sap flow offers an approximation of whole-tree transpiration (Granier 1987, Ladefoged 1960, Cohen et al. 1981, Hogg et al. 1997, Catovsky et al. 2002); although concerns exist that it may fail to account for variable tree anatomy (Clearwater et al. 1999, Lu et al. 2000, Burgess et al. 2001, Delzon et al. 2004), this method continues to provide one of the best approaches for capturing water fluxes in mature trees (Poyatos et al. 2016). Overall, the selected traits indicate water use and hydraulic performance, growth and productivity, and stress response. Associating the variability in particular traits - even small differences - with both the local and broader ranges and phylogenetic relationships of these three species can help us to subsequently understand how spatially and temporally varied habitats allow close relatives to coexist.

Methods

Study System

Site Description

Our study sites for mature trees were located in a continuous tract of forest within the Smithsonian Environmental Research Center (SERC), located in Edgewater, Maryland, along the Rhode River. Our study site was an approximately 50 ha tract (the “Big Tree Plot”, BTP) within the 1100 ha main forest situated around the SERC photobiology tower (38.89 N, 76.56 W) and included an elevation gradient ranging from sea level to 22m, shown in Figure 1.1a. Mean slope angle at sampled sites was 6.69°(SD = 4.70°), and compound topographical index (CTI, Moore et al 1991) was 3.62 (SD = 1.29). Historically used for

5 dairy farming, the study area was reclaimed as forest approximately 100 years ago, and is currently made up of 50-100 year old stands in the “tulip poplar” association. Since the time of data collection, a portion of this site has been added to the Forest Global Earth Observatory Network of the Center for Tropical Forest Studies (CTFS-ForestGEO). The elevation gradient in the plot was treated categorically, such that trees sampled at 0-5m were considered at low elevation and labeled “wet” sites, 10-22m were upland or “dry”, and those in between were at “mid” elevation. These elevation categories are characterized by different soil types with contrasting hydrologic qualities (Soil Survey Staff and Natural Resources Conservation Service 2018); six wells were installed in the Big Tree Plot from 1 to 10m in 2018, and the water table depth and soil moisture measurements show a strong relationship with elevation (Supplement Figures S3 and S4). The low elevation sites were dominated by “Widewater and Issue” (WBA) soils, a poorly drained soil with high flood frequency and a typical summer water table depth of 35 cm; the mean water table depth among all soil types at low elevation was 108 cm. Measured water table depth from May through September 2018 in wells at 1m and 2m elevation ranged from 12 cm to 105 cm, with a mean of 46 cm. The mid-elevation sites included several soil types, typically moderate- to-well drained but with lower flood frequency than the low elevation sites. Mean water table depth estimated from soil types was 158 cm, while measured depths ranged from 16 cm (immediately following heavy rain) to 330 cm. The high elevation sites from which trees were sampled were primarily Collington and Annapolis (CRD) soils, which are well-drained, sandy soils with a summer water table depth of more than 200 cm, which is the reporting threshold for USGS soils data. Soil moisture data for the study site during the experiment are given in Table 1.1a, and key differences in soil characteristics are summarized in Table 1.2. A map of the study trees including elevation and soil type can be found in Figure S2.

Water SWC (SE) Dry Year Wet 0.186 (0.016) Mid 0.246 (0.017) Water SWC (SE) Dry 0.157 (0.014) Dry 0.124 (0.012) Wet Year Wet 0.466 (0.003) Mid 0.263 (0.017) Mid 0.469 (0.005) Wet 0.462 (0.019) Dry 0.485 (0.005)

(a) Mature trees (b) Seedlings

Table 1.1: Mean soil moisture (volumetric water content, Vw/Vs) as measured by TDR probes in the mature tree field sites and seedling common garden. Differences among sites, years, and treatments are all significant. Standard error (SE) is reported for each value in parentheses.

6 Wet (<5m) Mid (5-10m) Dry (>10m) AWS (cm) 31.0 31.1 26.9 AWC (cm/cm) 0.17 0.16 0.14 Water Table Depth (cm) 108.2 157.8 >200 Ksat (µm/s) 15.7 16.3 13.4 % SOM 1.28 0.64 0.38

Table 1.2: Mean values of selected soil characteristics at SERC by elevation category. Available Water Storage (AWS) is the quantity of water available to plants for all soil layers. Available Water Capacity (AWC) is the water available for use by plants given in centimeters of water per centimeter soil. Water Table Depth is the average from May to September, matching the months of measurements on mature trees; the maximum water table depth measured is 2m and soils with a deeper water table were assigned this maximum value. Saturated hydraulic conductivity (Ksat) represents the rate of water movement through soil pores in a fully saturated soil. Soil Organic Matter (SOM) is measured as percentage by weight. Data were provided by the Web Soil Survey using a soil map of the minimum rectangular bounding box covering all trees measured in the experiment. All diﬀerences in means among elevation categories are signiﬁcant (ANOVA, p <0.0001).

Mature Tree Sampling

Physiological measurements were collected from June to October 2002 and 2003 on the three most common oak species in the SERC forest tract: Quercus alba L. (white oak), Quercus falcata Michx. (Southern red oak), and Quercus palustris Munchh. (pin oak). Q. palustris is commonly found in floodplains with limited drainage, and is considered water- loving; Q. falcata grows in drier areas, including slopes and ridges above the floodplain. Q. alba preferentially grows in more moderately watered areas and does not typically tolerate habitats with very high or very low water availability. Figure 1.1c shows the proportion of total basal area for each species found across the elevation gradient. The number of trees sampled per species and elevation category in each year is summarized in Table S1. Trees were all mature, with diameter-at-breast-height (DBH) between 50-70cm in similarly-aged forest stands and were selected to cover the elevation range of the site, with considerations made for proximity to power sources. A map of study trees and elevation categories is included as supplemental Figure S2. Soil moisture at each tree was measured approximately weekly each summer using time domain reflectometry (TDR): steel probes were installed to a depth of 1m and 5cm apart, and readings were collected with a metallic cable tester (Tektronix 1502C, Tektronix Inc., Beaverton, Oregon). Sapwood area (SA, cm2) was measured in all sample trees. Tree cores were taken in late summer each year at a height of 1.4m, away from the sap flow sensors and abnormal wood formations. Sapwood depth is the distance between the outermost ring of xylem and the point of color change marking the beginning of inactive heartwood. This approach was cross-validated with injection of Safranin-O dye. These cores were also used to estimate growth rate as basal area increment (BAI, cm2/year). Average values of sapwood depth and DBH are reported in supplemental Table S4.

7 Seedling Common Garden

In addition to in situ measurements of mature trees, a common garden of oak seedlings was established. Acorns from each species were collected from within a 2 ha region of the SERC forest and planted in three blocks of an experimental garden. Seedlings were grown under 50% shade cloth for their ﬁrst year of growth, then moved to an open-air rain-out shelter with an automatic irrigation system. Three water treatments were established: plants in the low water treatment were irrigated every 10 days, in the medium water treatment every four days, and in the high water treatment daily. Soil moisture was monitored using TDR probes; mean values are given for each treatment in Table 1.1b.

Species Geographic and Climatic Ranges

The geographic ranges for each species were captured using occurrence data aggregated by the Global Biodiversity Information Facility (GBIF, accessed December 2016); only occurrences in the United States with valid latitude and longitude coordinates were included. Climatic envelopes were produced for those ranges using the bioclimatic variables (chieﬂy mean annual temperature (MAT) and mean annual precipitation (MAP) generated by WorldClim Global Climate Data (Hijmans et al. 2005) and potential evapotranspiration (PET) and the aridity index (MAP over mean annual PET) data from the Consortium for Spatial Information (Zomer et al. 2008, Trabucco and Zomer 2010). We rename aridity index as ”wetness index” (WI) for clarity. All data were processed using R (R Core Development Team 2017).

Spatial and Temporal Variation in Water Availability

The SERC site falls within the humid subtropic climate zone, with warm summers and cool, wet winters. From 1990-2010, the mean daily temperature in the summer was 21.9 (SD = 7.1), with mean monthly summer rainfall of 28.1 mm (SD = 11.2 mm, Global His- torical Climatology Network Database), with a consistent pattern of interannual variation. Data were collected for this study over two summers with contrasting weather conditions. Weather during the “dry year” (2002) saw significantly less rainfall, warmer temperatures, more solar radiation, and higher vapor pressure deficit (VPD) than the “wet year” (2003) (Figure 1.2a, additional information in supplementary table S2). The differences in these weather conditions from 2002 to 2003 were consistent with year-to-year differences for the region (Figure 1.2b). All site-specific climate data were collected at the climate monitoring station at SERC; measurements include global solar flux between 285 to 2800 nm (Eppley Precision Spectral Pyranometer, The Eppley Laboratory, Newport, Rhode Island), temperature and relative humidity (Vaisala HMP45AC, Vaisala, Helsinki, Finland), and rainfall (TE525 “Tipping Bucket” rain gauge, Texas Electronics, Dallas, Texas). Saturated vapor pressure (VPsat) and vapor pressure deficit (VPD) were calculated from temperature and

8 relative humidity as per the National Weather Service.

Trait Measurements

The traits measured in mature trees and seedlings fall into three broad categories: water use, stress, and growth/productivity. In mature trees, water use and stress traits were compared among species and across both space and time; growth rate was calculated as an average basal area increment over 20 years and was thus only compared among species and along the elevation gradient.

Water Use: Sap Flow, Conductance, and Water-Use Eﬃciency

We used constant-heat dissipation sap flow sensors consisting of a heated temperature sensor inserted into the sapwood 4 cm (per manufacturer recommendation) above an unheated reference temperature probe (Granier 1985, 1987). We used both commercial sensors (TDP 30; Dynamax, Inc.; Houston, Texas) and constructed custom shorter sensors (Phillips et al. 2002, Meinzer et al. 2004); all probes used copper-constantin thermocouples to measure temperature. The current applied to constructed sensors was regulated by a circuit board to produce the same power density (wattage per unit volume of the resistor) to compensate for differences in resistance. The median temprature increase above ambient was 5.17 for the Dynamax sensors and 8.24 for the short sensors; this variation similar in magnitude to other studies (e. g. McCulloh et al. (2007)). Data from different sensor types showed no more variation than data from sensors of the same type in different positions in the tree (Supplemental Figures S5 and S6). Sap flow was measured for 15 weeks beginning in mid-August in 2002 and 17 weeks beginning in early July in 2003. Dynamax sensors were installed in each of 20 trees in both the dry and wet year: probes were inserted 0-30mm into the cambium at 1.4m in height on the north- and south-facing sides of each tree. In the wet year, when 19 additional trees were added to the study, two short sensors were also installed in each tree. These probes were inserted 11, 16, or 21mm (depending on probe length) into the cambium; if Dynamax probes were already installed, the short probes were inserted at the same height 20cm away. All sensors were insulated from water and heating, and connected to a current regulator (AVRD; Dynamax, Inc; Houston, Texas) and data logger (23X, 21X or 10X; Campbell Scientific, Inc.; Logan, Utah), powered by AC power with a battery backup. The temperature difference between the pairs of thermocouples for each probe were sampled every 10 seconds and averages were logged every 10 or 30 minutes. Data was downloaded weekly and potentially problematic data (due to malfunctioning sensors or electrical storms) was flagged.

Sap flow velocity (v, cm/s) was calculated from the maximum (∆T0) and actual (∆T ) temperature difference between probes at each time point, following the equations established by Granier (1987), Granier et al. (1994) as shown in equations 3 and 4; volumetric sap flow rate (F, cm3/s) is velocity multiplied by sapwood area. Total daily water loss (TDWL)

9 was calculated as the integral of sap ﬂow rate over a 24 hour period and maximum sap velocity (V, cm/s) is the maximum value of v in the same period.

v = 0.0119k1.231 (1.1) where ∆T − ∆T k = 0 (1.2) ∆T Sap flow measurements taken with Dynamax sensors, which were generally longer than the sapwood depth, and thus in contact with non-conducting tissue, were corrected per Clearwater et al. (1999) to account for overestimated sap flux velocity. −2 −1 In seedlings, transpiration (E, mol H2O m s ) was measured directly (n = 108, 12 plants per species per treatment) with a LI-COR 6400 Portable Photosynthesis System (LI- COR; Lincoln, Nebraska) rather than approximating via sap flux. Other water use traits, −2 −1 including stomatal conductance (gsw, mol H2O m s ) and intrinsic water use efficiency

(WUEi, A/gsw), were measured at the same time as E with the LI-COR 6400. Data were collected twice for each plant, over the last weeks of June and July, between 7:00 AM and 9:00 AM. In both mature trees and seedlings, predawn (3:00 am - 6:00 am) and midday (10:00

am - 3:00 pm) leaf water potential (ΨPD and ΨMD, respectively) were measured with a pressure chamber (Plant Water Status Console, 3000 series; Soilmoisture; Santa Barbara,

California). Leaves for measuring ΨPD were taken from the most accessible location on

tree, usually a low or mid canopy, while ΨMD was measured for high, mid and low canopy leaves. Between cutting and measurement, leaves were stored in moist, sealed plastic bags inside a dark cooler to minimize water loss. In mature trees, measurements were collected over the first three weeks of July in each year; in seedlings measurements were taken in the last two weeks of July. In mature trees, the change in water potential from predawn to midday and steady- state sap flow rate (F ) were used to calculate whole plant hydraulic conductance (K, 2 −1 −1 cm s MPa ): K = F /(ΨMD − ΨPD). Steady-state F is the average F over the hour- long period during mid-day leaf collection when the variance in F was smallest. If sap flow measurements were not available for a tree on the date water potential was measured, the value from the most recent day with similar VPD was used. Whole plant hydraulic conduc- −2 −1 −1 tance in seedlings (K l, mmol m s MPa ) was similarly calculated, using steady state transpiration instead of sap flow rate. Water use efficiency (WUE, A/E) in seedlings was calculated directly from gas exchange measurements. In mature trees, it was estimated from δ13C values (Farquhar et al. 1982), although this approach may be confounded by unknown mesophyll conductance (Warren and Adams 2006). In each monitored mature tree, leaves were collected at multiple canopy positions at four time points across both summers. Leaf samples were frozen upon collection

10 and then dried and ground for carbon isotopic analyses with an elemental analyzer (Carlo Erba Instruments, NA 2500 series; Wigan, England) coupled via continuous ﬂow to a stable isotope ratio mass spectrometer (ConﬂoII to Delta Plus XL; ThermoFinnigan; Waltham, Massachusetts) in the lab of Marilyn Fogel at the Geophysical Lab, Carnegie Institution of Washington, D.C. Stable carbon isotopic values are expressed as δ values according to the equation:

13 δ C = [(Rsample/Rstandard) − 1]1000 (1.3)

where R is the ratio of 13C to 12C and the standard was the Pee Dee Belemnite (PDB) standard. Instrument error was ±0.3. When making comparisons among species and water availability, only mature mid-summer leaves for each tree were analyzed to minimize the problem of early, heterotrophic growth inﬂuencing WUE estimates (Terwilliger et al. 2001).

Water Stress

The change in daily leaf water potential (∆Ψ) between midday and predawn was used to estimate leaf water stress, where lower values suggest a leaf is closing its stomata or otherwise conserving water during the day and higher values show more water loss relative to the equilibrium indicated by the predawn water potential. While measuring pre-dawn Ψ, maximum quantum yield of photosynthesis after dark incubation (Fv/Fm) was measured on seedlings with a portable chlorophyll fluorometer (MINI-PAM; Heinz Walz GmbH; Effeltrich, Germany). An indicator of the efficiency of photosynthesis, Fv/Fm is generally 0.8 in healthy plants and declines as plants experience stress (Maxwell and Johnson 2000).

Growth and Productivity

Basal area increment (BAI, cm2/year) from tree cores collected in 2002 was used in mature trees to compare growth rates among species across the elevation gradient. Basal area was estimated from 1980 to 2002 by subtracting all newer ring growth from the present DBH; average growth rate was the slope of least-squares regression between year and basal area.

Productivity was directly measured in seedlings as carbon assimilation (A, µmol CO2 m−2 s−1) with the LI-COR 6400 (n = 108, 12 plants per species per treatment, as with E). At the conclusion of the experiment, seedlings were harvested for biomass measurements. Leaves, stems, and roots were separated and dried at 70 for three days before weighing. In addition to biomass, leaf stable isotope ratios were measured following the same protocol as for mature trees.

11 Statistical Analysis

All statistical analyses were performed in R (R Core Development Team 2017). For each physiological trait measured in mature trees, we tested the effects of and interactions among species, elevation category, and year using Analysis of Variance (ANOVA) on a fixed effects model including all three attributes and all interactions. The same approach was used for the seedling trait data, with Species and Treatment as the explanatory variables. When ANOVA results were significant (p < 0.05), Tukey’s Honest Significant Differences (HSD) was used to make pairwise comparisons. Species climatic ranges were extracted from the raster BIOCLIM and aridity datasets at the coordinates of individuals identified in the GBIF data set using the raster package (Hijmans 2016). Coordinate system corrections and conversion of shapefile data to raster format were done using QGIS software (QGIS Development Team 2009). Pairwise species means were compared using a Tukey-adjusted t-test for multiple comparisons (Lenth 2016). All figures were produced using the ggplot2 package (Wickham 2009).

Results

Comparison of Broad and Local Distributions

Comparing the climatic distributions of the oak species across their full ranges, the three species differed in mean bioclimatic variables in a few critical ways that were suggestive of associations with their local distributions at SERC. In particular, Q. falcata had a more arid climatic distribution and was found in the sites that have the lowest water availability locally. Across its range, Q. falcata was found in locations which were significantly warmer than either Q. alba or Q. palustris, which were generally not different from each other. The average mean annual temperature (MAT, ) in Q. falcata’s range was 3.2 warmer than the range of Q. alba and 2.8 warmer than Q. palustris (p < 0.0001, Tukey-adjusted p- value). Q. falcata also occurred in regions with higher rainfall than the other species, with an average MAP was 79 mm higher (p < 0.0001, Tukey-adjusted p-value), but because the higher temperatures drove a higher rate of potential evapotranspiration (PET), its range had a lower WI value, indicative of a drier environment overall. The temperature and aridity distributions of these three species are shown in Figure 1.1b. For climate variables, the differences between Q. alba and Q. palustris were not significant; these and additional bioclimatic variables are summarized in Table 1.3. Figure 1.1c shows the distributions of each species of oaks for all trees in the Big Tree Plot at SERC; these distributions are also summarized in Table S3. Though all three species were found across the elevation gradient (from the sea level floodplain to 22m), each was concentrated in a distinct subset of the gradient from floodplain to higher elevation. Comparing the least-squares means of elevation by species, Q. palustris had the lowest mean

12 Q. alba Q. falcata Q. palustris Wetness (WI) 1.022 0.959 1.023 PET 1077.1 1219.6 1077.9 MAT () 11.12 14.28 11.51 Min. T() -7.08 -3.08 -6.71 Max. T() 29.39 31.48 29.87 MAP (mm) 1091.16 1168.00 1090.59 Wettest Month (mm) 112.86 122.84 112.51 Driest Month (mm) 68.71 74.49 67.14 Permeability (in/hr) 3.43 3.53 3.57 Flood frequency 3.77 3.70 3.67

Table 1.3: Mean values of bioclimatic and soil hydrology variables in the North American ranges if Q. alba, Q. falcata, and Q. palustris. elevation, showing a preference for locations where soils had higher water availability. As predicted, the largest difference in elevation was between the two red oaks, though both also occurred at significantly different mean elevations from Q. alba (p < 0.0001, Tukey-adjusted p-value).

Species, Spatial, and Temporal Performance Diﬀerences

Water Use

Figure 1.3 shows the sap velocity over the course of 24 hours averaged over the season (August - October in the dry year, July - September in the wet year) for each species; mean sap velocity for each species over time is shown in supplemental figure S7. The average maximum daily sap velocity (V, cm/s) was significantly different among species, elevation categories, and years; each interaction between pairs of variables was also significant (ANOVA, p = 0.0251 for the species by year interaction, p <0.0001 for all others). Mean values of V and other key traits measured in mature trees by species, elevation category, and year are summarized in Table 1.4.

13 Q. palustris Q. alba Q. falcata

Elev. (m) 20

-10

(a) Q. palustris Q. alba Q. falcata 1.4

1.2 WI 1.0

0.8

10 15 10 15 10 15

MAT (¡ ) (b)

Q. alba Q. falcata Q. palustris 0.2

0.1 Basal Area Proportion Basal Area

0.0

0 5 10 15 20 25 Elevation (m) (c)

Figure 1.1: Broad and local distributions of Q. alba,Q.falcata, and Q. palustris. 1.1a: Distribution of the three oak species across SERC’s Big Tree Plot (BTP), 700 m by 700 m. with elevation (m above sea level). 1.1b The climatic envelopes of the North American ranges of the three study species. Wetness Index, on the vertical axis, was developed by Zomer et al. (2008) and calculated as mean annual precipitation over mean annual evapotranspiration. The horizontal axis is mean annual temperature in degrees Celsius. The distribution of Q. falcata is signiﬁcantly drier (lower WI, p < 0.001) and hotter (p < 0.001) than the other two species. 1.1c Proportion of total basal area for each oak species found across the elevation gradient in the BTP. These distributions are further summarized in Table S3.

14 Max Temp (°C) Min Temp (°C) 30 30 )

t+1 2 20 20 - value

10 10 t 1

0 0 0 Rainfall (cm) VPD (kPa)

2.0 erence (value erence

0.02 ¡ -1 1.5

1.0 0.01 -2 0.5 Interannual Di 0.00 0.0 -3 Dry Year Wet Year Dry Year Wet Year Max Temp (°C) Min Temp (°C) Rainfall (mm) (a) (b)

Figure 1.2: 1.2a: Mean total daily rainfall, minimum and maximum daily temperatures, and VPD for each summer during which data was collected, showing that dry summer was significantly warmer and drier than the wet summer. Error bars are 2*SE. 1.2b:Year-to-year difference in average summer minimum and maximum daily temperature and monthly rainfall totals, 1980-2010. The vertical axis gives the difference in average summer weather from year t and year t + 1. Dark bar is the mean, boxes are interquartile distance, and whiskers are 95% confidence interval. Red dots highlight the difference in values between the study years, i.e. the value in 2003 minus the value in 2002.

15 Dry Year Wet Year Q. alba 0.006 Q. falcata Q. palustris

0.004 Wet

0.002

0.000

0.006 ) -1 s

0.004 Mid 2

V (cm 0.002

0.000

0.006

0.004 Dry

0.002

0.000 0:00 6:00 12:00 18:00 0:00 0:00 6:00 12:00 18:00 0:00 Time Figure 1.3: Average daily sap ﬂow patterns for each species at each elevation and in the wet (July- September) and dry (August-October) year; the error bars are standard error. Daily maximum velocity is more variable in the dry year (SD in wet year = 0.00194, SD in dry year = 0.00239; p = 0.0008, Welch’s Two-Sample t-test), and at low elevation (SD at low elevation = 0.00246, SD at high elevation = 0.00169; p < 0.0001, Welch’s Two-Sample t-test).

16 Species Site Year Trait Q. alba Q. falcata Q. palustris Wet Mid Dry Dry Wet V (cm s−1) 4.29 × 10−3 5.18 × 10−3 4.51 × 10−3 4.51 × 10−3 5.09 × 10−3 4.66 × 10−3 ** 4.91 × 10−3 4.55 × 10−3 TDWL (l) 13.17 12.28 12.28 8.72 15.56 14.07 12.83 12.47 K (cm2s−1MPa−1) 945.14 814.15 573.38 511.77 1165.68 744.52 ** 876.96 729.65 ∆Ψ (MPa) 1.58 1.43 1.68 1.61 1.48 1.60 . 1.66 1.47 * δ13C() -29.190 -29.241 -28.645 * -29.002 -29.142 -28.840 -28.791 -29.138 .

Table 1.4: Mean values of selected physiological traits measured in mature trees. Significance stars are the result of an ANOVA test and correspond to the following p-values: . : p < 0.1; * : p < 0.05; ** : p < 0.01, *** : p < 0.001. Significant interactions between variables are described in Figure 1.4. V: maximum sap flux velocity; TDWL: total daily water loss; K: hydraulic conductance; ∆Ψ: change in leaf water potential from pre-dawn to mid-day; δ13C: Water use efficiency. 17 Species Treatment Trait Q. alba Q. falcata Q. palustris Dry Moderate Wet Total Biomass (g) 10.36 8.96 10.89 * 7.28 14.05 8.59 *** Proportion Belowground 0.664 0.627 0.605 *** 0.625 0.645 0.608 ** Leaf Area (cm2) 201.41 219.26 288.95 *** 186.25 325.78 200.04 *** −2 −1 A(µmol CO2 m s ) 11.71 11.20 11.31 11.42 11.99 10.29 *** −2 −1 E (mol H2O m s ) 3.64 3.58 3.51 3.46 3.91 3.20 *** −2 −1 gsw(mol H2O m s ) 0.177 0.159 0.162 ** 0.149 0.190 0.153 *** WUEi (A/gsw) 75.21 77.54 74.73 81.52 72.81 70.31 *** δ13C() -28.780 -29.666 -29.632 * -28.752 -29.717 -29.688 * −2 −1 −1 Kl (mmol m s MPa ) 0.422 0.519 0.593 0.272 0.582 0.724 *** ∆Ψ 11.55 9.13 9.23 . 11.29 10.66 6.91 *** Fv/Fm 0.807 0.784 0.767 * 0.811 0.804 0.749 ***

18 Table 1.5: Seedling data means for a variety of physiological traits. Significance stars are the result of an ANOVA test and correspond to the following p-values: . : p < 0.1; * : p < 0.05; ** : p < 0.01, *** : p < 0.001. Total biomass, leaf area, photosynthesis (A), transpiration (E), stomatal conductance (gsw), and Fv/Fm each also show significant interactions between species and treatment. Maximum sap velocity was also slightly but significantly correlated with both VPD (Pearson’s r = 0.128, p < 0.0001) and with solar radiation (Pearson’s r = 0.107, p < 0.0001). The relationship between sap velocity and VPD was found in each species when considered separately and p-values were adjusted with the Holm method for multiple comparisons (Q. alba: r = 0.120, p < 0.0001; Q. falcata: r = 0.159, p < 0.0001; Q. palustris: r = 0.105, p = 1.343 × 10−4). The relationship between sap velocity and solar radiation persisted in both Q. alba and Q. falcata when these species were considered separately, but not in Q. palustris (r = 0.0008, p = 0.97). Average total daily water loss (TDWL) is shown in figure 1.4a. TDWL was significantly lower at low elevation than at either middle or high elevation sites (p = 0.013 and p = 0.046 respectively, Tukey’s HSD); mean values did not differ among species or between years. There was a significant (p = 0.024) interaction between elevation and species: Q. palustris exhibited a decline in water loss with increased elevation (and therefore decreased soil moisture), while both Q. alba and Q. falcata generally exhibited increased water loss. In Q. alba, peak TDWL in both years occurred at high elevation sites (dry), while in Q. falcata peak values were seen at mid elevation. In mature trees, whole-plant hydraulic conductance (K ) was similar to TDWL in its relationships with species, elevation, and year (figure 1.5a): there were significant differences in mean values among elevation categories (p= 0.002) but not species (p = 0.38) or year (p=0.13). Much of this difference was driven by the much higher K seen in Q. falcata growing at mid-elevation in the dry year. There was also a significant interaction (p = 0.003) between species and elevation: among both Q. alba and Q. falcata, the lowest values of hydraulic conductance occurred in the wet floodplain, while in Q. palustris, trees in the floodplain had higher values of K than at other elevations. Contrasting with mature trees, seedlings of all three species showed a significant decline in hydraulic conductance under the low water treatment; mean differences among species were not significant, and no significant interaction between species and water treatment when seedlings of all three species were included (Table 1.5). Q. palustris does show a steeper decline in hydraulic conductance than Q. falcata (Figure 1.5b), but this difference is marginal (p = 0.07). In mature trees, the strongest predictor of increased δ13C ratios (and thus increased WUE) was leaf developmental stage indicated by calendar day. There were significant differences in δ13C by species (p = 0.028) and marginal differences by year (p = 0.07). There was also a change in the relationship between water use efficiency and elevation between the years: on average, δ13C increased when comparing wet to dry sites in the dry year and decreased in the wet year (p = 0.023). Q. palustris had a higher WUE than the other two species in both years and at both wet and dry sites. It also exhibited the largest change in WUE at dry sites between the dry and wet years, as seen in figure 1.4c. Seedlings exhibited significant differences in transpiration rates (E) and stomatal con-

19 Dry Year Wet Year 25 Dry Year Wet Year

2.5 20

2.0 15

(MPa)

10 1.5 Total Daily Water Loss (l) Loss Daily Water Total

5 1.0

Wet Mid Dry Wet Mid Dry Wet Mid Dry Wet Mid Dry Site Site (a) (b) Dry Year Wet Year

-27.5

-28.0 C

13 ¡

-28.5

-29.0 Q. alba Q. falcata Q. palustris

Wet Mid Dry Wet Mid Dry Site (c) (d)

Figure 1.4: Differences by species, year, and elevation in four water-use traits measured in mature trees. 1.4a There were significant differences in total daily water loss (l) by elevation (ANOVA, p = 0.009), as well as a significant interaction between elevation and species (ANOVA, p = 0.024). 1.4b ∆Ψ was significantly higher in the drought year than in the wet year (ANOVA, p = 0.037), and there was a significant interaction between elevation category and year (ANOVA, p <0.0001). 1.4c There were significant species differences (ANOVA, p = 0.0167) in water use efficiency (δ13C) by species.

ductance (gsw) when grown under diﬀerent water-availability conditions ( E: p < 0.0001,

gsw: p < 0.0001), shown in ﬁgure 1.7. Performance in all species was highest at the mod-

erate water treatment for both traits; transpiration and gsw were significantly higher at moderate water availability than either dry or wet conditions (p < 0.0001 for both traits, Tukey’s HSD). There were no significant differences in either A or E among species, though

gsw was signiﬁcantly higher in Q. alba than in the other two species (p = 0.001, Tukey’s HSD). Water use eﬃciency in seedlings was measured using both carbon isotope ratio (δ13C)

and gas exchange measurements (A/gsw, abbreviated as WUEi). There were significant differences among species (p = 0.04) and treatments (p = 0.045) in δ13C, though pairwise differences were small. Q. falcata and Q. palustris were the most similar in their isotope

20 3000 Dry Year Wet Year

) 0.9 -1 ) -1 2000 MPa -1 MPa s -1 -2 0.6 s 2

1000 K (cm (mmol m

l 0.3 K

0 Wet Mid Dry Wet Mid Dry Wet Mid Dry a. Mature Trees b. Seedlings Q. alba Q. falcata Q. palustris

Figure 1.5: Differences in hydraulic conductance with water availability in mature trees (a) and seedlings (b). In mature trees, K (cm2s−1MPa−1) differed significantly by site-based water availability (ANOVA, p = 0.00225); interactions between water availability and species (ANOVA, p=0.003) and the three-way interaction between year, elevation, and species (ANOVA, p= 0.03) were also significant. In seedlings, conductance varied significantly by species (ANOVA, p < 0.0001) but not by water availability.

ratios (p = 0.99), while Q. alba showed slightly, though non-signiﬁcantly, higher WUE by

this metric. WUEi was not significantly different among species but was among treatments, and was highest under dry conditions (p < 0.0001, Tukey’s HSD). This pattern was also seen with δ13C, though the results were not significant.

Stress

Pre-dawn water potential (ΨPD) (shown in supplemental Figure S8) was significantly lower at all elevations and for all mature trees in the dry year, reflecting significant differences

in measured soil moisture. Mid-day water potential (ΨMD) was also significantly different between years. Here we focus on the difference (∆Ψ) between these values as an indicator of plant stress to incorporate information about both changing water availability and changing evaporative demand. Figure 1.4b illustrates the changes among species in ∆Ψ between years and elevation categories in mature trees. All species exhibited higher mean ∆Ψ in the dry year, though this general trend was not observed at all sites. The differences between years were most pronounced at dry sites, and the difference in ∆Ψ at wet and dry sites was significant in the dry year (p = 0.007, Tukey’s HSD) but not the wet year (p = 0.25, Tukey’s HSD). The compounding effect of the drought and elevation gradient on water stress appeared most pronounced in Q. palustris, though differences among species in mature trees were not significant. Q. palustris seedlings also exhibited higher levels of ∆Ψ in the low water treatment than at high water, as did Q. alba. Differences in ∆Ψ between water treatment categories and

21 species were significant (ANOVA, p = 0.0005 and p = 0.04, respectively). The interaction between species and water treatment was not significant when Q. alba was included, but differences among species in which water treatment caused the most stress were significant when only Q. palustris and Q. falcata seedlings were compared (p = 0.05).

Stress response measured by chlorophyll ﬂuorescence (Fv/Fm), however, suggested that seedlings exhibited increased photoinhibition (Fv/Fm below 0.8) at high water treatments (ANOVA, p < 0.0001). This response was seen in both Q. falcata and Q. palustris, but not in Q. alba (Figure 1.7).

Growth and Productivity

There was a weak (p = 0.08, linear least squares regression), positive relationship between increasing growth rate (average BAI per year) and elevation, shown in Figure 1.6a, suggesting slightly higher growth rates in individuals at drier sites at higher elevation. Q. palustris, however, had a significantly different (p = 0.02) relationship than the other two species, having its fastest growth in the floodplain and decreased growth rate at higher elevation.

50 40 ) ) 40 -1 -1

30 year year 2 2 30

20 20 Growth Rate (cm Rate Growth Growth Rate (cm Rate Growth 10 10 p

0 5 10 15 20 0 1000 2000 3000 Elevation (m) K (cm2s-1MPa-1) (a) (b)

Figure 1.6: Growth rate (basal area increment, cm2/year) versus 1.6a: elevation (m) and 1.6b: hydraulic conductance (K, cm2s−1MPa−1), measured in mature trees. There is a strong, positive linear relationship between growth rate and hydraulic conductance (Multiple R2 = 0.67), and the slope of that relationship is significantly higher (p = 0.0312) in Q. palustris, which also exhibits a significantly different (p = 0.0178) relationship between growth rate and elevation than the other two species.

In seedlings, the relationship between growth and water availability was not as strong; all three species produced less total biomass at both high water and low water availability, as compared to the moderate water treatment (Figure 1.7). However, the differences in biomass between high and low water were not significant, nor were the differences among species. Q. palustris seedlings did show a different pattern of biomass allocation than the other two species, with significantly lower allocation of biomass below ground. This was

22 especially apparent in the high water treatment. There was a significant difference in carbon assimilation (A) among treatment groups (p < 0.0001), with plants given moderate water showing higher A than those at high water (p < 0.0001, Tukey’s HSD). There were no significant differences in A among species, nor was a significant interaction between species and treatment observed. Mature trees in all three species did exhibit a strong (p < 0.0001), positive relationship between hydraulic conductance (K ) and average annual growth rate, shown in Figure 1.6b. The slope of this relationship was significantly (p = 0.03) higher in Q. palustris than the other two species, meaning for the same increase in K, Q. palustris had a larger annual basal area increment. In Q. palustris, this increased slope was the same at both dry and wet sites (slope = 0.02 at wet site and 0.01 at dry site, p = 0.23); by contrast, Q. falcata had a steeper slope at dry site (increasing from 0 to 0.016, p = 0.04) and Q. alba had a lower one (decreasing from 0.02 to 0.002, p = 0.07), suggesting that each species responded differently to environmental conditions that vary with elevation.

Discussion

These results provide evidence that the three most abundant species of oaks in the “Big Tree Plot” at SERC, Quercus alba, Quercus falcata, and Quercus palustris, partitioned an elevation (and thus hydrologic) gradient. Q. palustris and Q. falcata showed the largest differences in local distributions, while Q. alba was more evenly distributed from low to high elevation. The difference in local distribution between Q. falcata and Q. palustris was also reflected in differences in growth rate, with Q. palustris experiencing its highest growth rates at low elevation, in the floodplain, where Q. falcata exhibited its lowest growth rates. This habitat partitioning was supported in part by climatic differences in the broad geographic ranges of these species, as well as key differences in functional traits of both mature trees and seedlings. Considered in sum, these results underline the complexity of the factors that drive local species distributions in natural systems. Differences in climatic conditions across the broad geographic ranges of the three species were associated with local habitat partitioning, as hypothesized in Ackerly (2003) and Cavender-Bares et al. (2016), particularly in wetness index and mean annual temperature. The overall geographic range of Q. falcata was associated with significantly warmer and more arid climate than the other two species, despite higher overall rainfall, and locally was found in sites with the lowest seasonal water availability. Q. alba had a broad geographic and climatic range that largely overlaps the other two species, a trend consistent with the local distributions at SERC. However, the distribution of oaks in the BTP showed significant separation between Q. palustris and the other two species, while the full climatic distributions of Q. palustris and Q. alba across their ranges showed no significant differences in average temperature, rainfall, or aridity. One caveat to note is that we may

23 not have completely captured the full North American ranges of these species with GBIF data alone. Beck et al. (2014) demonstrated that the spatial bias in specimen records can significantly skew range reconstructions, and the accuracy of species identification and the precision of geographic location can introduce error (Goodwin et al. 2015, Wieczorek et al. 2004). Nevertheless the consistency between aridity and temperature ranges and habitat preference at SERC provides compelling evidence of a connection between broad scale and local distributions. Among plant functional traits, the hydraulic conductance of mature trees supported the hypothesis that contrasting water-use strategies help Q. palustris and Q. falcata exploit opposite ends of a hydrologic gradient. With decreasing water availability, in both a dry and wet year, the hydraulic conductance in mature trees of Q. palustris declined while that of Q. falcata increased or did not change. The conductance of Q. palustris also declined consistently with decreasing water in seedlings, while conductance in Q. falcata showed a small increase in the moderate water treatment, though the mean values were not significantly different among seedlings of different species. Conductance has been shown to be highly correlated with growth rate, a trend seen in both the the literature (e. g. Poorter et al. 2010) and in our data (Figure 1.6b). In our study, the relationship between growth and conductance was strongest in Q. palustris: the same increase in conductive ability was associated with a significantly larger increase in growth rate in Q. palustris than the other two species, suggesting it is adapted to take advantage of greater water availability. The higher conductance seen in Q. palustris may come at the cost of increased stress during drought years. Values reported in the literature show that Q. palustris typically has a larger vessel diameter than Q. falcata (Lobo et al. 2018, Robert et al. 2017), which suggests it may be trading high hydraulic efficiency when water is available for increased vulnerability when it is not (Sperry et al. 2008b). We observed mature Q. palustris trees experiencing the largest difference between predawn and midday water potential, indicative of drought stress, at the highest elevation in the dry year. ∆Ψ was also higher in Q. palustris seedlings when water was limited, and higher in Q. falcata without water limitation. Other traits in both mature trees and seedlings also provided evidence of partitioning. Q. palustris seedlings allocated less of their total biomass below ground, especially at high water availability, indicating a relatively shallow rooting system compared to the other species. Shallow roots have been shown to significantly decrease the survival of tree seedlings in drought (Padilla and Pugnaire 2007), and at a global scale lower rooting depth is associated with wet environments (Canadell et al. 1996). Though both species demonstrated an increase in water use efficiency with decreasing water, the change in WUE in drier conditions was the smallest in Q. falcata, consistent with the species’ preference for drier habitats. We found limited evidence to support the hypothesis that Q. alba’s broader distribution would be supported by an ability to maintain homeostasis under stress. In the high water

24 treatment, both Q. palustris and Q. falcata, but not Q. alba, seedlings exhibited stress (as indicated by low Fv/Fm). Though it might be unexpected to see a water-loving species like Q. palustris exhibit higher stress in very well-watered conditions, even wetland species show decline in photosynthetic rates in response to the oxygen deprivation caused by ﬂooding

(Pezeshki 2001), and lowered Fv/Fm is a documented response to flooding stress (Nash and Graves 1993). In general, oaks show a preference for drier, well-drained soils and do not grow in the wettest climates in their geographic ranges (Cavender-Bares et al. 2018). The depressed performance of seedlings under high water conditions illustrates that drought was unlikely to be the only environmental factor affecting plant function. Lower vapor pressure deficit or light limitation in the rainy season may have augmented plant response to water stress, helping to explain why we observed a smaller response than expected to the drought conditions of the dry year. We found sap flux to be correlated with both light levels and VPD; it is possible that decreases in transpiration from lower water availability were offset by stronger driving gradients in the dry year, explaining why we did not see a change in total daily water loss. Aranda et al. (2005) found a higher stress response to drought in cork oak (Quercus suber L.) in low light conditions compared to high light. High light could alternatively cause depressed performance or stress due to photoinhibition (Long et al. 1994), which we were not able to test for in this study. Finally, while three species are too few to draw strong conclusions about the effects of phylogeny on habitat sorting, the distributions of these three oak species at SERC did match the expectation that more closely related species will show greater habitat separation, drawn from microcosm experiments (Violle et al. 2011), across environmental gradients (Cavender- Bares et al. 2004a, Fallon and Cavender-Bares 2018), and on continental-scale observations of different subgenera (Cavender-Bares et al. 2018). Q. palustris and Q. falcata, both red oaks (Section Lobatae) are more closely related to each other and more separated along the elevation gradient than either is from Q. alba, a white oak (Section Quercus). The pattern suggested by these three oak species was consistent with phylogenetic relatedness as a driver for community structure and functional diversification. In addition to concerns about the accuracy of GBIF data and limited power for phylogenetic analysis, there are a few cautions which may limit the scope of these results. Heat dissipation sap flow measurements may fail to accurately estimate transpiration rate, in particular because there can be a high amount of radial and circumferential variation in sap flow that may not be captured by one or two measurements per tree (González-Altozano et al. 2008); we observed a high degree of dispersion in results from pairs of sensors installed in the same tree (Figures S5 and S6), which could be attributed to natural variation or could be an artifact of differences between sensors (Lu et al. 2004). Bush et al. (2010) have observed that the calibration constants published by Granier (1987) may not be accurate for ring-porous tree species, like oaks. Second, the design of this study was not optimal for testing competition or local adaptation directly. This was not a reciprocal transplant

25 experiment, nor were genotype or maternal line controlled (Bengtsson et al. 1994). Our results should, however, motivate further research that does explicitly control these variables, because the distribution pattern and trait diﬀerences we found warrant additional investigation.

Conclusion

We have provided evidence supporting the hypothesis that Quercus alba, Quercus falcata, and Quercus palustris coexist in the forest community at SERC by partitioning a hydrologic gradient driven by elevation. Our findings suggest that a combination of biogeographic legacy effects, functional traits, response to temporal variation, and phylogeny may play a role in driving this variation. Among functional traits, the hydraulic conductance of mature trees offers the clearest support to the idea that the two red oaks partition the gradient through contrasting water-use strategies. A lack of a single phenomenon among those we tested can explain the local distribution of our study species is consistent with other recent work (Morueta-Holme et al. 2016), and future research in habitat partitioning and community assembly will be strengthened by addressing multiple potential drivers of observed patterns.

26 a. b. c.

15.0 0.65 3.0

12.5 2.5

0.60

10.0 2.0 Biomass (g) 0.55 Leaf Biomass (g) Leaf 7.5 1.5

1.0 5.0 Biomass Belowground Proportion 0.50 Wet Mid Dry Wet Mid Dry Wet Mid Dry

d. e. 14 f.

4.0 ) ) -1 ) 12 -1 s -1 0.20 s -2 -2 s -2

3.5 m 2 O m

2 10 O m 2

0.15

3.0 mol CO (mol H

¤ 8 sw A ( E (mol H g

2.5 0.10 6

Dry Wet Mid Dry Wet Mid Dry Wet Mid

g. h. 1.50 i.

-0.2

-1.0 1.25

-0.3 (MPa)

(MPa) 1.00

(MPa)

¢ £ -1.5 midday

predawn -0.4 ¢ ¢ 0.75

-0.5 0.50

-2.0 Wet Mid Dry Wet Mid Dry Wet Mid Dry

j. k.

0.80 -27 Species C)

13 Q. alba

m 0.76 ¡ /F v Q. falcata F -28

WUE ( Q. palustris 0.72

-29

0.68 Dry Wet Mid Wet Mid Dry Figure 1.7: Seedling traits demonstrating (from top to bottom): growth (a. total biomass, b. proportion belowground biomass, and c. leaf biomass), gas exchange (c. transpiration rate, d. stomatal conductance, and e. photosynthesis), stress response and water status (g. Ψpredawn, h. 13 Ψmidday, i. ∆Ψ, and j. Fv/Fm), and water use (k. δ C). Signiﬁcant diﬀerences by treatment and species are summarized in Table 1.5.

27 Chapter 2

LeafGrapher: A software tool for network analysis of leaf venation

Background

Why analyze leaf venation

Patterns in leaf venation have been of interest to botanists for over 150 years, particularly for classification, even before the mechanisms of water transport were well understood (Et- tingshausen 1861, Hickey 1973). Characteristics of leaf venation have been used as key traits for identifying plant species using tools from the earliest dichotomous keys to cutting-edge neural network technology (Tan et al. 2018). Venation architecture is used by paleobotanists to identify extinct broad-leafed plant species and draw inferences about past climates (Uhl and Mosbrugger 1999). Plant vascular biologists focus on the important role venation architecture plays in plant physiological function; in particular, increased capacity for vascular transport increases the hydraulic supply to a leaf via increased conductance to water, which is strongly associated with greater maximum photosynthetic capacity (Brodribb et al. 2007, Sack et al. 2013). Venation structure of plants is also highly diverse, varying between plant groups and among individuals of the same species (Carr et al. 1986); improving our ability to quantify this diversity of structure is important for expanding our understanding of plant function. The range of this morphological variation in leaves becomes particularly interesting when considered in the context of the investment cost of building vascular tissue. Lignin and the other structural tissues required for building vascular bundles are energetically costly (Chapin et al. 1988). Optimality theory suggests organisms will tend toward structures with the lowest metabolic cost to “solve” a particular problem (Rosen 1967). Mammalian vasculature, for example, tends to conform to the optimal branching patterns predicted by a simple model attempting to maximize non-turbulent fluid flow while minimizing construction and maintenance costs (Rosen 1967, Labarbera 1990, Kamiya et al. 1993). The leaf

28 venation architecture of the major veins in many vascular plants does not conform to this optimal, cost-efficient branching structure (Price et al. 2013). Plant vasculature has an additional function, mechanical support, that is not required of animal vasculature. The quantity of vasculature required to supply water to an area of leaf lamina is not the same as the quantity required to mechanically support that area (Howland 1962). Simple models of leaf structure make predictions of a wedge-like system of primary and secondary veins to support typical leaf shapes (Givnish 1979). More sophisticated models incorporate folding and twisting forces that a leaf experiences in approximating optimal relationships between vascular structure and leaf shape (Kull and Herbig 1995, Niklas 1999, Corson et al. 2009). Neither the basic principles of fluid flow nor the requirements of mechanical stress suf- ficiently explain the evolutionary trend in leaf venation architecture, seen both within and among lineages, to become more dense, and notably, more net-like or interconnected (Triv- ett and Pigg 1996, Brodribb 2009). Segments of veins that form loops add to the cost of the venation architecture without directly increasing the flow of water to the leaf lamina or the amount of tissue that can be mechanically supported. They do, however, improve the safety of the flow of water through the leaf (Roth-Nebelsick et al. 2001, Price and Weitz 2014). Plants are vulnerable to interruptions in water flow both from physical damage due to herbivory and from cavitation of their vessels (Zimmermann 1983). Vascular plants have a variety of mechanisms to prevent or mitigate this loss of function at the cellular level. At the macro scale, increased reticulation or “loopiness” can allow plants to re-route flow around lost vessels, maintaining water supply to the leaf (Sack et al. 2008, Katifori et al. 2010, Blonder et al. 2018).

Quantifying leaf venation architecture

The most common approach for quantifying leaf venation, vein density, however, does not directly offer any information about the amount of reticulation in the leaf (Blonder et al. 2011). That quantity, the length of the venation per unit leaf area, can be used to predict other traits like maximum photosynthetic rate, and is still an important method of quantifying venation architecture. A variety of other measures have been proposed and used, including size and number of areoles (enclosed areas of leaf lamina) formed by veins, elongation of these areoles, diameter of veins and vein tapering, numbers of free-ending veins, and ratios of major to minor veins (Blonder et al. 2011, Sack et al. 2013). Each of these measures offers important information about topology, especially at the level of minor veins, but none provides an integrated picture of venation architecture of an entire leaf. Fundamentally, leaf venation is a network: a system of nodes and edges across which a resource flows (Figure 2.1). In these key characteristics, a plant’s vasculature shares much in common with a region’s transportation system, a city’s electrical grid, or the global Internet (Newmann 2010). The robust mathematical field of network (or graph)

29 theory thus offers plant biologists a set of tools that may help us better understand the three-way trade-off between minimizing cost, maximizing flow, and securing the safety of a leaf’s vascular system. Modeling leaf venation using network principles is not an entirely new idea. Venation architecture has been described as a mesh network (Kull and Herbig 1995), and terminology from topology and graph theory have been used to characterize the evolution of vein patterns and model water flow across a leaf (Roth-Nebelsick et al. 2001). Minimum spanning trees (MSTs) have been used to estimate a theoretical minimum amount of vasculature required to supply a leaf and quantify investment in venation (Price and Weitz 2014, Blonder et al. 2018). A hierarchical nesting algorithm based on network structure has been used to quantify the “loopiness” or amount of reticulation in a leaf network (Katifori and Magnasco 2012, Katifori 2018). The software described here, LeafGrapher, is an attempt to bridge the gap between traditional and well-used approaches to analyze venation architecture and topologically- informed network approaches. Starting with a leaf’s venation, represented as a set of line segments, the program generates an undirected graph data structure where edges are segments of vascular bundles and vertices (or nodes) are the intersection points between two segments. We have selected a set of metrics used in the analysis of spatial networks and flow through systems that can offer insight into plant physiological function. These include basic descriptors of graph structure, like the average degree of a vertex or the average shortest path between any two points. The program calculates estimations of “cost”, “efficiency”, and “transport performance” of a graph (Barthélemy 2011), as well as the responsiveness of these traits to sequential edge removal. The program also calculates “spectra” of a graph, illustrated in Figure 2: a set of characteristic values of the leaf venation analogous to optical spectra that have been shown in other systems to predict features like bottlenecks and resistance to flow (Chung and Graham 1997). Other, existing software tools for leaf vein analysis rely on automated image analysis to quantify key features of plant venation or generate network structures for analysis (i.e. Price et al. 2011). These tools have been criticized for being significantly less accurate at identifying and measuring leaf venation than measurements taken by hand (Sack et al. 2014); when compared to multiple automated methods for extracting venation from images, hand tracing was found to have consistently superior results (Clarke et al. 2006). These automated network extraction tools are often well-suited for other applications in plant science, such as plant identification (Kolivand et al. 2019), where the continuity of the network structure is not critical to the analysis. Other tools are quite accurate but require images of a quality and resolution that can be challenging to achieve (Ronellenfitsch et al. 2015). Our tool is therefore designed to work with hand tracings of leaf venation, and includes both an ImageJ extension to export files ready for analysis and a method for converting vector graphic images into networks. As both computer vision technology and imaging technology improve, our software can be easily updated to accept inputs from

30 Figure 2.1: Left An illustrative graph Graph: A set of vertices (or nodes) connected by edges. The mathematics underlying graphs were first formalized by Euler in 1736 (Newmann 2010). A spatial graph is constrained to physical, generally two-dimensional, space. In the leaf: the leaf venation. Node/Vertex (red circles): A set of points included in the graph which may or may not be connected by edges. Nodes can represent either physical or abstract entities, including locations, people, websites, or macromolecules. In the leaf: endpoints and intersections between veins. Edge (grey and blue lines): A connection between two vertices. These can be physical connections, like roads or vascular bundles, or abstract connections, like relationships, URLs, or biochemical processes. Edges can be unweighted, where all edges are the same, or weighted, where different edges are assigned different values. They can also be directed, where travel along an edge can only occur from the source node to the target node, or undirected, travel can occur between either node. In the leaf : the veins (vascular bundles). Weights might be size (length, width, area, or volume) or resistance to water flow. Degree: The number of edges connected to a node. In a directed graph, each node has an in-degree (the number of edges entering) and an out-degree). The circled node has a degree of 4. In the leaf : how many veins connect at a particular intersection. Path: The set of edges which connect any two nodes in the graph. The length of a path is either the number of unweighted edges needed to travel between the nodes, or the sum of the weights of those edges. There may be multiple paths between a pair of nodes. Two nodes are connected if there exists a path between them and disconnected otherwise. All nodes in this graph are connected. In the leaf: how can water (or sugars) travel between points on a leaf. Shortest path: The minimum-length path between two nodes. The average shortest path length is averaged among all possible pairs of nodes.In the leaf : ”shortest” may mean actual length or another quantity that can be minimized, like resistance. Minimum Spanning Tree (MST): The smallest subset of edges (blue edges) that leaves every node in the graph connected. In the MST, there is exactly one path between every pair of vertices. The “opposite” of the MST is the complete graph, where an edge exists between every pair of vertices. In the leaf : the least investment a leaf must make in venation to connect points all across the leaf. Centrality: The “importance” of a given node or edge to the network as a whole. The betweenness centrality (or simply “betweenness”) is a function of the number of shortest paths that contain a particular node or edge (Borgatti 2005). The green rectangle highlights the edge with the highest betweenness centrality in this graph; interestingly, it is not included in the minimum spanning tree. In the leaf : how important a particular section of vein is to water flow. Upper right Adjacency matrix: Numerical representation of the connectedness of a graph. Lower right Degree matrix: A diagonal matrix representing the degree of each vertex in the graph.

31 Figure 2.2: The “spectrum” of a graph, plotting the eigenvalues of the graph Laplacian from smallest to largest. This creates a “characteristic” curve of a graph. Two graph metrics are derived from these values: the Cheeger constant, an indicator of bottlenecks in graphs, and the spectral gap, the diﬀerence between the two largest eigenvalues and which may be related to clustering in a network (Chung and Graham 1997). these tools for automation, while still working with the hand-tracing approach that many researchers prefer. In this report, we detail the mathematical theory and practical implementation of the graph metrics calculated by this program. We also demonstrate their use by comparing the venation traits of a variety of species. Our goal is for LeafGrapher to be a tool that integrates with researchers’ existing methods for studying leaf venation and that oﬀers topologically-informed metrics to provide new insights into leaf form and function.

Implementation

Framework

LeafGrapher is a cross-platform software tool built primarily using Python 3.6 (Python Software Foundation). The user interface is based in Tcl/Tk, written using tkinter in Python. The majority of graph analysis relies on the graph-tool module (Peixoto 2014); matrix operations are performed with SciPy’s linear algebra toolkit (Virtanen et al. 2019). An additional ImageJ plug-in, written in Python 2.7 for ImageJ2, allows for the exporting of hand-traced leaf venation from ImageJ into a text CSV format compatible with LeafG- rapher. All code and documentation is freely available at github.com/jlevye/thesis. Because this software heavily uses the graph-tool module, it is most easily installed on Unix-based systems (ie. GNU/Linux and MacOS). Installation on Windows systems is possible if a Linux-based user environment is installed. Despite this limitation, we use graph-tool as a foundation for this software due to its underlying C++ framework, which greatly increases the speed and efficiency of calculations of graph metrics (Peixoto 2014). Rather than attempting to automate vein network extraction from images, LeafGrapher processes files that represent the network as a series of straight line segments. This is currently done in one of two ways: as a CSV exported from ImageJ or as a scalable vector graphics (SVG) image. An appropriate CSV file can be produced in ImageJ by tracing segments of the venation with the Line selection tool, saving these selections as an Overlay using the Region of Interest (ROI) manager, and processing this overlay with the export

32 plugin provided with this software. SVG image files can be produced using any appropriate vector graphics program; LeafGrapher generates the list of line segments required by the endpoints that define “path” objects. In both the ImageJ and SVG approach, segments can have width assigned by the user; in ImageJ this width is restricted to the nearest integer pixel value. Once the appropriate data is loaded, the program determines if there are any intersections between the line segments provided, and splits these into smaller segments if appropriate. Any segments shorter than a user-provided threshold are discarded, and then for each line segment in the list, a custom Edge object is created. Each Edge object stores two endpoints, as well as a length and width. Length is calculated as the straight-line distance between endpoints; width is either assigned from the value given in the input file or else set equal to one unit. Each endpoint of an Edge object defines a Vertex object. Each time a Vertex object is created, the distance between it and existing vertices is checked. If the newer Vertex is within a user-defined threshold of an existing Vertex, it is set to be a pointer to the existing object. This way, although each Edge is defined by two unique endpoints, those that intersect can be treated as the same node when the graph structure is generated. From the sets of these custom Vertex and Edge objects, a Graph data structure from the graph-tool module is generated; a visual example is shown in Figure 2.1. This Graph structure will be the base object for downstream analysis and stores all properties generated about the graph. After creation, the graph can be displayed to the user, as well as saved in the XML-based “gt” file format.

Graph Metrics

Appropriate Edge Weighting

Many of the graph metrics discussed here rely on an appropriate “weight” being assigned to each edge. All of the metrics call be calculated as if each edge were functionally equivalent, but this is not physically or biologically realistic. Depending on the metric in question, weightings that approximate investment (i), resistance (r) or conductance (k = 1/r) might be appropriate: we may be interested in minimizing the resources a leaf must use to create a graph or maximizing the ease of water ﬂow; multiple options for each metric are available for the user to select. Weightings are calculated as functions of the length (L) and vein diameter (also called width, D), omitting scalar factors that would be applied to every edge (such as pi). The weighting i, approximating investment in vascular tissue as volume, is given in 2.1 (Givnish 1979). Resistance (2.2) is based on the Hagen-Poiseuille law for water

ﬂow through pipes (Tyree and Zimmerman 2002), where dh is the approximate hydraulically weighted mean diameter and n is the estimated number of vessels. Both of these weighting options can be meaningfully summed to calculate path “length,” which either represents the total investment in a connection between two nodes or the total resistance to water along that path. Estimated hydraulic conductance (k) is the inverse of the estimated resistance

33 Figure 2.3: Three methods for calculating vessel size and number from the vein diameter. To the left (blue), a constant number of vessels which scale in size with bundle diameter. In the center (green), vessels of a ﬁxed size which decrease in number with vein diameter. To the right (red), vessels where the diameter equals the vein diameter raised 1 to the /6th power (after Coomes et al. (2008)), which both decrease in size and number as the vein diameter decreases.

(as deﬁned by Ohm’s law).

i = L × D2 (2.1) L r = 4 (2.2) ndh

Several options are provided for estimating dh from the measured vascular bundle width; these are illustrated in Figure 2.3. The user can select from: a fixed number of vessels that scale linearly in size based on bundle diameter, a fixed vessel size with a variable number of vessels, or a variable number of vessels which decrease in size as a fractional power (ie, non-linearly) of the decreasing measured vein width. The latter option is based on the observation that xylem vessels tend to be proportional to diameter of the vascular bundle raised to the power of 1/6, though this value varies by species (Coomes et al. 2008). In all cases, the proportion of the area of the vascular bundle which is occupied by vessels, set to 1 by default, can be defined by the user.

Basic Metrics

For a given leaf graph, several properties of edges and/or vertices are calculated; the actual values are stored as properties of a given edge or vertex, and mean value and standard deviation are reported for the graph as a whole. These core graph metrics are implemented using functions from the graph-tool module (Peixoto 2014). These include the degree of the vertices and the betweenness centrality of the edges (both deﬁned in Figure 2.1). Between- ness centrality is calculated using the algorithm developed using Brandes (2001) to identify the number of shortest paths a given edge is included in, and can be weighted using either the cost or the resistance of the edges. The shortest path between every pair of vertices is calculated using Dijkstra’s (1959) algorithm and can also be weighted using cost or resistance. The minimum spanning tree (MST), is the smallest set of edges (or the set of edges with the lowest total weight) needed to connect all the vertices. It is by default calculated using cost as the edge weighting, and is computed using the Kruskal (1956) method. Based on these core measures, three key metrics for quantifying redundancy in spatial

34 networks are calculated: Cost (CN ), Eﬃciency (EN ), and Transport Performance (PN ) (Barth´elemy 2011). Cost (Equation 2.3) is the total length of the graph over the length of the minimum spanning tree; “length” is calculated using the investment (i) of each edge. This value represents the excess investment in vascular connections over what is strictly necessary to span the set of vertices and has been used before to analyze leaf venation architecture (Price and Weitz 2014). In a leaf with no “extra” edges beyond those needed to connect all the

vertices, CN = 1. CN diﬀers from a more colloquial use of the term “cost” in that it is a relative metric, comparing the actual “size” of the vein network to the theoretical minimum

(the MST). Two leaves may have similar investment in vasculature but diﬀerent CN because the latter depends on the structure of the network.

lT CN = MST (2.3) lT Transport Performance (Equation 2.4) is one way to represent the beneﬁt gained by increased redundancy; it is the ratio between the average shortest path length in the full graph and the average shortest path length in the MST where path length calculated from the approximate resistance of the edge. A smaller value of PN represents a gain in performance, meaning a decrease in resistance to traverse between two points (or correspondingly, an increase in conductance). Like CN , PN compares the actual vein network to the theoretical minimum, quantifying the performance gain by including more connecting veins.

hli PN = (2.4) hlMST i Eﬃciency (Equation 2.5) is the average of the inverse of the shortest path lengths across all pairs of nodes (represented as i and j), where N is the total number of nodes in the graph.

In an unweighted graph, EN would equal 1 if an edge existed between every vertex. EN is similar to other uses of the term “eﬃciency” in that higher values indicate quicker movement

across a graph. In a leaf, EN approximates the average conductance (k) between any two points across a graph when the path lengths are calculated using resistance (r) as the edge weight, as k is the inverse of r.

1 X 1 EN = (2.5) N(N − 1) li,j i6=j

Fault Tolerance

Fault tolerance testing is used in engineering to determine the required level of redundancy needed to maintain a resilient network (Gao et al. 2016). LeafGrapher oﬀers several variations on a general fault tolerance testing approach wherein edges are removed sequentially and after each edge removal, several graph metrics are calculated. A user may have diﬀerent

35 hypotheses based on the order segments of vasculature fail: one might assume the largest veins will be the first to cavitate, or one may be interested in assessing the importance of edges based on a centrality metric. Therefore, edges can be removed in a random order, sorted by a given weight, or sorted by betweenness centrality (see Figure 2.1); in either sorting option, the removal can occur in ascending or descending order. Edge removal occurs by creating an array of “true” or “false” values matching the number of edges; the “true”/“false” array is used to filter the edges (including only those with a value of “true”) of the graph for analysis, which allows for manipulations without altering the underlying data structure. After each edge, or a user-set number of edges, is removed, the desired set of metrics is recorded. These include the size (number of nodes) in either the largest connected set of nodes or the number of nodes remaining connected to a user-defined source node, as well as the Cost, Transport Performance, and Efficiency of the graph. Edge removal can continue until either a selected metric drops below a set percentage of the original value, or until all the edges are removed. For each graph, a CSV file, including metadata, is generated for data export. Random edge removal can also be run iteratively, saving the number of edge removals required to reach a target threshold for each run to generate a distribution of values.

Spectral Graph Theory

All graphs can be represented as matrices. The simplest of these, the adjacency matrix, is made up of entries that represent presence and absence of edges between nodes. The degree matrix is a diagonal matrix where each non-zero value is the degree of that node; examples of these are shown in Figure 2.1. The Laplacian matrix, also called the graph Laplacian, found by subtracting the degree matrix from the adjacency matrix, works out to be the same matrix used in calculating the rate of diffusion of a fluid through a network (Newmann 2010). The graph Laplacian, and in particular its eigenvalues, provides a means to model the flow of materials through the leaf vasculature. The eigenvalues of a matrix are a set of characteristic values that define that matrix. The eigenvalues of the graph Laplacian in particular are useful as a “spectrum,” unique to a particular graph (of a leaf) allowing meaningful comparison among different graphs. The concept is analogous to an optical spectrum or spectral profile of an object to differentiate useful properties among them (Chung and Graham 1997). LeafGrapher computes and reports the set of real eigenvalues of the graph Laplacian using SciPy’s linear algebra functions for sparse matrices. The tool can either produce all the eigenvalues (equal to the number of vertices in the graph) or an even sampling of a fixed number of these values. The “spectral gap” is the difference between the two largest eigenvalues. In addition, the second-smallest eigenvalue (SSE) of the graph Laplacian is noted as approximating the Cheeger number of the graph (Alon 1986), a value which indicates the presence of a bottleneck to flow in the

36 graph (Cheeger 1970).

Data Management

All calculated metrics are stored as properties of the graph in the gt XML file generated when a graph is saved. In addition, all data produced is exported to a CSV file, either auto- generated or selected by the user. Every time data is exported, a metadata file containing all parameters used in analysis is generated. The exported headers of generated CSV files are standardized such that they can be used to set the desired metric calculations and parameter values automatically.

Results and Discussion

We demonstrate the use of this software with data from three scales of similarity: a set of Lespedeza capitata leaflets collected from a single 9m x 9m plot, leaves from a variety of Quercus species, and leaves from a variety of other species chosen for morphological diversity. We measured leaf hydraulic conductance (Kleaf ) on a subset of these species using the evaporative flux method detailed by Sack and Scoffoni (2012). More detailed methods, including a full list of species included, are given in the Appendix. Detailed leaf images of some of the species included are shown in Figure 2.4. These datasets have been both analyzed separately and considered in aggregate to capture the scales of variance in the graph metrics. In L. capitata and G. biloba, all visible veins were included. For the other species, major veins of the 1st through 4th orders were traced and included in the analysis, such that the midrib was the primary (1st order) vein, large veins branching directly from the midrib were secondary (2nd order), and so on. This typically meant including all veins of width 0.075 mm and greater. If there was ambiguity in the processed image regarding whether a possible segment was a vein or an artifact from staining or scanning, the segment was omitted. The reported results may, therefore, under-represent the vein network.

Core Metrics

Figure 2.5 illustrates the ranges of values for Cost, Efficiency, Transport Performance, and mean betweenness centrality, using the three different edge weighting methods and for each data set. We show these results aggregated among L. capitata, G. biloba, all Quercus species, and all other species. In many cases, especially Cost, the vein network of G. biloba was significantly different from all other species (Tukey’s Honest Significant Difference). We observed a large amount of variation in all other metrics, even within individuals of a single species. To ground the underlying assumption we make about the relationship between network- based efficiency and plant hydraulics, we measured Kleaf in a variety of species. Shown in

37 Figure 2.4: Example vein architectures in the demonstration data sets. a) Crescentia cujete; b) Doliocarpus major; c) Terminalia amazonia; d) Quercus aristata; e) Quercus crassipes; f) Quercus wislizeni; g) Ginkgo biloba; h) Lespedeza capitata. Source images for a-c were provided by C. Smith (personal correspondence); g was traced from Arnott 1959. d-f were collected from a greenhouse common garden of American oak species. The leaﬂet shown in h is representative of the a set which includes 4 individual plants, 2 leaves per plant, and 3 leaﬂets per leaf, collected in the summer from a monoculture plot at Cedar Creek Ecosystem Science Reserve. A full list of species included in these analyses can be found in the Appendix.

38 (a) (b)

Figure 2.5: Variation in a sample of core metrics (clockwise from upper left: Cost, Eﬃciency, Transport Performance, mean Betweenness Centrality) within and among four groups: within L. capitata and G. biloba, among Quercus species, and among a variety of other species (“Other”). In each of these examples, the metrics have been calculated from the unweighted graph (facet label “None”), a graph weighed by the approximate resistance of the edges (“Res”), and a graph weighted by the approximate volume of the edges (“Vol”). G. biloba leaves have a signiﬁcantly lower cost for all weighting types than other groups.

39 Figure 2.6: Measured Kleaf increases with estimated Efficiency. The estimated Efficiency (using resistance as the weighting method) was calculated for 2-4 leaves in 6 species of greenhouse-grown trees on which we measured hydraulic conductance using evaporative flux. There is a strong relationship between the theoretical and measured hydraulic performance, shown here with an ordinary least squares linear regression (slope = 3.91 × 10−3,p = 8.28 × 10−5, multiple R2 =0.655).

Figure 2.6, we do find a significant relationship with Efficiency (weighted using estimated resistance) and Kleaf (Pearson’s r = 0.81). This relationship may be driven largely by E. pulchellum: in this set of species, there was little variation in values of Kleaf except from E. pulchellum, which was significantly different from the other species (Tukey’s HSD, p = 0.01 - 0.06). These results do support the potential utility of this metric in assessing a plant’s hydraulic performance.

Fault Tolerance Testing

We illustrate our fault tolerance testing scheme by comparing the highly reticulate Q. wislizeni with the nearly completely branching G. biloba. We would expect the effects of edge removal by any method to be more severe in G. biloba because there are very few alternate pathways in the leaf, and our results match these expectations. In Figure 2.7 (left), we compare the proportion of edges removed to the proportion of the leaf still connected to the petiole under four different removal scenarios. In all cases, a larger proportion of the leaf’s vertices remain connected in Q. wislizeni than in G. biloba for the same proportion of edges removed. This difference is least pronounced when edges are removed from the least central to the most central as measured by betweenness centrality. When removal occurs from most central or largest first, however, removing just one percent of the edges in the graph leaves less than 15% of the ginkgo leaf still connected to the petiole but has almost no effect on the oak leaf. Iterated random edge removal illustrates this difference even more clearly. We randomly removed edges from each graph until the component of the graph connected to the petiole

40 (a) (b)

Figure 2.7: Upper: Comparison of fault tolerance, in terms of connectivity to the source (petiole) vertex between G. biloba and Q. wislizeni using betweenness centrality or investment in terms of estimated edge volume in ascending order (left) or descending order (right). In all cases, the highly reticulate Q. wislizeni retains a larger proportion of connectivity for the same loss of edges when compared to the branching G. biloba. Lower: Proportion of edges randomly removed before reaching 50% loss of connectivity, iterated 100 times. For G. biloba, the mean value is 2% of edges removed, while for Q. wislizeni, the mean value is 32% of edges removed.

41 Figure 2.8: Graphical representation of the eigenvalues of the graph Laplacian, calculated using the unweighted graph. Each graph has a total number of eigenvalues equal to the number of vertices and are ordered smallest to largest; to compare among graphs, 100 values are evenly selected from the ordered set for each graph. Points are the mean for a given species and error bars are the standard deviation from the mean. was 50% of the original, and ran this removal 100 times. A histogram of proportions of edges removed to hit this 50% threshold is shown in figure 2.7 (right). The distributions of values for the gingko and the oak do not overlap, and the means differ by an order of magnitude. This approach to testing the resilience of leaf venation clearly captures the differences in two extremely different architectures; further testing paired with empirical results will be needed to see if this simulation concurs with measured leaf hydraulic vulnerability.

Spectral Proﬁling

Curves representing the range of eigenvalues of the graph Laplacian for each genus in our testing data set are shown in Figure 2.8. Separation among species is observed in the largest 25% of eigenvalues; these larger eigenvalues might offer the most useful tool for differentiating among species. To test this idea, we generated dendrograms to find clusters of individuals based on the graph spectra. Euclidean distance was used to calculate the difference between leaf graphs, and clustering was performed using the default values of the “hclust” function in R. These results, however, were inconclusive, and further analysis is needed to determine what, if any, plant traits that graph spectra can capture.

Conclusions

LeafGrapher adds a new set of analysis tools to the options available to plant vascular biologists interested in venation architecture. It provides a user-friendly implementation of a suite of metrics drawn from network analysis which we believe provide new insights into the structure and function of leaf venation. The metrics chosen capture variation within and among species, and generally follow predicted expectations about the relationships between increased investment in vascular architecture, hydraulic safety, and performance. While empirical validation of these metrics was limited by a small dataset, the results we show highlight the promise of this software tool for future analyses. For example, the relationship between network Cost and any of the metrics that indicate performance (especially network Eﬃciency, Transport Performance, and fault tolerence) can

42 give us a way of quantifying the ”return on investment” in venation architecture. For a similar network Cost, different leaf architectures may gain more benefit from the additional linkages present in the network. Following the framework of the leaf economic spectrum (Wright et al. 2004), we may expect leaves in resource-limited areas or plants with longer leaf lifespans to exhibit leaf architectures with a higher return on investment. This software has been built to be portable and flexible. The classes and functions that provide the core utility of the tool can be imported as a Python module to be used in other applications or interactive sessions. All steps in the analysis pipeline which produce output also generate metadata files in plain text, designed for easy reproducibility of settings. The graph data structures created for analysis are stored as archives in the gt binary file format provided by the graph-tool, storing both the graph structure and all the properties calculated in the analysis. This archive format can easily be converted to the XML-based GraphML file format, which can easily be parsed by many other programs, including R (Brandes et al. 2002). The graph data structure in general will enable the use of any quantifier used in network theory to be applied to leaf venation. As with traditionally measured vein density, the metrics calculated by LeafGrapher are only as useful as the source data provided is accurate. This has been a barrier to automating the extraction of veins from leaf images, such that hand tracing has consistently provided better results than automated processing (Clarke et al. 2006, Sack et al. 2014). Improvements in both imaging technology and extraction approaches might remove this barrier: two-dimensional X-ray and three-dimensional micro chromatography tools have begun to gain more widespread use in the study of plant vasculature (Schneider et al. 2018), and more easily provide the resolution and image-quality required by accurate vectorization schemes like that of Ronellenfitsch et al. (2015). In future releases of LeafGrapher, we aim to implement the hierarchical loop decom- position algorithm developed by Katifori and Magnasco (2012), which provides a novel approach to understanding redundancy in network systems. We also hope to integrate tools for modeling flow and changes in fluid pressure across a graph; modeling the drop in pressure across a leaf (or leaf-like network) is a clearer way of demonstrating resilience of the network (Roth-Nebelsick et al. 2001, Katifori et al. 2010). We also plan to improve the speed of processing and calculations, especially in our fault tolerance testing protocol. As further empirical testing of these metrics continues, we expect that our preliminary results will become more robust and the relationships between these metrics and plant physiological function to become clearer. We believe LeafGrapher to be a flexible and valuable new tool for plant vascular biologists.

43 Chapter 3

Network-derived traits help demonstrate resource-allocation trade-oﬀs in oaks

Introduction

Understanding leaf vasculature is fundamental to our ability to understand plant productivity and function. The structure of the leaf vascular system can act as a key limit to a plant’s maximum photosynthetic rate because of its dual role in supplying water to and transporting sugars from photosynthetic tissue (Brodribb et al. 2010, Adams et al. 2018, Polutchko et al. 2018). Venation architecture is also highly diverse (Hickey 1973), with important structural differences found between closely related species (e.g Carr et al. 1986) and within species across changing climates or resource gradients (e.g. Uhl and Mosbrugger 1999, Scoffoni et al. 2015). Variation in hydraulic traits like vein architecture is closely linked to other variation in leaf form and function (Sack and Frole 2006). Venation traits also play an important role in a plant’s ability to resist drought (Blackman et al. 2018). Venation architecture offers a compelling case study for considering plant function in an ecological context because of the critical trade-offs involved in allocating resources to vascular tissue. Though critical for supporting gas exchange and metabolism, vascular tissue is energetically costly for a plant to produce and represents a substantial portion of a plant’s total biomass (Brodribb 2009). This trade-off depends not only on the quantity of vascular tissue developed, but also the proportions of veins of different sizes and the connectivity of the network (McKown et al. 2010). Requirements for water and solute transport must also be balanced with the mechanical support provided by the vein network to the leaf, and the mechanical traits and hydraulic traits both driven by vein architecture do not necessarily correlate with each other (Kawai and Okada 2016). One major framework for understanding trade-offs in plant resource allocation is the

44 leaf economic spectrum (LES): a suite of traits which, considered collectively, characterize strategies plants have evolved for managing resource use (Wright et al. 2004). Plants may grow thin or broad leaves with short lifespans, able to quickly take advantage of available nutrients with very high maximum photosynthetic rates, or they may trade lower rates of productivity for thick, long-lasting leaf tissues that may be less vulnerable to damage. The roles that water use and plant hydraulic traits play in this framework have been identified as important sources of uncertainty (Reich 2014). Whether venation architecture, especially vein density, acts as a foundational trait underlying much of the rest of the leaf economic spectrum, or is instead part of a complex network of traits related to resource fluxes, has been a source of significant debate (Blonder et al. 2011, Sack et al. 2013, Blonder et al. 2014). One source of uncertainty in studying the functional implications of leaf venation architecture has been a lack of a widely used approach to quantifying the topology of venation. Vein density, or vein length per area (VLA) is the most widely used and best understood way of understanding leaf vasculature (Sack et al. 2013), but it does not capture differences in the structure or connectivity of the system. Many approaches to understanding and quantifying leaf venation have been proposed (Roth-Nebelsick et al. 2001); here we use an approach that focuses on the network structure of a leaf’s vasculature to quantify how resilient the vascular system might be to damage (see Chapter 2; Katifori and Magnasco 2012, Katifori 2018). Our aim in this study is to use these network-informed vein architecture traits to better understand the relationships between leaf hydraulics and other plant functional traits in the context of environmental variation in oak species found in the Americas. The Quercus L. genus is ecologically important, diverse, and abundant in the Americas (Cavender-Bares et al. 2016). Oaks exhibit a high degree of functional diversity that helps support the species richness found at a regional scale (Cavender-Bares et al. 2004a), especially in the context of drought and water-use traits (Skelton et al. 2018, Cooper et al. 2018). We consider the leaf venation architecture of 16 species of oaks grown in a greenhouse common garden experiment. These species include representatives from the major sub- clades (section Quercus [white oaks], section Lobatae [red oaks], as well as sections Proto- balanus, Virentes, and Cerris) across a large climatic gradient (Kaproth and Cavender-Bares 2016). An experimental drought treatment was imposed on the plants in their second year of growth; in addition to venation architecture, we measured relative growth rates, gas exchange, osmotic potential, and stomatal characteristics of these plants. We also use the network traits that we measured to develop a simple approach to assessing “return on investment” in leaf venation architecture (Figure 3.1). We use this data to ask the following core questions:

1. What are the relationships between venation traits (both vein density and network- informed traits) and known functional traits?

45 Figure 3.1: If we consider “investment” as an increase in the size, complexity, or redundancy of a leaf’s vascular network, and “performance”” is the beneﬁt a plant gets (in either overall hydraulic performance, or in resilience to damage), we might expect to see a generally consistent increase in performance with increased investment. We may also not observe a direct linear relationship, but can still consider whether an individual leaf is performing better than average (above the black line) or worse than average (below the line).

2. How do venation traits vary among taxa within the oaks, considering both phylogenetic groupings (sub-clades) and functional ones (especially leaf habit)?

3. How do venation traits change with climate, either climate of origin or imposed drought treatment?

We expect to observe traits indicating a higher leaf hydraulic conductivity (higher vein density and higher network efficiency [see Chapter 2 Figure 6]) to be associated with higher rates of transpiration and photosynthesis across all species (Brodribb 2009, Scoffoni et al. 2016). However, this association may be complicated by the fact that if venation characteristics are highly conserved within Quercus species, the variation in leaf hydraulics may be more driven by non-xylem hydraulic pathways than by venation (Scoffoni et al. 2016, Rockwell and Holbrook 2017). Venation architecture has been observed to vary significantly based on light availability (Scoffoni et al. 2015), and we expect to see a similar degree of plasticity in response to drought.

46 Species Section Leaf Habit n Q. acutissima Cerris Deciduous 2 Q. alba Quercus Deciduous 1 Q. castanea Lobatae Brevideciduous 1 Q. chapmanii Lobatae Evergreen 2 Q. chrysolepsis Protobalanus Evergreen 2 Q. douglasii Quercus Deciduous 2 Q. garryana Quercus Deciduous 1 Q. laevis Lobatae Deciduous 1 Q. lobata Quercus Deciduous 1 Q. lyrata Quercus Deciduous 3 Q. macrocarpa Quercus Deciduous 1 Q. myrtifolia Lobatae Evergreen 3 Q. robur Quercus Deciduous 1 Q. rubra Lobatae Deciduous 3 Q. virginiana Virentes Brevideciduous 1 Q. wislizeni Lobatae Evergreen 4

Table 3.1

Methods

Study System: Oak Common Garden

The leaves included in this analysis were collected from a small subset of oak trees grown in common garden greenhouse experiment in 2013 and 2014. Oaks from forty species found in the Americas were grown from seed at three water availability treatments. Plants were grown in 1.5 m pots in a potting soil-sand mixture and were fertilized bi-monthly (Kaproth and Cavender-Bares 2016). Included in this study are 29 individuals (representing 16 species, summarized in Table 3.1) which were grown at either the low (7% volumetric water content) or moderate (14% VWC) water treatment. Leaves from these individuals were collected after the drought treatment was ended, and in coordination with leaves which were sampled to measure osmotic potential.

Physiological Measurements

All functional trait measurements were collected on the same plant as venation metrics, though not the same leaves. Stomatal density (SD), stomatal aperture length (mm), and the stomatal pore index (SPI,= SD × aperture length2; Sack et al. 2003) were calculated using stomatal peels taken from newly developed mature leaves. Gas exchange (photosynthetic −2 −1 −2 −1 rate (µmol CO2 m s ), transpiration rate (mol H2O m s ), and stomatal conductance −2 −1 (mol H2O m s )) measurements were collected mid-way through the growing season using a LI-COR 6400 (LI-COR Biosciences, Lincoln, Nebrasca). Osmotic potential was collected near the end of the second growing season following the method outlined in Bartlett

47 et al. (2012); pre-dawn water potential was also measured during this collection period. Chlorophyll content was measured using a SPAD meter (Spectrum Technologies, Aurora, Illinois). Speciﬁc leaf area (SLA) was calculated as leaf dry mass (g) over leaf area (cm2), and leaf thickness (mm) was measured with a micrometer, avoiding the largest veins during measurement.

Climate

Global occurrence information for all 19 species was accessed through the Global Biodiver- sity Information Facility (GBIF); records from direct observations and preserved specimens with location information were included. These records were manually veriﬁed to remove occurrences in arboreta and botanical gardens or if the location given was likely an herbarium rather than source tree. All data were downloaded November 5, 2019. Mean values of climatic variables for each species were calculated using the bioclimatic variables (chieﬂy mean annual temperature (MAT, ) and mean annual precipitation (MAP, mm) generated by WorldClim Global Climate Data (Hijmans et al. 2005), and potential evapotranspiration (PET mm, day−1), actual evapotranspiration (AET, mm day−1), and the aridity index (MAP divided by mean annual PET) data from the Consortium for Spatial Information (Zomer et al. 2008, Trabucco and Zomer 2010).

Venation Analysis

Leaves collected for venation were dried at 70 for at least three days prior to storage for ultimate processing. Dried leaves were cleared of pigments and non-structural tissue by soaking in a 5% sodium hydroxide solution for approximately one week before bleaching and staining in Safranin-O and ethanol. Leaves were mounted on plastic film in Permount mounting medium (Fisher Chemical), then scanned and archived. Scanning was performed with a flatbed scanner (Epson) at a resolution of either 600 DPI or 800 DPI. For each of the individual plants with both scanned leaves and physiological data for the greenhouse experiment, the highest quality leaf image was chosen to be traced and analyzed. The major venation of scanned leaves was traced using a vector graphics program (Inkscape v0.92). All vein segments larger than 0.075 mm were traced into straight line segments; this threshold included all primary and secondary veins, as well as most tertiary and some quaternary veins and thus captured what would typically be considered the “major veins” (Hickey 1973). The image files were exported in scalable vector graphics (SVG) format, producing a text file able to be parsed for conversion into graphs. These files were then converted into graph data structures using the software LeafG- rapher v0.1; see Chapter 2 for more details. The set of metrics calculated is summarized in Table 3.2, which also lists the “weighting” method used to calculate each metric. Un- weighted metrics treat each edge in the graph as identical, regardless of length or width. “Volume” based metrics are weighted by the product of the length and width of the vein,

48 Graph Units Description Notes Trait Cost * Increase in investment in vein network Increases with graph over theoretical minimum (MST) redundancy Efficiency mm3 Average inverse of shortest path lengths Weighted using es- across network timated resistance; increase associated with increased hydraulic conductance Transport * How much shorter the average shortest Smaller values indi- Performance path is in the actual network over the cate faster movement minimum spanning tree. across graph Betweenness * Mean value reported. Number of short- Centrality est paths an edge finds itself on. Total Length mm Total length of vein network (major veins) Major Vein mm/mm2 Length of vein network (width > 0.075 Density mm) over leaf area Max. width mm Width (i.e. diameter) of largest vein segment Avg. width mm Weighted average (based on length) of edge width Cheeger con- * Square root of the second smallest eigen- Low values indicate stant value of the graph Laplacian bottlenecks in a network Spectral gap * Difference between largest and second largest eigenvalue of the graph Lapla- cian. Fault toler- % Mean percentage of edges removed (in Higher values suggest ance 100 iterations) until only 50% of vertices increased resistance to are connected to source (ie, petiole). damage

Table 3.2: Major graph traits, with units and notes. * = unitless and “resistance” based metrics are weighted an approximation of the Hagen-Poiseuille Law given in equation 2.2, where dh is the approximate hydraulically weighted mean diameter of the xylem vessels and n is the estimated number of vessels. In this analysis, we calculated dh using the relationship described by Coomes et al. (2008), that the diameter of a xylem 1 vessel tends to be proportional to the diameter of the vascular bundle raised to the /6 power. For each of these leaves, we also calculated leaf area (mm2), perimeter (mm) and length (mm) using ImageJ2 with Fiji (Rueden et al. 2017, Schindelin et al. 2012). A unitless “lobedness” index was calculated as (perimeter/area)×length. Correlations between pairs of functional, venation, and climatic traits were tested using

Spearman’s rank correlation coeﬃcient (rs). Other statistical tests are noted where appropriate in the Results; all analysis were performed using R (R Core Development Team 2017).

49 Figure 3.2: Correlations between graph traits and leaf functional traits.

Results

Venation and Functional Traits

Venation traits were found to correlate with a variety of anatomical and physiological leaf traits (Figure 3.2). The strongest associations found were with leaf area: larger leaves had more overall venation (rh = 0.96), though somewhat lower vein density (rh = -0.46).

Increased leaf size was also strongly associated with a lower graph Eﬃciency (rh = -0.95)

and increased risk of bottlenecks (i.e. a lower Cheeger constant, rh = -0.97). Stomatal aperture length, though not stomatal density, was positively correlated with venation Cost (rh = 0.669 ), total length (rh = 0.588 ), and average vein width (rh = 0.519); each of these correlations is stronger than the relationship between stomatal aperture length

and leaf area (rh = 0.493). This suggests that there is some relationship between larger stomata and a more complex venation network beyond that which might be expected to be associated with increasing leaf size.

Leaf thickness was positively correlated with graph Eﬃciency (rh = 0.603), Cheeger con-

stant (rh = 0.588), and major vein density (rh = 0.519), suggesting an association between increased investment in leaf tissue (via thickness and vein density) with higher performance (higher hydraulic conductance and reduced bottlenecks). Neither photosynthetic rate nor stomatal conductance were strongly associated with any of the venation traits we expected

50 Figure 3.3: Principle component analysis including 12 venation and functional traits. Deciduous and evergreen leaves differ significantly along both axes (p = 0.012 for PC1 and p = 0.031 for PC1, Student’s t-test). to be related to hydraulic performance. Transpiration rate did show weak positive correlations with efficiency (rh = 0.208) and mean removed edges (rh = 0.205), as well as a weak negative correlation with the mean vertex degree (rh = -0.233). There was, however, a fairly strong correlation between both transpiration rate and stomatal conductance and the

“spectral gap” calculated by eigenvalues of the graph Laplacian(rh = 0.522 and rh = 0.512,

respectively). The spectral gap is also weakly (rh = 0.269) correlated with mean number

of removed edges from fault tolerance testing and with osmotic potential (rh = 0.321); it was the only vein trait which showed any correlation with osmotic potential. Some of the relationships demonstrated via correlation also emerge in a principle com- ponents analysis, which helps highlight how these traits differ in deciduous and evergreen (including brevideciduous) trees (Figure 3.3). Efficiency is tightly coupled with the Cheeger constant, while network Cost groups with both average and maximum vein width and leaf area and major vein density and thickness group together but are distinct from network cost and vein width. The separation of evergreen and deciduous leaves along these two axes is significant, especially in mean value of PC1 (p = 0.012, Student’s t-test).

51 Figure 3.4: Hydraulic return on investment in leaf venation architecture. The slope of the black line is mean Eﬃciency over mean Cost. A point lying above this line suggests a leaf is getting a better- than-average gain in hydraulic performance for a given amount of investment in vascular tissue.

Figure 3.5: Resilience return on investment in venation architecture. The number of edges which can be removed from a vascular network before a 50% loss of connectivity is positively correlated (Spearman’s r = 0.64). The regression line fit for evergreen leaves has a significantly higher (p = 0.0397) than the line fit for deciduous leaves, suggesting a better gain in fault tolerence for the same investment in a vascular network.

Return on Investment

Figures 3.4 and 3.5 illustrate two ways we consider the benefit a plant may gain by increasing the network cost of the venation - hydraulic performance (Figure 3.4) or resistance to damage (Figure 3.5). While graph Cost and Efficiency are not themselves strongly correlated, we can consider the ratio of Efficiency to Cost as a way to assess return on investment. Each leaf was categorized as performing “better” than average if its’ Efficiency:Cost ratio was higher than the ratio of mean Efficiency to mean Cost, and “worse” if its relationship was lower. We found that leaf habit was a significant predictor of return on investment category (binomial regression, p = 0.015); evergreen leaves were more likely to exhibit a better-than-average return on investment. Several traits, both venation and functional, were significantly different (Student’s t-test, p < 0.05 unless otherwise noted) between leaves with better or worse than average return on investment, shown in Figure 3.6. Leaves with a better return tended to be smaller and thicker, with a lower SLA and slightly lower lobedness (p = 0.07). Their venation networks tended to have a lower average degree and a higher Cheeger constant, implying lower risk of bottlenecks. In Figure 3.5, we use the mean percentage of edges which can be removed before 50% of the venation network becomes disconnected as the assessment of performance compared to vein network cost. Cost and mean edges removed are correlated (rh = 0.65), so we compared

52 Figure 3.6: Trait values of selected leaf and graph traits in over- and under-performers. Diﬀerences in mean trait values for all plots shown are signiﬁcant (Student’s t test, p < 0.05) except lobedness (p = 0.07).

53 Figure 3.7: Correlations among venation traits and climate variables linear regressions between the leaf habit categories and found that evergreen leaves have a signiﬁcantly higher slope than deciduous leaves (p = 0.04). As the Cost of a vascular network increases, evergreen leaves become more fault tolerant than deciduous leaves.

Venation and Climate

The imposed drought treatment had no effect on any of the venation traits calculated or functional and physiological traits measured, at least for the subset of plants included in this study. We did find some associations between vascular network traits and climatic variables (Figure 3.7). In particular, Transport Performance was positively correlated with each of the four climatic variables included, most strongly with MAP (mm, rh = 0.559) and AET (mm −1 day , rh = 0.427). Lower values of Transport Performance indicate faster “movement” across the network; thus improved performance is associated with drier, cooler climates. Figure 3.8 shows several graph traits varying with aridity index (AI); a low AI indicates a more arid environment. We observed higher Efficiency and Cheeger constants, and a higher density of major veins, in drier climates, while the total length of major veins and average vein width was lower. Drier climate was also associated with smaller (rh = 0.464) and thicker (rh = -0.55) leaves. Species with higher than average Efficiency to Cost ratio were also found in more arid

54 Figure 3.8: Selected graph traits versus aridity index (AI). Each graph trait shown has a correlation coefficient of at least 0.4. Low values of AI suggest highly arid climates. climates when comparing AI than those with lower than average ratios (Student’s t-test, p = 0.004), and also came from slightly warmer environments, though the difference in MAT was not significant.

Venation and Taxonomic Groupings

Most differences in venation traits between the red (section Lobatae) and white (section Quercus) oaks can be best explained by leaf habit: 10 of 14 white oak specimens were from deciduous species (experiencing full, seasonal leaf loss), while 8 of 10 red oak specimens were evergreen (or brevideciduous, experiencing only partial leaf loss). To attempt to identify venation traits that might differ with lineage, we tested for differences in venation traits, leaf area, and lobedness in red versus white deciduous leaves. Of the 14 traits tested, only the fault tolerance metric was significantly different between the two sections. The venation networks of deciduous red oaks could lose a mean of 12.8% of edges before half of vertices were separated from the petiole vertex, while white oaks could lose 10.9% of edges (Student’s t-test, p = 0.019; Figure 3.9). No other trait differences between deciduous red and white oaks were significant.

55 Figure 3.9: Venation networks of deciduous red oaks (n=4) are more resiliant than white oaks (n = 8; Student’s t test, p = 0.02). No other leaf traits exhibited significant differences between the different sections.

Discussion

Our results highlight some important ways that network-based metrics can be used to understand the relationship between venation architecture and resource allocation. Venation traits can be used to estimate the benefit a leaf gains from increased investment in vascular tissue, and a higher return on investment in vasculature appears to fit expectations based on other traits in the leaf economic spectrum (LES) like specific leaf area and leaf lifespan. We observed significant differences in venation traits based on both leaf habit and climate of origin, though not based on imposed drought treatment. The calculated metrics we theorized as related to leaf performance, especially the Cheeger constant and the ratio of Efficiency to Cost, were higher in smaller, thicker leaves with lower SLA. These functional traits are associated with drought tolerance (Nardini et al. 2014), and they were, along with their correlated graph traits, related to higher aridity in the species’ range. Leaves with low SLA and high construction costs are typical of evergreen plants (Villar and Merino 2001); evergreen leaf habit was a strong predictor of higher Effi- ciency:Cost ratio. These relationships form the core conclusion of this study: that we can fit some network-derived venation traits into a resource-allocation schema like the leaf economic spectrum (Wright et al. 2004, Reich 2014). Our results offer a different perspective to the debate on how venation architecture relates to the LES - we show that instead of serving as the theoretical foundation for traits like SLA (Blonder et al. 2011, 2013, 2014) or an indirectly-related componenet of a flux system (Sack et al. 2013, 2014), a vein network with a high return on investment might help plants with a “slow” strategy in the LES get the most benefit from limited available resources. More empirical analysis will needed to determine if these results are generalizable. We found some surprising associations among calculated graph traits and leaf functional traits. The approximate Cheeger constant and graph Efficiency, two graph traits which are calculated from very different aspects of the network (Barthélemy 2011, Chung and Graham 1997), are very tightly correlated. This correlation may be driven largely by leaf area, which is correlated with both. However, like the Cheeger constant, the spectral gap is calculated

56 from eigenvalues of the Laplacian matrix of the graph; in our data set, the spectral gap was completely unrelated to both the Cheeger constant and leaf area. Similarly, Transport Performance and Cost are both functions of the minimum spanning tree of the graph: Cost measures the increase the size of the graph compared to the minimum spanning tree while Transport Performance measures the decrease in shortest path lengths. In our data set, these metrics were uncorrelated. Based on known relationships between venation, leaf hydraulic conductance, and photosynthetic rate (Brodribb et al. 2007), we expected to observe relationships between vein network traits indicating higher investment and gas exchange traits. The only venation trait we found correlated with gas exchange (transpiration rate and stomatal conductance) was the spectral gap. While this value has known applications in abstract networks for identifying clusters or subgroups within a graph (e.g. Popa 2007), the significance of this value in spatially explicit networks is not generally known. If the relationship between this value and gas exchange traits is supported by future analyses, it could open a novel intersection between plant physiology and mathematical theory. We were unable to make any conclusions about the plasticity of vascular traits in response to drought. There were no differences in any vein traits between plants in the two treatments, but there were also no significant differences in plant functional traits measured as part of the drought experiment. The individuals included in this study did not include representatives of both treatments for all species, leaving us unable to capture the varying responses to drought observed by Kaproth and Cavender-Bares (2016), or see if these trends also applied to vein traits. The problematic aspects of this study, especially low sample size, the exclusion of minor venation, and gaps in data, limit our ability to make strong conclusions about the role of network-based venation traits in plant function. Many of the associations we observe may be driven more by leaf size than other factors. Minor venation tends to be more independent of leaf size than major venation (Sack and Scoffoni 2012), so including more minor venation in the calculation of graph traits may allow more meaningful relationships among traits to be detected. Oaks also offer a somewhat limited range of venation architectures: all are pinnately veined, and are of a small number of the venation categories described by Hickey (1973). Some major physiological differences driven by venation may only be detectable when comparing more disparate architectures (e.g. pinnate versus palmate leaves; Sack et al. 2008). Despite these limitations, the relationships found between measured functional traits and calculated venation traits highlight the potential strength of using network-informed vein analysis to understand plant physiology in scenarios where direct measurements cannot be made. Venation is one of a handful of leaf traits preserved in the fossil record (Wolfe et al. 1975). Simple vein traits have been used to demonstrate changing climate through the plant fossil record (Uhl and Mosbrugger 1999), and the traits we have highlighted here

57 might enable novel analyses of fossilized vascular plants, expanding our understanding of paleoenvironments. By quantifying leaf venation with the same metrics used for understanding networked infrastructure systems (like transit systems and the Internet), engineers and designers may be able to learn the solutions plants have evolved to similar problems with similar constraints. This study has validated many of the theoretical assumptions of these new venation metrics. Ultimately, these results provide the most evidence that network-derived venation traits may be an exciting avenue to further our understanding of plant vascular biology.

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71 Appendix

Supplementary ﬁgures for chapter 1

Dry Year Wet Year Wet Mid Dry Wet Mid Dry Sap Flow Data (Installed) Q. alba 3 (3) 3 (3) 1 (1) 4 (4) 6 (7) 3 (3) Q. falcata 3 (3) 1 (1) 3 (3) 3 (3) 4 (4) 5 (6) Q. palustris 3 (3) 0 (0) 3 (3) 4 (4) 0 (2) 3 (7) Carbon Isotope Sampling Q. alba 2 6 1 4 10 2 Q. falcata 2 5 2 3 6 6 Q. palustris 4 2 3 5 4 7

Table S1: Mature tree sample sizes by year, species, and elevation. In the upper half of the table, the number of trees which were included in all sap ﬂow-related calculations is given ﬁrst, with the number of trees with sensors installed following in parentheses. This total number was the sample size for all water potential measurements in mature trees. Eight trees in the wet year are missing data from all sensors due to failure. Additional trees were sampled for stable carbon isotope measurements; these numbers are given in the lower half of the table.

Year Dry Wet p Min. Temp (°C) 19.58 16.92 2.6 × 10−5 Max. Temp (°C) 28.86 25.25 1.7 × 10−9 Daily Precipitation (cm) 0.0094 0.019 0.03991 Vapor Pressure Deﬁcit 2.16 1.55 < 2.2 × 10−16 Solar Radiation (Watt/m2) 306.0 275.8 5.2 × 10−12

Table S2: Mean weather conditions as recorded at the photobiology tower at SERC from July- October of each year. The p-values given are from the results of Welch’s Two Sample t-test

72 Species N Mean Lower Median Upper SD Peak Q. alba 361 7.10 1.58 6.21 16.40 4.11 3.96 Q. falcata 346 8.57 1.29 8.14 15.75 3.57 7.35 Q. palustris 80 3.13 0.45 2.08 10.62 3.04 1.53

Table S3: Descriptive statistics of the elevation ranges of each of the study species, reflecting abundance weighted by basal area. All values, except N (number of individuals), are given in m above sea level. ”Peak” indicates the elevation at which the proportion of total biomass for a species is at its highest. Pairwise comparison of means among species shows significant differences between all pairs, in each case with the Tukey-adjusted p-value <0.0001.

Species DBH (cm) SW Depth (cm) % Sapwood Area Q. alba 58.0 (5.88) 2.63 (0.43) 16.7 (1.54) Q. falcata 56.7 (5.26) 2.55 (0.17) 16.78 (1.71) Q. palustris 42.3 (4.30) 3.40 (0.40) 29.57 (3.63)

Table S4: Tree wood characteristics by species. Mean and standard error (in parentheses) values of diameter at breast height (DBH) in cm, sapwood (SW) depth in cm, and percent of total area (cm2 that is sapwood for each species. SW depth was determined by the color change between conductive and non-conductive wood measured from tree cores.

73 Phylogenetic Relatedness Q. alba

Q. palustris

Q. falcata

Geographic Distribution Local Distribution

Wet Dry Climate Elevation

Wet Dry Wet Dry

Figure S1: Schematic of the principal hypotheses explaining distribution and habitat partitioning at SERC. Phylogenetic relatedness can drive distributions: closely related species are hypothesized to co-occur than more distantly related ones (Donoghue 2008) ; this phenomenon appears at both broad and narrow spatial scales. Broader geographic distribution can also drive local distribution (Cavender-Bares et al. 2016). Finally, the interaction between spatial and temporal variability in climate may allow the persistence of a species which may have lower performance than other species across the gradient under optimal conditions, but which can maintain consistent performance when stressed.

74 Low Mid High

Q. alba Q. falcata Q. palustris

Figure S2: Upper: Satellite images of the region surrounding SERC. The BTP is highlighted in blue; the region covering all sampled trees is highlighted in yellow. Lower: Soil types and elevation categories across the study area. Elevation categories are: low (<=5m), mid (>5m, <10m), high (>=10m). Soil types are labeled as per the standard abbreviations of the USGS Web Soil Survey.

75 Figure S3: Water table depth after drydown at SERC, measured in 8 wells May-September 2018. ”Drydown” refers to measurements taken 10 or more days since there was >1cm total daily rainfall. Mean depth to water table decreases signiﬁcantly (slope = -16.2, p ¡ 0.0001) with elevation, and the relationship between water table depth and days since last rainfall gets steeper (more negative) with increasing elevation (interaction coeﬃcient = -0.26, p = 0.0002).

76 Figure S4: Actual and predicted volumetric water content (VWC, %) by elevation at SERC, measured from May-September 2018 at twelve 10cm depth-intervals. Observed values are daily soil moisture averages (from 15-minute measurements) during the time interval, lines are least-squares linear regression.

77 Figure S5: Sap velocity as measured in one sensor versus the velocity measured in the second sensor of the same type. Data from the commercial Dynamax sensors is split by year (2002 = dry year, 2003 = wet year); all ”short” sensor data is from 2003. The black line is the 1:1 line for each plot. Pearson’s correlation coeﬃcients are: 0.79 for Dynamax 2002, 0.60 for Dynamax 2003, and 0.75 for Short sensors.

78 Figure S6: Sap velocity as measured in short (custom) versus Dynamax (commercial) sensors. Data is from 2003 (the year when both sensors were used), and the 5 trees included were the only ones to have sensors of both types produce valid data. The blue line is the least squares linear regression (slope = 0.78, R2 = 0.85), the black line is the 1:1 line. Pearson’s correlation coeﬃcient is 0.93.

80 iueS:Spﬂxvlct vrgdb pce yya n iecategory. site and year by species by averaged velocity ﬂux Sap S7: Figure

V (cm2 s-1) Dry Year Date

Wet Year

Mid Wet Dry Dry Year Wet Year Dry Year Wet Year -1.0

-0.2 -1.5 (MPa)

(MPa)

¡ ¡

-2.0

-0.4 Midday Predawn Predawn

-2.5 Species Q. alba Q. falcata Q. palustris -0.6 -3.0

Wet Mid Dry Wet Mid Dry Wet Mid Dry Wet Mid Dry Site Site Figure S8: Predawn (left) and midday (right) water potential values measured in mature trees

81 Supplement to Chapter 2

Methods: Hydraulic Conductance

Plants were chosen based on qualitative variation in venation architecture from the collections of the CBS Conservatory (College of Biological Sciences, University of Minnesota, St. Paul, Minnesota). Small branches with a minimum of 4 mature leaves were cut and immediately placed in distilled water. Branches were cut in late morning, and allowed to hydrate for at least one hour before measuring. Once rehydrated, individual leaves were cut under water and initial water potential was measured using a Scholander pressure bomb. Leaves were then connected to the water supply and positioned between a fan for air circulation and a high intensity halogen light. The water supply was placed on a balance and mass was logged every 30 seconds until the flow rate was steady, at least 40 minutes. Following logging, the water potential of the leaf was measured a second time. The average flow rate from the final five minutes was divided by this second water potential measurement to calculate conductance, based on (Sack and Scoffoni 2012). Following measurement, leaf area was measured and leaves were cleared in NaOH and stained in Safranin-O. Stained leaves were scanned at 800DPI and major venation was traced for calculation of metrics using LeafGrapher software.

Species List

Crescentia cujete

Doliocarpus major

Eranthemum pulchellum

Ginkgo biloba

Lespedeza capitata

Medinilla scortechinii

Quercus aristata

Quercus castanea

Quercus crassipes

Quercus ellipsoidales

Quercus wislizeni

Terminalia amazonia