American Journal of Botany 101(2): 348–356. 2014.

THE DISPERSAL PROCESS OF ASEXUAL PROPAGULES AND THE CONTRIBUTION TO POPULATION PERSISTENCE IN

MARCHANTIA (MARCHANTIACEAE)1 CHRISTOPHER R. STIEHA2,3,4, AUREA R. MIDDLETON2, JOSEPH K. STIEHA2, SKYLAR H. TROTT2, AND D. NICHOLAS MCLETCHIE2 2Department

of Biology, University of Kentucky, Lexington, Kentucky 40506-0225 USA; and 3Department of Entomology, Cornell University, 4128 Comstock Hall, Ithaca, New York 14853 USA.

• Premise of the study: The dispersal process involves emigration from a focal source, dispersal through the landscape, and immigration into a new population or habitat. Despite the fact that dispersal is vital for the long-term persistence of a species, key stages of the process are unknown or understudied for many species, including the importance and contribution of asexual reproduction. Focusing only on a single stage in the dispersal process may give an incomplete and potentially flawed picture of the effects of asexual reproduction on metapopulation dynamics in plant species. • Methods: Using a multifaceted approach that combines laboratory experiments, field studies, and mathematical models, we quantify the production, dispersal, and survival of immigrants of water-dispersed asexual offspring (gemmae) of the clonal liverwort Marchantia inflexa. • Key results: Compared to female plants, male plants of Marchantia inflexa produce gemmae more quickly and in higher numbers, but due to desiccation have lower gemmae survival rates. Gemmae move up to 20 cm per minute in light rain, suggesting they can leave the source population. Long distance dispersal of gemmae is supported by the mathematical analysis of unisexual metapopulations. Upon reaching the new habitat, gemmae survival is high if they stay moist. • Conclusions: By integrating multiple experiments to quantify the effects of gemmae on metapopulation dynamics, we found that different stages of dispersal can lead to different conclusions on which sex has an advantage. Gemmae are critical for the maintenance of both sexes, the persistence of single-sex metapopulations and species, and the invasibility of clonal organisms. Key words: bryophytes; clonal organism; dispersal; gemmae; Marchantia inflexa; metapopulation; propagules.

Dispersal of individuals among populations is required for the persistence of populations and species in landscapes where populations form an aggregated network (metapopulation; Hanski, 1999), but large gaps exist in our knowledge of many components of the dispersal process (Bullock et al., 2006). Understanding the effects of dispersal on populations and metapopulations requires understanding the three stages of dispersal: emigration, dispersal, and immigration (Ims and Yoccoz, 1997; Baguette and Van Dyck, 2007). In organisms with dispersing propagules as opposed to dispersing individuals, understanding dispersal requires knowledge of propagule production (Longton, 1992), dispersal (Bullock et al., 2006; Cousens et al., 2008),

and survival (During, 2006; Cousens et al., 2008). The process of dispersal is the combination of these three stages, i.e., studying only one stage will give an incomplete and potentially flawed understanding of the effects of dispersal on metapopulation dynamics. However, studies that incorporate all three stages are rare (see Klinkhamer et al., 1988 and Ronsheim, 1994 for examples). In many organisms, sexual propagules are the main or only form of dispersal (Longton and Schuster, 1983; Ashton and Mitchell, 1989; Hansson et al., 1992; Starfinger and Stöcklin, 1996; Santamaría, 2002; Laaka-Lindberg et al., 2003), but organisms from many taxa ranging from bacteria to fungi, plants, and animals produce asexual offspring in the form of propagules, fragments, or individuals that are capable of dispersal (algae in DeWreede and Klinger, 1988; seaweeds reviewed in Santelices, 1990; plants reviewed in Eckert, 2001; and animals in Bell, 1982; Avise, 2008). Although we focus on asexual propagules, the concepts apply to any form of dispersal involving clonal material, such as dislodged vegetative material. Asexual propagules have the potential to alter population dynamics of the source population (Longton and Schuster, 1983; McFadden, 1997) and of other populations via dispersal (Cousens et al., 2008), but their dispersal capabilities are not well studied. Asexual propagules vary in their contribution to dispersal between populations (Laaka-Lindberg et al., 2003), contributing negligible and unobservable amounts for some systems (Walser, 2004; Mizuki and Takahashi, 2009; Kohn, 1995), and being the main form of interpopulation dispersal for other systems (for examples, see Fry et al., 1992; Kohli et al., 1995; and references

1 Manuscript received 22 September 2013; revision accepted 20 December 2013. The authors thank Sara Cilles, Phil Crowley, Scott Gleeson, and Daehyun Kim and two anonymous reviewers for reviewing earlier versions of this paper. They are grateful to the Wildlife Section of the Forestry Division of The Republic of Trinidad and Tobago for collection permits and to the Water and Sewage Authority in Trinidad for access to research sites. Funding for the research by C.R.S. was provided by the US National Science Foundation (DEB 9974086 to D.N.M. [PI] and Phil Crowley [coPI]), the US Department of State, the Institute of International Education Fulbright Program 2006-2007, the University of Kentucky Graduate School and Biology Department, and the Gertrude Flora Ribble Fund (to C.R.S. and J.K.S.). An NSF Research Experience for Undergraduates supplement supported A.M. 4 Author for correspondence (e-mail: [email protected])

doi:10.3732/ajb.1300339

American Journal of Botany 101(2): 348–356, 2014; http://www.amjbot.org/ © 2014 Botanical Society of America

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in Santelices, 1990), such as species with two separate sexes that have lost one sex (single-sex populations of dioecious clonal plants in Longton and Schuster, 1983; Longton, 1992). Clonal growth and dispersal are thought to contribute greatly to the wide distributions of aquatic plants (Santamaría, 2002). Single-sex populations, metapopulations, and species have persisted for long periods of time exclusively via asexual reproduction (Longton and Schuster, 1983; Judson and Normark, 1996), despite the idea that asexually reproducing populations are considered “evolutionary dead ends” (Maynard Smith, 1978). In these systems the interpopulation dispersal of asexual propagules is vital for persistence (Longton and Schuster, 1983; Longton, 1992). In species with separate genetically determined sexes, we can use single-sex metapopulations to quantify the dispersal capabilities of asexual propagules independent of the dispersal of sexual propagules. Quantifying dispersal requires the study of multiple processes, including propagule production, dispersal both within (intrapopulation dispersal) and between (interpopulation dispersal) populations, and survival after dispersal. We used a multifaceted approach, combining laboratory experiments, field experiments, and mathematical models to assess the dispersal capabilities of asexual propagules of the clonal liverwort Marchantia inflexa Nees & Mont. We quantified the production of asexual propagules using a laboratory experiment, determined intrapopulation dispersal with a field experiment, estimated interpopulation dispersal using a mathematical model, and determined the survival of propagules with laboratory experiments. Although the interpopulation dispersal is the standard concept of dispersal (how are propagules dispersed through space?), the multiplicative effect of all these components is required for dispersal. As an extreme example, if many propagules are produced, disperse to unoccupied sites, but then die, studying only production or dispersal would conclude that dispersal is important. In actuality, the dispersal process of the propagules would have no impact on the generation of new populations at these sites. MATERIALS AND METHODS Study organism—Marchantia inflexa is a New World liverwort found along streams from northern Venezuela to the southern United States as far north as Tennessee (Bischler, 1984, Schuster, 1992). Plants are found on rocks within the stream or along the banks of the stream in discrete areas separated by water or obvious habitat breaks, producing quantifiable populations. Males and females are separate individuals determined by sex chromosomes (Bischler, 1986). Streams containing only one sex are found in the southern United States, while most streams in the Caribbean contain both sexes (Bischler, 1984; Fuselier and McLetchie, 2004). Asexual dispersal can occur by two mechanisms: (1) dislodged vegetative material or; (2) distinct asexual propagules. Asexual propagules, known as gemmae, are assumed to be the main form of asexual dispersal and are the focus of this study. Gemmae are produced by both male and female plants in specialized structures known as gemma cups, which function as splash cups as described by Brodie (1951). Gemmae of M. inflexa are about 0.2 mm in diameter and are dispersed by water. Spores, sexual propagules of M. inflexa, are about 28 μm in size (Schuster, 1992) and are wind dispersed. Because spores are smaller and wind-dispersed, they are thought to travel farther than gemmae and be the main mechanism of colonization (see assumptions in García-Ramos et al., 2007). In other bryophytes, asexual propagules are thought to stay within the patch (Kimmerer, 1991, but see Skotnicki et al., 2000 and references therein; Pohjamo et al., 2006; Rudolphi, 2009). Single-sex metapopulations are proposed to be the products of post-Pleistocene unisexual colonization events of suitable habitat due to the changing environment (Longton and Schuster, 1983). Therefore, gemmae must be able to disperse out of the

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source population and colonize suitable habitat along the stream. These singlesex populations are ideal natural systems in which to study interpatch dispersal using metapopulation theory. Production of asexual propagules—Male and female plants differ in resource allocation to asexual reproduction (McLetchie and Puterbaugh, 2000; Brzyski et al., 2013). This difference can influence the number and sex ratio of dispersing asexual propagules. Two male and two female plants collected along the Quare River, Trinidad, West Indies, were crossed to produce offspring. The offspring were propagated asexually to produce stock plants. From these stock plants, 20 male and 20 female plants supplied gemmae for the experiment. Some plants were clones, which left us with 14 unique female parents and 15 unique male parents in the experiment. On 17 and 18 December, 2001, we planted three gemmae from the same plant in a well of a 50-well plug tray filled with steam-sterilized soil. Each plant was used only once. After eight weeks, all wells were weeded to leave only one individual. All plants were grown in a greenhouse at the University of Kentucky, Lexington, Kentucky, USA. Plants developed gemma cups in February, March, and April 2002. After a gemma cup developed, gemmae were extracted once per week for nine weeks by pipetting 0.1 μL of distilled water into the cup and extracting the gemmawater solution using a 1000 μL pipette, which provided the necessary force to extract the gemma-water solution from the cup. The water extraction process did not damage the gemma cups. To ease counting of the gemmae by preventing clumping, the extraction was combined with 500 μL of 5% Tween 20 solution (Sigma-Aldrich, St. Louis, Missouri, USA) in an Eppendorf 1.5 ml tube. Each cup was extracted twice per sampling event. At most, we extracted from three cups for each individual. Gemmae from each cup were counted using a grid-lined culture plate under a dissecting microscope. We extracted each week, but many cups stopped producing gemmae before the end of the nine weeks. Only the first extraction after gemma production stopped was included in the analysis. To determine the effects of sex and extraction time on the number of gemmae, we analyzed our data with a generalized linear mixed-effects model with a Poisson error distribution and log link function using the lme4 library (Bates et al., 2011) for R (R Development Core Team, 2013). Categorical fixed effects were the sex of the individual, the extraction time, and the interaction between sex and extraction time. The random effect was cup-nested within individual within parent. We developed the model sequentially, comparing models that initially started with only the random factor, then sex, then sex and extraction time, and finally sex, extraction time, and the interaction. Models were compared using a χ2 test to determine if the term significantly increased the explanatory power of the model compared to a model without the term (Crawley, 2007). Intrapatch dispersal—The movement of gemmae during a rain shower determines whether they stay within the source population or emigrate. On average, gemmae must travel at least 0.85 ± 0.14 m (mean ± SE) to leave the source population (n = 49, C. Stieha, unpublished data). At the Simla Research Station, Trinidad, West Indies, we constructed a 1.23 m by 1.23 m platform from porcelain tiles. The platform was covered with a moistened capillary mat to prevent water from pooling and three layers of white cotton fabric to make the gemmae easily observable. The platform had a negligible slope between 0° and 5°. In a preliminary study on a platform with a slope of 42°, the average slope of substrate with a population, all gemmae traveled farther than 0.61 m in a light rain and were lost. A slope of 0° produces a conservative estimate of gemma movement. Trials occurred at least twenty minutes apart on 27 and 28 August 2007, and 10 through 14 September 2007. The platform was cleaned between trials and excess water was removed. For each trial, ten gemmae from plants of unknown sex from Quare River, Trinidad, West Indies were placed in a two-centimeter circle on Whatman 70 mm filter paper (GE Healthcare, Little Chalfont, UK). Gemmae were subjected to natural rain and observed. Once a gemma had moved, we stopped the experiment 30 s later to increase the chance of finding the gemmae. Trials ran for 30 s to 5 min. We exhaustively searched for all gemmae within a 45 cm radius from the center of the platform. For each gemma, we measured the distance the gemma moved from the center of the filter paper. Gemmae that remained in the 2 cm circle were assigned a distance of 0 cm. Gemmae that were not found were assumed to have moved off the platform and assigned a distance of 45 cm. For each trial, we computed the average velocity of the gemmae. We measured rainfall rate using a HOBO tipping bucket rain gauge (0.2 mm sensitivity, Onset Computer Corporation, Bourne, Massachusetts, USA). Because

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the tipping of the bucket did not coincide with the beginning or end of the trial, tipping points up to two minutes before or after the trial were used to determine the rainfall time. The rainfall time was longer than the length of the trial, but this procedure ensured that the tipping bucket was empty as opposed to about to tip. The rainfall rate is the amount of rain that fell during this time. Rainfall events ranged from 0 mm·min−1, which consisted of no rainfall and slight rainfall that did not tip the bucket, to 3 mm·min−1, which will completely soak a person in a few seconds. Results were analyzed using linear regression in the statistical program R (R Development Core Team, 2013). Because 92% of all observed rainfall events had a rainfall rate less than 1 mm·min−1 (Fig. 1), we fit two lines to the data, i.e., one containing all trials and one containing trials with rainfall rates less than 1 mm·min−1. Interpatch dispersal—Single-sex metapopulations persist only through the dispersal of asexual propagules. We use these metapopulations to study the dispersal of asexual propagules without the confounding effects of dispersal by sexual propagules. Field surveys combined with mathematical techniques can be used to estimate interpatch dispersal without costly dispersal experiments (Moilanen, 1999, 2004). Two single-sex metapopulations (Fuselier and McLetchie, 2004) were surveyed in Oklahoma, USA: (1) the all-female metapopulation at Bird’s Mill Creek (lat./long.: 34°31′36″N 96°38′1″W) with 17 populations on 10 June 2006; and (2) the all-male metapopulation at Honey Creek (lat./long.: 34°26′49″N 97°07′59″W) with 23 populations on 9 June 2006. We measured the size of each population by measuring the length of the population along the stream and the width perpendicular to the stream at the largest point in the population. Population size was computed as area due to the difficulty in discerning individuals in this clonal system. Distances and degrees from north were collected between adjacent populations and used to compute distances among all populations in the metapopulation. The distance between populations was calculated as the distance along the stream. We combined data from the survey with a mathematical model of Marchantia inflexa (McLetchie et al., 2002; García-Ramos et al., 2007) that incorporated population size and distances among populations (C. Stieha, unpublished manuscript). The mathematical model simulates population dynamics and metapopulation persistence of M. inflexa (see McLetchie et al., 2002; García-Ramos et al., 2007).

Fig. 1. Distribution of rainfall rates from the 12 December 2006 to 26 September 2007. In total there were 396 rainfall events, where an event is defined as a series of bucket tips with no more than one minute between tips. The median rainfall rate was 0.53 mm·min−1 with 95% of the rainfall rates falling between 0.21 mm·min−1 and 1.37 mm·min−1. Only 8% or 33 out of 396 rainfall events had a rainfall rate greater than 1 mm·min−1. We removed all rainfall events with a duration of only 0.5 s.

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In the model, dispersal of asexual propagules is described by the probability density function y = αe-αd, where d is the distance and α is the dispersal capability of the gemmae. For dispersal capability α, 1/α is the mean dispersal distance of gemmae. We varied the mean dispersal distance of gemmae to determine the effect of dispersal on metapopulation persistence. We incorporated two different dispersal functions: (1) a 1-dimensional dispersal kernel (see García-Ramos et al., 2007); and (2) a 2-dimensional dispersal kernel (C. Stieha, unpublished manuscript). A 1-dimensional dispersal function focuses on the linear aspect of the stream, while a 2-dimensional dispersal function accounts for the increase in area with an increase in distance from the source population. We predict the actual dispersal function falls between these two extremes. Parameter values were derived from laboratory experiments and modified to account for differences in growth and survival between the laboratory and the field (see McLetchie et al., 2002 and García-Ramos et al., 2007 for a detailed description of the mathematical model). For the carrying capacity of suitable substrate (patch), we assumed that all patches had a carrying capacity of either 1 m2 or the field-observed population size. Populations experienced two types of disturbance: (1) disturbance, where 20% of the occupied area was removed every five months, on average (McLetchie et al., 2002); and (2) extinction, where all individuals within a population were removed once every 40 yr, on average (García-Ramos et al., 2007). We assumed that the extinction probability was independent of population size. All patches within the metapopulation were initialized with 20 individuals of the sex found in the stream, females for Bird’s Mill Creek and males for Honey Creek. For each mean dispersal distance (1/α), we ran fifty simulations for 500 yr and excluded the first 100 yr to remove transient dynamics. We report the average proportion of occupied patches within the metapopulation. All simulations were run in MATLAB R2011a (Mathworks Inc., 2011). Asexual propagule survival under water—Gemmae are dispersed by water and may be submerged, especially during the early stages of establishment. Therefore, we quantified the survival of gemmae under prolonged submergence. On 10 July 2006, male and female gemmae were collected from stock plants grown in a greenhouse at the University of Kentucky. From these collections, 336 male gemmae and 336 female gemmae were placed individually in 10 × 75 mm test tubes filled with 25% Hoagland’s solution (Hoagland and Arnon, 1950). We randomly assigned 48 gemmae from each sex to each of our six treatments: (1) zero days submerged; (2) seven days submerged; (3) 18 d submerged; (4) four wk submerged; (5) eight wk submerged; or (6) 12 wk submerged. Test tubes were gently agitated and placed in a single container in a growth chamber (22°C/18°C 12/12 d/night). After one week, gemmae were forced to sink. Treatment times were computed from this date. At the end of a treatment, gemmae were planted in soil-filled wells of 96-well plates (Falcon 353911, Corning, Tewksbury, Massachusetts, USA) and placed in a growth chamber (22°C/18°C 14/10 d/night) for two weeks. After two weeks, gemmae were classified as either alive or dead. We used logistic regression in R (R Development Core Team, 2013) and model reduction (Crawley, 2007) to determine whether sex, time spent under water, or the interaction had significant effects on survival. Initial analysis revealed underdispersion (residual deviation 5.65 for 8 degrees of freedom (df)). Therefore, we used a quasi-binomial error distribution (Wilson and Hardy, 2002). The analysis was weighted for sample size. Asexual propagule survival after desiccation—After dispersing, gemmae may land on substrate that may dry out. To quantify the effect of desiccation on gemmae, we allowed gemmae to remain dry for various lengths of time and measured survival. Three 96-well plates (Falcon 353911, Corning) were filled with steamed sterilized soil and allowed to dry for one week. Male and female gemmae were collected from stock plants and planted on 20 March 2012 at the University of Kentucky. A total of 144 males and 144 females were placed singly in a well with a drop of water. Because gemmae are dispersed by rainfall (Brodie, 1951; Equihua, 1987) and water, using water and moist soil mimics the immigration process. Gemmae were randomly assigned to one of five drying treatments: (1) zero days dry; (2) one day dry; (3) two days dry; (4) three days dry; or (5) four days dry. The plates were allowed to dry for 24 h at 21°C and 54% humidity (temperature and humidity sensor RHT03, MaxDetect Technology Co., Ltd., Shenzen, China). Gemmae assigned to the zero-days dry treatment were kept moist throughout this period. Gemmae in the one-day dry treatment were kept dry from the time they were planted until 24 h later, after which the soil was constantly moist. Other treatments followed a similar protocol. After the initial 24 h drying out period, well plates were lidded and placed in a growth chamber (22°C/18°C 14/10 d/night).

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After the final treatment received water, all wells were kept moist for 13 d. After 13 d, we observed each gemma with a dissecting microscope and determined if the gemma was green and alive or brown and dead. If the gemma was alive, we slowly filled the well with water to determine if the gemma was attached to the substrate or floated. Results were analyzed using multinomial logistic regression using the multinom function in the nnet library (Venables and Ripley, 2002) in R (R Development Core Team, 2013). The status of the gemmae (dead, floating, or germinating) was the response variable and the number of days without water and the sex of the gemmae were the explanatory variables.

RESULTS Production of asexual propagules— Gemma production within cups peaked at week 4 (males 150.5 ±11.6 (mean ± SE); females 132.9 ±11.0 (mean ± SE); Fig. 2). Sex by itself did not significantly explain gemma production (compared to interceptonly model, χ2 = 0.62, df = 1, P = 0.43). The age of the gemma cup, denoted as extraction time, significantly increased the explanatory power compared to a model containing only sex and the random intercept (χ2 = 24275, df = 8, P < 0.001). The order that main effects were included in the model did not affect the results. The interaction between the age of the gemma cup and sex was significant when compared to a model containing only sex and age of the gemma cup (χ2 = 226.97, df = 8, P < 0.001). Male production of gemmae increases until week 4, at which point production decreases and then stops around week 9. On the other hand, female production is stable for the first three weeks, increases sharply at week 4, and declines after week 4. Intrapatch dispersal— The rate of rainfall was a good predictor of gemma speed (F1,17 = 195.5, P < 0.001, adjusted r2 = 0.915). The speed of gemma movement (y, cm of gemma movement per minute) was positively related to the strength of the rainfall (x, mm of rainfall per minute; y = −1.35 (±1.40 cm·min−1)

Fig. 2. Production of gemmae by the two sexes of Marchantia inflexa. Number of gemmae extracted per cup for each sex (means ± SE) are offset for clarity. All measurements are analyzed based on the age of the cup, not the age of the plant. Males increase production of gemmae faster than females (interaction between time and sex: χ2 = 226.97, df = 8, P < 0.001).

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+ 25.27 (±1.81 cm·mm−1) x, β (± SE); Fig. 3). The removal of the heaviest rainfall event did not change the results (F1,16 = 16.34, P < 0.001; y = −0.097 (±1.833 cm·min−1) + 20.332 (±5.031 cm·mm−1) x, β (± SE); Fig. 3). Interpatch dispersal— Figures 4A and 4B show the paths of the streams and the sizes of the populations. Dispersal capabilities of gemmae greatly affected the proportion of occupied patches in our simulations (Figs. 4C and D). For Bird’s Mill Creek (Fig. 4A), a mean dispersal distance of 0.1 m or less led to an extinct metapopulation, where no individuals were found in any patches after 500 yr (Fig. 4C). From 0.1 m to 1 m, the proportion of occupied patches increased and a mean dispersal distance of greater than 1 m ensured that almost all patches were occupied. For simulations of Honey Creek (Fig. 4B), only short mean dispersal distances and field-observed patch sizes led to the extinction of the metapopulation (Fig. 4D). A mean dispersal distance greater than 2 m was required for persistence of the single-sex metapopulations. For both metapopulations, whether we assumed patches had a carrying capacity of 1 m2 or had the measured carrying capacity, the results did not change. Asexual propagule survival under water— Average gemma survival across both sexes and all treatments was 92.9% (range of 90.7–94.6%, mean ±2 SE) survival. There were no significant differences in gemma survival given the sex of the gemma (F1,8 = 0.577, P = 0.465), the amount of time the gemma spent submerged (F1,9 = 0.086, P = 0.776) or the interaction between time submerged and sex of the gemma (F1,8 = 4.327, P = 0.071).

Fig. 3. Intrapatch movement speed of Marchantia inflexa gemmae vs. rainfall rate (n = 19). The solid line (all points) represents the equation y = −1.35 (±1.40 cm·min−1) + 25.27 (±1.81 cm·mm−1) x, β (± SE). The dashed line (only rainfall rates less than 1 mm min-1) represents the equation y = −0.097 (±1.833 cm·min−1) + 20.332 (±5.031 cm·mm−1) x, β (± SE). In both cases, rainfall rate positively affects the gemma speed. The intercepts were not forced through zero because very light rains were often not recorded, but gemmae still moved. Light rainfall may not have enough force to eject the gemmae from the cup. This requires further experimentation.

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Fig. 4. (A) Spatial configuration of Marchantia inflexa populations found along Bird’s Mill creek, female-only, n = 17 populations. One large population dominates the upstream segment of the stream. (B) Spatial configuration of populations found along Honey Creek, male-only, n = 23 populations. Both Honey Creek and Bird’s Mill Creek have very large or aggregates of larger populations toward the upstream end (right side) of the metapopulation. Relationship between mean gemma dispersal and proportion of metapopulation occupied for (C) the female-only Bird’s Mill Creek and (D) the male-only Honey Creek. Means ± SE are the average of 50 simulations. The 1d and 2d dispersal define the spatial component of the dispersal kernel, whether it is only 1-dimensional (along the stream) or 2-dimensional (along and across stream), see text at Methods—Interpatch dispersal. Patch size, whether 1 m2 or the area measured in the field, does not appear to affect the proportion of populations occupied.

Asexual propagule survival after desiccation— Gemma attachment ranged from a low of 34.5% for male gemmae that had experienced four days without water (Fig. 5A) to a high of 82.1% for female gemmae that experienced zero days without water (Fig. 5B). The interaction between sex and the number of days without water was not significant (likelihood ratio = 0.169, df = 2, P = 0.919) and therefore removed from the model. Male

and female gemmae differed in their fundamental survival rates (likelihood ratio = 79.912, df = 4, P < 0.0001); female gemmae were 14 times less likely to die than germinate, while male gemmae were only five times less likely to die than germinate. Female gemmae were 6.75 times less likely to float than germinate, while male gemmae were 4.55 times less likely to float than germinate. For each day without water, the probability of

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Fig. 5. Proportion of Marchantia inflexa gemmae germinating after desiccation: (A) males, total n = 143; and (B) females, total n = 141. Individuals not germinating were either brown and dead or were still green but not attached to the substrate and showed no signs of growth. Germinating individuals could have the beginning of a vegetative tip or have tripled in size.

not attaching to the substrate increased by 1.31 times and the probability of dying increased by 1.55 times compared to the probability of attaching to the substrate and germinating (likelihood ratio = 19.647, df = 2, P < 0.0001). DISCUSSION We focused on the production, dispersal, and survival of asexual propagules for an integrative perspective on the importance of asexual propagules on population and metapopulation persistence. Understanding the factors that influence population or metapopulation persistence is vital for developing plans for the conservation or control of species. Using field, laboratory,

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and modeling approaches, we quantified the production, emigration, dispersal, and immigration of asexual propagules. The modeling of interpopulation dispersal stresses the importance of asexual propagules on population and metapopulation persistence. Because each component of dispersal (emigration, dispersal, and immigration) depends on the results of the previous stages, the study of each stage and combination of experiments is vital for quantifying the effects of asexual propagules on metapopulation dynamics. Focusing only on a single experiment gives an incomplete picture of the effects. For example, focusing only on gemma production, one would conclude that asexual dispersal is dominated by males. However, focusing only on survival in the desiccation experiment, one would conclude asexual dispersal is dominated by females. Only through the integration of all stages of the dispersal process do we come to the complete picture. On average, a male gemma cup produces 529 gemmae during its lifetime, while a female cup produces 492 gemmae. Overall, males make more cups than females (10 vs. 7, Fig. 3 in McLetchie and Puterbaugh, 2000). The combination of these results suggests that males (females) can produce 5290 (3444) copies of themselves in only 9 weeks. Comparable high levels of production are found in other species as well (Laaka-Lindberg, 1999). Depending on the rainfall rate, these gemmae can easily move up to 20 cm per minute of rainfall along a flat substrate and have been observed to move faster on an inclined substrate (C. Stieha, personal observation). Intrapopulation dispersal of gemmae from splash cups has been shown to be large, ranging from greater than half a meter (Brodie, 1951) to 1.2 m (Equihua, 1987). Propagules can be dispersed via abiotic factors (Equihua, 1987; Johansson and Nilsson, 1993; Walser, 2004) or biotic factors (Kimmerer and Young, 1995; Heinken, 1999; Parsons et al., 2007; Rudolphi, 2009). For example, ants are capable of dispersing propagules of some plant species (Dalling et al., 1998; Rudolphi, 2009). Despite the presence of ants on many populations of Marchantia inflexa, ants do not appear to disperse gemmae (McLetchie and C. Stieha, personal observations). Water appears to be the main mechanism for intrapopulation and interpopulation dispersal of asexual propagules of M. inflexa. Traps along the edge of populations of M. inflexa caught many gemmae leaving the populations and entering the stream without much rainfall (C. Stieha, unpublished data). In M. inflexa, asexual propagules must travel a mean of two meters for Bird’s Mill Creek and a mean greater than five meters for Honey Creek for the persistence of unisexual metapopulations. Once the asexual propagules disperse outside of the focal population, they persist and are able to colonize and initiate a new population, as long as they remain moist. Our experiments predict that gemma mortality mainly occurs via desiccation. The number of successfully establishing gemmae is probably lower than the 90% predicted from the desiccation experiment performed in the benign laboratory. In the tropical research station, gemmae turn brown (suggesting death) after only a couple of hours on unmoistened filter paper (C. Stieha, personal observation). Often the asexual propagules survive better than the sexual counterparts (Kimmerer, 1991), but asexual propagules can suffer high mortality (Johansson and Nilsson, 1993). Accounting for dispersal and increased mortality, a 90% reduction still suggests 529 and 344 colonizing gemmae for males and females, respectively.

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With the number of asexual propagules produced and the difference in male vs. female production, it is difficult to envision a scenario where asexual propagules do not affect metapopulation dynamics and the ratio of males-to-females in the individual population as well as in the metapopulation. The dispersal of asexual propagules can bias sex ratios at the population level and metapopulation level. Biased sex ratios have been shown to affect population growth (Bisang et al., 2004; Rydgren et al., 2010; Miller and Inouye, 2011). However, the importance of asexual propagules in interpatch dispersal and metapopulation dynamics has been downplayed either due to the nature of asexual reproduction (large vegetative pieces (Johansson and Nilsson, 1993); larger asexual propagules (Ronsheim, 1994); or data suggesting small dispersal scales (Kimmerer, 1991; Heinken, 1999). Recently, there has been a call to better quantify the dispersal capabilities of asexual propagules (Laaka-Lindberg et al., 2003), and results suggest that asexual propagules can and do disperse out of the focal population (Innes, 1987; Johansson and Nilsson, 1993; Skotnicki et al., 2000; Pohjamo et al., 2006; Rudolphi, 2009). In some cases, the dispersal capability of asexual propagules is very similar to the dispersal capability of the sexual propagules (Ronsheim, 1994; Pohjamo et al., 2006). For Allium vineale L., the mean dispersal distances of asexual bulbils and sexual seeds from scapes of the same height are the same, although the maximum distances differ. Asexual bulbils dispersed a maximum of 0.95 m while sexual seeds dispersed a maximum distance of 1.3 m (Ronsheim, 1994). In other cases, asexual propagules are thought to disperse farther along the river than sexually produced seeds due to differences in floating abilities (Johansson and Nilsson, 1993). In lichens, molecular techniques have been used to determine that clones can be found up to 230 m from one another (Walser, 2004). Evidence in bryophytes also suggests interpatch dispersal of asexual propagules. Populations of three liverworts, Anastrophyllum hellerianum (Nees ex Lindenb.) R.M. Schust., Lophozia longiflora (Nees) Schiffn., and Lophozia silvicola Buch are aggregated, which suggests limited distribution of asexual offspring, as opposed to randomly or uniformly distributed, which would suggest widespread dispersal of sexual propagules. Populations of the asexual A. hellerianum and L. silvicola are aggregated at distances up to 16 m and 20 m, respectively, whereas populations of the highly sexual L. longiflora are aggregated only up to 10 m (Laaka-Lindberg et al., 2006). In the liverwort Barbilophozia attenuate (Mart.) Loeske, only one instance of asexual dispersal between populations was documented with molecular evidence (Korpelainen et al., 2011), but in three other bryophytes, no identical individuals were found in different populations (Snäll et al., 2004; Pohjamo et al., 2008). However, individuals within a specific distance of one another were likely to be related, to 8 m as noted in Korpelainen et al. (2011) and 300 m in Snäll et al. (2004). One explanation for high relatedness is asexual dispersal coupled with mutations. Mutations in asexual offspring would limit the ability to find genetically identical individuals (see Skotnicki et al., 2000 for an example). We expect dispersal distances for asexual propagules of Marchantia inflexa to be 2 to 5 m, on average. The combination of these experiments with molecular techniques would help us refine the dispersal capabilities of asexual propagules. The dispersal capabilities of asexual propagules could also affect evolutionary trajectories and resource allocation strategies. When interpopulation dispersal of asexual propagules is assumed not to affect metapopulation fitness, there is no difference

in the optimal allocation strategy when competition is lottery (allows utilization of unoccupied resources) vs. overgrowth (competition for currently used resources; Crowley and McLetchie, 2002). Because colonizations are vital for the persistence of the metapopulation, we would expect that single-sex metapopulations would contain individuals that invested more in dispersal (Mattei, 2012), therefore increasing interpopulation dispersal and the likelihood of colonizations. But recent research shows that individuals in single-sex metapopulations of M. inflexa actually invest more in vegetative growth and less in gemma production than their counterparts found in two-sex metapopulations (Fuselier, 2008), suggesting competition among clones (Mattei, 2012). Dispersal capabilities are greatly affected by the environment through which the propagule must travel (Wiens,1997). Given the stream-based dispersal mechanism of asexual propagules of M. inflexa, pools, riffles, and the meanderings of the stream could influence dispersal among populations and the location of new populations. The effects of the environment through which the propagule must disperse may be evident in the mean dispersal difference between Honey Creek and Bird’s Mill Creek. Although the locations of pools and ripples were not collected, comparison of the spatial configuration of populations along both streams suggests that streams were relatively straight (Figs. 4A, B). In the aquatic plant Ranunculus lingua L., curved parts of the stream captured more asexual propagules (rhizomes) than did straight parts but there was no difference between pools and rapids (Johansson and Nilsson, 1993). The observed dispersal difference between metapopulations of M. inflexa may be due to water flow differences between the two streams. As proposed by Laaka-Lindberg et al. (2003), gemmae have the capability of emigrating from the source population and influencing population and metapopulation dynamics. Understanding the dispersal capabilities of asexual propagules is vital for determining the persistence of single-sex metapopulations and for describing the population dynamics of two-sex clonal organisms. Two-sex models of population dynamics already include clonality (Crowley and McLetchie, 2002; Rydgren et al., 2010; Shelton, 2010); metapopulation models are only beginning to incorporate asexual dispersal (García-Ramos et al., 2007; Mattei, 2012). Ignoring asexual propagules could lead to erroneous predictions of growth and persistence for both populations and metapopulations of natural populations, invasive organisms (Lyman and Ellstrand, 1984), and pathogens (Kohli et al., 1995; Kohn, 1995). LITERATURE CITED ASHTON, P. S., AND D. S. MITCHELL. 1989. Aquatic plants: Patterns and modes of invasion, attributes of invading species and assessment of control programmes. In J. A. Drake, H. A. Mooney, F. di Castri, R. H. Groves, F. J. Kruger, M. Rejmanek, and M. Williamson [eds.], Biological invasions: A global perspective, 111-147. Wiley, Chichester, UK. AVISE, J. C. 2008. Clonality: The genetics, ecology, and evolution of sexual abstinence on vertebrate animals. Oxford University Press, Oxford, UK. BAGUETTE, M., AND H. VAN DYCK. 2007. Landscape connectivity and animal behavior: Functional grain as a key determinant for dispersal. Landscape Ecology 22: 1117–1129. BATES, D., M. MAECHLER, AND B. BOLKER. 2011. lme4: Package to fit linear and generalized linear mixed-effects models. Version 0.999375-42. Website http://lme4.r-forge.r-project.org/

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