Modeling the life history of sessile : larval substratum selection through reproduction

Andrea N. Young, Rick Hochberg, Elizabeth J. Walsh & Robert L. Wallace

Hydrobiologia The International Journal of Aquatic Sciences

ISSN 0018-8158

Hydrobiologia DOI 10.1007/s10750-018-3802-x

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https://doi.org/10.1007/s10750-018-3802-x (0123456789().,-volV)(0123456789().,-volV)

ROTIFERA XV

Modeling the life history of sessile rotifers: larval substratum selection through reproduction

Andrea N. Young . Rick Hochberg . Elizabeth J. Walsh . Robert L. Wallace

Received: 14 July 2018 / Revised: 13 October 2018 / Accepted: 15 October 2018 Ó Springer Nature Switzerland AG 2018

Abstract Although the theoretical underpinnings of cohort of larvae. Our Basic Model assessed fitness as habitat selection by marine larvae have simply settling on a substratum using only the larval been well studied, this theory has been neglected for elements and revealed statistically greatest fitness freshwater sessile rotifers. To study how substratum when swimming speed decreased with age and when selection affects larval fitness, we developed a substratum preference was constant or exhibited mid- dynamic model to examine influences of three age competence. The Reproductive Model assessed elements of larval life (survival, substratum accep- fitness (mean number of offspring adult-1)asa tance, substratum encounter probability) and substra- function of substratum. We compared reproduction tum-dependent reproductive success in adults. Monte on neutral substrata to substrata where quality varied Carlo simulation models were run using an initial and separately as a function of adult population density: coloniality (synergism) versus competition. The model showed fitness was statistically greatest Guest editors: Steven A. J. Declerck, Diego Fontaneto, Rick Hochberg & Terry W. Snell / Crossing Disciplinary when larval swimming speed decreased with age and Borders in Research when coloniality increased reproduction. We also explored conditions where populations of planktonic Electronic supplementary material The online version of adults could survive. The model is applicable to sessile this article (https://doi.org/10.1007/s10750-018-3802-x) con- tains supplementary material, which is available to authorized organisms and may be modified to examine other life users.

A. N. Young R. L. Wallace (&) Department of Mathematical Sciences, Ripon College, Department of , Ripon College, Ripon, WI 54971, Ripon, WI 54971, USA USA e-mail: [email protected] R. Hochberg Department of Biological Sciences, University of Massachusetts at Lowell, Lowell, MA 01854, USA

E. J. Walsh Department of Biological Sciences, University of Texas at El Paso, El Paso, TX 79968, USA

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Hydrobiologia history activities including selection of mates, prey, or et al., 2004; Kinlan et al., 2005; Toonen & Tyre, 2007; territory. Burgess et al., 2012). However, the life history characteristics of sessile rotifers (: Gne- Keywords Behavior Á Dynamic modeling Á siotrocha: Atrochidae, Collothecidae, and Flosculari- Gnesiotrocha Á Planktonic Á Substratum-dependent idae) differ from those of marine . For reproduction Á Rotifera example, often release large numbers of relatively long-lived (days, weeks, months) larvae that may disperse over short Larvae … are indeed not helpless, for they are endowed with the power of choice, and with a period of time during which that choice (* 1 m) to long ([ 750 km) distances and have may be made. — Wilson (1952). extended development times (days to months) (Kempf, 1981; Hadfield, 1998; Shanks, 2009). They also exhibit extreme diversity in size (* 200 to [ 3000 lm) and form (Levin & Bridges, 1995), and as a group use varied energy sources: endosymbiotic Introduction autotrophy, lecithotrophy, osmotrophy, and plank- totrophy, as well as poecilogony (Vance, 1973; Understanding a species requires comprehending its McEdward, 1995; Chia et al., 1996; Allen & Pernet, entire life history, not just the morphological and 2007). Additionally, during their free-swimming ecological features attendant to the adult (Werner & phase, marine larvae usually experience an extensive, Gilliam, 1984; Werner, 1988). Undeniably many relatively uniform, open-water existence, where suit- studies have documented ontogenetic (developmental) able substrata are generally not encountered. As a shifts; these include shifts in diet (e.g., polychaetes: consequence many, but certainly not all, marine larvae Hentschel, 1998; harpacticoid copepods: Decho & are capable of postponing settlement in the absence of Fleeger, 1988; fishes: Daly et al., 2009; amphibians: suitable habitat (Pechenik, 1980). In contrast, sessile Schriever & Williams, 2013), behavior (Despland & rotifers release relatively few, short-lived (hours to Hamzeh, 2004), physiology (Woods & Wilson, 2013), days) larvae that exhibit little variation in size (ca. and habitat use (Richards, 1992) (see de Roos & 400 lm) or form (Wallace et al., 2015), and which Persson, 2013). appear to be lecithotrophic or possess limited ability to Interpreting the life history of sessile invertebrates feed (Wallace et al., 1998; Hochberg, 2014; Hochberg is no different; it requires an understanding of their et al. (in this volume). Moreover hatchlings immedi- distinct bipartite existence: larval life is transitory, ately encounter a mosaic of habitats dominated by ending either in death or with a cascade of searching diverse hydrophytes that provide a rich landscape for and settling behaviors culminating in attachment and settlement with variable morphologies and chemis- subsequent metamorphosis into an adult (Crisp & tries that often differ over short distances (Meksuwan Meadows, 1963; Wallace, 1980; Pawlik, 1992; et al., 2014). Burgess et al., 2009). Accordingly, a successful Free-swimming larvae may provide sessile rotifers must survive planktonic life, encounter at least one several advantages including (1) colonization of a substratum, attach, metamorphose to adulthood, and preferred substratum, including new hydrophyte reproduce. Clearly, if settlement is irreversible, choice growth that has not been weakened by herbivores, of a high-quality substratum becomes critical to pathogens, or age; (2) establishment of a colony or maximize fitness (Hodin et al., 2015). Thus, one may alternatively avoidance of competition; and (3) wider infer that sessile invertebrates must make evolutionary dispersal that may reduce inbreeding. In contrast, tradeoffs that are not intuitively obvious. disadvantages include (1) death in the due to Undeniably there is a rich literature on the life starvation and/or predation; (2) delayed metamorpho- history of most marine invertebrate larvae (Chia & sis with subsequent inability to complete it; and (3) Rice, 1978; Young, 1990; McEdward, 1995; Hadfield, poor adult reproduction due to selection of an inferior 1998), including conceptualizing the process of sub- habitat (Pechenik, 1999). stratum selection (Doyle, 1975; Roughgarden et al., To better understand the life history of sessile 1985; Strathmann, 1985; Rumrill, 1990; Marechal rotifers, we developed a dynamic model with the 123 Author's personal copy

Hydrobiologia capacity to vary environmental and sessile rotifer life with the potential for reproduction. Components of the history features including (a) relative availability of model are fully described in Supplemental Document. potential substrata, (b) cohort size, (c) planktonic In the basic model (BM), we defined fitness simply as survival, (d) substratum choice, and (e) adult survival settling and metamorphosing, with the assumption that and subsequent reproduction. Here we present our metamorphosis leads to equal reproduction on all model, explore some of its results, offer testable hy- substrata (Doyle, 1975). In the reproductive model potheses regarding sessile rotifer life histories based (RM), we defined reproductive fitness as metamor- on outcomes of model runs, and suggest areas where phosing with subsequent reproduction, which could additional research is needed. vary as a function of substratum or density of settled larvae. The RM followed the behavior of the original population and one generation of offspring. We also Materials and methods explored conditions where adults could survive in the plankton. Following, we provide a brief overview of Model development the environmental and life history functions (LHF) that we incorporated into the model (Table 1). Our model reflects ideas from several previously LHF 1 Larval survival in the plankton. Larval published models of sessile (Doyle, 1975; survival was set such that during each time step of the Pineda & Caswell, 1997; Toonen & Tyre, 2007; model a certain percentage of larvae die in the Burgess et al., 2009), but emphasizes characteristics of plankton due to predation, parasitization, or starvation the freshwater littoral habitat and life history features (dP). This is a classic Type II survivorship curve of sessile rotifers (Fig. 1). This dynamic model was (Kempf, 1981). Further, we added the assumption that developed as a system of difference equations that larvae have a maximum length of life (l). Those that follow a cohort of larvae to potential endpoints of reach that point immediately die due to starvation. either death in the plankton or survival to adulthood

Fig. 1 Schematic overview of the life history of sessile rotifers conceptual model was used to develop the fitness functions in used in this model. The model starts with a cohort of planktonic, our simulations. A more complete development of the model is free-swimming larvae. Boxed regions indicate endpoints for explained in the text and in the Supplemental Document larvae and Italic print indicates their behaviors. This simplified, 123 Author's personal copy

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Table 1 Environmental and life history functions (LHF) used in modeling substratum selection by sessile rotifer larvae Life history functions Description

Larval life LHF 1. Larval survivorship Larval population decreases over time, either by settling or dying, such that a certain percentage of free-swimming larvae die at each iteration, but total lifespan is fixed (l), at which point all remaining larvae die LHF 2. Substratum acceptance and Values for acceptance probabilities varied over l in one of three ways: (A) autonomous metamorphosis (constant), (B) decreasing choosiness, (C) intermediate competence (follows a quadric choosiness function). Total likelihood of settling of larvae over l was kept equal among these functions LHF 3. Substratum availability Values for encounter probabilities were varied over l in one of three ways: (A) autonomous (Encounter rates) (constant), (B) increases linearly, (C) decreases linearly. But among them, total likelihood of encounter over l was kept equal Adult fitness Basic model Assumed that all settled adults reproduce equally Adult reproduction Adult reproduction is a function of habitat

LHF 4. Reproductive model (A) Substratum type alone affects Ro

(1) Positive: Ro higher for one or more substratum

(2) Negative: Ro lower for one or more substratum

(B) Adult density alone affects Ro

(1) Autonomous: Ro equal for all substrata

(2) Synergistic: Ro increases with increasing population sizes (e.g., coloniality), until a critical value is reached above which no additional advantage is accrued

(3) Competition: Ro decreases with increased population size until a critical value is reached above which no additional disadvantage is accrued LHF 5. Facultatively sessility Larvae may settle or metamorphose in the plankton and reproduce Additional details of these functions are described in the text; descriptions of the mathematical functions of the model are specified in the Supplemental Document

LHF 2 Larval substratum acceptance (i.e., choice, competence (quadratic choosiness): mid-aged larvae preference, or selection) and settling. Larvae accept are more likely to settle in response to suitable cues substrata (j =1ton) at rates (aj) that may vary with than either younger or older larvae (Hodin et al., 2015; time over their life; this corresponds to the behavioral Wallace, 1980). In this case, we employed a quadratic concept of larval ‘choosiness’ based on substrata function to model competence. We kept the total possessing the appropriate settlement cue(s). We likelihood of settling constant for the three acceptance assumed that the level of cues possessed by each scenarios. substratum does not vary. Rather, acceptance rate is LHF 3 Larval substratum encounter. The model viewed as a change in the behavior of larvae with can incorporate any number of potential substrata respect to the substratum as a function of their age. (j =1ton), with larvae encountering substrata at rates

Three acceptance scenarios were explored. (A) Au- (ej) that may vary with time. This constraint may be tonomous (constant): aj were set as constants that were interpreted in either of two ways. It may be seen as a randomly generated over a set range of amin =0to change in larval swimming speed with age. Thus, amax = 0.5. This assumes no change in acceptance rate larval swimming speed influences its likelihood of with larval age. (B) Decreasing choosiness: probabil- encountering a substratum. It can also be interpreted as ity of attachment increases with time. That is, as they a change in the amount of substrata available over age, larvae increase their propensity to attach to any time. This second interpretation is unlikely for sessile substratum they encounter. This behavior was termed rotifers; while a change in relative substratum ‘‘desperate’’ by Hodin et al. (2015). (C) Intermediate

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Hydrobiologia availability will change seasonally, for a larva these possibility that planktonic larvae could, after a period changes will be insignificant during its planktonic life. of time, abandon substratum searching to metamor- Three encountering scenarios were considered. phose in the plankton. This LHF allows larvae to

(A) Autonomous (constant): ej rates were set as become unattached, reproductive adults (Fig. 1). constants that were randomly generated within the Confounding factors We ignored six factors that range of emin =0 to emax, depending on the total allow us to simplify the model. (1) Substrata distribu- number of substrata. This assumes no change in tion and architecture: spatial distribution of hydro- swimming speed with larval age. (B) Increasing: the phytes was discounted by assuming that all substrata probability of encountering substrata increases with are randomly dispersed within the habitat. We also time. (C) Decreasing: the probability of encountering ignored potential influences of hydrophyte architec- substrata decreases with time. The total likelihood of ture on larval encounter, as well as their potential to encountering substrata was kept constant across the influence community structure (Kuczyn´ska-Kippen, three models. 2003, 2005; Kuczyn´ska-Kippen & Nagengast, 2006; LHF 4 Adult fitness (substratum-dependent sur- Lucena-Moya & Duggan, 2011). (2) Water flow: the vival and reproduction). We examined two different model does not account for effects of prevailing types of substratum-dependent survival and reproduc- currents or their velocity on larval dispersal or their tion (Ro). In the first of these variations (LHF 4A), tendency to settle (Olson, 1985; Koehl & Hadfield, adult Ro was defined as a function of the substratum to 2010; Hodin et al., 2015). (3) Variation in energy which a larva settled with two variations. (1) Positive: content of embryos: embryo size (egg volume) varies at least one substratum supports increased settling depending on species for both marine invertebrates according to specific criteria. (2) Negative: at least one and sessile rotifers (McEdward, 1995; Wallace et al., substratum results in decreased settling according to 1998). Similarly, in some marine invertebrates, specific criteria. In the second variation (LHF 4B), embryo size and presumably energy content can vary fitness was varied as a function of adult density in three as a function of the substratum occupied by its parent ways. (1) Autonomous (constant): reproduction was (Burgess et al., 2009). Disregarding these factors independent of substratum. In this case, reproduction eliminated the need to add components varying larval rates were randomly generated and independent of lifespan or altering the probability of metamorphic substratum quality. (2) Synergism: reproduction competence and subsequent reproduction, i.e., a latent increased as a function of population density. This effect based on larval experience (Marshall et al., variation may be seen as reflecting the improvement in 2003; Marshall & Keough, 2003; Pechenik, 2006). (4) lifespan and Ro seen in conifera (Hudson, Larval memory: we discounted the possibility for 1886) when two or more adults form a colony larvae to sequentially evaluate substrata that they (Edmondson, 1945). We modeled synergism such that encounter; thus in our model larvae have no memory reproduction increased linearly as a function of the of past encounters with substrata (Thiyagarajan, density of settled larvae. (3) Competition: reproduc- 2010). (5) Geminative colony formation behavior: tion decreased as a function of population density. For we ignored geminative colony formation (larvae example, the aggregation of large numbers of Col- swimming together) as is seen in floscu- lotheca campanulata (Dobie, 1849) colonists on the losa (Mu¨ller, 1773) and Sinantherina socialis (Lin- abaxial (under) surface of Elodea canadensis naeus, 1758) (Wallace et al., 2015). (6) Predation: all Michaux, 1803 leaves has the potential to reduce larvae were assumed equally vulnerable to predation adult reproduction through competition (Wallace and regardless of the presence of species-specific defen- Edmondson, 1986; Wallace, 1987). We modeled sive traits of the rotifer (Wallace et al., 2015) or the competition such that reproduction decreased linearly architecture of the plant species (Walsh, 1995). as a function of settled larvae. LHF 5 Larval abandonment of substratum selec- Model runs tion behavior. Some sessile species have been col- lected in planktonic samples, a condition that we have There are 54 possible combinations of the various termed facultative sessility (reviewed below). To LHF that could be examined by our model, and many explore this, we expanded our model to include the more are possible by making adjustments to the 123 Author's personal copy

Hydrobiologia functions employed. For example, the BM had three Basic model (BM): fitness defined substrata acceptance and three substrata encounter as metamorphosis (LHF 1–3) functions, yielding nine possible combinations. In the RM, these nine scenarios were linked to variations in Although we did not attempt to parameterize the reproduction by substratum type (n = 2) and adult model using real-world data, we did use values that are density (n = 3) (Table 1) for a total of 54 combina- likely to approximate actual conditions. As a conse- tions. In the remainder of the paper, we will refer to the quence, our results should be interpreted as compar- combination of these functions as a mechanism. For isons between mechanisms rather than being example, one mechanism in the BM would be predictive scenarios. Were appropriate data to be decreasing speed and intermediate competence; in collected, this model could be easily adapted to serve a the RM a mechanism could be decreasing speed, predictive purpose. intermediate competence, and synergistic reproduc- Results of this simple model were, as expected, tion. Surveying all of the possible variations within mixed with the outcomes (the fraction of the larval this model is beyond the scope of this paper, but we do cohort that settled) ranging from * 7 to 18% provide analyses into a variety of features of the (Table 2; also see Supplemental Document, ‘‘Model model. To check the robustness of our results, we development’’ section). Surprisingly, of the 36 possi- performed sensitivity analyses on our model with ble pairwise combinations, only one was not signif- respect to different parameters (Pannell, 1997). icantly different (P \ 0.001). In our model, the We have not parameterized our models with real- highest fitness levels were reached when larvae had world data because only a few studies on sessile a choosiness (LHF 2) that was either constant or rotifers provide data that could be used to quantify quadratic and decreasing larval swimming speed (LHF environmental and life history functions (e.g., 3). On the other hand, the lowest fitness levels Edmondson, 1945; Butler, 1983; Wallace & Edmond- occurred when larval acceptance was constant or son, 1986; Sarma et al., 2017). However, with decreasing and when larval swimming speed was suitable values the model may be modified to do that. increasing. To test the model’s robustness and to account for the The sensitivity analysis that examined the degree to stochasticity of environmental processes, we used which our results depended on the value of dP, death Monte Carlo simulations with 10,000 runs for each of rate in the plankton, showed that this parameter the scenarios being examined (Mooney & Swift, appeared to be related to early life behavior (see 1999). The initial cohort of larvae in any run of the Supplemental Document, Table 3 and Figs. 6, 7). For model can be varied, but for convenience we used 100 example, the larvae with the mechanism of constant individuals. choosiness (LHF 2) and decreasing speed (LHF 3) We used the Bonferroni multiple-significance-test settled on a substratum at the fastest rate of all nine correction (Armstrong, 2014) when all pairs of the mechanisms. Under moderate to high levels of preda- sample means were compared. However, because our tion, this mechanism yielded the highest overall study was exploratory, we did not hold to the normal fitness. However, with little to no predation, the rigor of the Bonferroni correction, which requires quadratic choosiness and decreasing speed mechanism accepting the null hypothesis for the complete set even yielded the highest overall fitness. Additionally, the when only one pair within the set was not significant decreasing choosiness and increasing speed mecha- (Streiner & Norman, 2011). nism performed well under no predation, but per- formed the worst among all mechanisms under moderate to high predation. Results The sensitivity analysis also revealed dependence on the length of life parameter, l, related to end of life Here we examine some of the interesting outcomes of behavior (see Supplemental Document, Table 4 and our model, recognizing that these results reflect the Figs. 8, 9). In particular, for medium to large values of specific LHF we used in each scenario (also see l, the constant choosiness and decreasing speed Supplemental Document). mechanism gave the highest overall fitness, whereas for small values of l, the quadratic choosiness and 123 Author's personal copy

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Table 2 Results of the nine variations of the Basic Model (BM). In the BM fitness was defined as larval settling on a substratum LHF 3 Larval substratum encounter (speed) Constant Decreasing Increasing

LHF 2 Larval substratum acceptance Constant 0.134 (0.08) 0.175 (0.10) 0.082 (0.05) Decreasing 0.086 (0.05) 0.100 (0.06) 0.067 (0.04) Increasing 0.126 (0.07) 0.157 (0.09) 0.087 (0.05) Here we report means and standard deviations for 10,000 simulations for the nine different scenarios (3 substratum encounter 9 3 substratum acceptance functions), each with three potential substrata, medium predation rate, and medium length of life. The Life History Functions, LHF 2 (Acceptance) and LHF 3 (Speed) employed in these runs are as described in the text. All but one of the pairwise t-Tests of the sample means were significantly different at P \ 0.05. That comparison was between the mechanisms of acceptance = decreasing and speed = constant versus acceptance = quadratic and speed = increasing. See text for a description of the statistics decreasing speed mechanism gave the highest overall The results of the autonomous reproduction model fitness. were compared to the two variations (see below): LHF It is also interesting to note that for most of the 4A (reproduction as a function of substratum type) and mechanisms, there appears to be a global maximum LHF 4B (reproduction as a function of adult density). for fitness values as a function of l under moderate to high loss of larvae from the plankton. Specifically, the LHF 4A—Substratum-dependent reproduction: mechanisms with quadratic and decreasing choosiness positive versus negative habitats display this behavior, whereas the mechanisms with constant choosiness do not. For mechanisms with When reproduction was dependent on habitat, we quadratic and decreasing choosiness, there is a value found that having one positive substratum (low such that the length of life, which governs the time encounter, high acceptance value) yielded overall larvae have to search for acceptable substratum before higher reproductive fitness for a given mechanism they die due to starvation, has a diminishing return as it than did having one negative substratum (high means more opportunity for mortality due to encounter, low acceptance value) (Table 3, Substra- predation. tum-dependent reproduction). This result held for a range of choosiness and encounter rates (see Supple- Reproductive models (LHF 1–4) mental Document, Fig. 10).

In the first version of the reproductive model, we LHF 4B—Adult density reproduction: synergism modeled the nine scenarios of the BM with fitness versus competition defined as settling and subsequent reproduction (Table 3, Autonomous reproduction). This established Overall, the mechanisms with the highest fitness were a baseline against which we could compare the other those with constant choosiness and decreasing speed two reproductive models (below). In the autonomous coupled with synergistic or constant reproduction reproduction model, we found that the mechanisms (Table 4). These results were robust across a variety of with the highest juvenile fitness corresponded exactly critical density values (see Supplemental Document, to those having the highest fitness in the basic model. Table 5 and Fig. 11). However, relative fitness among For example, under medium death in the plankton due different reproductive functions depended greatly on to predation and medium length of life conditions, the the number of substrata available (see Supplemental constant choosiness and decreasing speed mechanism Document, Fig. 12). In that case, the constant choosi- had the highest reproductive fitness. This was ness and decreasing speed mechanism displayed expected, as the autonomous reproduction model greater fitness when coupled with a competitive assumed a rate of reproduction proportional to the reproduction than with either a constant or synergistic number of larvae surviving to reproduce. reproduction. This was due to the fact that, with more

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Table 3 Results of the first variation of the reproductive model (RM) Choosiness/Speed Autonomous reproduction Substratum-dependent reproduction Positive Negative

Autonomous/autonomous 1.31 0.86 0.72 Autonomous/decreasing 1.85 1.22 0.97 Autonomous/increasing 0.71 0.45 0.40 Decreasing/autonomous 0.68 0.43 0.37 Decreasing/decreasing 0.84 0.54 0.45 Decreasing/increasing 0.48 0.29 0.26 Quadratic/autonomous 1.18 0.76 0.63 Quadratic/decreasing 1.50 1.00 0.81 Quadratic/increasing 0.72 0.47 0.39 This model defined fitness as the average number of offspring per settled larvae. These data are the means for 10,000 simulations for each scenario with three potential substrata for one of the variations of Life History Feature 4A in which reproduction was dependent on substratum only

Table 4 Results of the second variation of the reproductive model (RM) Mechanisms examined Adult fitness

Constant choosiness, decreasing speed, synergistic reproduction 2.23 Constant choosiness, decreasing speed, constant reproduction 1.84 Quadratic choosiness, decreasing speed, synergistic reproduction 1.76 Constant choosiness, constant speed, synergistic reproduction 1.54 Constant choosiness, decreasing speed, competitive reproduction 1.50 This model defined fitness the average number of offspring per settled larvae. These data are the mean reproductive fitness values for the highest ranked mechanisms, using 10,000 simulations for each scenario with three potential substrata for one of the variations of Life History Feature 4B substrata options available, the likelihood of a large encounter and low acceptance rates, the highest number of larvae settling on a given substratum reproductive fitness was achieved when the larvae decreased. That is, density never reached a critical metamorphose and reproduce in the plankton without level on any substratum, which gave the competitive searching for a substratum. For conditions with high- mechanism an advantage. quality and high-quantity substrata, the highest repro- ductive fitness was achieved when the larvae never Facultative sessility (LHF 5) metamorphosed in the plankton. In other words, the likelihood of reproductive success on a substratum Our model has the capacity to allow larvae to was so great, that it was not worth the risk of metamorphose and reproduce in the plankton, as well metamorphosing in the plankton. However, there is a as settling and reproducing on a substratum. By boundary zone between these two regions that yield a systematically varying substratum encounter and maximum fitness when some portion of larvae settle larval acceptance rates, we found that under most and some metamorphose in the plankton. It is within conditions, larvae are likely to either immediately this range that facultatively sessile species may be abandon a search for substrata or to never metamor- found. Given that we have no information on larval phose in the plankton (see Supplemental Document, choosiness and substratum encounter rates, we have Fig. 13). Specifically, under conditions with low not studied this aspect of the model any further (see

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Supplemental Document, section 4 for additional before that time.’’ Moreover, our BM simulations information). indicate that the highest fitness values were achieved under two circumstances: when larval substratum choice was either constant or followed a quadratic Discussion function (i.e., so-called mid-life competence) and larval speed decreased with age (Table 2). This result Our study provides the first model that specifically supports observations by Wallace (1975)onP. examines the life history functions of sessile rotifers beauchampi in which both young and older larvae that includes both larvae and adults. Most previous were less likely to settle. We hypothesize that larvae of research focused on larval behaviors and/or adult species exhibiting exacting preferences for particular presence on substrata, usually with little exploration of substrata will have behavioral patterns as noted here substratum survival or reproduction (Edmondson, (decreasing speed and either constant acceptance or 1944, 1945; Wallace, 1977a, 1980; Wallace & mid-life competence), but species settling on a wide Edmondson, 1986; Delbecque & Suykerbuyk, 1988; array of substrata will not. Meksuwan et al., 2014). As a result of these studies, we know something of larval life before settlement, Reproductive models (RM) (LHF 1–4) e.g., swimming speed and reaction to surfaces (Wal- lace, 1975, 1980) and their energy sources (Hochberg Here we modeled reproduction in three ways: (1) et al. (in this volume); Wallace, 1993; Wallace et al., unrelated to either substratum or adult density (au- 1998). And for transition to adult life, we know tonomous), (2) affected by substratum (positively or something about their development and metamorphic negatively) (LHF 4A), or (3) dependent on adult processes, but only for a few species (e.g., Edmond- density, either positively (coloniality) or negatively son, 1944, 1945; Wright, 1959; Wallace & Edmond- (competition) (LHF 4B). son, 1986; Kutikova, 1995; Fontaneto et al., 2003; Hochberg, 2014). Overall, our understanding of the LHF 4A—Substratum-dependent reproduction evolutionary forces driving larval and adult life histories remains relatively poor. This study modeled Our model showed that larval fitness depended on the larval behavior and subsequent adult reproduction quality of substratum and that small quantities of high- with the aim of developing areas where additional quality substrata were preferable to large amounts of research is needed. poor-quality substrata. Unfortunately, we know little about substratum-dependent survival and reproduc- Basic model (BM) (LHF 1–3) tion in sessile rotifers. Wallace (1980) showed that populations of (Linnaeus, 1758) The BM defined fitness simply as larvae settling on a and Stephanoceros fimbriatus (Goldfuss, 1820) substratum and metamorphosing into adults, thus attached to Nymphaea sp. were shorter than the offering an uncomplicated outcome to assess substra- individuals attached to other vascular hydrophytes. tum selection. This view of fitness is similar to the one This could have resulted from processes unique to the used by Doyle (1975) in his Markov chain model. substrata, e.g., biotic (unequal growth or predation However, because our model is more general than his, rates) or abiotic (increased abrasion on the undersur- we did not attempt a direct comparison. Nevertheless, face of the lily pads by submerged objects). Col- it is interesting to note that Doyle’s model yielded a lotheca campanulata produced more offspring when surprising prediction: ‘‘… that fitness is highest for a attached to the under versus the upper surfaces of E. larva [that] either settles immediately on a substratum canadensis leaves (Wallace & Edmondson, 1986). or never settles on it at all.’’ While that conclusion Butler (1983) suggested that the reproductive effort of does not seem to make biological sense, Wallace Cupelopagis vorax (Leidy, 1857) might be correlated (1975) described a similar behavior in Ptygura to substratum quality, but to our knowledge this beauchampi Edmondson, 1940. If not provided with hypothesis has not be tested. Clearly, additional their preferred substratum, P. beauchampi ‘‘… larvae research is needed to understand the scope of can delay metamorphosis for up to 50 h; most die 123 Author's personal copy

Hydrobiologia substratum-dependent survival and reproduction surface of sediments (i.e., biogenous or organogenous) across taxa and what makes one substratum better in a few habitats in Sweden. These were Collotheca than another. edentata (Collins, 1872), Collotheca edmondsoni Be¯rzin¸sˇ, 1951, and Collotheca heptabrachiata LHF 4B—Adult density-dependent reproduction (Schoch, 1869). Unfortunately, it is not known whether the specimens observed were adults that had Here we modeled a positive effect for gregarious survived dislodgement from their substratum or settlement leading to the development of colonies as whether they came from larvae that metamorphosed Edmondson (1945) demonstrated for F. conifera. in the plankton and subsequently sank to the bottom. Presumably the juxtaposition of two or more coronae Regardless of the validity of these reports, the concept of microphagous suspension feeders will reinforce of facultative sessility is intriguing and represents an each other, perhaps making feeding more efficient interesting Evolutionary Stable Strategy (ESS) that (Wallace, 1987). On the other hand, we also modeled a should be examined. No doubt such a switch in the life negative effect of density on reproduction. Our history of a population must be determined by local assumption was that closely opposed coronae of conditions, i.e., the combined effects of larval death raptorial gnesiotrochans (Atrochidae, Collothecidae) rate coupled with reproductive potential of sessile as would obstruct with each other’s predatory activities compared to planktonic populations. Although those via interference competition. As with other aspects of conditions suggest outcomes whereby planktonic, our model, we are hampered by the lack of data on sessile, or facultative taxa might exist, lack of adult survival and reproduction as a function of information to parameterize our model hampers substratum and/or population density. understanding of this phenomenon. Thus, additional data on larval and adult survival in the plankton and Facultative sessility (LHF 5) the reproductive ability of planktonic species are needed. Without those data, facultative sessility Reports of sessile species collected in planktonic remains an intriguing, but untested supposition. samples are uncommon and often difficult to interpret; On the other hand, many motile rotifers may also it has been assumed that sessile rotifers may become attach to surfaces. Examples of this behavior include dislodged from their substratum and thus are present in species of Seison, Paraseison, bdelloids, and numer- plankton samples after a net has been towed through a ous monogononts (May, 1989; Wallace et al., 2006; bed of hydrophytes, e.g., F. ringens (Green, 2003). Fontaneto & Ambrosini, 2010;Drazˇina et al., 2018). Nevertheless, four sessile species have been reported For example, Brachionus rubens Ehrenberg, 1838 to exhibit facultative sessility. (1) The intra-subspeci- opportunistically settles on the carapaces of cladocer- fic form of Collotheca ornata (Ehrenberg, 1830) is ans thereby receiving a respite from interference known to be sessile (Edmondson, 1944; Koste, 1978), competition and predation (Iyer & Rao, 1995; Die´guez but its subspecific variation C. ornata natans (Tschu- & Gilbert, 2011; Gilbert, in this volume). Ptygura gunoff, 1921) is planktonic (Koste, 1978; Sendacz seminatans Edmondson, 1939 has been termed semi- et al., 2006). (2) While sessile, Lacinularia flosculosa sessile (Edmondson, 1944). When disturbed, adults of is also known to occur in the plankton as adult colonies this species detach and swim away, but return to a (Koste, 1978; RLW pers. obs). (3) Ptygura wilsonii substratum after the disturbance has subsided. Sinan- (Anderson & Shepard, 1892) has been described as therina semibullata (Thorpe, 1889) also attaches to both free-swimming and sessile (Murray, 1913; hydrophytes for short periods of time (RLW, pers. Edmondson, 1949). (4) Although ceratophylli obs.). These species exhibit the behavior of being Schrank, 1803 is considered to be sessile (Nilsen & sequentially sessile, a strategy whereby temporary Larimore, 1973; Koste, 1978; Meksuwan et al., 2014), attachment leads to a gain in fitness due to reduced Beach (1960) reports it to be an ‘‘adventitious swimming costs and perhaps increased feeding effi- plankter.’’ Because no photographic evidence was ciency (Vadstein et al., 2012). We suggest that such provided, we should treat Beach’s account with some temporary attachment behaviors be studied by apply- skepticism (Wallace et al., 2018). Also Be¯rzin¸sˇ (1951) ing concepts of Ideal Free Distribution theory (van der reported the occurrence of sessile species on the Hammen et al., 2012). 123 Author's personal copy

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When sessile rotifers are not sessile Obviously, obligatorily sessile and obligate plank- tonic rotifers have their own evolutionary constraints. Some species within Collothecidae and While there are evolutionary tradeoffs between these are obligatorily planktonic. Examination of the taxo- extremes, we cannot yet appreciate their scope until nomic literature pertaining to those families indicates much more information on the life history of sessile that * 12% are obligatorily planktonic (Koste, 1978; taxa has been obtained. Indeed, we need to understand Segers et al., 2012; Jersabek & Leitner, 2015). that the behavioral and morphological characteristics Therefore, obligatorily planktonic existence must be of sessile rotifers, or their planktonic counterparts, considered to be an ESS. Thus, gnesiotrochans may cannot be optimized simultaneously. According to the have four major life history strategies: obligatorily Pareto Optimality Theory, evolutionary tradeoffs sessile, facultatively sessile, sequentially sessile, and occur such that the performance function of each obligatorily planktonic. In our conceptual model, we feature collectively contributes to fitness (Tendler envision loss of the sessile condition in these families et al., 2015). After additional data are obtained, as we to be delimited by three evolutionary constraints: (1) have noted here, a next logical step is an integration of larval survival before metamorphosis, (2) availability the behavioral space of the sessile taxa with their of substrata allowing adequate reproduction, and, in morphological space (Dera et al., 2008). Once those contrast (3) relative fitness of planktonic adults data are available, performing phylogenetic general- (Fig. 2). However, the transition barrier between the ized least squares or logistic regression analyses may two endpoints of these life history strategies must be provide a better understanding of the forces driving difficult as only a few species occupy the middle evolution of the sessile taxa. region in this behavioral space, i.e., facultative (n = 4) and sequential (n = 2) sessility. In contrast, obligate Comparisons with models of other sessile species sessility has two extremes (monopatry and polypatry). These extremes are probably regulated by the quality As we noted previously a large number of models have of the substrata available and the niche requirements explored substratum selection by marine inverte- of each species. The unusually restricted habitat of P. brates; while we developed our model within that beauchampi for certain trap doors of the carnivorous context, we focused specifically on life history func- hydrophyte Utricularia macrorhiza Le Conte, 1824 tions likely to be experienced by sessile rotifers. Our (Wallace, 1978) illustrates an extreme example of a model allows for flexibility in each life history monopatric species. On the other hand, propensity of function, and thus it accounts for the behaviors C. campanulata larvae to settle everywhere including employed by different species. the bottom of culture dishes represents a polypatric Although it is possible, we did not use either the species (Wallace & Edmondson, 1986). Two species BM or RM to explore the intensification effect (IE) as serve as examples of intermediate substratum selec- defined in the model developed by Pineda & Caswell tivity. Floscularia conifera will settle on a variety of (1997). In the IE, larval settlement is disproportion- hydrophytes, but has a strong propensity for settling on ately higher in circumstances ‘‘… where the amount of conspecifics thus forming colonies (Edmondson, suitable [substratum] is reduced, either due to occu- 1945; Wallace, 1977a); Ptygura crystallina (Ehren- pation by other individuals or to physical processes.’’ berg, 1834) accepts a wide variety of substrata, as does However, both aspects of the IE may have been Limnias melicerta Weisse, 1848 (Wallace, 1977a; observed in sessile rotifers. For example, as noted Meksuwan et al., 2014). Additionally, the molecular above the preferred substrata of P. beauchampi phylogenetic analysis of family Conochilidae by includes the trap doors of U. macrorhiza (Wallace, Meksuwan et al. (2015) must also be considered in 1977b). In his study, Wallace reported some of the this discussion. That study offers support for aligning greatest densities ([ 25 individuals/mm2) occurred on this planktonic, colonial taxon to Ptygura, thereby the doors of intermediate size; smaller and larger doors asserting that the family is really a group of special- did not achieve that density. In addition, Wallace ized Flosculariidae. Using that perspective raises the (1980) speculated that individuals of both F. ringens percentage of sessile taxa that have an obligatorily and S. fimbriatus achieved smaller stature when planktonic life style to * 16%. attached to the undersurfaces of lily pads (Nymphaea) 123 Author's personal copy

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Obligatorily planktonic Larvae Adult Predation rate: unknown Predation rate Substratum suitability: low Attached: high Planktonic: low Collotheca libera, Adult R Collotheca pelagica, Planktonic o Ptygura libera, suitability Attached: low Sinantherina spinosa, Plankton: high Conochilidae

Facultative sessility Sequential sessility Larvae Larvae Predation rate: varies Predation rate: low Substratum: varies Life history Substratum: high Adult Ro Adult Ro Attached: high transition Attached: high Plankton: high barrier Plankton: low Collotheca ornata, Bdelloids, Lacinularia flosculosa, Brachionus rubens, Limnias ceratophylli Ptygura seminatans, Ptygura wilsonii Sinantherina semibullata Polypatry Collotheca algicola, Collotheca ambigua Octotrocha speciosa Limnias melicerta Ptygura beauchampi Floscularia ringens Floscularia armata Ptygura barbata

worraN Range of adult substratum suitability ediW

Monopatry Larvae - Predation rate: low; Substratum suitability: high Adult -- Predation rate: low; R o: high Obligatorily sessile

Fig. 2 A working conceptual model of the behavioral land- and obligatorily planktonic taxa are discussed in the text. We scape for sessile versus planktonic gnesiotrochan rotifers. note the behavior of sequential sessility in bdelloids and Obligatorily sessile taxa noted along the range of adult Brachionus rubens (Monogononta, Ploima) for comparative substratum suitability axis were inferred from Fig. 1 of purposes Meksuwan et al. (2014). Facultatively and sequentially sessile than on either Lemna or Myriophyllum. Our model assessment of its energetics as Toonen & Tyre (2007). could easily be adapted to explore the IE by tracking Our model shares features with Burgess et al. (2009)in the number of settled larvae as a function of time and that both take a discrete dynamical systems approach performing a sensitivity analysis to see how that to modeling the reproductive behavior of larvae. depends on different parameter choices. However, our model offers much more flexibility in We also did not take into account larval substratum the five life history functions and thus it is likely to be selection behaviors as a function of an instantaneous more reflective of real-world behaviors.

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Conclusions histories of other sessile invertebrates; because of its flexibility, it could be applied to other selection While others have explored rotifer populations using behaviors in animals including mate, habitat, and diet. mathematical models (e.g., Fussmann et al., 2000; We encourage others to adapt our model to address Serra et al., 2011; Kovach-Orr & Fussmann, 2013), these questions. ours is the first study to model settling dynamics of sessile rotifers. However, we emphasize that our study Acknowledgements We thank Diego Fontaneto, Holger is exploratory; our purpose was to examine aspects of Herlyn, Mark Kainz, Menuma Khan, McKenzie Lamb, George Wittler, and three anonymous reviewers for their sessile rotifer life history and in doing so to suggest comments that improved this manuscript. This research was topics for additional research and to propose supported in part by funds for faculty development (Ripon testable hypotheses. As such our model provides a College), from the National Science Foundation: DEB 1257068 flexible, tractable, mechanistic approach to examine (EJW), 1257110 (RH), and 1257116 (RLW), and by Grant 5G12MD007592 from the National Institutes on Minority substratum selection of sessile rotifers by varying Health and Health Disparities (NIMHD), a component of the several environmental and life history features. While National Institutes of Health (NIH). The content is solely the we recognize that models are inherently inaccurate, responsibility of the authors and does not necessarily represent loss in accuracy in this model is balanced by a gain in the official views of the National Institutes of Health or the National Science Foundation. simplicity (e.g., Shertzer et al., 2002). Still, lack of observational data on sessile rotifer life history features across all taxa is a weakness to our study. 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