Between semelparity and iteroparity: Empirical evidence for a continuum of modes of parity

Abstract The number of times an organism reproduces (i.e., its mode of parity) is a fundamental life‐history character, and evolutionary and ecological models that compare the relative fitnesses of different modes of parity are common in life‐history theory and theoretical biology. Despite the success of mathematical models designed to compare intrinsic rates of increase (i.e., density‐independent growth rates) between annual‐semelparous and perennial‐iteroparous reproductive schedules, there is widespread evidence that variation in reproductive allocation among semelparous and iteroparous organisms alike is continuous. This study reviews the ecological and molecular evidence for the continuity and plasticity of modes of parity—that is, the idea that annual‐semelparous and perennial‐iteroparous life histories are better understood as endpoints along a continuum of possible strategies. I conclude that parity should be understood as a continuum of different modes of parity, which differ by the degree to which they disperse or concentrate reproductive effort in time. I further argue that there are three main implications of this conclusion: (1) that seasonality should not be conflated with parity; (2) that mathematical models purporting to explain the general evolution of semelparous life histories from iteroparous ones (or vice versa) should not assume that organisms can only display either an annual‐semelparous life history or a perennial‐iteroparous one; and (3) that evolutionary ecologists should base explanations of how different life‐history strategies evolve on the physiological or molecular basis of traits underlying different modes of parity.


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HUGHES 2013; Young, 1981). In such models, two modes of parity are considered, classified by whether they express all reproductive effort in a single year (semelparity), or in more than one (iteroparity). Here, I refer to this simplified conception as the "discrete conception of parity." The main advantage of the discrete conception of parity is its analytical simplicity; given population growth data, intrinsic rates of increase can be easily computed and directly compared. Some intraspecific comparisons between phenotypically similar semelparous and iteroparous congeners conform to the predictions of demographic models based on the discrete conception of parity (Fritz, Stamp & Halverson, 1982;Iguchi & Tsukamoto, 2001;Young, 1984Young, , 1990.
However, in this review I will argue that despite the successesboth theoretical and empirical-of evolutionary explanations rooted in the discrete conception of parity, there is widespread evidence that, like many other life-history traits, parity is a continuous variable and that semelparity and iteroparity are the endpoints of a continuum of possible strategies that define the distribution of reproductive effort through time, rather than simple alternatives describing whether an organism fatally reproduces in a given year or not. On this account, semelparity can be understood as the strategy defined by concentrating reproductive effort in time and iteroparity as the strategy defined by distributing reproductive effort over longer timescales. I refer to this idea hereafter as the "continuous conception of parity." It is important to note that the continuous conception of parity should not be conflated with the related terms "annuality" and "perenniality." These terms specify strategies defined by the "digitization" of reproduction in response to seasonal effects supervening on the process of reproduction, rather than describing how concentrated reproductive effort is in time. This distinction is further discussed later.
However, to date the degree to which empirical evidence supports the continuity of parity has not yet been examined. Furthermore, evolutionary explanations comparing life-history differences between clades with differing modes of parity continue to rely on the discrete conception of parity (e.g., Lopes & Leiner, 2015), and mathematical models based on the formalization of this assumption continue to be produced (Benton & Grant, 1999;Davydova, Diekmann, and van Gils, 2005;Vaupel et al., 2013). However, because of the ubiquity of evolutionary transitions from iteroparity to semelparity (Table 1), understanding parity as a continuous trait is important for understanding the underlying eco-evolutionary dynamics that affect the fitness of life-history strategies.
In this review, I begin by reviewing the development of both the discrete and continuous conceptions of parity as evolutionary hypotheses and/or models. Next, I review empirical work that highlights the existence of natural variation in reproduction along a semelparity-iteroparity continuum, focusing on three distinct patterns found in natural populations that are neither abstractly semelparous nor iteroparous: facultative iteroparity, facultative semelparity, and multiple modes of parity. I conclude by exploring the implications of the continuous conception of parity for: (1) the study of seasonality as a "digitization" of reproduction, (2) the process of mathematically modeling life-history optimization, and (3) the study of the molecular regulation of reproductive traits linked to parity.

| "Cole's Paradox" and the development of the discrete conception of parity
Although the first mathematical model of the intrinsic rate of increase in annual plants was constructed by Linnaeus (1744), Lamont Cole (1954) was the first to categorize life histories into dichotomous "semelparous" and "iteroparous" groups: A semelparous organism is one that "dies upon producing seed" and therefore, "potential population growth may be considered on the assumption that generations do not overlap" (p. 109), while iteroparous organisms include a variety of cases, from those where "only two or three litters of young are produced in a lifetime" as well as "various trees and tapeworms, where a single individual may produce thousands of litters" (p. 118). Thus, Cole created, and contemporary theorists have inherited, a conception of parity as a discrete variable: An organism either reproduces more than once or it does not.
Cole also identified "the paradox of semelparity," and wrote that "for an annual species, the absolute gain in intrinsic population growth which could be achieved by changing to the perennial reproductive habit would be exactly equivalent to adding one individual to the average litter size." (Cole, 1954, p. 118). Consequently, according to the model he developed, a semelparous or iteroparous strategy evolves in response to strong directional selection for trait values that: (1) maximize the annual rate of intrinsic increase; and (2) are subject to trade-offs, since reproductive effort is always limited by resource availability. The "paradox of semelparity" is that the relative intrinsic rates of increase for semelparous and iteroparous strategies are very similar (i.e., they differ only by one individual-the mother), which suggests that iteroparity, not semelparity, should be rare, while in nature, iteroparous life histories are generally more common than semelparous ones. Cole's articulation of the paradox of semelparity motivated many studies searching for theoretical selective advantages of traits linked to discrete semelparous and iteroparous strategies (Cushing, 2015;Murdoch, 1966;Murphy, 1968;Omielan, 1991;Su & Peterman, 2012;Vaupel, Missov, and Metcalf, 2013), as well as attempts to detect these selective advantages in natural systems (Fisher & Blomberg, 2011;Franklin & Hogarth, 2008;Gagnon & Platt, 2008;Kraaijeveld, Kraaijeveld-Smit & Adcock, 2003;Murphy & Rodhouse, 1999). Following Cole, semelparous strategies considered in later life-history models were usually also annual (García, 2003;Young & Augspurger, 1991), and thus, the primary goal of many models purporting to explain the evolution of semelparity was to provide reasons why a perennial-iteroparous strategy might confer higher fitness than an annual-semelparous one.
Cole's "paradox of semelparity" was resolved by acknowledging that differences in age-specific rates of mortality affect the relative fitness of semelparous and iteroparous habits. Building on prior analytical work (Bryant, 1971;Emlen, 1970;Gadgil & Bossert, 1970;Murphy, 1968), Charnov and Schaffer (1973) and Schaffer (1974b) noted that the expected fitness value of individuals at juvenile (i.e., prereproductive) and adult (i.e., reproductively mature) developmental stages often differed. They then argued that when the survival of adults was more assured than the survival of juveniles, an iteroparous habit would have a comparative growth advantage over a semelparous one. Thus, their model emphasized that the reproductive value of members of the age class with a lower age-or stage-specific rate of mortality would beassuming equal fitness across age classes-greater than the value of the members of the age class with a higher rate of mortality. This approach can also be used to analyze the age structures of iteroparous populations; thus, it is a "discrete" rather than a "binary" model. Young (1981) extended this insight into a more general model of intrinsic rates of increase, which incorporated not only differences in age-specific survivorship, but also differences in prereproductive development time and time between reproductive episodes. This model provided three major reasons why semelparity might be favored by natural selection.
First, high adult mortality-or the early onset of reproductive senescence-might prevent iteroparous species from accruing fitness gains from established parents over long timescales. Second, a high population growth rate should favor semelparity outright. Third, when the marginal cost of additional offspring is inversely proportional to the number of offspring produced, fecundity is maximized by investing all reproductive effort into a single episode, that is, adopting an extreme annual-semelparous life history-see also Schaffer (1974aSchaffer ( , 1974b and Schaffer and Gadgil (1975).

| Further theoretical work on parity as a discrete trait
Given that earlier work sought to explain the prevalence of semelparous and iteroparous strategies by identifying differences in agespecific mortality, recent work has sought to explain why differences in age-specific mortality persist, as well as how varying environmental conditions facilitate the co-existence of different modes of parity. Models used to predict age and size at first flowering for semelparous plants have been found to be more appropriate for long-lived than short-lived species (Metcalf, Rose & Rees, 2003;Rees and Rose 2002).

| Empirical support for the discrete conception of parity
Empirical support for the predictions made by discrete-conception models is strongest where perennial-iteroparous and annualsemelparous (or, rarely, perennial-semelparous) congeneric species coexist and have starkly different life histories. For instance, in a comparison of Mount Kenya species of the genus Lobelia, Young (1984) found that juvenile and adult mortality of the annual-semelparous species L. telekii were higher than in the closely related perennialiteroparous species Lobelia deckenii (syn. L. keniensis). Young concluded that the difference in age-specific rates of mortality would strongly influence the expected value of future reproduction for each species, leading to perennial-iteroparity in one species and annualsemelparity in the other (see also Young, 1990). Similar comparisons between semelparous and iteroparous congeners or confamilials have been conducted in insects (Fritz et al., 1982;Stegmann & Linsenmair, 2002), salmon (Crespi & Teo, 2002;Dickhoff, 1989;Kindsvater, Braun, Otto & Reynolds, 2016;Unwin, Kinnison, and Quinn, 1999), snakes (Bonnet, 2011), algae (De Wreede & Klinger, 1988, and dasyurid marsupials (Kraaijeveld, Kraaijeveld-Smit, and Adcock, 2003;Mills, Bradshaw, Lambert, Bradshaw & Bencini, 2012). Other studies have focused on reproductive effort, as a declining marginal cost of offspring in terms of reproductive effort should select for an annual-or perennial-semelparous life history over an perennial-iteroparous one. This is the cited cause of the evolution of semelparity in Digitalis purpurea (Sletvold, 2002), and in Antechinus agilis (Fisher & Blomberg, 2011;Smith & Charnov, 2001). The interaction between intrinsic rate of increase and phenology also has important fitness implications; in two subspecies of Yucca whipplei, the semelparous variant showed higher viability and faster time to germination than the iteroparous variant did (Huxman & Loik, 1997

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HUGHES mortality differences between juveniles and adults, which explains the evolution of semelparity in a variety of long-lived semelparous plants (Foster, 1977;Kitajima & Augspurger, 1989;Young & Augspurger, 1991), as well as in salmonids (Crespi & Teo, 2002;Fleming, 1998;Hendry, Morbey, Berg & Wenburg, 2004;Sloat et al., 2014). Taken together, even when not biologically plausible, conceptual models have proven to be heuristically valuable and have been used to draw stark contrasts between the different effects density dependence has on annual-semelparous and perennial-iteroparous strategies. In cases where such extreme strategies coexist, existing theories seem to do a good job of predicting how they evolved.

| From uniparity to continuous reproduction
However, in many cases substantial unexplained variation in parity exists even after factors such as age-specific mortality, density dependence, and environmental effects are taken into account. For this reason, it seems as though models based on the discrete conception of parity describe a limited range of special cases and not the majority of systems with congeneric or confamilial species with a spectrum of different reproductive strategies. This problem arises because theoretical models of the discrete conception of parity make two characteristic assumptions. First, it is assumed that reproductive output is allocated among cycles (typically seasons or years) rather than expressed continuously. This means that offspring produced at two different times within a single season are "counted" as being part of the same reproductive episode, while offspring produced at two different times in two different seasons are counted as part of categorically different reproductive episodes. This permits the calculation of threshold values (e.g., of size or age) beyond which selection should begin to favor one mode of parity or the other, but this is based on a distinction that is arbitrary. Second, each individual is assumed to express a single reproductive strategy; models do not predict phenotypically plastic modes of parity, or facultative switching between modes.
These assumptions do not hold in many cases. There are relatively few examples of semelparous reproduction occurring exactly "once"that is, in exactly one place, at exactly one time. Moreover, "annuality" and "perenniality"-terms that refer to the number of years in which organisms reproduce-cannot be used interchangeably with "semelparity" and "iteroparity," which refer to the number of reproductive episodes organisms have (Fritz, Stamp, and Halverson, 1982;Kirkendall & Stenseth, 1985). In "The Evolution of Life Histories", Roff (1992) noted that, "if we consider our unit of time to be a single year, annuals can be termed semelparous and perennials iteroparous. A further division is possible within annuals, for some reproduce once and are, therefore, semelparous within any time scale, while others flower repeatedly throughout the summer and, hence, are iteroparous with respect to annuals that flower only once, but semelparous with respect to perennials" (p. 248). That is, it is the simultaneity and the finality of the reproductive episode (i.e., the concentration of reproductive effort) that defines "perfect" semelparity. Therefore, the continuous conception characterizes "extreme" semelparity to be a single, complete, and exhaustive reproductive episode where all reproductive effort is invested at once. Examples of this strategy-which Kirkendall and Stenseth (1985) termed "uniparity"-include mayflies and mites of the genus Adactylidium (Corkum, Ciborowski & Poulin, 1997;Edmunds, Jensen & Berner, 1976). Both male and female mayflies die shortly after mating and dispersing fertilized eggs. In Adactylid mites, offspring devour the mother from the inside out and are thus obligately annual-semelparous (Elbadry & Tawfik, 1966;Goldrazena, Jordana & Zhang, 1997). The correspondingly "extreme" perennial-iteroparous strategy is a long-lived perennial strategy that spreads reproductive effort out evenly among a very large number of reproductive cycles.
Intermediate strategies complete reproduction over a shorter timescale than bristlecone pine, but over a longer timescale than Adactylid mites.
The continuous conception of parity is therefore very simple: Parity should be understood as a composite trait, and, rather than considering only whether organisms complete reproduction within a given year, life-history strategies should be compared by the degree to which they concentrate or disperse reproductive effort-and hence risk of reproductive failure-in time. For example, a mature biennial strategy (where an organism reproduces once per year in two consecutive years) distributes reproductive effort over a shorter timescale than does a long-lived perennial congener (where an organism reproduces once per year in many years); although the biennial strategy is not semelparous, it is further toward the "uniparous" end of the continuum of modes of parity than is the perennial strategy. Similarly, an annual-semelparous life history that reproduces rapidly lies further toward this end of the continuum than does an annual-semelparous life history in which reproduction is spread over a longer period of time. In extending the underlying logic of the discrete conception in this way, the insights gained by comparing "extreme" semelparous and iteroparous strategies are included, but the explanatory power of this logic is extended to apply to intermediate strategies as well.

| Empirical support for the continuous conception of parity
There is considerable empirical support, from laboratory and field studies alike, for the notion that parity varies continuously. Many species are facultatively semelparous, others reproduce irregularly or opportunistically, and many comparisons between related iteroparous and semelparous species do not show measurable differences in factors affecting intrinsic rates of increase, including age-specific rates of mortality. These situations are not uncommon in nature. The problem they present is significant because the evolutionary transition from semelparity to iteroparity (and back) is ubiquitous, and has occurred in a wide variety of taxa (see Table 1 for an example using data from angiosperm orders).
There are important consequences for adopting the continuous conception of parity as a starting point for modeling the evolution of different modes of parity. Mathematical models based on the discrete conception of parity often predict threshold values-in mortality rate, size at initiation of reproduction, or expected growth rate-that do not agree with empirical observation (Lessells, 2005;Omielan, 1991;Piñol & Banzon, 2011;Su & Peterman, 2012;Trumbo, 2013;Vaupel, Missov, and Metcalf, 2013). In particular, ESS models derived from assumptions rooted in the discrete conception of parity frequently underestimate the adaptive value of semelparous reproductive strategies; even after accounting for the effects of environmental stochasticity and density dependence, ESS models predict that semelparous strategies should be less abundant-and less fit-than they have been found to be (Benton & Grant, 1999). In addition, there are empirical cases that explicitly do not conform to the predictions of the discrete model.
For example, an analysis of 12 winter-establishing primrose species (Oenothera: Onagraceae) found no significant differences in mortality estimates or in environmental determinants of fitness for semelparous and iteroparous species (Evans et al., 2005). In some cases, the problem may be that life histories are too complex for organisms to follow discrete strategies; many salmon species also do not fit neatly into "classical" annual-or perennial-semelparous and perennial-iteroparous classifications (Hendry et al., 2004;Unwin et al., 1999). Other research has suggested that deterministic models of investment may provide more accurate demographic predictions for long-lived than short-lived semelparous species, given that many annual-semelparous species (usually plants) show substantial phenotypic plasticity in phenology (e.g., size at first flowering), offspring quality, and overall fecundity (Burd, Read, Sanson, Jaffre & Jaffré, 2006 (Hop and Gjøsaeter, 2013;Hop, Trudeau & Graham, 1995). However, males and females of this species also seem to have different life histories-males begin to reproduce at an earlier age and can, in response to environmental stressors of varying strength, allocate varying (and even extreme) amounts of reproductive effort to a single instance of reproductive activity; parity in this species is thus also continuously varying and phenotypically plastic, and populations display multiple modes of parity at once (Nahrgang et al., 2014). Although examples of each life history are provided below, many more have been added to

| Facultative iteroparity
Many semelparous species have shown the ability to facultatively reproduce one or more times after an initial bout of reproduction has begun and ended-this is termed "facultative iteroparity." Facultative iteroparity can be adaptive when it either: (1) provides an opportunity to realize fitness gains from an unexpected abundance of resources, or (2) shifts reproductive effort from inopportune to opportune times. The first type of adaptive facultative iteroparity occurs when additional bouts of reproduction increase fitness by permitting unexpected "bonus" resources to be invested in new offspring. For example, mothers of the semelparous crab spider Misumena vatia (Araeae, Thomsidae) typically lay and provision a single brood of eggs (Gertsch, 1939;Morse, 1979); however, in response to high food availability and/or usually warm environmental conditions, they are capable of laying and caring for a second brood if sperm supplies are not depleted (Morse, 1994). A similar facultative double-broodedness in response to unusually favorable environment has been observed in the green lynx spider Peucetia viridans (Fink, 1986). In addition, a small proportion of Chinook salmon (Onchorhynchus tshawytscha), which typically reproduce only once, have been found to survive and reproduce in two or three additional seasons (Unwin et al., 1999). Tallamy and Brown (1999)

Sthenoteuthis oualaniensis
Cephalopod Timing of reproduction x Rocha et al. (2001) T A B L E 2 (Continued) (Continues) more than once, despite the fact that small females can typically breed only once.
The second form of adaptive facultative iteroparity occurs when deferral of reproductive effort-from a primary reproductive episode to a secondary one-allows an organism to reproduce at a more opportune time. Reproduction is deferred to seek the highest marginal fitness return on invested reproductive effort. For example, when high organic pollution levels disrupt primary reproduction in the freshwater leech Erpobdella octoculata, reproduction ceases and remaining reproductive effort is deferred to a second reproductive bout produced the next year (Maltby & Calow, 1986). Similar behavior has been seen in another Erpobdellid leech, Erpobdella obscura (Davies & Dratnal, 1996;Peterson, 1983) as well as in many cephalopods (Rocha, Guerra & González, 2001). Adaptive deferral of reproductive effort is common in crab spiders. In Lysiteles coronatus, artificial brood reductions resulted in the production of a second brood, and the degree of deferral was proportional to the degree of the original reduction (Futami & Akimoto, 2005). This was also observed in the field in Eresid spiders of the genera Anelosimus and Stegodyphus, both of which facultatively produce a second brood in response to nest predation (Grinsted, Breuker & Bilde, 2014;Schneider & Lubin, 1997;Schneider, Salomon & Lubin, 2003). Although the adaptive potential of facultative iteroparity is often apparent, facultative iteroparity may also be vestigial instead of adaptive. In this case, the organism's life history merely reflects an ancestral state, and the second (or additional) bout of reproduction should confer little or no adaptive value (Golding & Yuwono, 1994;Hughes & Simons, 2014b).

| Facultative semelparity
Facultative semelparity occurs when species that are normally perennial-iteroparous-that is, they have multiple, discontinuous reproductive episodes that span more than one year-are capable of expressing only a single reproductive bout (Christiansen, Praebel, Siikavuopio & Carscadden, 2008). This is a useful strategy for organisms to use to take advantage of unusually good environmental conditions for reproduction. For example, in the short-lived mustard Boechera fecunda (syn. Arabis fecunda; Brassicaceae), plants are capable of wide range of reproductive strategies, from nearinstantaneous semelparity to multiyear iteroparity. This is because B. fecunda can produce many small axillary inflorescences in any given year, and their production does not preclude flowering by the same rosette in the subsequent year. However, plants can also produce large "terminal inflorescences" that exhaust remaining resources and lead to senescence and death. Although some plants produce axillary inflorescences for several years before a terminal inflorescence, others produce a terminal inflorescence in their first year (Lesica & Shelly, 1995;Lesica & Young, 2005). A similar system is seen in common foxglove, Digitalis purpurea (Scrophulariaceae), which is predominantly biennial or perennial-iteroparous, but can be facultatively semelparous if resource availability in the first year is high (Sletvold, 2002). Facultative semelparity has also been observed in capelin (

| Multiple modes of parity
The realization of multiple modes of parity at once is a major source of confusion for mathematical models that predict a single optimal value for all individuals, regardless of whether they are all supposed to express an annual-semelparous or perennial-iteroparous habit. The range of different modes of parity expressed need not be dramatic and may be due to phenotypic plasticity, but, as a consistent response to environmental triggers, even small differences in the degree of concentration of reproductive effort should significantly affect fitness. In Strong empirical evidence of multiple modes of parity realized at once is found in sea beets (Beta spp., Amaranthaceae), which display reproductive strategies along "a gradient from pronounced iteroparity to pronounced semelparity" (Hautekèete et al., 2001, p. 796).
Interestingly, the production of multiple modes of parity is elicited as an adaptive response to variable selective pressures faced by these species (e.g., predation and disturbance). High levels of environmental stress cause individuals to trade off future fecundity for increased immediate reproductive effort, resulting in a parity gradient tending to semelparity wherever environmental stress becomes intense Van Dijk, 2001, 2009). This pattern is consistent with the prediction that higher current reproductive effort can prevent organisms from being exposed to uncertain or risky environments (Rubenstein, 2011;Trumbo, 2013;Vahl, 1981;Williams, 1966). Many insect species are also capable of displaying a range of modes of parity among individuals (Trumbo, 2013). In the assassin bug (Atopozelus pallens), females deposit eggs in small clutches, approximately every two days. However, the number of clutches-and hence how prolonged this reproductive episode is-varies substantially (Tallamy, Walsh & Peck, 2004). Similarly, female European earwigs (Forficula auricularia) show continuous variation in clutch size and can even become semelparous by laying only a single one (Meunier et al., 2012;Ratz, Kramer, Veuille & Meunier, 2016). Most insects showing variation in the number of clutches produced do so in response to abiotic cues, particularly temperature and day length (Bradshaw, 1986). This behavior can also be found in ascidians (Grosberg, 1988) and semelparous mammals (Mills et al., 2012;Wolfe, Mills, Garkaklis & Bencini, 2004).
Phenotypic plasticity within a reproductive episode of a single individual is noticeable when a semelparous organism displays a changing reproductive strategy-varying along the continuum of parity-that cannot be attributed to developmental, environmental, or architectural constraints (Diggle, 1995(Diggle, , 1997. This pattern is more difficult to detect than phenotypically plastic strategies that differ between individuals, but in many systems observable differences exist between the "packaging" of reproductive effort, resulting in adaptive variation in phenology or offspring quality through time. This can also be difficult, because-since they reproduce only once-semelparous organisms are expected to show high reproductive effort (Bonser & Aarssen, 2006). However, the development of fruits of the semelparous plant Lobelia inflata varied continuously; in this system, late fruits showed accelerated phenology and higher offspring quality relative to early fruits. This pattern, which indicated that more reproductive effort was invested in later fruit, shows that L. inflata does not "reproduce once" but dynamically allocates reproductive effort throughout a sequence of repeated fruiting events (Hughes & Simons, 2014a, 2015

| Evolutionary transitions between modes of parity are ubiquitous
Transitions between different strategies along the semelparityiteroparity continuum are common throughout the tree of life.
Similar lability in these traits is also present in other clades, including both angiosperms and animals (Crespi & Teo, 2002;Hautekèete, Piquot, and Van Dijk, 2001;Maltby & Calow, 1986;Tallamy & Brown, 1999;Varela-Lasheras & Van Dooren, 2014). Therefore, since transitions from mode of parity to another have occurred throughout the tree of life, a continuous understanding of parity may clarify the relationship between life-history strategy and speciation.

| UNDERSTANDING THE EVOLUTION OF PARITY AS A CONTINUOUS TRAIT
What changes should be made in light of the evidence that parity is a continuous trait? In this section, I will focus on three main recommen-

| Seasonality and mode of parity
One major implication of treating parity as a continuous variable is that this reconception allows us to distinguish between parity and seasonality. Parity describes the concentration or diffusion of reproductive effort in time, which is distinct from the question of seasonal reproduction-that is, how organisms should distribute reproductive effort among seasons, when seasonal cycles determine the favorability of establishment, growth, and reproductive conditions (Bulmer, 1994;Calow, 1979;Charnov & Schaffer, 1973;Cole, 1954;Evans et al., 2005;Ranta, Tesar, Alaja & Kaitala, 2007;Schaffer and Gadgil (1975); Schaffer, 1974b;Young, 1981). It is, of course, clear that seasonality is related to parity. Insofar as an annual-semelparous organism is defined by the fact that it has a single reproductive episode that occurs within one year, it is likely to experience selection for strategies that optimize its reproductive schedule relative to season-specific environmental effects; this means that an annual-semelparous organism is more likely to show predictable seasonal patterns than a perennial-iteroparous congener that can escape a poor season by overwintering. However, the explanatory power of such seasonal adaptations may be much weaker when we compare a fast-reproducing semelparous organism with a slower-reproducing semelparous congener, or when we compare an iteroparous strategy where reproductive effort is distributed over two seasons with another where reproductive effort is distributed among ten seasons. Seasonal effects are likely to supervene on reproduction whenever regular intervals occur that have an impact on the favorability of reproduction. Thus, it may be more fruitful to understand annuality and perenniality as strategies defined by the "digitization" of reproduction in response to seasonality. The advantage of this approach is that it makes it easier to understand flexible life histories, regardless of whether a species is semelparous or iteroparous.
There is widespread empirical evidence that seasonality and parity can vary independently. One common pattern is integer changes in voltinism among organisms that share a common mode of parity. For example, the Muga silkworm (Antheraea assamensis) is semelparous and multivoltine throughout its natural range (from India to Borneo).
This species produces up to six generations per year, with the number of reproductive cycles depending on length of the season (Ghorai, Chaudhuri & Senapati, 2009;Singh & Singh, 1998). However, the closely related Chinese tussar silkmoth, Antheraea pernyi, is bivoltine at the southern margins of its range, but is univoltine in northern China and Korea. Moreover, this continuous variation in voltinism along an ecological cline is due to continuous variation in environmentdependent biogenic monoamine production in the brains of diapause pupae (Fukuda, 1953;Liu, Li, Li & Qin, 2010;Matsumoto & Takeda, 2002). Life histories also vary continuously among populations of the wild silkmoth (Bombyx mandarina) and its domesticated counterpart (Bombyx mori), where populations in colder climates (e.g., European Russia) are univoltine, whereas those in China and Korea are bivoltine or multivoltine (Xia et al., 2009). Similar examples can also be found in crucifers (Springthorpe & Penfield, 2015;Williams & Hill, 1986), orchids (Chase, Hanson, Albert, Whitten & Williams, 2005), freshwater mollusks (Mackie & Flippance, 1983;McMahon & Bogan, 2001), and Centaurea (Asteraceae; Acker et al., 2014), among others. In each of these systems, a distinct continuum of reproductive strategies despite the supervening effect of seasonality is readily observable.
Additionally, new models are being developed that consider generation length independently from parity (Waples, 2016). Thus, we can easily tease apart the question of whether reproduction is concentrated in time-that is, whether a given species is semelparous-from the question of whether seasonality requires that, in temperate climates, late-reproducing individuals should enter diapause rather than reproduce immediately. These new models will have to build on and learn from a considerable body of existing models detailing the eco-evolutionary dynamics of semelparous and iteroparous life-history strategies. Early conceptual and mathematical models of optimal semelparous reproduction were generally simple and deterministic and were designed to predict a single "threshold" value that optimized life-history characters such as size at first reproduction (Bell, 1980;Young, 1981). Threshold models of this type include senescence-threshold models based on the Penna aging model (Piñol & Banzon, 2011), as well as development-threshold models such as age-structured life-history models. Age-structured models treat age at reproduction, and hence parity, as a discrete variable, and assess the evolutionary consequences of the degree of overlap between juvenile (i.e., prereproductive) and adult (reproductive) classes in a population (Wikan, 2012). Among the best known of these are Leslie models, which predict either few evolutionary stable states for semelparous organisms (Cushing, 2009(Cushing, , 2015Cushing & Henson, 2012;Cushing & Stump, 2013) or even that populations should consist entirely of individuals of a given age class (Rudnicki & Wieczorek, 2014). Still other threshold models make similar predictions for survival traits (Da-Silva, Martins, Bonato & Dos Reis, 2008).

| Mathematical models of parity
Some of the assumptions made by threshold models may be resolved by incorporating a wider range of possible life histories. For instance, Rees et al. (1999) showed that those deterministic agestructured models, which rest on the assumption that parity is discrete, consistently overestimate time at first reproduction in monocarpic plants. This result is the problem of the discrete conception writ large: Empirical data does not conform to model predictions because empirically, the concentration of reproductive effort in time is not as extreme as would be predicted by if the annual-semelparous life history were as extreme as it was predicted to be (see also Marshall and Keough, 2007). Such variability-caused by developmental plasticity and stochastic variation in the timing of cues-confounds threshold models, in which semelparous reproduction is held to be optimized closely within a given environment and has therefore prompted the formulation of new modeling approaches that consider a range of semelparous strategies in response to environmental heterogeneity (reviewed in Metcalf et al., 2003).
Recent mathematical models also fall into several types, each with a particular ecological focus. Integral projection models, which incorporate random fluctuations in environmental parameters related to reproduction, were developed to more accurately predict time to first reproduction and size at reproduction, both in iteroparous species (e.g., Kuss, Rees, Aegisdottir, Ellner & Stocklin, 2008) and in semelparous species with a prolonged semelparous reproductive episode (Ellner & Rees, 2006;Rees, Sheppard, Briese, and Mangel, 1999;Sletvold 2005). Time-lagged integral projection models attempt to account for the temporal discounting of reproductive value as well as size-specific effects on reproductive effort (Kuss et al., 2008). Newer age-structured stochastic models incorporate continuous variation in life-history traits to predict optimal timing of reproduction; while these resemble earlier models that treat parity wholly as a discrete variable, the life-history traits in these models are treated continuously (Davison & Satterthwaite, 2016;Oizumi, 2014;Oizumi & Takada, 2013).
Several recent models have been developed to predict reproductive trait values given other (measured or measurable) life-history parameters. This modeling methodology is intuitive and compatible with the idea that parity is a continuous trait. For example, Kindsvater et al.
(2016) used a stage-structured model to assess the degree to which trait covariation constrained life-history adaptation in salmonids.
Other kinds of data-driven models fall into two main types: (1) models that highlight the importance of phenotypically plastic reaction norms as maximizing fitness despite stochastic variability in environment (e.g., Burd et al., 2006); and (2) models that emphasize the innate variability in reproductive characters within species (Austen, Forrest & Weis, 2015;Drouineau, Rigaud, Daverat & Lambert, 2014). Both of these ideas may be useful in modeling selective pressures on a continuum of modes of parity. Moreover, rather than using a single model to characterize semelparous investment in flowers and offspring, authors are now proposing a "meta-modeling" approach to annual plant reproduction, recognizing that semelparous reproduction can be fine-tuned by natural selection through phenotypic plasticity (Hughes & Simons, 2014a).
Because parity may be most fruitfully understood as the concentration of reproductive effort in time, another class of model that may prove to be useful is the dynamic state variable model (DSVM).
DSVMs are powerful dynamic optimization models used to characterize mechanistic relationships in ecology and have the benefit of being able to be solved computationally (Clark & Mangel, 2000).  (Peterson & Roitberg, 2010;Skubic, Taborsky, McNamara & Houston, 2004;Yerkes & Koops, 1999). Although the specification of mathematical models is complex, and a thorough articulation and validation of a mathematical model of continuously varying parity is beyond the scope of this review, this approach offers hope for a simple, iterative improvement of the discrete-conception threshold and age-class models that have been validated in the past.

| Molecular regulation of parity
The third implication of understanding parity as a continuously varying trait is that life-history models should be rooted in mechanistic detail, and identifying the mechanistic basis of different modes of parity  (Table 3). In this section, I will briefly explain how parsing out the contributions of a single gene can improve our understanding of how modes of parity can vary continuously. To do so, I will discuss an important example: the control of the initiation of flowering in response to vernalization as it is regulated by FLOWERING LOCUS C (FLC) and its orthologues in the Brassicaceae.

| CONCLUSIONS
We still know far too little about why the evolutionary transition from semelparity to iteroparity (or vice versa) is as common as it is, or under which ecological conditions intermediate strategies-such as facultative semelparity-will thrive. Models rooted in the conception of parity as a binary trait do a good job of accounting for the fitness differences between discrete semelparous-annual and iteroparous perennial alternative strategies, and, even when they do not make accurate quantitative predictions, they have heuristic value (e.g., they permit the consideration of the impact that factors such as density dependence and environmental stochasticity will have on parity). However, systems characterized by only these possibilities-and no others-are special cases, and thus their insights. In most cases, the life-history question at hand is subtle: Why does a given species evolve a facultative strategy, or why does another show intraspecific variation in the length of its semelparous reproductive episode?
1. The main conclusion of this work is that parity should be understood as the concentration of reproductive effort in time and should therefore be treated as a continuous trait rather than a discrete one. This generalization of parity offers several notable advantages for life-history theory. First, treating parity as a continuous trait allows us to treat parity as a distinct life-history syndrome, itself the result of correlated selection on a suite of continuously varying traits affecting the concentration of reproductive effort in time, and which may show finely graded correlated variation within species or populations. This is advantageous because parity is a composite trait, and the act of reproducing at a given time, for a given duration, etc. involves the recruitment and coordination of many independent traits, each of which may affect the expression of others. A similar integrative approach has proven to be valuable in studying other multifactorial composite traits, such as dispersal and risk spreading (Buoro & Carlson, 2014). Second, whether they share a common genetic basis or not, obvious or visible life-history characters may not be primary targets of selection, and evolution of such traits may occur as an epiphenomenon of selection on (one or many) other apparent or nonapparent underlying traits.

2.
Next, the question of parity should be separated from the question of seasonality; this is a source of abundant confusion. The question of the concentration of reproductive effort within a reproductive episode is simply not the same as the question of the optimal pattern of the distribution of risk in and among seasons. These questions are undoubtedly related: Reproductive characters of long-lived semelparous species are generally easier to model than characters of short-lived species, and while environmental heterogeneity plays an important role determining the optimal allocation of reproductive effort in annual-semelparous species, long-lived semelparous species can afford to be "choosier" about when they reproduce, and therefore have been shown to more closely approximate model predictions. This may be especially true when, as in many long-lived perennial-iteroparous species, the relationship between age and cost of reproduction is nonlinear. Thus, developing models that accurately model the fitness dynamics of short-lived semelparous species should be a priority.

3.
Third, life-history theorists should work to extend the insights from abstract discrete-conception conceptual and mathematical models to next-generation models that treat parity as a continuously varying trait. Considering only annual-semelparity and perennial-iteroparity as discrete alternatives, although a useful simplification for many models, is biologically accurate only in a limited number of special cases, and the continuous conception of parity is more likely to approximate the eco-evolutionary dynamics of natural systems that show intraspecific or plastic variation in the expression of parity.

4.
Lastly, treating parity as a continuous variable that represents a syndrome of associated traits makes it easier to integrate life-history studies with mechanistic details deriving from molecular ecology, insofar as composite life-history traits such as parity are unlikely to be the result of a simple presence or absence of a single gene or allele. Instead, parity is likely to be the product of complex systems of genetic, translational, and post-translational regulation.
Systems in which discrete modes of parity are found may therefore reflect those cases where continuous variation in underlying traits is masked by the supervening effect of developmental thresholds that can trigger reproduction (or not).