Probing of mortality rate by staying alive: The growth-reproduction trade-off in a spatially heterogeneous environment

1. In many annual plants, mollusks, crustaceans and ectothermic vertebrates, growth accompanies reproduction. The growth curves of these organisms often exhibit a complex shape, with episodic cessations or accelerations of growth occurring long after maturation. The mixed allocation to growth and reproduction has poorly understood adaptive consequences, and the life-history theory does not explain if complex growth in short-lived organisms can be adaptive. 2. We model the trade-off between growth and reproduction in a short-lived organ­ ism evolving in a metapopulation. Individuals occupy risky or safe sites throughout their lives, but are uncertain regarding the risk of death. Modelled organisms are allowed to grow and produce offspring at specified time points (moults), although we also consider scenarios that approximate continuous growth and reproduction. 3. Certain combinations of risky to safe sites select for strategies with mixed alloca­ tion to growth and reproduction that bet-hedge offspring production in safe and risky sites. Our model shows that spatially heterogeneous environments select for mixed allocation only if safe sites do not become the prevailing source of recruits, for example, when


| INTRODUCTION
Th e evolution of grow th tactics is key to understanding the diversity of life histories m ediated by the body size of organism s (Gotthard, 2001;Kozlow ski, 1996). Th e adaptive consequences of grow th by mature plants, fish, am phibians, reptiles, crustaceans, m ollusks and other invertebrates are far from being understood (H eino & Kaitala, 1999). G row th can be seen as an investm ent in future reproduction because the net am ount of acquired resources scales positively with b ody size (Kozlow ski, 2 0 0 6 ; Peters, 1983). In an aseasonal en vironm ent, maximal fitness is reached by determ inate grow ers that instantaneously sw itch the allocation of resources from growth to reproduction Zió łko & Kozłow ski, 1983).
Several studies in life-history th eory predict the grow th of re producing organism s, but these studies are often founded on sim plifying assum ptions that may alter the generality of the reported findings. For exam ple, grow th after m aturity and mixed allocation were suggested to evolve in annual plants and cladocerans as an adaptive response to m ortality rate or season lengths that flu ctu ate on a per generation basis (G urney & M iddleton, 1996;King & Roughgarden, 1982;Taylor & Gabriel, 1993;W ong & A ckerly, 2005).
A fluctuating environm ent selects against an instantaneous sw itch ing from grow th to reproduction because the production of a low num ber of offspring in som e years d rastically reduces the overall geom etric mean fitness (Lew ontin & Cohen, 1969). Mixed allocation to grow th and reproduction bet-hedges against fluctuating envi ronm ent and is predicted to evolve by the life-h istory w ork that as sum es immediate offsp rin g recruitm ent (G urney & M iddleton, 1996;King & Roughgarden, 1982;Taylor & Gabriel, 1993). T h is assum ption contrasts with the fa ct that annual plants and cladocerans produce diapausing propagules that m ay recruit m any years after the time they were released (Cham bers & M acmahon, 1994;H airston, 1996). In plants, the mixed allocation to grow th and reproduction is likely a consequence of the plant-herbivore arm s race. Th e synthesis of non-degradable defensive chem icals that decrease the rate of vege tative parts loss due to h erbivory selects fo r grow th that accom pa nies reproduction (Janczur, 2009). W hereas this explanation seem s plausible fo r plants, it cannot be applied to the m ajority of inde term inately grow ing anim als. Th e proportional (linear) relationship betw een fecu nd ity or m ortality risk with reproductive allocation prom otes a 'bang-bang' sw itch between grow th and reproduction.
However, the mixed allocation can be adaptive when birth rates, death rates or both scale nonlinearly with reproductive allocation (for details see. Joh ansson , Brannstrom , M etz, & Dieckm ann, 2018;Leon, 1976;Sibly, Calow , & Nichols, 1985;Taylor, Gourley, Lawrence, & Kaplan, 1974). T h is general hypothesis, deriving grow th tactics from a link between reproductive allocation, fecu nd ity and mor tality rate, aw aits em pirical verification; it is unclear to w hat extent taxa that share sim ilar grow th patterns are also sim ilar with respect to the w ay vital rates scale with reproductive allocation. In contrast to our work, the aforem entioned life-h istory literature, as well as ta xa -sp e cific studies reviewed in the discussion below, unrealistically assum es that grow th tactics evolve in spatially hom ogenous environm ents.
M any short-lived indeterm inate grow ers evolve in m etapopu lations of dynam ic spatiotem poral structure. Plant-pathogen inter actions can produce a dynam ic m osaic of populations that undergo phases of local extinction and the colonization of annual species (Burdon & Thrall, 1999). Populations of cladocerans are connected by the m igration of resting eggs, with occupied sites d iffering co n siderably with respect to the level of m ortality risk, as these small organism s are capable of colonizing large w ater bodies but also tem porary fishless ponds (Ebert, 2005). Sim ilar structure of m eta populations, with patches d iffering in m ortality risk, shapes the life-h istory evolution of other indeterm inately grow ing crustaceans, such as short-lived am phipods (M unguia, M ackie, & Levitan, 2007;W ellborn, 1994;W ellborn & Broughton, 2008). Th e spatial variab il ity in the m ortality risk translates into dem ographic prospects that are not neutral to the evolution of body size. In fishless ponds, large daphnia species out-com pete small ones (Ebert, 2005), with sim ilar sh ifts to bigger b ody size reported in freshw ater am phipods living in the absence of predators (W ellborn, 1994;W ellborn & Broughton, 2008). Th ese size -sh ifts are driven by the fa ct that the lifetim e ex pected offsp rin g production is greater for those m aturing late and with larger body size but only if conditions are safe (Kozlow ski, 2006). Spatial variab ility in m ortality risk im poses a dilemma on the adopted grow th strate gy as well as on the age and size at m aturity of dispersing individuals. O u r life-h istory model investigates the grow th strategy of a short-lived organism that evolves in a spatially structured m etapopulation.
In m any adult fish, reptiles, cladocerans and plants, and also som e mammals, the grow th rate can periodically drop to zero, re main constant, or accelerate at certain periods of life (Bogin, 1999;Folkvord et al., 2014;Laver et al., 2012;Lynch, 1980;M urugan & Sivaram akrishnan, 1973;Rideout, Rose, & Burton, 2 005;Sheehy et al., 2 004;Xu et al., 2016). Com plex shapes of grow th cu rves are routinely associated with adverse conditions or sex reallocation in herm aphroditic species (e.g. H iggins, Diogo, & Isidro, 2015). An alternative explanation links com plex grow th patterns with adap tive consequences of m ultiple shifts in the allocation of resources to grow th and reproduction (Kozlow ski, 2006). Com plex shapes of grow th cu rves in perennials often arise as a result of intensive grow th occurring in years of skipped reproduction (Folkvord et al., 2014;J 0rgensen, Ernande, Fiksen, & Dieckm ann, 2006;Rideout et al., 2005). How ever, skipped reproduction has limited utility for e x plaining the origin of com plex grow th patterns in short-lived organ isms. Annual plants and short-lived crustaceans, even when raised in a controlled environm ent or laboratory conditions, display multiphasic grow th curves with grow th that stops, rem ains constant, or accelerates at certain periods of adult life (Lynch, 1980;Murugan & Job , 1982;Murugan & Sivaram akrishnan, 1973;Sh eeh y et al., 2004).
T h e phases of accelerating grow th by adults, w hich are docum ented in studies on the individual grow th trajectories of cladocerans, are som etim es associated with decreased egg production (Lynch, 1980;M urugan & Sivaram akrishnan, 1973). W hereas it is optimal to ac celerate grow th in the juvenile stage to com pensate for adverse

| The model
T h e presented m odel in ve stig ates the g ro w th -re p ro d u ctio n tra d e -o ff in a sho rt-lived organism (e.g. an in verteb rate or annual plant) in w hich m aturation does not preclude fu rth e r grow th . In T h e co de fo r the algorithm used in this stu d y is p u b licly available (see Data A v a ila b ility Statem ent).

| RESULTS
T h e final evolutionary outcom e of sim ulations run in hom ogenous environm ents is a resource allocation strate gy that co nsists of a w ell-defined grow th phase early in life and reproduction thereaf ter ( Figure 1a). Th e duration of the grow th period depends on the m ortality risk, with larger body size attained in environm ents char acterized by a low risk of death ( Figure 1b). Allocation decisions with a i < 0.9 and a i > 0.1 were indistinguishable from pure growth (af = 1) and pure reproduction (a i = 0) due to the persisting variab il ity in a maintained by the stoch astic character of our sim ulations ( Figure 1a). Note that, although sw itching from grow th to reproduc tion can be classified as a 'bang-bang' sw itch, one-tim e episode may be dedicated to mixed allocation if the optimal age/size of sw itching is placed within the time episode and not at its end ( Figure 1a). To avoid the p ossibility of mixed allocation resulting from the stochastic character of our sim ulations, we defined that mixed allocation in our model as a strategy for which allocation decisions a i fall between 0.1 and 0.9 for more than 15% of the time episodes per generation, that is, more than three per 20 episodes assum ed in the base scenario. G row th strategies with sim ultaneous allocation to grow th and reproduction, including those with allocation to grow th accelerating in the m iddle of life span, can evolve also in more com plex environ ments that consist of several differen t typ es of sites ( Figure S1 in A p p e n d ix S1).

| DISCUSSION
A n organism unable to perceive reliable inform ation about m ortality risk m ust bet on its fate when deciding when to maturate. In a het erogeneous environm ent, with respect to m ortality risk, mixed allo cation to grow th and reproduction allow s an organism to bet-hedge against m aturing at a suboptim al time. In the presented model, grow th accom panying reproduction evolves when 70% or more sites in the environm ent are risky (see Figure 2c), because safe sites select for large fem ales capable of producing num erous offspring. Staying alive m akes an organism more optim istic about its fate as it becom es more likely that it occupies a safe spot. Th is 'probing of m ortality by living' becom es a selective force for mixed allocation as it perm its the gradual building of size and reproductive potential. Probing of m ortality in heterogeneous environm ents by staying alive has also been suggested to influence oviposition behaviour in parasitic in sects (Tammaru, Javo is, & Larsson, 2005).
Heterogeneous environm ents, with respect to m ortality risk, that are stable over time but spatially structured, can select for indeter minate grow th and mixed allocation to grow th and reproduction in short-lived organism s. Previous contributions to life-h istory theory reveal that mixed allocation is an optimal bet-hedging strate gy when m ortality risk changes tem porarily in a per generation basis (Gurney & M iddleton, 1996;King & Roughgarden, 1982;Taylor & Gabriel, 1993;W ong & Ackerly, 2005). In our model, grow th accom panying reproduction selected for in spatially heterogeneous environm ents also serves as a bet-hedging strategy because offsp rin g produced by fem ales are dispersed am ong risky and safe sites in the environm ent.

FIGURE 2 Optim al allocation strategies and resulting resource allocation patterns in hom ogenous and heterogeneous environm ents. (a)
In a heterogeneous environm ent, the mixed allocation is selected for (red squares), w hereas hom ogenous environm ents select for a 'bang bang' sw itching (green triangles and black diamonds). (a, b) The shaded area d epicts sim ultaneous allocation to grow th and reproduction. Th e m odelled environm ent consists of risky and safe sites with a survival probability of one-tim e episode equal to p R = 0.7 and pS = 0.875. A llocation strategies, grow th increm ents and egg production are presented for episodes to which organism s survive with a probability >0.005. (c) Th e proportion of time episodes with mixed allocation per generation is illustrated by the coloured spheres (see the legend). The em pty space m atches scenarios with a 'bang-bang' sw itch (see the main te xt for the definition of mixed allocation). For certain com binations of survival probabilities p S and p R, the mixed allocation appears at more than one level of the considered proportion of risky sites S R (the num ber of levels with mixed allocation is illustrated by the grey contour plot). Th e blue dashed line indicates the survival chance in risky and safe sites of the scenario investigated in a and b. (a-c) Th e presented allocation strategies are median values calculated across 20 sim ulation replicates. For illustration of individual variation in allocation strategies see Figure S3 in A p p e n d ix S1 G row th rate in the m odelled fem ales varies throughout life with p e riods of decelerating but also accelerating grow th. Prolonged and variable allocation to grow th by adults m ay produce com plex growth curves that arise as an adaptation to spatially heterogeneous e n vi ronm ents. O u r stu d y provides the first theoretical evidence of spa tially heterogeneous environm ents selecting for com plex growth curves. However, more w ork is needed to explore the evolution of grow th strategies under com plex spatiotem poral variation of the en vironm ent and with explicitly considered evolution of dispersal rate.
Living organism s undertake actions that are dependent on the cues and signals perceived from their environm ent, but the ability G row th that accom panies reproduction in short-lived w ater in vertebrates has been suggested to evolve when both the assim ila tion of resources and m ortality risk increase along with body size (Perrin, Sibly, & N ichols, 1993;Taylor & Gabriel, 1992). Th e death rates of m any planktonic crustaceans are stron gly affected by the a ctivity of visual predators, with large species or individuals being e x posed to a higher risk of death than small ones (Ebert, 2005  rate and m ortality rate predict that the rate of adult grow th deceler ates along with body size (e.g. . Shapes of growth cu rves of cladocerans, including those raised in laboratory condi tions, can be com plex with periodic term ination or acceleration of allocation to grow th observed long after m aturation (Lynch, 1980;Murugan & Sivaram akrishnan, 1973 Lester, 2008). However, these m odels do not capture the nature of com plex growth curves that arise due to shifts in resource allocation, including episodic cessations or accelerations of growth (Lynch, 1980;Murugan & Job, 1982;Murugan & Sivaram akrishnan, 1973;Sheehy et al., 2004). In our model, allocation to growth that accelerates or remains constant throughout certain periods of adult life results in the com plex shape of growth curves (see Figure 3c,d). Com plex growth curves, routinely associated with adverse conditions in ecological lit erature, arise in the model as an adaptive response to spatial heterogeneity of the environm ent. Th ese curves are more likely to arise when fem ales in the model are able to enlarge their body size only during a moulting, and there are several m oults per generation (see Figure 4).
Cladocerans that enlarge their body size by changing exoskeleton through moulting (Ebert, 2005;Lynch, 1980) indeed display com plex growth patterns (Lynch, 1980;Murugan & Job, 1982;Murugan & Sivaram akrishnan, 1973). Further studies are needed to investigate if high overhead costs of reproduction that cause fem ales to reproduce discontinuously would also select for mixed allocation to growth and reproduction when environm ents are spatially heterogeneous.
To conclude, spatial heterogeneity with respect to m ortality should be added to the list of factors that shape grow th strategies of indeterm inate growers. However, the m odelled setup fits well with a life history of annuals or those with a sho rter life cycle; more com plex trad e -offs need to be considered in the case of perennials (Ejsm ond et al., 2015). Th e adults of short-lived organism s that moult during life can accelerate the allocation to grow th as an adaptive response to heterogenic environm ents. O u r w ork also show s that com plex grow th curves are more likely to evolve in short-lived or ganism s, when individuals need to change their exoskeleton to grow and there are only several m oults per adult life.

ACKNOW LEDGEM ENTS
T h e research w as financed by the National Science Centre in Poland project nr. 2 0 1 4 /1 5 /B /N Z 8 /0 0 2 3 6 and Jagiellonian U n ive rsity funds