domain: sde sdv

text:
Rebecca Rimbach
email: rrimbach@gmail.com

Neville Pillay

Carsten

Carsten Schradin

Prolonged growth during the food

Keywords: Eco-physiology, pace-of-life, plasticity, postnatal growth, rodents, senescence

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Growth, especially during early life, can have important consequences for reproduction and survival [START_REF] Lindström | Early development and fitness in birds and mammals[END_REF]. Some species show competitive growth, where individuals increase their growth rate in response to increases in the growth rate of potential competitors [START_REF] Huchard | Competitive growth in a cooperative mammal[END_REF]. Fast growth and good body condition can positively affect survival [START_REF] Wauters | Body mass at weaning and juvenile recruitment in the red squirrel[END_REF][START_REF] Festa-Bianchet | Body mass and survival of bighorn sheep[END_REF]; can lead to an earlier age of sexual maturity (Altmann and Alberts 2005); and influence fecundity [START_REF] Mahlert | Implications of being born late in the active season for growth, fattening, torpor use, winter survival and fecundity[END_REF]), competitive ability [START_REF] Schradin | Territorial defense in a group-living solitary forager: who, where, against who?[END_REF][START_REF] English | Early growth, dominance acquisition and lifetime reproductive success in male and female cooperative meerkats[END_REF]) and fitness [START_REF] Svendsen | Body mass and first-time reproduction in female chipmunks (Tamias striatus)[END_REF][START_REF] Schradin | Relative fitness of alternative male reproductive tactics in a mammal varies between years[END_REF]). Yet, fast growth also can have negative consequences (reviewed in [START_REF] Metcalfe | Growth versus lifespan: perspectives from evolutionary ecology[END_REF], and has been linked to faster senescence [START_REF] Kim | Quantitative genetic evidence for a trade-off between growth and resistance to oxidative stress in a wild bird[END_REF][START_REF] Geiger | Catching-up but telomere loss: half-opening the black box of growth and ageing trade-off in wild king penguin chicks[END_REF][START_REF] Douhard | The cost of growing large: sex-specific costs of post-weaning growth on body mass senescence in a wild mammal[END_REF]. Growth rates represent a potential source of within-species variation in fitness, and thus studying factors that influence -either promote or limit -growth is fundamental to understanding the evolution of different growth strategies and life histories [START_REF] Dmitriew | The evolution of growth trajectories: what limits growth rate?[END_REF].

Environmental parameters, such as resource availability and ambient temperature, can affect growth rates [START_REF] Voltura | Effects of ambient temperature, diet quality, and food restriction on body composition dynamics of the prairie vole, Microtus ochrogaster[END_REF][START_REF] Eifler | Effect of weather on individual growth rates in cotton rats, Sigmodon hispidus[END_REF][START_REF] Dmitriew | The evolution of growth trajectories: what limits growth rate?[END_REF].

Typically, high levels of food availability enhance growth [START_REF] Nicieza | Growth compensation in juvenile Atlantic salmon: responses to depressed temperature and food availability[END_REF][START_REF] Mcadam | Dietary protein constraint on age at maturity: an experimental test with wild deer mice[END_REF][START_REF] Mcadam | Effects of food abundance on genetic and maternal variation in the growth rate of juvenile red squirrels[END_REF]Altmann and Alberts 2005), whereas food limitation restricts growth [START_REF] Dmitriew | The evolution of growth trajectories: what limits growth rate?[END_REF]. Physiological processes may be limited by the ability to dissipate heat to maintain body temperature (i.e. heat dissipation limit hypothesis; Speakman and Król 2010a, b). Reduced food intake is a common consequence of heat stress [START_REF] Renaudeau | Adaptation to hot climate and strategies to alleviate heat stress in livestock production[END_REF][START_REF] Beale | A hot lunch for herbivores: physiological effects of elevated temperatures on mammalian feeding ecology[END_REF][START_REF] Camp | Interacting effects of ambient temperature and food quality on the foraging ecology of small mammalian herbivores[END_REF], and is thought to be driven by the interaction between the increase in metabolic heat production after food ingestion (diet-induced thermogenesis) and the need to balance heat dissipation to maintain body temperature [START_REF] Renaudeau | Adaptation to hot climate and strategies to alleviate heat stress in livestock production[END_REF]. Somatic growth also produces heat, and thus, high ambient temperature can indirectly affect growth via an influence on heat dissipation, food intake and digestion. Thus, we predict trade-offs between body temperature maintenance, digestion, and growth.

Previous studies reported that the relationship between ambient temperature and growth depends on season, taxon, and habitat type occupied [START_REF] Eifler | Effect of weather on individual growth rates in cotton rats, Sigmodon hispidus[END_REF][START_REF] Gardner | Declining body size: a third universal response to warming?[END_REF]. For example, adult size of fish decreases with increasing ambient temperature (Atkinson 1994; [START_REF] Barneche | Warming increases the cost of growth in a model vertebrate[END_REF]. Similarly, growth rates of meerkat (Suricata suricatta) pups are reduced at high ambient temperature, likely because of an increased cost of thermoregulation [START_REF] Russell | Factors affecting pup growth and survival in co-operatively breeding meerkats Suricata suricatta[END_REF][START_REF] Van De Ven | Effects of climate change on pup growth and survival in a cooperative mammal, the meerkat[END_REF]. In rodents, results are mixed; some species show an increase and others a decrease in body size [START_REF] Gardner | Declining body size: a third universal response to warming?[END_REF]). Because of the potential trade-off between body temperature maintenance and food intake at high ambient temperature, it is conceivable that high ambient temperature limits growth, for example during summers. Rarely has the effect of both ambient temperature and food availability on growth rates been studied simultaneously, particularly in animals inhabiting arid areas in the subtropics, where variation in ambient temperature and food availability is pronounced. Nonetheless, such studies would be important to promote an understanding of whether and how food availability and/or ambient temperature affect growth rate. Such information will become increasingly important given the progressively hotter and drier conditions predicted to occur as a consequence of climate change [START_REF] Karl | Modern global climate change[END_REF][START_REF] Seager | Model projections of an imminent transition to a more arid climate in southwestern North America[END_REF]) and the associated changes in selection for body size [START_REF] Ozgul | The dynamics of phenotypic change and the shrinking sheep of St. Kilda[END_REF]).

Here, we studied postnatal growth in African striped mice (Rhabdomys pumilio) living under a variety of environmental conditions. We focused on changes in body length as an indicator of skeletal growth. We did not consider body mass here because mass can change seasonally without reflecting growth depending on fat stores and muscle mass, such that body mass does not always reflect skeletal size [START_REF] Campbell | Growth and size in meadow voles (Microtus pennsylvanicus)[END_REF]. Body size is an important trait in striped mice because it confers an advantage in competitive interactions [START_REF] Schradin | Territorial defense in a group-living solitary forager: who, where, against who?[END_REF]) and as such, also influences reproductive tactics adopted by both sexes (Schradin et al. 2009a;[START_REF] Hill | Alternative reproductive tactics in female striped mice: heavier females are more likely to breed solitary than communally[END_REF]. Large males are the most competitive individuals and follow a tactic that has a much higher reproductive success than smaller and less competitive males which follow alternative tactics [START_REF] Schradin | Relative fitness of alternative male reproductive tactics in a mammal varies between years[END_REF].

Heavier females are more likely to breed solitarily than communally [START_REF] Hill | Alternative reproductive tactics in female striped mice: heavier females are more likely to breed solitary than communally[END_REF], thereby avoiding reproductive competition with other females and female infanticide (Schradin et al. 2010a).

Striped mice are sensitive both to low and high temperatures, basking in the sun to warm up in winter and resting in the shade in summer [START_REF] Schradin | Regulation of activity in desert-living striped mice: the importance of basking[END_REF][START_REF] Rimbach | Young but not old adult African striped mice reduce their activity in the dry season when food availability is low[END_REF][START_REF] Zduniak | Basking African striped mice choose warmer locations to heat up: evidence from a field study[END_REF]. Dry seasons are energetically challenging periods for striped mice because of low food availability, and they show physiological signs of fasting, such as increased ketone body concentrations [START_REF] Rimbach | Both thyroid hormone levels and resting metabolic rate decrease in African striped mice when food availability decreases[END_REF]. When food resources decline and conditions become harsher, their health status deteriorates and non-survivors exhibit signs of permanent pathology [START_REF] Schoepf | The pathophysiology of survival in harsh environments[END_REF]). To reduce their daily energy expenditure, striped mice reduce their metabolism and activity during the dry season [START_REF] Rimbach | Both thyroid hormone levels and resting metabolic rate decrease in African striped mice when food availability decreases[END_REF](Rimbach et al. , 2018b;;a). Thus, since breeding season for striped mice is followed by a food restricted dry season, we expect them to have reduced growth rates but over a period of longer growth to reach a larger body size that enhances their competitive abilities in the following breeding season.

In temperate climates, mammals typically reproduce seasonally: young are born in spring and grow during summer when food availability is high, before they enter the food restricted winter [START_REF] Bronson | Mammalian reproduction: an ecological perspective[END_REF][START_REF] Bronson | Climate change and seasonal reproduction in mammals[END_REF]. Similarly, striped mice have a short 3 -4 month spring breeding season but the following 5-month summer represents the food restricted dry season, likely limiting growth. Thus, to reach a greater body length, growth might continue slowly during the dry season and then accelerate again when rain falls and food again becomes abundant. Some years are characterized by high summer rainfall and a subsequent increase in food availability (although food availability during summer breeding is less than 60% of that during the spring breeding season; see results), which allows for summer breeding. In this study, we repeatedly recorded body length of 369 striped mice with a known age (from 6 to 890 days old) to examine which environmental factors are associated with growth. Specifically, we tested three predictions. (i) Growth would be faster when food availability is high and ambient temperature low, compared with when food availability is low and ambient temperature high. (ii) Growth rate of striped mice would be slower in the dry season than in the moist season, when food is more abundant. Thus, we expected fast growth in the moist season after birth which would then decrease as food availability decreased and then accelerate again as food availability increased again after winter rains.

(iii) Because of the higher ambient temperature and relatively lower food availability in summer compared with spring, we predicted that individuals born during an atypical summer breeding season to grow slower than individuals born during the typical spring breeding season.

MATERIALS AND METHODS

Study site and species.-We collected data from November 2015 to January 2019 in Goegap Nature Reserve, Northern Cape Province, South Africa. The reserve lies within the semidesert biome of the Succulent Karoo, characterized by cold and moist winters (June -August), in which most of the annual rain falls (average rainfall 2004 -2018: 155.2 ± 76.6 mm; Supplementary Data SD1). Striped mice breed in spring, which typically lasts from August to November and is characterized by high food abundance (Supplementary Data SD1). Food availability is lower in the hot and dry summers (December -May; Supplementary Data SD1; [START_REF] Schradin | Demography of the striped mouse (Rhabdomys pumilio) in the Succulent Karoo[END_REF].

In the study area, striped mice are facultatively group-living. Groups typically consist of one breeding male, 2 -4 breeding females and their philopatric offspring of both sexes [START_REF] Schradin | The striped mouse (Rhabdomys pumilio) from the Succulent Karoo, South Africa: a territorial group-living solitary forager with communal breeding and helpers at the nest[END_REF]. Individuals of both sexes can become solitary if population density is low during the breeding season (Schradin et al. 2010a). Females can give birth to 2 -3 litters during the 3 -4 month breeding season, with an average of 5 pups per litter [START_REF] Schradin | Demography of the striped mouse (Rhabdomys pumilio) in the Succulent Karoo[END_REF]. Most individuals born during the breeding season remain in their natal group as non-breeders (i.e. philopatric) until the next breeding season. Striped mice can reach sexual maturity at around 6 weeks of age [START_REF] Schradin | Absence of reproductive suppression in young adult female striped mice living in their natal family[END_REF]Schradin et al. 2014a), but typically delay reproduction until the next spring [START_REF] Schradin | The striped mouse (Rhabdomys pumilio) from the Succulent Karoo, South Africa: a territorial group-living solitary forager with communal breeding and helpers at the nest[END_REF].

Both sexes disperse, but female striped mice show a higher level of natal philopatry than males [START_REF] Solmsen | Highly asymmetric fine-scale genetic structure between sexes of African striped mice and indication for condition dependent alternative male dispersal tactics[END_REF]. Approximately 30% of young adult striped mice present at the start of the dry season survive until the next breeding season [START_REF] Schradin | Demography of the striped mouse (Rhabdomys pumilio) in the Succulent Karoo[END_REF], and survival rate is much lower in some years. We determined body mass (± 0.1 g) using a portable electronic balance (Yamada HC-3, Yuet Hing Company, Kowloon, Hong Kong).

We measured body length using a ruler from the tip of the nose to the anus to the nearest 0.1 cm every 2 -4 weeks. We collected body length measurements only in the morning to avoid a circadian influence on body size. Body length measurements were repeatable; the difference between body length measurements collected within 3 days for the same individual (190 body length measurements of 107 individuals) was 0.53 ± 1.66 mm (range: -4 -4 mm; Supplementary Data S2), and there was a strong correlation between the first and the second length measurement (Pearson's product-moment correlation: t = 94.58, df = 188, P < 0.0001, R 2 = 0.97; Supplementary Data S2).

The study population has been monitored continuously since 2001 and striped mice within the field site are regularly trapped using Sherman-style live-traps (26 x 9 x 9 cm) baited with bran flakes, raisins, salt, and sunflower oil. For identification, we marked all mice permanently with ear tags (fish & small animal tags size 1, National Band and Tag Co., Newport, KY, USA) at the first trapping event. We set traps in front of nest sites at dawn and in the afternoon, and checked them twice in the morning and once at dusk, 30 -45 minutes after being set. For 3 consecutive days, we placed traps at the nest of several groups on a rotation schedule that allowed us to biweekly trap of each group throughout the year.

We carried out fieldwork under the necessary licenses. We collected all data following protocols approved by the Animal Ethics Screening Committee of the University of the Several different growth models, including Gompertz, logistic, von Bertalanffy, and Richards, have been used to describe mammalian growth, and earlier studies have assumed that sigmoid curves, like the Gompertz equation, adequately describe mammalian growth [START_REF] Zullinger | Fitting sigmoidal equations to mammalian growth curves[END_REF]. However, subsequent studies have demonstrated species-specific variation in growth curves [START_REF] Gaillard | Variation in growth form and precocity at birth in eutherian mammals[END_REF]) and thus, using more flexible growth functions, such as the Richards equation (which allows for both sigmoidal and non-sigmoidal curves) should aid in accurately describing growth curves [START_REF] Karkach | Trajectories and models of individual growth[END_REF][START_REF] Teleken | Comparing non-linear mathematical models to describe growth of different animals[END_REF]. Consequently, we used an approach without a priori assumptions of curve trajectories and describe striped mouse growth curves using the R package "FlexParamCurve" [START_REF] Oswald | FlexParamCurve: R package for flexible fitting of nonlinear parametric curves[END_REF][START_REF] Oswald | FlexParamCurve: tools to fit flexible parametric curves[END_REF]. This package includes functions to estimate parameters for 32 different monotonic and non-monotonic curves and can model many sigmoidal forms (e.g. Richards, logistic, Gompertz, and von Bertalanffy).

Growth rate.-We calculated growth rate (mm day -1 ) as the change in body length (length 2 -length 1/ days between measurements) of individuals over approximately one month (depending on the trapping intervals, average: 27.3 ± 12.2 days). We chose the interval of one month to represent monitored monthly changes in food availability (see below). To examine which intrinsic and environmental factors influence growth rate, we used 1668 data points of growth rate from a total of 369 individuals (179 females and 190 males; 4.5 ± 3.5 growth rates per individual, range: 1 to 24). We calculated birthdates from the body mass at first capture, using a population specific growth curve based on body mass (Schradin et al. 2009b), only for individuals with a body mass < 30 g at first capture (22.4 ± 11.1 days of age at first capture, range: 3 -56 days; 15.6 ± 5.7 g at first capture, range: 6.0 -29.7 g). We excluded individuals whose birthdate we could not calculate reliably. No body length measurements were taken before 2015, thus some mice already were adults (older than 3 months with a known birthdate) when we started collecting body length data. We included these older individuals because it enabled us to examine the growth rate of adult striped mice.

Consequently, there was variation in age at the first body length measurement included in this study.

Food availability.-Striped mice feed on all parts (leaves, flowers and seeds) of annual and periannual plants [START_REF] Schradin | Female striped mice (Rhabdomys pumilio) change their home ranges in response to seasonal variation in food availability[END_REF]. Biweekly, we conducted plant surveys in the home ranges of eight different groups in the field site on eight monitoring plots (4 m² each).

Briefly, we recorded the number of palatable plant species in all plots and used the average number of plant species as a measure of food availability (as done previously, for example (Schradin et al. 2014b;Rimbach et al. 2018b)). Palatability of plants was known from behavioral observations [START_REF] Schradin | Female striped mice (Rhabdomys pumilio) change their home ranges in response to seasonal variation in food availability[END_REF]. For each mouse, we established average food availability during the period for which its growth rate was determined. We defined dry seasons as periods in which food availability was < 2.9 species/ plots and moist seasons as periods in which food availability was ≥ 2.9 species/ plots (Supplementary Data S1), as physiological measures indicate fasting (decreased blood sugar and increased ketone levels) when food availability drops below 2.9. Ambient temperature.-We recorded ambient temperature daily in the shade 10 cm above ground (where mice roam) using a digital thermometer (TFA Dostmann, Wertheim-Reicholzheim, Germany) that was installed permanently in the same location. For data analysis, we used the average daily minimum and maximum ambient temperature (Supplementary Data SD1).

Data analyses.

Growth curves of striped mice.-We used the R package "FlexParamCurve" [START_REF] Oswald | FlexParamCurve: R package for flexible fitting of nonlinear parametric curves[END_REF][START_REF] Oswald | FlexParamCurve: tools to fit flexible parametric curves[END_REF], which includes functions to estimate parameters for 32 different monotonic and non-monotonic curves and to select the models that best fit the growth data.

Male striped mice reach a larger body size relative to females, so we analyzed growth curves separately for each sex [START_REF] Schradin | Demography of the striped mouse (Rhabdomys pumilio) in the Succulent Karoo[END_REF]. We grouped body length data by ID and used the functions 'pn.mod.compare' (compares all possible positive-negative Richards models) and 'pn.modselect.step' (backwards stepwise model selection) to select the most suitable model [START_REF] Oswald | FlexParamCurve: tools to fit flexible parametric curves[END_REF]. Subsequently, we fitted a nonlinear least-squares model, and plotted one curve per sex using the package "lattice" [START_REF] Sarkar | Lattice: multivariate data visualization with R[END_REF]. To examine body length as a function of age, we included data of 280 mice for which at least 5 measurements were available (a total of 2870 body length measurements; 10.2 ± 5.1 measurements per individual). Growth curves could be fitted for 94.6% of females (141 of 149 individuals) and 92.3% of males (121 of 131 individuals). We used one Mann-Whitney-U test to examine whether final body length differed by sex.

Influence of intrinsic and environmental factors on growth rates.-To analyze the influence

of intrinsic and environmental factors on growth rates of striped mice, we used linear mixed models (LMMs) with Gaussian error structure and identity link using the R package 'lme4' [START_REF] Bates | lme4: Linear mixed-effects models using S4 classes[END_REF]. As response variable we used the square root of the growth rates to reduce heteroscedasticity when fitting the models. We compared growth rates seasonally using 1668 data points of growth rate and included season (moist season 1, dry season 1, moist season 2 and dry season 2) as a fixed factor (Model 1). To investigate which environmental factor (food availability and/ or ambient temperature) influenced growth rates of striped mice, we also used 1668 growth rates, with food availability and ambient temperature treated as fixed factors (Model 2). For each mouse, we established average food availability and average ambient temperature for each measurement period (days between measurements: 27.3 ± 12.2 days) for which its growth rate was determined. In both models, we also included age at initial length (as older mice grow slower; see results) and sex, and initial body length as a continuous variable to account for allometric effects. We included year and ID as random factors in both models because most mice were measured repeatedly.

Using likelihood ratio tests, we tested for all two-way interactions by comparing a model which included the interaction with a model excluding the interaction and dropped nonsignificant interaction terms (P ≥ 0.05). We examined sex differences in initial body length, and age at initial body length in the four seasons using Mann-Whitney-U tests. We split the data into four equally sized subsets represented by the quartiles of mean ambient temperature: (i) 9.88 to 18.4 °C; (ii) 18.4 to 21.5 °C; (iii) 21.5 to 23.9 °C; and (iv) 23.9-29.6 °C to illustrate how interactions between ambient temperature and food availability and ambient temperature and age at initial length influenced growth rates (Model 2).

Growth rates of individuals born in summer vs spring.-Some mice were born in the summers of 2016 (February -April) and 2018 (January -February) because of unusually high rainfall (in January 2016 and November 2017) and subsequently increased food availability (Supplementary Data SD1).

We used a LMM (Model 3) with Gaussian error structure and identity link using the R package 'lme4' [START_REF] Bates | lme4: Linear mixed-effects models using S4 classes[END_REF] to examine whether growth rates differed between striped mice born in spring and summer. The response variable used was the square root of the growth rates to reduce heteroscedasticity when fitting the model. We included the season in which mice were born (spring vs summer), sex and age at initial length as fixed predictors, and we included initial body length as a continuous variable to account for allometric effects. We used individual ID and year as random factors. Using likelihood ratio tests, we tested for all two-way interactions by comparing a model including the interaction with a model excluding the interaction and dropped non-significant interaction terms (P ≥ 0.05). We assessed differences in food availability and ambient temperature during summer and spring breeding seasons using Mann-Whitney-U test.

We tested all three LMMs for temporal autocorrelation of residuals using the 'check_autocorrelation' function in the package "performance". To account for the temporal autocorrelation between data points (i.e., non-random residual error), we included an autoregressive structure of order 1 (i.e., autocorrelation declines exponentially with time) using the ('corAR1' function) in all three LMMs [START_REF] Pinheiro | Mixed-effects models in S and S-Plus[END_REF]. For the validation of all three LMMs, we visually inspected Q -Q plots and scatterplots of residuals plotted against fitted values, to check for the assumptions of homogeneous and normally distributed residuals. In all models, we standardized (z-transformed) all numeric predictors for more accurate model fitting and to facilitate comparisons of model estimates [START_REF] Schielzeth | Simple means to improve the interpretability of regression coefficients[END_REF]. We derived variance inflation factors (vifs) using the vif function of the "car" package [START_REF] Fox | An R companion to applied regression[END_REF], which did not indicate collinearity (all vifs < 4; [START_REF] Zuur | Mixed effetcs models and extensions in ecology with R[END_REF]).

We determined marginal and conditional R² [START_REF] Nakagawa | A general and simple method for obtaining R2 from generalized linear mixed-effects models[END_REF]) for all models with the function r.squaredGLMM from the "MuMIn" package [START_REF] Bartoń | MuMIn: multi-model inference[END_REF]. Marginal R² (R²m) represents the variance explained by the fixed effects and conditional R² (R²c) represents the variance explained by the entire model (fixed and random effects).

RESULTS

Growth curves of striped mice.-Growth of female and male mice were fit best by the Richards curve [START_REF] Nelder | Note: an alternative form of a generalized logistic equation[END_REF] 1). Only 13.4 % of females and 14.2 % of males survived until the age when the growth asymptote was reached; females disappeared at a mean age of 193.0 ± 151.9 days and males at 213.8 ± 157.0 days. Mean body length after reaching the asymptotic body length was larger for males (123.7 ± 2.7 mm at 367 ± 170.4 days) than for females (117.1 ± 3.0 mm at 388 ± 175.3 days; Mann-Whitney-U test: U = 768, P < 0.0001).

Influence of intrinsic and environmental factors on growth rates.-Growth rate was higher in the moist season when mice were born (mean ± SD; 0.493 ± 0.367 mm day -1 ) compared with the following dry season (Dry 1: 0.151 ± 0.188 mm day -1 ), the following moist season of their first reproduction (Moist 2: 0.133 ± 0.191 mm day -1 ) and the subsequent dry season (Dry 2: 0.124 ± 0.174 mm day -1 ; Table 1; Fig. 2). Growth rates did not differ between the other three seasons (moist season 2 and both dry seasons; Table 1; Fig. 2). The interaction between initial length and sex influenced growth rates, where males with a large initial length grew faster than females of the same initial length (Table 1).

Growth rate was influenced by the interactions between ambient temperature and food availability, ambient temperature and age at initial length, and sex and initial length (Model 2). Growth rate increased with increasing food availability and was most pronounced at 21.5 -23.9°C (3 rd quartile) and least pronounced at higher temperatures of 23.9 -29.6°C (4 th quartile; Fig. 3A). At low temperatures (quartiles 1 -2), growth rate also increased with increasing food availability but at an intermediate level. Growth rate decreased with increasing age from low to medium high ambient temperature (quartiles 1 -3), and growth rate did not change with age at 23.9 -29.6°C (4 th quartile), but remained stable at a low rate (Table 2; Fig. 3B). The interaction between initial body length and sex influenced growth rates, where males with a large initial length grew faster than females of the same initial length (Table 2).

Growth rates of individuals born in summer vs spring.-At the first body length measurement, striped mice were (mean ± SD) 36.4 ± 16.4 days old (range 6 -77 days) and at the second measurement they were 61.3 ± 16.3 days old (range 19 -90 days). Mice born in spring (583 growth rates of 116 females and 142 males) had a faster growth rate (0.483 ± 0.35 mm day -1 ) during the first three months after birth than individuals born in summer (0.337 ± 0.29 mm day -1 ; 60 growth rates of 17 females and 10 males; Table 3; Fig. 4A). Sex and the interaction between age at initial length and initial body length influenced growth rates (Table 3). Specifically, during the first month of life, growth rates were related inversely to initial body length (smaller animals grew more rapidly; Fig. 4B). During the second and third month, the relationship between initial length and growth rate was weaker (Fig. 4B).

Food availability was higher during spring breeding (4.4 ± 1.3 plant species/ plot) compared with summer breeding (2.5 ± 0.4 plant species/ plot; Mann-Whitney-U test: U = 32643, P < 0.0001). Average ambient temperature did not differ between spring (18.8 ± 3.7°C) and summer breeding (22.2 ± 1.2°C; U = 17328, P = 0.90).

DISCUSSION

Striped mice can reach sexual maturity at an age of 45 days [START_REF] Schradin | Absence of reproductive suppression in young adult female striped mice living in their natal family[END_REF]. Here we demonstrated that they grow more than 5 times as long, for more than 250 days, which means they grow for most of their adult life. At our study site, some (less than 1%) striped mice live up to 3 years, but approximately 70% of mice disappear between the onset and the end of the dry season [START_REF] Vuarin | Elevated basal corticosterone levels increase disappearance risk of light but not heavy individuals in a long-term monitored rodent population[END_REF]. Striped mice born in the atypical summer breeding season had slower growth rates, showing that harsh environmental conditions (low food and high ambient temperature) constrain growth of striped mice. Continued growth to attain a large body size can confer fitness benefits such as increased fecundity [START_REF] Mahlert | Implications of being born late in the active season for growth, fattening, torpor use, winter survival and fecundity[END_REF] and competitive ability [START_REF] Schradin | Territorial defense in a group-living solitary forager: who, where, against who?[END_REF][START_REF] English | Early growth, dominance acquisition and lifetime reproductive success in male and female cooperative meerkats[END_REF]). Thus, a prolonged growth period is adaptive for striped mice whose postnatal growth starts under harsh environmental conditions. Finally, striped mice reached an asymptote in growth of body length, indicating that they show determinate growth, which is nearly ubiquitous in mammals and birds [START_REF] Sebens | The ecology of indeterminate growth in animals[END_REF][START_REF] Karkach | Trajectories and models of individual growth[END_REF]). Nevertheless, the asymptote occurred late in adult life at an age of 9 months. Most striped mice do not survive until the asymptote, including most individuals that survived the dry season and reproduced successfully during the spring breeding season when they were less than 9 months old. These results indicate a possible effect of senescence stopping growth in a few very old individuals.

To understand the growth strategy of striped mice one must look at the two distinct types of postnatal growth strategies that exist: determinate and indeterminate growth.

Determinate growth is characterized by an initial phase of fast (often linear) growth which is followed by an asymptotic growth phase [START_REF] Sebens | The ecology of indeterminate growth in animals[END_REF][START_REF] West | A general model for ontogenetic growth[END_REF]. Growth slows considerably or ceases after sexual maturity [START_REF] Sebens | The ecology of indeterminate growth in animals[END_REF]. Determinate growth is nearly ubiquitous in mammals and birds [START_REF] Sebens | The ecology of indeterminate growth in animals[END_REF][START_REF] Karkach | Trajectories and models of individual growth[END_REF]. Indeterminate growth is characterized by rapid growth in early age and continued growth, albeit at a slower pace, after reaching maturity [START_REF] West | A general model for ontogenetic growth[END_REF]). Indeterminate growth is nearly ubiquitous in invertebrates, fish, amphibians, and reptiles [START_REF] Dutta | Growth in fishes[END_REF][START_REF] Shine | Patterns of survival, growth and maturation in turtles[END_REF][START_REF] Kozlowski | Optimal allocation of resources explains interspecific life-history patterns in animals with indeterminate growth[END_REF][START_REF] Charnov | Reproductive constraints and the evolution of life histories with indeterminate growth[END_REF]. While striped mice stop growing, and thus do not show indeterminate growth, they also do not cease growth soon after reaching sexual maturity, as most small mammals do.

Both male and female striped mice showed a linear and an asymptotic growth phase.

Females reached the asymptotic body length at 258 days and males at 285 days, well after reaching sexual maturity, which they can reach at around 45 days of age. They can reproduce in the same breeding season in which they are born (Schradin et al. 2010b), but typically delay reproduction until the subsequent breeding season when they are 250 to 300 days old [START_REF] Schradin | The striped mouse (Rhabdomys pumilio) from the Succulent Karoo, South Africa: a territorial group-living solitary forager with communal breeding and helpers at the nest[END_REF]. Parents that do not delay reproduction produce offspring late in the breeding season that would be exposed to low food availability and high ambient temperature at an earlier age than offspring born earlier in the breeding season. Consequently, these offspring would have slower growth rates than early-born mice. Similarly, early-born roe deer (Capreolus capreolus), little brown bats (Myotis lucifugus), and common voles (Microtus arvalis), grow faster than late-born individuals [START_REF] Reynolds | Variation in life history traits in the little brown bat, Myotis lucifugus (Chiroptera: Vespertilionidae)[END_REF][START_REF] Jacob | Body weight dynamics of common voles in agro-ecosystems[END_REF][START_REF] Plard | Disentangling direct and growth-mediated influences on early survival: a mechanistic approach[END_REF]. Therefore, investment into growth and survival until the next breeding season might be more beneficial than investment into immediate reproduction.

Our study indicates that striped mice show determinate growth, that they have an extended growth period, and that most individuals grow during their entire life because they do not reach old age when growth terminates. The average age at disappearance was 200 days for both sexes, which likely is an overestimation because individuals that died very young (e.g. before weaning) were not included. Striped mice enter the second dry season at approximately 300 days of age and only 10 % lived beyond that point. Most mammals reach sexual maturity before they reach a growth asymptote [START_REF] Ricklefs | Life-history connections to rates of aging in terrestrial vertebrates[END_REF]. Many small rodents attain an asymptote in body length at a much younger age than striped mice and around the time of reaching sexual maturity. For example, Cabrera voles (Microtus cabrerae) reach an asymptote at 70 days [START_REF] Fernández-Salvador | Reproduction and postnatal growth of the Cabrera vole, Microtus cabrerae, in captivity[END_REF], meadow voles (Microtus pennsylvanicus) at 30 -50 days and simultaneously attaining sexual maturity [START_REF] Campbell | Growth and size in meadow voles (Microtus pennsylvanicus)[END_REF]. Multimammate mice (Mastomys natalensis and M. coucha) reach an asymptote at 100 -120 days [START_REF] Jackson | Sex-and species-specific growth patterns in cryptic African rodents, Mastomys natalensis and M. coucha[END_REF]. Female house mice (Mus musculus) reach a growth asymptote close to when they attain sexual maturity [START_REF] Monteiro | Compensatory growth and sexual maturity in mice[END_REF]. Similarly to striped mice, hispid cotton rats (Sigmodon hispidus), garden dormice (Eliomys quercinus), and fossorial tuco tuco (Ctenomys talarum), attain sexual maturity before reaching a growth asymptote [START_REF] Malizia | Reproductive parameters and growth in the fossorial rodent Ctenomys talarum (Rodentia: Octodontidae)[END_REF][START_REF] Cameron | Growth and reproduction of hispid cotton rats (Sigmodon hispidus) in response to naturally occurring levels of dietary protein[END_REF][START_REF] Schaub | Annual and seasonal variation of survival rates in the garden dormouse (Eliomys quercinus)[END_REF][START_REF] Stumpfel | Differences in growth rates and pre-hibernation body mass gain between early and late-born juvenile garden dormice[END_REF]. In some species, such as common voles (M. arvalis), precocious fertile mating of non-weaned females occurs before reaching the growth asymptote [START_REF] Tkadlec | Precocious breeding in female common voles and its relevance to rodent fluctuations[END_REF], but this early onset of reproduction is associated with an early reaching of the growth asymptote at an age of 1 to 2 months [START_REF] Jacob | Body weight dynamics of common voles in agro-ecosystems[END_REF]. Thus, relative to many other rodents, striped mice show a prolonged period of growth, which might be associated with their specific environment and resulting life history.

Whereas our study species lives in a highly seasonal and arid environment with a short breeding season, its sister species Rhabdomys dilectus lives in a moist grassland environment with a long breeding season [START_REF] Schradin | When to live alone and when to live in groups: ecological determinants of sociality in the African striped mouse (Rhabdomys pumilio, Sparrman, 1784)[END_REF]. Captive R. dilectus reach an asymptotic length of 107.8 mm at 112 days [START_REF] Brooks | Aspects of the reproduction, growth and development of the fourstriped field mouse, Rhabdomys pumilio (Sparrman, 1784)[END_REF]. Thus, R. dilectus reaches a shorter asymptotic length than R. pumilio (females: 113.0 mm; males: 120.8 mm) at a younger age (R. pumilio: females at 258 days, males at 285 days), at least in captivity. R. dilectus also does not show sex-specific differences in growth [START_REF] Brooks | Aspects of the reproduction, growth and development of the fourstriped field mouse, Rhabdomys pumilio (Sparrman, 1784)[END_REF]). The differences in growth curves might be related to socio-ecological differences between both species. Rhabdomys pumilio is group-living, has a 3 -4 month (short) breeding season, juveniles have a low mortality, and most delay reproduction for one year [START_REF] Schradin | When to live alone and when to live in groups: ecological determinants of sociality in the African striped mouse (Rhabdomys pumilio, Sparrman, 1784)[END_REF]. These traits indicate that for young adults, the short breeding season makes investment into growth and survival to the next breeding season more adaptive than immediate investment into reproduction.

Rhabdomys pumilio also is territorial and body size is an important predictor of competitive interactions [START_REF] Schradin | Territorial defense in a group-living solitary forager: who, where, against who?[END_REF]). Thus, a prolonged growth period can result in fitness benefits via access to mates and territories. In contrast, R. dilectus occurs in mesic grasslands, is solitary, occupies large territories, has a 7-month (long) breeding season, and juveniles have high mortality and reproduce in the breeding season in which they were born [START_REF] Schradin | When to live alone and when to live in groups: ecological determinants of sociality in the African striped mouse (Rhabdomys pumilio, Sparrman, 1784)[END_REF]. Consequently, R. dilectus likely would benefit from immediate investment into positive influence of food availability on growth rate was strongest at medium ambient temperature of 20°C. This relationship was weaker, although still positive, at lower and higher ambient temperatures. Similarly, high ambient temperature reduced growth rates of meerkat pups [START_REF] Russell | Factors affecting pup growth and survival in co-operatively breeding meerkats Suricata suricatta[END_REF]. These results might explain why striped mice rarely breed when it is very cold in winter even though food availability might be sufficient, and offer insights into why young females do not reproduce at the end of the breeding season, when offspring would suffer from slow growth because of high temperatures. That high temperatures and low food availability constrain growth of striped mice also is evident in the reduced growth rates of mice born in the atypical summer breeding season compared with individuals born in the typical spring breeding season. Growth rate decreased with increasing ambient temperature for individuals younger than 6.5 months, whereas growth rate of mice older than 6.5 months was not influenced by ambient temperature. The negative influence of ambient temperature on growth rate might indicate that the need to dissipate excess body heat created during growth constraints growth rate, especially at high ambient temperature (Speakman and Król 2010a;b). Heat stress also can result in reduced food intake [START_REF] Renaudeau | Adaptation to hot climate and strategies to alleviate heat stress in livestock production[END_REF][START_REF] Beale | A hot lunch for herbivores: physiological effects of elevated temperatures on mammalian feeding ecology[END_REF][START_REF] Camp | Interacting effects of ambient temperature and food quality on the foraging ecology of small mammalian herbivores[END_REF], and thereby negatively influence growth rate. These results demonstrate that the interplay of food availability and ambient temperature determines growth rate in this harsh semi-arid environment. A temperature-mediated growth of striped mice could explain why striped mice restrict breeding mainly to spring, when ambient temperature is close to the optimum for growth of their offspring, but switch investment into survival and slow growth when ambient temperature is too high in summer or too low in winter to produce offspring that could grow into competitive adults.

In conclusion, growth in striped mice was enhanced by high food availability but affected negatively by high ambient temperature, which might indicate that growth is constrained by the need to dissipate excess body heat, especially at high ambient temperature. a Factors included in significant interaction terms cannot be interpreted as independent variables.

  Witwatersrand (AESC 2014/40/B), and followed the animal care guidelines of the American Society of Mammologists (Sikes et al. 2016) Growth curves.-To determine growth curves of striped mice, we collected a minimum of five measurements of body length per individual. This resulted in a total of 2870 body length measurements of 280 individuals (1474 measurements of 149 females, 1396 measurements of 131 males) with 10.2 ± 5.1 measurements per individual; range was 5 -40 measurements.

  Fig. 1) described by this formula: 𝑦 𝐴/ 1 𝑚 exp 𝑘 𝑥 𝑖 / where A = asymptote, k = rate parameter, i = inflection point and m = shape parameter. Growth parameters for female striped mice were A = 113.06, k = 0.007, i = -206.76, m = -4.143, and for males were A = 120.86, k = 0.008, i = -184.10, m = -4.144. Females reached asymptotic body length of 113.0 mm at (mean ± SD) 257.7 ± 84.3 days and males reached asymptotic body length of 120.8 mm at 284.4 ± 101.2 days (Fig.

Fig. 1 .

 1 Fig. 1.-Parametric curves fitted to growth data for female (left panel; N = 1474 measurements of 149 individuals) and male (right panel; N = 1396 measurements of 131 individuals) striped mice sampled between November 2015 and January 2019 in Goegap Nature Reserve, South Africa. The dotted curves represent the Richards curve fit to the data and the dashed vertical line indicates the earliest age of sexual maturity at 6 weeks.

Fig. 2 .

 2 Fig. 2.-Growth rates of striped mice sampled between November 2015 and January 2019 in Goegap Nature Reserve, South Africa during the moist season in which they were born (Moist 1; N = 516), the subsequent dry season (Dry 1; N = 862), the second moist season (Moist 2; N = 195) and the subsequent dry season (Dry 2; N = 95).

Fig. 3 .

 3 Fig. 3.-(A) The interaction effect of food availability (plant species/ plot) and ambient temperature on striped mouse growth rate sampled between November 2015 and January 2019 in Goegap Nature Reserve, South Africa (the vertical line at 2.9 for food availability indicates the threshold for dry season vs moist season). (B) The interaction effect of ambient temperature and age at initial body length on growth rate. For illustration, the data are split into four subsets representing the quartiles of mean ambient temperature: (i) 9.88º -18.4°C (purple); (ii) 18.4º -21.5 °C (blue); (iii) 21.5º -23.9 °C (green); and (iv) 23.9º -29.6°C (yellow). Linear regression lines are shown and shaded areas indicate 95% CI.

Fig. 4 .

 4 Fig. 4 .-(A) Growth rates of striped mice sampled between November 2015 and January 2019 in Goegap Nature Reserve, South Africa born during spring (N = 583 growth rates) and summer (N = 60 growth rates). Black lines indicate the median, boxes the 1 st and 3 rd quartile, whiskers minimum and maximum values of non-outlier data and yellow circles show raw data. (B) The interaction effect of initial body length and age at initial body length on growth rate. For illustration data are split into three subsets representing the first (purple dots), second (green dots) and third (yellow dots) month after birth. Linear regression lines are shown and shaded areas indicate 95% CI.

Table 2 .

 2 -Results of the linear mixed model to test for an association between striped mouse (Rhabdomys pumilio) growth rate, average ambient temperature, food availability, sex, age at initial length and initial length (N = 1668 growth rates) sampled between November 2015 and January 2019 in Goegap Nature Reserve, South Africa. Factors in bold type indicate significant predictors of growth rate.

	Model 2	Estimate	SE	t value	P
	R²m = 0.58; R²c = 0.61
	(Intercept) Food availability a Average ambient temperature a Sex a Age at initial length a Initial length a	0.352 0.056 -0.015 0.114 0.044 -0.264	0.010 0.008 0.006 0.012 0.011 0.011	34.249 6.918 -2.282 8.780 3.859 -23.363 0.0000 0.0000 0.0000 0.0226 0.0000 0.0001
	Food availability:ambient temperature	0.023	0.006	3.977	0.0001
	ambient temperature:age at initial length	0.016	0.005	2.881	0.0040
	Sex:age at initial length	0.001	0.015	0.080	0.9359
	Sex:Initial length	0.045	0.014	3.157	0.0016

reproduction rather than from a prolonged growth period as observed in R. pumilio. Thus, we hypothesize that environmentally driven differences in the trade-off between reproduction and growth explain the evolution of alternative growth strategies in the two Rhabdomys sister species.

Striped mice grew fastest in their first moist season (i.e., the season in which they were born). We did not find evidence of accelerated growth in the second moist season when food availability recovered. Therefore, striped mice show a typical growth curve for mammals with an initial period of rapid growth followed by a second period of less rapid growth. As predicted by allometric rules [START_REF] West | A general model for ontogenetic growth[END_REF], growth rate decreased with increasing initial body length, a relationship that has previously been reported in birds [START_REF] Ton | Metabolism correlates with variation in post-natal growth rate among songbirds at three latitudes[END_REF] and mammals [START_REF] Sadowska | Genetic correlations in a wild rodent: grass-eaters and fast-growers evolve high basal metabolic rates[END_REF][START_REF] Larivée | Associations between over-winter survival and resting metabolic rate in juvenile North American red squirrels[END_REF]. Males with a large initial length grew faster than females of the same initial length, and males also grew to a larger final length than females, a pattern found in many species [START_REF] Campbell | Growth and size in meadow voles (Microtus pennsylvanicus)[END_REF][START_REF] Lima | Body mass dynamics and growth patterns of leaf-eared mice Phyllotis darwini in a semi-arid region of the Neotropics[END_REF]. The 6% sexual size dimorphism in body length is the same as previously reported for body mass in striped mice [START_REF] Schradin | Demography of the striped mouse (Rhabdomys pumilio) in the Succulent Karoo[END_REF]. The largest males are able to defend a group of communally breeding females and have a 10-times higher reproductive success than males of a medium size and 100-times greater reproductive success than small males, at least in years of high population density [START_REF] Schradin | Relative fitness of alternative male reproductive tactics in a mammal varies between years[END_REF]. In contrast, all adult females present at the onset of the breeding season produce litters [START_REF] Schradin | Relative fitness of alternative male reproductive tactics in a mammal varies between years[END_REF]. Thus, a stronger selective pressure on reaching a large body size in males than on females might explain the sexual dimorphism in body length.

A positive relationship between food availability and growth is intuitive and has been documented previously in many species [START_REF] Nicieza | Growth compensation in juvenile Atlantic salmon: responses to depressed temperature and food availability[END_REF][START_REF] Mcadam | Effects of food abundance on genetic and maternal variation in the growth rate of juvenile red squirrels[END_REF][START_REF] Auer | The optimal combination of standard metabolic rate and aerobic scope for somatic growth depends on food availability[END_REF]. Our results demonstrate that the growth of striped mice is positively linked to food availability and that this relationship is mediated by ambient temperature. The Striped mice enter the food-restricted dry season before postnatal growth is terminated. The following harsh environmental conditions with low food ability can explain why growth slows down considerably, while the proposed fitness benefits of reaching a competitive body size can explain why it does not terminate. This causes a prolonged growth period in striped mice, long past the age of sexual maturity.

ACKNOWLEDGMENTS

This study was made possible by support of the Succulent Karoo Research Station (registered South African NPO 122-134). We thank several field assistants for helping with data collection. All applicable international, national, and institutional guidelines for the care and use of animals were followed. This work was supported by the University of the Witwatersrand, the Claude Leon Foundation, the National Research Foundation (grant code: a Factors included in significant interaction terms cannot be interpreted as independent variables.