Telomere heritability and parental age at conception effects in a wild avian population

Individual variation in telomere length is predictive of health and mortality risk across a range of species. However, the relative influence of environmental and genetic variation on individual telomere length in wild populations remains poorly understood. Heritability of telomere length has primarily been calculated using parent–offspring regression which can be confounded by shared environments. To control for confounding variables, quantitative genetic “animal models” can be used, but few studies have applied animal models in wild populations. Furthermore, parental age at conception may also influence offspring telomere length, but most studies have been cross‐sectional. We investigated within‐ and between‐parental age at conception effects and heritability of telomere length in the Seychelles warbler using measures from birds caught over 20 years and a multigenerational pedigree. We found a weak negative within‐paternal age at conception effect (as fathers aged, their offspring had shorter telomeres) and a weak positive between‐maternal age at conception effect (females that survived to older ages had offspring with longer telomeres). Animal models provided evidence that heritability and evolvability of telomere length were low in this population, and that variation in telomere length was not driven by early‐life effects of hatch period or parental identities. Quantitative polymerase chain reaction plate had a large influence on telomere length variation and not accounting for it in the models would have underestimated heritability. Our study illustrates the need to include and account for technical variation in order to accurately estimate heritability, as well as other environmental effects, on telomere length in natural populations.

to be used first (Monaghan et al., 2020). In contrast, fathers produce sperm throughout their life, and there is cross-sectional evidence from humans that sperm telomere length is positively correlated with age and older fathers have offspring with longer telomeres (Aston et al., 2012;Broer et al., 2013;Eisenberg et al., 2012;Kimura et al., 2008;Unryn et al., 2005). Such effects may be due to the activity of telomerase in the testes resulting in elongated telomeres with age Kimura et al., 2008). A second (not mutually exclusive) hypothesis is the selective survival or proliferation of germ stem cells with longer telomeres (Hjelmborg et al., 2015;Kimura et al., 2008). Alternatively, the positive association between paternal age and offspring telomere length may arise through selective disappearance, whereby males with short telomeres are lost from the population (Bauch et al., 2019;Noguera et al., 2018).
Studies in nonhuman vertebrates report conflicting results; while some have found a positive correlation between offspring telomere length and paternal (Eisenberg et al., 2017) or maternal age (Asghar et al., 2015), others have found negative paternal age correlations (Bauch et al., 2019;Bouwhuis et al., 2018;Criscuolo et al., 2017;de Frutos et al., 2016;Noguera et al., 2018;Olsson et al., 2011) or no parental age effects (Belmaker et al., 2019;Froy et al., 2017;Heidinger et al., 2016;McLennan et al., 2018;van Lieshout, Sparks, et al., 2020). Importantly, only two of these studies have looked at longitudinal changes in offspring telomere length within mothers and fathers as they aged (Bauch et al., 2019;van Lieshout, Sparks, et al., 2020). This is important because the selective disappearance of parents with shorter telomeres may obscure age-related patterns (Bauch et al., 2019;Noguera et al., 2018). Work on a wider range of species, separating within-from between-parental age at conception effects, is required to identify the drivers of variation in parental age at conception effects.
In addition to parental age effects, genetic variation also influences the maintenance of telomeres from the first mitotic division, and thus telomere dynamics across an individual's lifetime (Delgado et al., 2019;Eisenberg, 2019). Environmental effects and life-history events are also associated with telomere shortening due to the stress they exert on organisms, and such effects will accumulate with age (Hall et al., 2004;Heidinger et al., 2012). The majority of the pioneering studies quantifying the contribution of genetic variation to telomere length have been in human populations and typically implicate significant heritability .
It is, however, difficult to interpret heritability estimates from human studies where processes, such as industrialization and medical interventions, limit their evolutionary interpretation. Importantly, biologists wanting to understand the ecological and evolutionary significance of telomere dynamics will be interested in studying telomere heritability in wild populations, experiencing natural environmental variation and where natural selection is occurring. To date, very few studies have attempted to separate genetic from environmental contributions to variation in telomere length within wild populations. Consequently, our understanding of the heritability of telomeres in wild populations is limited . This is important as the amount of additive genetic variance underlying a trait, such as telomere length, limits the variation that selection can act on and, therefore, a trait's evolutionary potential (Lynch & Walsh, 1998).
In wild populations, telomere length heritability estimates range from 0 to 1 . Heritability estimates have, however, been based primarily on parent-offspring regressions, which assume that the similarity between parents and offspring is genetic, when, in fact, relatives often also share environments. These shared environmental effects, including cohort and maternal effects (Asghar et al., 2015;Becker et al., 2015), will artificially inflate heritability estimates (Kruuk & Hadfield, 2007;Kruuk et al., 2008). Additionally, telomere length will change throughout life, so measures across the lifetimes of individuals will be the product of inherited telomere length, attrition and restoration/lengthening . Not all telomere studies have taken individual age at sampling into account , or sampled both offspring and parents at the same age, as both sampling and accurate ageing are difficult in wild populations (but see Becker et al., 2015 andAsghar et al., 2015). Subsequently, it is unclear whether the variation in heritability estimates of telomere length in wild populations reflects biological variation, or methodological or analytical differences between studies.
Quantitative genetic "animal models" offer a strong analytical framework to estimate the relative effects of additive genetic and environmental variation on phenotypic traits (Kruuk, 2004). Animal models utilize the relationships in a pedigree to estimate additive genetic variance, thus maximizing data and increasing the power to detect heritabilities . Additionally, animal models can account for, and estimate the contribution of, other factors known to influence telomeres, to get more accurate estimates of the proportion of phenotypic variance due to additive genetic effects.
However, the power to estimate heritability will depend on the number of individuals phenotyped, pedigree size, pedigree structure (e.g., depth, completeness and family sizes), the confidence with which pedigree relationships were estimated (either using molecular data or observational data), as well as the complexity of the animal model . For wild populations, these conditions are often less than optimal compared to animal breeding studies, with large sample sizes of phenotyped individuals often difficult to obtain, and with molecular pedigree relationships unlikely to be perfect . Furthermore, statistical power will increase with the heritability in the population of interest . While heritability estimates vary greatly in wild populations , calculation of the repeatability -the amount of variance explained by individual identity in a data set with multiple measures -will provide the upper limit to ordinary heritability (Falconer & Mackay, 1996). Using this estimate, and given a data set and pedigree structure, simulation studies can predict the power to detect the expected range of heritabilities . In humans, 10 studies using variance partitioning approaches have detected considerable genetic variation underlying telomere length, with heritabilities ranging from 0.07 to 0.70 (Blackburn, Charlesworth, et al., 2015;Broer et al., 2013;Coutts et al., 2019;Delgado et al., 2018;Faul et al., 2016;Honig et al., 2015;Kim et al., 2020;Lee et al., 2014;Njajou et al., 2007;Zhu et al., 2013).
Currently, the six studies using animal model approaches in wild or captive animal populations have found heritabilities ranging from 0 to 1 (Asghar et al., 2015;Becker et al., 2015;Atema et al., 2015;van Lieshout, Sparks, et al., 2020;Boonekamp et al. 2020;Foley et al., 2020). However, power analyses were only provided for one study (van Lieshout, Sparks, et al., 2020) and only a few of these studies were able to separate out (some) common environment effects from additive genetic effects (Asghar et al., 2015;Becker et al., 2015;van Lieshout, Sparks, et al., 2020). In addition to calculating heritability, evolvability (a mean standardized measure of additive genetic variance) facilitates comparison between studies of the evolutionary potential of a given trait (Houle, 1992). There is a need for more studies assessing the heritability and evolvability of telomere length using large data sets with multigenerational pedigrees and animal model approaches.
In this study, we used long-term individual-based multigenerational data from an isolated population of the cooperatively breeding Seychelles warbler (Acrocephalus sechellensis) to investigate additive genetic and environmental variance components underlying telomere length. Telomere length declines with age, and adult survival is positively associated with telomere length, independent of age, in this population (Barrett et al., 2013). Telomere length decline is greatest in early life in the Seychelles warbler, and telomere length shows strong cohort effects and is positively associated with islandwide food abundance (Spurgin et al., 2018). However, telomeres also appear to elongate within individuals in this population (Spurgin et al., 2018). Telomere dynamics have helped reveal the costs of factors such as inbreeding (Bebbington et al., 2016), social conflict (Bebbington et al., 2017) and parental care (Hammers et al., 2019).
In the Seychelles warbler, telomere length is therefore an important biomarker of condition and senescence and is impacted by environmental conditions. The individual repeatability of relative telomere length (RTL) is 0.068 in this population (Spurgin et al., 2018), which sets a low upper limit on ordinary heritability (Falconer & Mackay, 1996). However, the relative contribution of other environmental components, such as parental, catch period and hatch period effects, is unknown.
Here, we estimate the heritability of telomere length in the Seychelles warbler using 2,663 telomere measures from 1,317 birds within a 10-generation genetic pedigree. First, we test for effects of parental age at conception on offspring telomere length accounting for the age at which offspring were sampled. We then estimate the heritability and evolvability of telomere length using animal models where we control for expected confounding effects. We predict estimates of heritability will be higher when we included fewer common environmental effects (due to the upward biasing of heritability as a result of shared environments). Finally, we discuss the broader implications of our results for understanding the evolutionary potential of telomeres in this population.

| Study system
The Seychelles warbler is a small passerine endemic to the Seychelles archipelago . The entire population (~320 adult individuals in 115 territories) on Cousin island (29 ha; 04°20′S, 55°40′E) has been monitored intensively since 1985 (Hammers et al., 2019;Komdeur, 1992;Raj Pant et al., 2019;Richardson et al., 2007). Seychelles warblers defend year-round territories in which a dominant male and female breed and most clutches contain just one egg (Komdeur, 1994;Richardson et al., 2001). The major breeding season runs from June to September, although some pairs also breed in the minor breeding season between January and March Komdeur & Daan, 2005). Senescence has been documented in the Seychelles warbler (Hammers et al., 2015) with age-dependent declines in both reproduction and survival (Hammers et al., 2012. Seychelles warblers are largely insectivorous, and variation in rainfall drives variation in insect abundance (Komdeur & Daan, 2005), which is positively associated with telomere length (Spurgin et al., 2018).
In addition, this study benefits from being able to separate genetic and social parent effects on telomere variation, due to the presence of extra-group paternity (41% of offspring) and subordinate female cobreeding (11% of offspring) (Raj Pant et al., 2019).
All protocols were ethically reviewed and approved by the BIO Ethical Review Committee, University of East Anglia, UK, and ratified by the University of Leeds. Each breeding season as many birds as possible are caught using mist nets and all territories are monitored for the presence and identity of individually colour-ringed birds. The majority (96%) of individuals have been individually marked with a British Trust for Ornithology ring and a unique colour ring combination (Richardson et al., 2001). Age of unringed birds was estimated using lay, hatch or fledge dates, or alternatively if these dates were unknown, we used eye colour to determine whether the individual was in the first year of its life or not (Komdeur, 1991). Since 1990, blood samples (~25 µl) have been taken and stored at room temperature in absolute ethanol, thus allowing molecular sexing, parentage assignment (Hadfield et al., 2006;Richardson et al., 2001), pedigree construction (Edwards et al., 2017) and telomere length measurement (Barrett et al., 2013). The population is virtually closed (<0.1% dispersal; Komdeur et al., 2004) and extrinsic mortality is low, so birds live long lives (maximum observed lifespan =19 years).
Furthermore, the population is intensively monitored with high annual resighting rates (~0.92 ± 0.02 for birds ≤2 years and 0.98 ± 0.01 for older birds, Brouwer et al., 2010), so accurate hatch and death years are known (Hammers et al., 2015). Each fieldwork period (a minor and major breeding season each year) is assigned a unique identifier (for each unique combination of year and season) and catch records are assigned to the fieldwork period ID in which they occurred (henceforth "catch period ID") or hatch records to the closest fieldwork period ID (henceforth "hatch period ID").

| Telomere data
We used the telomere data set generated in Spurgin et al. (2018), which included birds caught and blood sampled between 1995 and 2014, when the data were most complete. RTL was estimated using qPCR (quantitative polymerase chain reaction; Barrett et al., 2013;Bebbington et al., 2016;Spurgin et al., 2018). DNA integrity (agarose gel) and 260/280 ratios were checked in all samples before running any qPCR, and any samples with signs of degradation were removed, 2018). All repeatability estimates were calculated on RTL measurements from the same DNA extraction and may be lower if DNA extractions were also repeated. There were no storage time effects (of the blood samples) on telomere length (Spurgin et al., 2018). Our cleaned data set included 2,664 samples from 1,318 individuals that passed quality control (Bebbington et al., 2016) and filtering steps (sample removal criteria: telomere cq ≥25 or cq replicate difference ≥0.5; GADPH cq ≤21 or ≥26 or cq replicate difference ≥0.5; RTL values ≥3). To investigate plate variance (by including qPCR plate as a random effect in our statistical models), where samples had replicates across plates (n = 388), an RTL value for a given blood sample was taken at random.

| Genetic pedigree
Protocols for genotyping, quality control tests and parentage assignments (MasterBayes 2.5.2; Hadfield et al., 2006), and pedigree statistics are provided in the Supporting Information (Supplementary parentage methods, Figures S1-S3 and Tables S1-S3). Parentage was assigned at p ≥ .8. The pruned pedigree, calculated using pedantics 1.7 , included parentage assignments for individuals born in 1992-2014 and contained 1,482 informative individuals for telomere length with 1,217 maternities and 1,268 paternities (Table S3).

| Statistical analyses
2.4.1 | Paternal age at conception effects on offspring telomere length Statistical analyses were performed in r 3.5.3 (R Core Team, 2019).
We first investigated associations between parental ages at conception and RTL in offspring using linear mixed effects models with Gaussian error distribution in lme4 1.1-21 (Bates et al., 2015). RTL was square-root transformed to improve linear mixed model fits (from checking model diagnostics) and to be consistent with previous work on this system (Spurgin et al., 2018), and in each model subset RTL was subsequently z-transformed (mean centred and divided by 1 SD) for comparability of telomere studies (Verhulst, 2020). Distributions of nontransformed and the square-root and z-transformed RTL data are provided in Figure S4 and conclusions were the same when nontransformed RTL was used in these models (see Tables S4-S5). Collinearity between the fixed effects was checked by calculating variance inflation factors (VIFs); all VIFs were <3. We fitted offspring RTL across all ages that offspring were sampled at as the response variable and included offspring sex (factor), offspring age in years (log-transformed for all ages and juvenile models following Spurgin et al., 2018), parental age at conception (maternal and paternal) and technician identity (factor: two levels) as our fixed effects. Random effects included offspring identity, maternal identity, paternal identity, catch period ID and qPCR plate.
Based on our data set and model structure we had ≥80% statistical power to detect paternal age at conception effect sizes of ≥0.02 ( Figure S5) using a simulation-based power analysis in the package simr 1.0.5 (Green & MacLeod, 2016). This was equivalent to a correlation coefficient of .059 (r=β*[SD x /SD y ] following Froy et al., 2017) which is sufficient power to detect paternal age at conception effects of the correlation coefficients previously published (De Meyer et al., 2007;Eisenberg et al., 2012Eisenberg et al., , 2017Nordfjäll et al., 2010).
There was considerable variation in maternal and paternal ages at conception ( Figure S6a,b) and a significant but weak correlation between the two (r = .12, t 1154 = 4.08, p < .001, Figure S6c) which allowed us to include both variables in the same model. Significance was determined using likelihood ratio tests where the fixed effect of interest was dropped from the full model.
We also investigated paternal (PAC) and maternal age at conception (MAC) effects where offspring RTL was restricted to the first measurement as a nestling (n = 304), or all juvenile measures (<1 year old, n = 1,137 measures of 958 offspring). The model structure was identical to the model of all ages, except offspring identity was not included as a random effect for the nestling model, and for the juvenile model paternal identity was not included to allow model convergence.
To investigate whether effects on offspring telomere length were driven by within-parental age rather than between-parental age (selective disappearance) at conception effects, we used withinsubject centring (van de Pol & Wright, 2009). In the model of RTL across all ages, we first removed PAC and MAC and included mean age at conception per parent (between-parental age effects) and the deviation from the mean age at conception of the parent (withinparental age effects). To test whether the within and between slopes differed from each other, we included parental age at conception (within-individual age effects) and mean parental age at conception (difference between the within-and between-individual slopes) in a second model. The significance of mean parental age at conception in this second model indicates that these within and between slopes in the first model are significantly different (van de Pol & Wright, 2009). We found within-PAC and between-MAC effects but effect sizes were small (see Results). To aid interpretability and comparability between studies, we then calculated the correlation coefficient of these effects using the equation r = β*(SD x /SD y ) where r is the correlation coefficient, β is the regression slope and SD is the standard deviation for x (within PAC or between MAC) and y (RTL). Our correlation coefficients using this method were very similar to those estimated using the formula t/sqrt(t 2 + df) using df = n − 1 − k (since error degrees of freedom are difficult to ascertain in linear mixed models) from Nakagawa & Cuthill, 2007 (r = −.058 for the within-PAC effect and .056 for the between-MAC effect).

| Heritability of telomere length
We investigated the heritability of telomere length in quantitative genetic "animal models" in MCMCglmm2.26 (Hadfield, 2010). We used a Bayesian approach to provide accurate estimates of our variance components. Our pruned pedigree had ≥80% power to detect heritabilities of ≥0.17 ( Figure S7), determined in pedantics 1.7 . These univariate models were fitted with nontransformed RTL as the response variable to estimate variance components on the scale the trait was measured (de Villemereuil et al., 2016). We used a z-transformation in the parental age at conception models to improve comparability of the effect sizes of fixed effects between qPCR studies (Verhulst, 2020). Because we are interested in the partitioning of variance components rather than investigating fixed effects in these animal models, z-transformation was not performed. Animal models were fitted with an increasingly complex fixed and random effect structure. This allowed us to test for confounds between random effects, and to investigate how the inclusion of random effects affected our estimates of heritability.
Model 1 included only individual identity to account for repeated measures (to calculate between-individual variation or "repeatability", n = 1,317 individuals). In model 2, individual identity was partitioned into additive genetic and permanent environment components using the pruned pedigree. In model 3, we included fixed effects of sex (factor), age (log-transformed following Spurgin et al., 2018) and technician (factor: two levels) to investigate how heritability was impacted by the inclusion of fixed effects (following: de Villemereuil et al., 2018;Wilson, 2008). In model 4, we estimated technical variance by adding qPCR plate ID as a random effect (271 levels). We subsequently added maternal (model 5; 380 mothers) and paternal (model 6; 354 fathers) identity, determined from the genetic pedigree, to investigate parental effects underlying telomere length. Maternal effects have previously been observed in other species (Asghar et al., 2015), and maternal inbreeding effects, but not paternal inbreeding effects, on offspring telomere length have been documented in our population (Bebbington et al., 2016). We then added the random effects of catch period ID (model 7; 37 levels) and current territory (model 8; 166 levels), to account for spatiotemporal factors associated with telomere length (Spurgin et al., 2018). Finally, we tested for early-life effects of hatch period ID (model 9; 39 levels) to account for long-lasting effects of natal conditions on telomere variation. Although we had information on natal territory, models including natal territory did not converge, and simpler models suggested that natal territory explained no variance in RTL.
We defined fixed effects as significant if the 95% credible intervals (CrI) of the posterior modes did not overlap zero. Heritability estimates, and the proportion of phenotypic variance explained by other variance components, were calculated by taking the posterior mode of the ratio of the additive genetic variance to total phenotypic variance for each sample of the posterior distribution. In addition, we also calculated evolvability (a mean standardized measure of additive genetic variance) of telomere length by dividing the additive genetic variance by the squared trait's mean (I A = V A /x̄2 where I A is evolvability, V A is the additive genetic variance and x̄ is the trait mean) (Houle, 1992).
To confirm the robustness of our estimates of telomere length heritability, we also ran the final model in a frequentist framework using ASReml-R 3 (Butler et al., 2009) using the same structure as model 9. The significance of random effects was determined by dropping each random effect from a model containing all random effects and performing a likelihood ratio test using twice the absolute difference in log-likelihoods between the two models.
We then tested whether parental effects were present when using the social (i.e., the dominant breeding pair) rather than the genetic parents, which is possible due to extra-group paternity (41% of offspring) and cobreeding (11% of offspring; Raj Pant et al., 2019).
To do this, we compared the model with genetic parents (model 7) to that where the genetic parents were replaced with social parents (model 10: specifications: 1 × 10 7 iterations, burn-in =4 × 10 6 , thinning =3,000) using model 7's structure, as other random effects in models 8 and 9 explained a small proportion of the phenotypic variance (see Results).

| RE SULTS
Maternal and paternal age at conception (MAC and PAC, respectively) were not significantly associated with offspring RTL when using telomere lengths across all ages, or when the data set was restricted to the first offspring measurements taken as nestlings, or when all measurements were taken from juvenile offspring (<1 year old; Figure S8, Table S6). However, when parental age at conception effects were separated into within-vs. between-parental age effects for lifelong RTL, there was a significant negative within-paternal age effect and a significant positive between-maternal age effect TA B L E 1 Linear mixed model results investigating between vs. within maternal and paternal age at conception (MAC and PAC, respectively) effects on offspring telomere length in the Seychelles warbler using the within-subject centring method ( Associations were investigated in offspring telomere length of all ages (2,361 RTL measures of 1,156 offspring) and included are the estimated effects (estimate), standard errors (SEs), and significance of fixed effects based on a likelihood ratio test (LRT; p-value) where df =1. Relative telomere length was square-root then z-transformed in both models and age was log-transformed. Model 1 investigates within-MAC/PAC effects (deviation from the mean age at conception of the parent: DevMeanMAC/PAC) and between-MAC/PAC (mean age at conception for each parent: meanMAC/PAC) effects. Model 2 investigates whether these within and between slopes are significantly different from each other (mean MAC/PAC representing the difference between the slopes and MAC/PAC which becomes the within-MAC/PAC slope identical to Model 1). p values <.05 are shown in bold.
(Table 1, Figure 1). As fathers aged the offspring they produced had progressively shorter telomeres, while females that survived to older ages had offspring with longer telomeres (Figure 1). Within-vs.
between-parental age slopes were significantly different from each other for both maternal and paternal age at conception (Table 1).
However, both the within-paternal (r = −.059) and between-maternal (r = .060) age effects on offspring RTL were small when converted to a correlation coefficient (Figure 1). There was no difference in lifelong RTL between the sexes, but there was a logarithmic association with age and an effect of technician ( Table 1; Table S6).
We estimated heritability with a quantitative genetic animal model using a hierarchical approach (Figure 2). Individual repeatability of RTL, the amount of variance due to individual identity, was low across all models and ranged from 0.056 (95% CrI: 0.016-0.092; ASReml-R produced similar results: repeatability was 0.057 ± 0.023 SE and heritability was low but significant at 0.041 ± 0.018 SE (Table   S8). Without plate included in the total phenotypic variance, repeatability was 0.074 ± 0.030 SE and heritability was 0.053 ± 0.023 SE.
Parental effects were compared when social parents (dominant breeding pair) or genetic parents (from the pedigree) were included.
Maternal and paternal effects were close to zero in both models and did not differ significantly between models based on overlapping 95% credible intervals ( Table 3). Heritability estimates were not significantly different based on the 95% credible intervals of the two models ( Table 3).

| DISCUSS ION
We found a negative within-paternal age at conception effect, and a positive between-maternal age at conception effect on offspring telomere length in the Seychelles warbler, but both of these effect sizes were small. These results add to the growing literature report- F I G U R E 2 Estimated variance components as proportions of total phenotypic variance in relative telomere length determined using univariate models in the Seychelles warbler. Models were fitted additively with increasing random or fixed effects as follows: Model 1individual identity (V ID ), 2 -partitioning of V ID into additive genetic (V A ) and permanent environment (V PE ) components, 3 -the addition of fixed effects (age, sex, technician), 4 -qPCR plate ID (V Plate ), 5 -maternal identity (V Mat ), 6 -paternal identity (V Pat ), 7 -catch period ID (V CP ), 8 -current territory (V Terr ) and 9 -hatch period ID (V HP ). Five variance components (V PE , V Mat , V Pat , V Terr , V HP ) explained <0.001 of the total phenotypic variance in all models so do not show up on the graph. For full model results see Table 2 and  Unryn et al., 2005). Including just paternal and maternal age at conception in the model, we found no evidence for cross-sectional parental age at conception effects on offspring telomere length in the Seychelles warbler, even with sufficient power to detect paternal age at conception effects of the size of the correlation coefficients previously published (De Meyer et al., 2007;Eisenberg et al., 2012Eisenberg et al., , 2017Nordfjäll et al., 2010). However, using within-subject centring we found weak but significant within-paternal age at conception and between-maternal age at conception effects on offspring telomere length. In contrast to cross-sectional findings in humans (Broer et al., 2013;Eisenberg et al., 2012;Unryn et al., 2005), we found that males produced offspring with shorter telomere lengths as they aged. Furthermore, we also found that females that lived longer had offspring with longer telomeres. However, both these effects on offspring telomere length were relatively small when considered as correlation coefficients.
Despite the consistency in human studies, studies in nonhuman vertebrate populations are providing mixed evidence of paternal age at conception effects (Eisenberg, 2019). While a few have documented positive paternal age at conception effects (Dupont et al., 2018;Eisenberg et al., 2017), most find a negative paternal age at conception effect (Bauch et al., 2019;Bouwhuis et al., 2018;Criscuolo et al., 2017;de Frutos et al., 2016;Noguera et al., 2018;Olsson et al., 2011). Furthermore, many studies have documented no parental age at conception effects (Belmaker et al., 2019;Froy et al., 2017;Heidinger et al., 2016;McLennan et al., 2018;van Lieshout, Sparks, et al., 2020), while one study found a positive maternal but no paternal age at conception effect (Asghar et al., 2015). Such mixed results in natural populations may be due to the majority of studies on parental age at conception effects being cross-sectional.
Where telomere length is known to be positively associated with survival in a population , this could lead to the selective disappearance of parents with shorter telomeres from older age groups. Such selective disappearance could obscure within-parental age at conception effects when analysing data at a cross-sectional level (Bauch et al., 2019;Noguera et al., 2018). So far, only two published studies investigating parental age at conception effects have separated within-from between-parental age effects: a negative paternal age at conception effect was found in wild jackdaws (Bauch et al., 2019) while no parental age at conception effects were found in wild European badgers (van Lieshout, Sparks, et al., 2020). More studies using a within-subject centring approach (van de Pol & Wright, 2009) are now needed in both human and natural populations to determine whether such heterogeneous findings are indeed driven by cross-sectional approaches.
We investigated heritability using an animal model approach.
Telomere length had a low individual repeatability (without plate variance: 0.077; 95% CrI: 0.028-0.125) and a low heritability   variance. Variance component estimates are reported as the posterior mode along with their 95% credible intervals (Lower 95% CrI, Upper 95% CrI) and the proportion of the total phenotypic variance explained by the term (Prop V P ) with their associated 95% credible intervals.
<0.001-0.042, to 0.060, 95% CI: 0.023-0.106 depending on prior specification, Foley et al., 2020) et al. 2020). However, whether such differences represent true biological variation between species, or whether these differences may also reflect methodological differences is unclear. While qPCR is the most common method used in nonmodel vertebrate studies (because it is cheaper and of higher throughput), terminal restriction fragment (TRF) analyses or southern blot methods are more technically repeatable (Aviv et al., 2011). Despite the lower technical repeatability of the qPCR method compared to the TRF method, there is evidence of high correlations (r = .847-.896, p < .001) between these two measures (Aviv et al., 2011;Tarik et al., 2018). Higher individual repeatabilities (i.e., the proportion of phenotypic variance explained by individual identity), or within-individual correlations, have been documented in TRF studies (Bauch et al., 2013;Bichet et al., 2020;Boonekamp et al., 2014) than those in qPCR studies in wild populations Foley et al., 2020;van Lieshout, Sparks, et al., 2020;Spurgin et al., 2018). The presence of telomere lengthening, which has been documented in qPCR studies including our study population van Lieshout et al., 2019;Spurgin et al., 2018), may be an important factor contributing to a lower between-individual repeatability.
Of the six studies using animal models in nonmodel species, the two captive studies which found high heritabilities of ~1 used the TRF method (Atema et al., 2015;Boonekamp et al. 2020), while the remaining qPCR studies which were conducted in wild populations found heritabilities of 0-0.48 (Asghar et al., 2015;Becker et al., 2015;Foley et al., 2020;van Lieshout, Sparks, et al., 2020).
In humans there is also some evidence that within-individual correlations in telomere length measures are higher with TRF studies than qPCR studies (Benetos et al., 2013;Martin-Ruiz et al., 2005;Svenson et al., 2011). Despite this, the mean heritability estimate in 10 studies of humans using both qPCR measures and a variance partitioning approach was moderate at 0.47 (range 0.07-0.70) (Blackburn, Charlesworth, et al., 2015;Broer et al., 2013;Coutts et al., 2019;Delgado et al., 2018;Faul et al., 2016;Honig et al., 2015;Kim et al., 2020;Lee et al., 2014;Njajou et al., 2007;Zhu et al., 2013). Furthermore, a qPCR study in dairy cattle found heritabilities of 0.32 and 0.38 in the calf and cow data set, respectively (Seeker et al., 2018). In a recent simulation study of qPCR telomere data, measurement error alone produced patterns of low correlations between consecutive telomere measures within an individual, although this study highlights that this does not necessarily mean that all low correlations are due to measurement error (Nettle et al., 2019). The presence of these differences highlights the need for studies that apply both qPCR and TRF methods to the same samples in order to understand how repeatabilities and heritabilities are influenced by each methodology.
The low heritability of telomere length in the Seychelles warbler is consistent with individuals with longer telomeres having a higher probability of surviving until the next year, independent of age (Barrett et al., 2013). Although it is unclear whether the links between telomere length and fitness are causal (Young, 2018), it is possible that selection for longer telomeres in this population has reduced the genetic variation, and hence the heritability, of this trait (Falconer & Mackay, 1996). Previously we found a weak but significant positive association between food availability and telomere length (see Figure 3c, Spurgin et al., 2018), suggesting a relationship between environmental variation and telomere length. However, we could not identify any considerable sources of environmental and year of hatch effects (0.46 ± 0.13 SE) on telomere length variation (Becker et al., 2015). In comparison, in the great reed warbler Acrocephalus arundinaceus, high heritability (0.48 ± 0.12 SE) and equally large maternal effects (0.47 ± 0.09 SE) appeared to underlie telomere variation (Asghar et al., 2015). In the European bad- Indeed, we previously found cohort effects on juvenile telomere length that did not extend to measures beyond the natal year (Spurgin et al., 2018).
The lack of parental or early life environment effects in our study may also reflect the sampling regime of our population whereby only a small proportion of samples in the data set were measured as nestlings (12% chicks). Due to the inaccessibility of nests, which may be up to 30 m high in trees, individuals are usually caught as fledglings during their first 3 months when they remain dependent on their parents (Brouwer et al., 2006;Komdeur, 1994). While early-life measures of telomeres will be closer to the inherited telomere length, by using a measure of telomere length across the lifetimes of birds we are measuring a product of inheritance, attrition and restoration/lengthening. After birth, telomere attrition occurs rapidly (Hall et al., 2004;Salomons et al., 2009) and telomere length decreases with age quickest in the first few weeks of life in the Seychelles warbler (Spurgin et al., 2018).  (Ponzi et al., 2018).
Heritabilities can be re-evaluated with the total phenotypic variance excluding any technical variance to reflect true biological variance (de Villemereuil et al., 2018). Measurement error in qPCR studies could come from various factors such as between-and within-plate effects, technician, storage time and method, changes in reagents, and extraction method effects (Eisenberg et al., 2015;Reichert et al., 2017;Seeker et al., 2016;van Lieshout, Froy, et al., 2020). Such systematic measurement error should be incorporated into analyses and reported to prevent it from biasing results (Nettle et al., 2019).
Furthermore, other nonsystematic sources of error are present in qPCR studies due to the calculation of RTL from the ratio of telomeric DNA to a control gene. Measurement errors in both of these measures can magnify the error in the resulting ratio (Nettle et al., 2019).
While our technical repeatability was high (Spurgin et al., 2018) this was estimated based on RTL measurements from the same DNA extraction. Although we check for DNA integrity and quality prior to running the qPCR, it may be that our technical repeatability would be lower if we also repeated the DNA extraction. Importantly, while there was more error in our between-plate repeatability estimates, it must be noted that these were calculated based on plates run with a considerable time gap between the repeats to more accurately reflect technical error in our data set. In this study, while we have accounted for technician effects, tested for storage time effects and accounted for between-plate variation (both with the golden sample and also by including plate ID in models), we cannot rule out that the remaining large residual variance (although not uncommon in quantitative genetic studies Bérénos et al., 2014) may also be due to within-plate variation (Eisenberg et al., 2015). Within-plate variation can occur due to edge effects, from poor sealing and/or from thermal gradient distortion at plate edges (Rogers-Broadway & Karteris, 2015), and in one study these row effects explained 1.3% of telomere length variance (van Lieshout, Sparks, et al., 2020). As a result, our heritability estimates may actually represent a lower limit of true heritability in this population. We currently run, on the same plate, three technical replicates of each sample, from the same DNA extraction, of both the telomere and control gene sequences (Barrett et al., 2013), with samples randomly assigned to plates (Spurgin et al., 2018). In future, a better solution would be to repeat this process with a separate DNA extraction with sample identity and well location added as an extra variance component in analyses. Importantly, between-plate repeatability estimates should also be carried out at two different time points representing the maximum time difference between the first and last samples being run in the data set.
In conclusion, our results find a low lower limit on the heritability of telomere length in this wild avian population. In our population, telomere length variation across an individual's lifetime was not driven by environmental variation in early life (hatch period or parental effects). Instead, telomere length was largely driven by unexplained variation, caused either by unmeasured technical or by environmental variation. In addition, there was evidence for a negative, but weak, within-paternal age at conception effect and a positive but weak among-maternal age at conception effect on offspring telomere length. Further work is needed to see how heritability estimates of telomere length, and telomere loss, calculated using the appropriate power and analytical tools, compare across wild populations.

ACK N OWLED G EM ENTS
We thank the Department of Environment and Seychelles Bureau of Standards for research permits and Nature Seychelles for facilitating work on Cousin Island. We thank all those who have contrib-

DATA AVA I L A B I L I T Y S TAT E M E N T
Data are available from the Dryad Digital Repository: https://doi. org/10.5061/dryad.vt4b8 gtr1 (Sparks et al., 2021). r scripts for the analysis are available at https://github.com/Seych elle-Warbl er-Proje ct/Sparks_2021_MolEcol