Allele Frequency Dynamics in a Pedigreed Natural Population

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Andrew Chen Nancy population pedigreed natural a in dynamics frequency Allele www.pnas.org/cgi/doi/10.1073/pnas.1813852116 genetics population date. to population natural in a change in frequencies evolutionary allele short-term of the gene of descriptions one with complete provides study success, most This reproductive contribution. primarily smaller and a are making survival change flow in changes frequency variation frequency allele to allele due in Observed variance time. of through par- proportion we directional size, the population under in titioned changes SNPs for account few that flow. a models gene actually Using for identified accounting selection appropriately We after to selection flow. short-term attributed gene been to have due shifts may frequency allele otherwise large that some of with recent contributions of substantial, contribution is genetic genetic immigrants the pre- different that show well the results Our generally found for founders. are We accounting changes pedigree. by known frequency dicted the allele the on observed to drift that dropping contributions model genetic gene and individual performed population estimate We of to patterns time. simulations shaping through in variation relative processes genetic the evolutionary different characterize informa- of directly genomic roles Scrub-Jays to Florida and of coerulescens) population pedigree (Aphelocoma natural extensive long-studied a use from through tion population we the Here, in individuals time. all among set relationships the of pedigree, under- population Fully the quantify. requires processes to these difficult standing often movement—are suc- how and reproductive fre- cess, survival, understand allele individual in underlying shape to processes changes—variation flow actual these is the gene However, time. genetics and 2018) through 10, selection, quencies population August natural review for of drift, (received 2018 genetic goal 19, November approved central and Norway, A Oslo, Oslo, of University Stenseth, C. Nils by Edited 38152 TN Memphis, Memphis, of 33960; University FL Venus, Station, Biological Archbold 44195; OH Cleveland, Foundation, Clinic c a eei otiuino nidvda sa niiulsrepro- individual’s an is individual an of expected long-term contribution The (4). genetic descendants of pedigree alleles their dropping of down gene transmission Mendelian via of or simulations (1–3) i.e., simulations, analytically estimated be contri- can individual, genetic Individual given butions generations. a future by in contributed population allele the neutral to a of copies num- of expected ber the i.e., contributions, genetic individual expected segregation. 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EVOLUTION polymorphism (SNP) data for nearly every individual in the Using the detailed population pedigree, we calculated both the population over the past two decades to demonstrate how genealogical and expected genetic contribution of each individ- decreased immigration into the population led to increased levels ual to the study population from 1990 to 2013. Fig. 1 A and B of inbreeding and decreased mean fitness over time. In this study, shows results for two illustrative males, both of whom first bred we link individual lifetime reproductive success with long-term in 1994. Male A lived until 2006 and had 41 offspring, whereas genetic contributions and allele frequency change. We show Male B only lived until 2000 and had 7 offspring. We define how the population pedigree presents a powerful opportunity an individual’s genealogical contribution to a given year as the to directly elucidate the relative roles of drift, gene flow, and proportion of nestlings in the birth cohort who are genealogi- selection in governing allele frequency dynamics over time. cally descended from the focal individual, while an individual’s expected genetic contribution is the expected proportion of alle- Results les at a locus in the nestling cohort that comes from the focal Individual Fitness and Genetic Contributions. First, we consider a individual. Beyond a few generations, few genealogical descen- series of inferences that can be made purely with the pedigree, dants are expected to inherit any genetic material, so the number ignoring the SNP genotypes for the moment. We estimated fit- of genealogical descendants should quickly outnumber the num- ness for all 926 individuals who bred in our study population ber of genetic descendants. Fig. 1 A–C nicely demonstrates this in 1990–2013 and were born before 2002 (the age cohorts who pattern in our data, providing empirical illustration for a sub- are all dead by the end of 2014). Lifetime reproductive success stantial body of theory on the relationship between genetic and was highly variable in our study population: The total num- genealogical ancestry (8, 22, 23). An individual’s genealogical ber of nestlings produced over an individual’s lifetime ranged contribution in 2013 is correlated with its expected genetic con- from 0 to 43, with 197 individuals (21%) producing no nestlings tribution in 2013 (Spearman’s ρ = 0.99, p < 2 × 10−16), but its despite having at least one breeding attempt (SI Appendix, Fig. genealogical contribution is significantly larger (paired Wilcoxon S1). Only 43% produced any grand-offspring (range 0 to 189), test, p < 2 × 10−16; Fig. 1C). and 33% produced great-grand-offspring (range 0 to 210). As Individual fitness is a central concept in evolutionary biol- might be expected in these monogamous birds in which the sexes ogy but is notoriously difficult to measure (24). Here, we tested experience equal annual mortality (20, 21), we found no signifi- for a relationship between various proxies for fitness and the cant differences in individual fitness between males and females expected genetic contribution to the population. All three mea- (Wilcoxon rank sum test, p > 0.65 for all three measures of sures of fitness (number of offspring, grand-offspring, and great- fitness). grand-offspring) are significantly correlated with both the total

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Fig. 1. Genealogical (Top) and expected genetic contributions (Bottom) to the study population over time for two males who first bred in 1994 with total lifetime reproductive success of (A) 41 and (B) 7. Blue lines indicate the proportion of nestlings each year who are genealogical descendants. Black lines indicate mean expected genetic contribution for each year, and gray shading is the 95% confidence interval for their contribution at a neutral locus. The pedigree of all descendants of each individual in the study population is shown, with an arrow indicating the focal individual, and solid symbols denoting individuals still alive in 2013. (C) Genealogical contributions and expected genetic contributions to the population in 2013 for all breeders born before 2002 who first bred in 1990 or later (926 individuals). The dotted line indicates a one-to-one relationship. (D) Predicted versus observed change in allele frequencies from 1999 to 2013.

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Fig. 3. (A) Distribution of expected allele frequency shifts between 1999 and 2013 for the SNP shown in B (gray histogram). The blue line indicates the observed allele frequency change. (B) Observed (blue) and simulated (black) allele frequency trajectories for one of the significant SNPs in 1999–2013. Gray bars indicate 95% confidence intervals for the gene dropping simulations. (C) Manhattan plot for allele frequency shifts in 1999–2013. Significant SNPs (FDR < 0.25) are highlighted in orange.

change from year to year due to survival/reproduction and gene contributions to both individual fitness measures and allele fre- flow using a model that accounts for variation in population sizes quency change over time. In our population of Florida Scrub- over time and overlapping generations (Fig. 4). The change in Jays, we observed huge variation in individual fitness: 75% of allele frequency due to births is a result of both variation in fam- the 445 individuals who first bred in our population before 1997 ily size and Mendelian segregation of alleles in heterozygotes. have no living descendants by 2013, but 6 of these individuals We further divided the variance in allele frequency change due are each genealogical ancestors to >25% of the birth cohort in to births into these two components and found that the noise due 2013. However, many of these genealogical descendants receive to Mendelian segregation comprises 24 to 48% of the variance little genetic material from a particular ancestor, thanks to the due to births, and 12 to 23% of the overall variance. Our model vagaries of Mendelian segregation and recombination during results reflect patterns we observed in the field. For instance, meiosis (8, 22, 23). Here, we empirically show how genealogical the number of nestlings born in 2012 was unusually low (SI contributions outstrip expected genetic contributions after just a Appendix, Fig. S6), leading the survivors to have a disproportion- few generations. ate impact on allele frequency variation in 2011–2012. Overall, we found that 90% of the variance in allele frequencies is driven by variation in survival and reproductive success (fitness) among individuals. If variation in fitness is heritable, then the effects of drift can be compounded over the generations, even at unlinked loci (28–30). Simulations of allele frequency change on pedigrees in which we randomized family sizes over breeding individuals showed that heritable variation in reproductive success has no detectable effect on the variance in allele frequency change in 1999–2013: The mean difference between randomized and observed pedigrees was −0.8%, with a 95% confidence interval of (−11.3%, 8.7%). These results suggest that drift is the pre- dominant force driving allele frequency change over time, which is consistent with our small population size. Discussion We capitalized on a long-term demographic study of Florida Fig. 4. Schematic and results for our model of the variance in autosomal allele frequency change from year to year due to survival (Surv)/reproduc- Scrub-Jays with extensive pedigree and genomic data to demon- tion (red/orange/yellow) or gene flow (Imm; blue). The variance in allele strate how short-term evolutionary processes operate in a natural frequency change due to births is further partitioned into the variance due population. We estimated genealogical and expected genetic to variation in family size (Fam size) and additional noise due to Mendelian contributions for hundreds of individuals, and linked genetic segregation of heterozygotes (Mend noise).

4 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1813852116 Chen et al. 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Figshare Genetic Expected at individuals. found be frequency 3,404 can in allele study SNPs minor this autosomal 7044368. in with 10,731 used SNPs of data removed consists All dataset we found final Here, be Our can Informa- 19. verification (19). pedigree ref. 1999–2013 and and in genotyping, genome- discovery, 1995, SNP 1989–1991, 15,416 on in at tion territories breeders and individuals core nestlings these all 3,984 1990. of in sampling genotyped in near-complete in starting we resulting monitored SNPs, study, wide consistently previous been a has In that area geographic a en fsrn s1--l etig teaea hc hyaefirst are they which at 2014 age of (the end we nestlings the Here, at 11-d-old grand-offspring, great-grand-offspring. banded). alive as additional additional still offspring still produce produce were define may were may who and who therefore grand-offspring 2014 offspring and had of had repro- 13% end 5% lifetime and of the individuals, the survey at before these unbiased died and alive Of all accurate indi- who an success. ensure breeders (926 ductive to of 2002 2014 cohorts We or of age before lifetime. grand-offspring, end to its adults born offspring, sample over all were individual our of given restricted for and number a by fitness later total produced the or individual great-grand-offspring counting 1990 estimate individu- by in 6,936 to viduals), bred of pedigree truncated first consists the and who pedigree used 1990 final in We analyses Our als. our accordingly. tract all study pedigree and began by detailed the we caused a 1990, artifacts have any before we avoid expansion To 36), pedigree. (19–21, population population accurate this in distances dispersal Commission Conservation Wildlife and Fish Wildlife Florida (LSSC-10-00205). and the permits and Fish (banding Archbold 23098), US Survey Geological 07732, and the US Univer- the by (0667), TE-117769), Cornell permitted Memphis (TE824723-8, Service and at of (AUP-006-R) Committees approved University Station Use was the Biological and fieldwork 2010-0015), Care All (IACUC population. Animal sity the Institutional in the reproductive are individuals by and groups all survival family all for of of success documentation nests all providing and monitored, months, pop- closely few entire every The banded, year. censused uniquely each is are individuals ulation population in immigrant entire of half the and identification in southern 33), allowing individuals the (19, All monitoring 35). 1969 Bowman, (34, began in 1989 Fitzpatrick, colleagues half and Woolfenden, northern Schoech, the decades. Biolog- Mumme, monitoring for Archbold began population at colleagues FL) A monitored and (Venus, (33). intensively Florida Station been in has ical scrub Scrub-Jays oak Florida to of restricted bird breeding atively Dataset. and System Study Methods and Materials increase will evolution short-term of dramatically. the consequences observe for and directly resources to causes ability genomic our As expand, time. populations pedigree pedigreed over governing population dynamics forces frequency a evolutionary allele the on to fitness. analyses insights to substantial SNP provide linked single haplotypes across even specific immigrants However, pinpoint quan- recent and of material, genome, contribution genetic the genetic surviving reproductive pedi- actual of between the the distribution tify relationship down the the blocks and explore genomic value could of we inheritance gree, the contributions. tracing genetic expected By just contributions of instead genetic individual actual each would realized, for information of quantification haplotype the and allow linkage of incorporation The in in variance variation decrease heritable frequencies. significantly that allele not found does and success year reproductive permuting by each fitness to within linked families alleles for dropping gene of mance o u eoi nlss efcsdo oestof set core a on focused we analyses, genomic our For natal limited and paternity extra-pair of rate low very the of Because pedigree. the down alleles single only traced have we Here G h lrd cu-a sannirtr,cooper- nonmigratory, a is Scrub-Jay Florida The = n 1 eqatf niiulgntccontribution genetic individual quantify We X m X p 2 1 g NSLts Articles Latest PNAS , 8trioisin territories ∼68 | <0.05. f7 of 5 [1]

EVOLUTION where n is the total number of nestlings born that year, m is the num- we generated a list of individuals present in our population each year in ber of nestlings related to the focal individual, p is the number of paths 1990–2013 and categorized them as survivors, immigrants, or nestlings (new in the pedigree linking the focal individual and the nestling, and g is the births; SI Appendix, Fig. S6A). We only included an individual in a given number of generations separating the focal individual from the nestling in year if it was observed in at least two months during March through June. that path (1–3). We used pedigree-based simulations to estimate expected We conservatively considered individuals who left our study population but individual genetic contributions instead. Our simulation results match the- later returned as survivors during the intervening time period to minimize oretical expectations but also provide estimates of the variance around the inflating the variance in allele frequencies. expected values. Let Nt be the total number of individuals in the population in year t, Ns We used gene dropping simulations to obtain expected genetic contri- be the number of individuals who survived from year t − 1 to t, Ni be the butions of individual breeders and of different immigrant cohorts to our number of new immigrants into the population in year t, and Nb be the population over time. A founder is by definition any individual in the pedi- number of individuals born in year t. Thus, the population size in year t is gree whose parents are unknown. Thus, all immigrants are founders. We Nt = Ns + Ni + Nb. If we denote the allele frequencies in each category as assigned genotypes to all founders as follows: For individual simulations, pj, then we can write the change in allele frequencies between years t − 1 we assigned the genotype “22” to the focal individual and “11” to all and t for a given SNP as other founders. To assess the expected genetic contributions of different immigrant cohorts, we assigned immigrants appearing in different years dif- Ns Ni Nb ∆p = (ps − pt−1) + (pi − pt−1) + (pb − pt−1). [4] ferent alleles. We then simulated Mendelian transmission of alleles down Nt Nt Nt the pedigree 1,000,000 times using custom C code. The distribution of allele counts in the nestling cohort each year gives the distribution of expected The variance in allele frequency change over time is then genetic contributions over time. Ns 2 Ni 2 Var(∆p) = Var(ps − pt−1) + Var(pi − pt−1) N N Immigrant Contribution Projection. The proportion of resident alleles in the t t N N N birth cohort over time [r(t)] can be written as + b 2Var( − ) + 2 s b Cov( − , − ) pb pt−1 2 ps pt−1 pb pt−1 Nt Nt t r(t) = (1 − i) , [2] N N +2 i b Cov( − , − ). 2 pi pt−1 pb pt−1 [5] Nt where i is the per-year replacement rate by immigrant alleles, and t is the number of years following 1992. We began in 1992 because no parents in Note that we assume that survivors and immigrants in a given year are 1990–1992 were recent immigrants. We fitted this model using nonlinear unrelated and accordingly set Cov(ps − pt−1, pi − pt−1) = 0. least squares to estimate i, then used Eq. 2 to calculate the expected time We further partitioned the change in allele frequency due to the birth until neutral alleles were 95% replaced by immigrant alleles. cohort Var(pb − pt−1) into the change due to variation in family size and the deviation due to Mendelian segregation of alleles from heterozygotes

Allele Frequency Predictions. In the absence of selection, the allele frequency (∆pb,mend) (29). If pm and pf are the allele frequencies of the parents of an autosomal SNP in any given year can be written as a function of the weighted by the number of offspring they produced in year t, then individual genetic contributions of each founder and the founder allele frequencies. Let F be the number of founders, Gi,y be the expected genetic 1 pb − pt−1 = (pm + pf ) − pt−1 + ∆pb,mend, [6] contribution of founder i to the population in year y, and pi be the allele 2 frequency of founder i. We can predict the expected allele frequency in year y as follows: where the first term denotes the expected change in allele frequencies due F to the variation in family size, and the second term denotes the additional X pˆy = Gi,y pi. [3] independent noise due to Mendelian transmission. We can then estimate i=1 the variance due to Mendelian noise as Here we iteratively trimmed the population pedigree until all founders were 1 genotyped, and estimated individual genetic contributions using simula- Var(∆pb,mend) = Var pb − (pm + pf ) , [7] tions on the trimmed pedigree. We evaluated prediction accuracy by fitting 2 linear regressions. with the alternate term for the variance due to family size variation following from Eq. 6. To generate expected allele frequency distributions Neutral Allele Dynamics. We estimated each of the terms on the left and right sides of Eq. 5 aver- over time, we used gene dropping simulations on a trimmed pedigree. For aged across all autosomal SNPs. We then divided each of the terms on the each SNP, we iteratively trimmed the pedigree until all founders in the final right by the total to quantify the proportion of allele frequency change due trimmed pedigree had a known genotype. Briefly, we removed all ungeno- to which individuals survive to the focal year, appear as new immigrants, typed founders and set all offspring of these individuals as founders, then or are born, as well as the contribution of survivors and immigrants to the repeated these two steps until all remaining founders had observed geno- birth cohort and Mendelian segregation of heterozygotes. We verified our types. Note that the trimmed pedigree can differ across SNPs because of model using simulations. variable missing data across individuals; however, missing data rates are low Although we have genomic data from nearly every individual present < ( 5%), so these differences are slight. Using the observed genotype for each in the population from 1999 to 2013, we still have a small number of founder, we simulated Mendelian transmission of alleles down the pedigree ungenotyped individuals in each year (SI Appendix, Fig. S6B). To account a million times and estimated allele frequencies each year in genotyped for missing genotypes, we corrected each term in Eq. 5 for sampling. Nor- nestlings from a core set of 54 to 76 territories. mally, the error in allele frequency estimation due to sampling can be We used Mann–Kendall tests from the R package Kendall (37) to test statistically modeled, but relatedness among individuals and nonrandom for trends in the allele frequencies of incoming immigrant cohorts through sampling make error estimation more complicated in this case. Therefore, time. We tested for net directional selection between 1999 and 2013, as we empirically calculated the error in allele frequency estimation using well as between all adjacent years during that time period, by comparing simulations. observed allele frequency shifts to the distribution of expected allele fre- To assess the effect of heritable variation in reproductive success on quency shifts generated from the gene dropping simulations. For each test, allele frequency change, we performed simulations that permuted parental we calculated p values by counting the number of simulations in which the assignments within each birth cohort, effectively breaking any inheritance simulated value is more different from the median value of all of the sim- of reproductive success while keeping variation in family sizes consistent. We ulations compared with the observed value. We used an FDR threshold of then simulated genotypes for 10,000 loci on the randomized pedigree and 0.25 for significance. the observed pedigree and compared the variance in net allele frequency change in 1999–2013. See SI Appendix for the full derivation of the model Variance in Allele Frequencies Model. To quantify the proportion of variance and more details on our simulations. All statistical analyses were done in R in the change in allele frequencies due to gene flow and variation in individ- (38). All code is available from Figshare 10.6084/m9.figshare.7044368. ual survival and reproductive success, we modeled the population as follows: Adults who survive or immigrate into the population then produce off- ACKNOWLEDGMENTS. We thank the many students and staff who collected spring. From our detailed census and other population monitoring records, the field data at Archbold Biological Station over the past half century.

6 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1813852116 Chen et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 8 ueoaA,e l 21)Rdfxgnm sebyietfisgnmcregions genomic identifies assembly genome fox Red human (2018) a al. against et selection natural AV, neutralizes Kukekova curse 18. Mother’s (2017) the al. of et estimate E, An Milot (2015) 17. M Przeworski C, Ober a M, in Stephens cryptic D, are Waggoner pattern Z, coat Gao of microevolution 16. and Selection (2012) al. et forward. way J, The Gratten pedigrees: Wild 15. (2008) J Pemberton 14. of (1986) effect equivalents EA The Thompson Founder pedigrees: (2005) 13. in representation YS founder Aulchenko of Analysis CM, (1989) Duijn RC van Lacy Quebec B, 12. of Oostra I, contribution MacKay genetic LM, the Pardo of 11. Variability (1995) M Tremblay E, Heyer 10. 0 un S olednG,FtptikJ,WieB 19)MlilcsDAfin- DNA Multi-locus (1999) BN White JW, con- Fitzpatrick Genomic GE, (2016) Woolfenden AG JS, Clark Quinn JW, 20. Fitzpatrick R, Bowman EJ, Cosgrove N, Chen 19. a upre yNtoa cec onain(S)Gat DEB0855879 Grants work (NSF) This Foundation comments. helpful Science for Arvid for National reviewer Coopons, Buffalo by anonymous the Vince supported an to and was and go help Jensen, Thanks Jeff statistical randomization. Agren, for pedigree Edge on Doc discussions to go Thanks hne al. et Chen .OBinE ebrR od ,Rgr 19)Fudrefc:Assmn fvariation of Assessment and effect: Founder value (1994) A reproductive Rogers L, between Jorde R, relation Kerber E, The O’Brien (2011) 9. AM Etheridge value. NH, reproductive Fisher’s of Barton theory A 8. (2006) A Grafen 7. (2010) D Charlesworth B, Charlesworth computer 6. by (1930) R analysis Fisher Pedigree (1986) 5. population. 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EVOLUTION