Effects of genomic homozygosity on total fitness in an invertebrate: lethal equivalent estimates for Drosophila melanogaster

doi:10.21203/rs.3.rs-2118841/v1

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Effects of genomic homozygosity on total fitness in an invertebrate: lethal equivalent estimates for Drosophila melanogaster

https://doi.org/10.21203/rs.3.rs-2118841/v1

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published 29 Dec, 2022

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Estimates of susceptibility to inbreeding depression for total fitness are needed for predicting the cost of inbreeding and for use in population viability analyses, but no such valid estimates are available for any wild invertebrate population. I estimated the number of lethals equivalents for total fitness in recently wild-caught populations of Drosophila melanogaster using published data on the total fitness of homozygosity versus heterozygosity for each of the major chromosomes (the X, second, and third) under competitive conditions. As there are no data for the fitness effects of homozygosity for the small fourth chromosome which represents 1.0% of the euchromatic genome, this was accounted for by attributing the homozygosity for the three large chromosome to an inbreeding coefficient of 0.99 when computing lethal equivalents for total fitness. Total genomic homozygosity is predicted to be essentially lethal in D. melanogaster. The corresponding haploid lethal equivalents estimate for total fitness was 5.4. The lethal equivalent value lies within the range for vertebrates but tends to be higher than for most outbreeding plants which are often purged as they exhibit up to 20% selfing (by definition). As D. melanogaster has its genome sequenced and annotated and has lethal equivalent estimates for total fitness for individual chromosomes as well as its total genome, it provides an excellent opportunity for evaluating genomic estimates of mutation load.

Drosophila melanogaster

Genomic homozygosity

Inbreeding depression

Invertebrates

Lethal equivalents

Mutation load

Inbreeding reduces fitness in essentially all outbreeding species of animals and plants investigated, but nearly all the data are for fitness components, rather than total fitness (Darwin 1876; Wright 1977; Lynch and Walsh 1998; Crnokrak and Roff 1999; Keller and Waller 2002; Frankham et al. 2017). However, information on susceptibility of species to inbreeding depression for total fitness is crucial information for:

modelling the fate of species in population viability analyses (PVAs) (O’Grady et al. 2006; Lacy and Pollak 2014)
predicting the impacts of inbreeding depression on fitness for devising rules of thumb or evaluating proposed changes to the Convention on Biodiversity (Frankham et al. 2014; Frankham 2022)
assessing the importance of genetic factors in conservation biology (Frankham 2005; O’Grady et al. 2006)
evaluating the validity of estimates of mutational load from genomic analyses (Ralls et al. 2020; Kardos et al. 2021; Bertorelle et al. 2022).

Estimates of inbreeding depression needs to be for total fitness in wild or simulated wild conditions in natural populations to be relevant for PVAs or other modelling for species in the wild.

The usual quantitative measure of susceptibility to inbreeding depression is lethal equivalents (Morton et al. 1956). This is the number of completely lethal alleles required to account for the observed inbreeding depression i.e. “a lethal equivalent is a group of mutant genes that, if dispersed in different individuals, they would cause on average one death, e.g. one lethal mutant, two mutants each with 50% probability of causing death, etc.” The Morton et al. (1956) model is as follows (couched in terms of the probability of survival [S] of individuals with an inbreeding coefficient of F):

$${\text{S}}_{F}= {\text{e}}^{-A-BF}$$

Where e^− A is the survival in a non-inbred random mating population (F = 0), and B is haploid lethal equivalents, a measure of the hidden genetic damage that would be expressed fully only in a complete homozygote (F = 1). Inherent in this method is that the impacts of loci combine multiplicatively. This expression can be linearized by taking natural logarithms (ln), yielding:

$$ln S = - A – BF$$

This leads to the usual means of estimating B from the regression of natural logarithm of survival on the inbreeding coefficient. If the multiplicative assumption is upheld the regression of lnS on F is predicted to be a linear decrease with slope of B (Morton et al. 1956). While the original estimates were couched in term of survival, the same approach can be used with relative fitness of inbred versus outbred individuals (W_I/W_O) (O’Grady et al. 2006; Frankham et al. 2017), as follows:

$${W}_{I}/{W}_{O}= {e}^{-BF}$$

Taking natural logarithms and rearranging yields an alternative method for estimating B (O’Grady et al. 2006):

$$B = - ln \left(\frac{{W}_{I}}{{W}_{O}}\right)/F$$

This method can not only be used for genomes, but also for individual chromosomes as I shall describe below.

The multiplicative assumption was checked by Latter and Robertson (1962) for populations from the same base population of Drosophila melanogaster fruit flies with inbreeding coefficients between 0 and 0.89. They found an excellent fit to the expectations, with no data points being more than one standard error from the predicted value and quadratic and cubic terms for departure from linear regression on the logarithmic scale non-significant. Others have reported deviations in either direction from multiplicative combinations (often not significant), (Charlesworth and Charlesworth 1987; Seager and Ayala 1982; Seager et al. 1982; Charlesworth and Charlesworth 2010). However, the Latter and Robertson (1962) work is most appropriate here as it is not the separate interactions of every locus or individual chromosome sample that matters, but that the average interactions of groups of loci or samples of chromosomes behave multiplicatively.

There are very few estimates of lethal equivalents for total fitness in the wild (Frankham et al. 2017) and no valid estimates for any wild invertebrate population, despite invertebrates comprising ~ 72% of all eukaryotes and 95–97% of all animal species (Chapman 2009), with 23% currently classified as threatened (IUCN 2022). Two studies have claimed to provide estimates of lethal equivalents for D. melanogaster in wild or competitive conditions, but there are defects in both. Enders and Nunney (2012) reported lethal equivalent estimates for D. melanogaster in the wild of 0.45 and 1.20 by comparing the wild fitness of inbred and outbred populations. However, they are not valid as they ignored the effects of extinctions during the development of their inbred lines (see Latter and Robertson 1962; Brown and Kelly 2020) meaning that the mutation load could be 10–20 times higher than their estimates (Rumball et al. 1994; Frankham 1995; Reed et al. 2003).

The nearest relevant estimate is that from Latter and Robertson (1962), who used a single generation competitive index of near total fitness. They estimated that their old laboratory strain (~ 160 generations in a laboratory cage with an N_e of 185–253; Briscoe et al. 1992) contained 2.67 lethal equivalents (though they did not identify the parameter by this name). However, this is likely to be considerably less than expected for a wild population as their cage population had much reduced genetic variation compared to new wild strains (Briscoe et al 1992) and mutation load declines due to drift in finite populations (Crow and Kimura 1970; Frankham et al. 2014, Figures S1 and S2; Kardos et al 2021). Further, Latter and Robertson’s (1962) single generation fitness assessment method yields lower estimates of inbreeding depression than the Sved and Ayala (1970) multigenerational one described below, likely due to age-dependent fitness components that do not contribute in single generation experiments (Latter and Sved 1994). Thus, the Latter and Robertson (1962) value for lethal equivalents is expected to be an underestimate. Further, the fitness estimation method used by Latter and Robertson (1962) combines fitness components in a less than ideal manner (Sved 1989). However, their estimate sets a lower limit on lethal equivalent estimates in D. melanogaster.

Fortunately, it is possible to obtain an estimate of lethal equivalents for total fitness in D. melanogaster fruit flies from published information on total fitness of chromosomal homozygotes versus heterozygotes. D. melanogaster has only four pairs of chromosomes and most of the genome resides in the three larger pairs (Fig. 1) and there are published estimates for the total fitness effects of homozygosity for the three major chromosomes. The method I will describe combines data on the effects of homozygosity for total fitness of X, second and third chromosomes and accounts for the fourth chromosome for which there is no such data via a reduction in the inbreeding coefficient by the proportion of the euchromatic genome it represents.

The objectives of this work were to obtain an estimate of lethal equivalents for total fitness for recently wild caught populations of D. melanogaster and to compare it with estimates from other species. This is provided in the context of conservation biology as a crisis discipline where decision often must be made urgently in the face of limited information (Soulè 1985), i.e. to fill an important information gap.

How might lethal equivalents in D. melanogaster differ from that in other species? There are several issues with some reducing and others increasing the mutation load compared to other species, as follows:

The large sex chromosome (X ~ 20% of genome) leads to the expectation of a lower mutational load compared to many other outbreeding animals with smaller sex chromosomes (other things being equal), as selection in haploid males reduces mutational load compared to that in diploid autosomes (Turelli and Begun 1997; Avery 1984). In mammals the X chromosome typically only represents ~ 5% of the genome (Schaffner 2004), while some other species lack differentiated sex chromosomes.
D. melanogaster has low recombination with only four pairs of chromosomes and no recombination in males, indicating that linked selection will be more prominent than in most species with higher chromosome numbers (Charlesworth and Jensen 2021). In many cases linked selection will reduce genetic diversity due to background selection (Charlesworth et al. 1993; Charlesworth 2013) and selective sweeps (Maynard Smith and Haigh 1974; Stephan 2019), but in some cases associative overdominance slows loss of genetic diversity under inbreeding (Rumball et al. 1994; Latter 1998; Charlesworth and Jensen 2021). However, this latter effect does not apply to chromosomes made homozygous instantaneously using marked balancer chromosomes as in the present context.
The high effective populations size (N_e) in D. melanogaster (~ 1.5–2.5 million: Lange et al. 2021) leads to the expectation of a higher mutation load than in the many other species with lower N_e, especially those of conservation concern (Crow and Kimura 1970; Frankham et al. 2014; Kardos et al. 2021).

My simple expectations are that lethal equivalent estimates for total fitness will be similar for chromosomes 2 and 3 due to their similar sizes, but the effects on the X will be much less. Relative chromosome sizes are used in these computations as they are used to determine the relevant inbreeding coefficients. The relative euchromatic chromosomal sizes are expected to be the best guide to expected mutation loads, since the vast majority of functional DNA is in the euchromatin (Weiler and Wakimoto 1995), and it is functional DNA that will mutate to the harmful alleles that cause inbreeding depression or where the loci subject to balancing selection that also contribute will be found.

The method to estimate the total fitness of chromosomal homozygotes in Drosophila species was devised by Sved and Ayala (1970). The key features of the methods used to make chromosomes homozygous are illustrated for chromosome 2 in D. melanogaster in Fig. 2.

Multiple chromosomal homozygote lines are obtained, and the total fitness of each chromosomal homozygote genotype assessed individually in populations set up with Cy/+ and +/+ individuals and run over multiple generations. Fitness is assessed by following the frequency of Cy/+ flies, with low fitness chromosomes yielding an equilibrium with both the Cy and the + chromosomes present. Conversely, populations with high fitness wild type chromosomes lose the Cy chromosome (note that Cy/Cy is lethal). Data from these assessments are used to estimate the total fitness of +/+ homozygotes relative to Cy/+.

To allow determination of homozygous chromosomal fitness relative to heterozygous fitness, a second set of populations is set up, each containing multiple different wild-type chromosomes (termed chromosomal heterozygotes in the literature but actually representative of chromosomes in random mating outbred populations). From these, the fitness of chromosomal heterozygotes is estimated relative to Cy/+ flies. This is then used to convert the above chromosomal homozygote fitnesses to ones relative to wild-type chromosomal heterozygotes. This method yields a measure of relative fitness that encompasses all relevant component of fitness (total fitness) under competitive conditions.

Similar principles apply to determining the total fitness of chromosomal homozygotes for chromosome 3 and the X chromosome, except that different marked balancer chromosomes are used. Readers are referred to Sved and Ayala (1970), Sved (1975), and Wilton and Sved (1979) for further details.

I have used all relevant data on chromosomal homozygote fitnesses of wild D. melanogaster populations that I could find. The flies used by Sved (1971, 1975) and Wilton and Sved (1979) were from Australia, while those used by Tracey and Ayala (1974) and Mackay (1985) came from the western USA. I did not include data from the study by Seager et al. (1982), as their sampling of non-lethal chromosomal homozygotes on which they estimated total fitness was seriously biased.

A few total fitness estimates were negative, but I did not set them to zero as that would have risked upwardly biasing the fitness estimates. Environmental conditions were similar in the fitness assays done by the different authors, with temperatures of 23 or 25 C, typical laboratory culture media, and overlapping generations in cages except for Mackay (1985) who used discrete generations in multiple culture bottles (but her results were not outliers). Critically, the chromosomal homozygotes and chromosomal heterozygotes in each study were compared under the same conditions.

I treated the different estimates as ”replicates” to reflect the mutation load in the species, and as the results from the different studies were similar. Further, global D. melanogaster populations are connected despite quarantine restrictions as the species has spread around the world from its African origins (Clark et al. 2007), and an identical P450 allele associated with insecticide resistance alleles has spread throughout the world (Daborn et al. 2002).

From these data I obtained mean, median and weighted mean total relative fitnesses for each of the major chromosomes. The weighting was the product of the number of wild chromosomes sampled and the number of homozygous chromosomes whose total fitness was estimated. It made little difference which of the median/means I used, so I concentrate on the weighted means in what follows. The effects of genomic “homozygosity“ on total fitness were obtained as the product of the fitness effects of the X, 2nd, and 3rd chromosomes.

Estimates of lethal equivalents were obtained for X, 2nd and 3rd chromosomes as well as for the “total” genome by inserting the weighted mean total fitness values into Eq. 4. The F values were based on the euchromatic sizes of the four chromosomes as a proportion of the total genome, with the chromosomal homozygotes having an inbreeding coefficient of 1.0 for this proportion, and an inbreeding coefficient of 0 for the remainder of the genome. The euchromatic arms have DNA contents of 21.9 (X), 22.2 (2L [long arm]), 20.3 (2R [right arm]), 23.4 (3L), 27.9 (3R) and 1.2 (4) Mb (Celniker and Rubin 2003). Further, the gene densities of the different chromosomal arms are similar in D. melanogaster (Celniker and Rubin 2003). Thus, the X represents 18.7% of the genome, chromosome 2 36.4%, chromosome 3 43.9% and chromosome 4 1.0%.

Data on the effects of chromosomal homozygosity on relative total fitness for chromosomes X, 2 and 3 in D. melanogaster compared to relative total fitness of chromosomal heterozygotes are shown in Table 1, along with lethal equivalent estimates. To capture the full effects of inbreeding depression both the lethal and sterile and non-lethal non-sterile chromosomes must be included, so the estimates of “genomic” homozygosity and lethal equivalents are based on “Relative fitness of homozygotes/heterozygotes: all chromosomes” in column 7 of Table 1. Chromosomal homozygotes for every one of the 34 sampled X chromosome, 100 2nd chromosomes, and 149 3rd chromosomes had a total fitnesses less than the mean of the corresponding chromosomal heterozygotes, confirming that inbreeding depression is ubiquitous for X, 2nd, and 3rd chromosomes in this outbreeding species.

The lethal equivalent estimate for total fitness for the X chromosomes (2.7) was less than half those for chromosomes 2 and 3 (6.5 and 6.0, respectively), in the direction expected from theory. Note that these individual chromosome values are extrapolated to the whole genome, so they are not additive.

The combined effect of genomic homozygosity for the three major chromosomes was obtained as the products of the effects of chromosomal homozygosity relative to chromosomal heterozygosity for X, 2nd and 3rd chromosomes as follows:

Relative fitness of genomic homozygotes for X, 2 and 3 = 0.599 x 0.092 x 0.086

= 4.739 x 10³

Thus, near total genomic homozygosity is expected to be essentially lethal.

As the effects of homozygosity for the small fourth chromosome is not included, I attributed this to an inbreeding coefficient of one minus the proportion of the genome that the fourth chromosome represents. As Celniker and Rubin (2003) reported that the euchromatic chromosome 4 was 1.0% of the total euchromatin, I attributed the genomic homozygosity for chromosomes X, 2 and 3 to an inbreeding coefficient of 0.99 and estimated lethal equivalents (B) using Eq. 4, as follows:

B = - ln (W_I/W_O)/F = - ln (4.739 x 10^− 3)/0.99 = 5.41

If only data on Australian populations were use, the estimate of lethal equivalents was 6.0. If the data on the Australian X chromosome was used with data for the autosomes from the US populations, the estimate of lethal equivalents was 5.6 not materially different. I favour the weighted mean estimate of 5.4 as it is based on all data, takes account of sample size of the different estimates, and is more likely to be representative of the species.

Table 1

Effects of chromosomal homozygosity on relative total fitness for chromosomes X, 2 and 3 in *D. melanogaster* compared to relative total fitness of chromosomal heterozygotes. The relative fitnesses for lethal and sterile free chromosomes is shown, along with the lethal plus sterile frequencies, the sample sizes for lethal tests and for fitness tests, the weighting factors, the relative fitnesses for all chromosomes, and lethal equivalent estimates.
Chromosome	Relative fitness of homozygotes/heterozygotes: non-lethal, non-sterile chromosomes	Frequency of lethal plus sterile chromosomes	n_l^a	n_f^b	n_w^c	Relative fitness of homozygotes/heterozygotes: all chromosomes^d	Lethal equivalents (B)	References
X	0.600 ± 0.030	0.19%^e	-	34	-	0.599 ± 0.030	2.74	Wilton and Sved (1979); ^eLewontin (1974)
2	0.140 ± 0.038	20.0%	~ 50	24	1200	0.112 ± 0.032	6.01	Sved (1971)
2	0.112 ± 0.050	36%	50	23	1150	0.072 ± 0.043	7.24	Tracey and Ayala (1974)
2 median						0.092
2 mean						0.092
2 weighted mean			100	47	2350	0.092	6.54
3	0.103 ± 0.039	63.16%	38	14	532	0.038 ± 0.016	7.46	Sved (1975)
3	0.318 ± 0.037	60%	50	14	700	0.127 ± 0.034	4.70	Tracey and Ayala (1974)
3	0.127 ± 0.016	32.8%	61	41	2501	0.085 ± 0.013	5.61	Mackay (1985)
3 median						0.085
3 mean						0.083
3 weighted mean			149	69	3733	0.086	5.59
Genomic “homozygosity” weighted means (all data)						4.739 x 10^− 3	5.41
Genomic “homozygosity”: Sved and colleagues (Australian data)						2.549 x 10^− 3	6.03

^a Total number of chromosomes sampled.

^b Number of homozygous non-lethal, non-sterile chromosomes that had their fitness measured.

^c Weighting factors used to estimate weighted means (n_l x n_f). Using the square root of this number for weighting yielded very similar results.

^d Data used to estimate total fitness impacts of genomic “homozygosity” and lethal equivalents for the species.

^e Wilton and Sved (1979) sampled adult males and consequently could not detect sex-linked lethals, so information reported by Lewontin (1974) on the median level of sex-linked lethals over 27 populations from across the world was used.

There were three major finding of this study. First, the X chromosome contained a mutation load for total fitness of less than one-half that on the two large autosomes per unit length of the euchromatic genome, the first such comparative estimate of which I am aware. Second, nearly complete genomic homozygosity is essentially completely lethal in D. melanogaster. Third, recently caught wild populations of D. melanogaster under competitive conditions contained 5.4 haploid lethal equivalents for total fitness.

The lower estimates of lethal equivalents for the X chromosome than for the large autosomes is expected because of the much greater efficiency of selection in removing recessive and partially recessive harmful alleles in the haploid X in males than in diploid autosomal chromosomes. In part, the difference is due to the much lower frequency of sex-linked recessive lethals than autosomal recessive lethals, as expected from theory (Table 1). My conclusion is different from that of Wilton and Sved (1979), but they relied on the fitness of lethal and sterile free chromosomes, while the total fitness effect of all chromosomes is appropriate. My finding is concordant with the finding that haplodiploids exhibit substantially less inbreeding depression than do diploid insect species (Henter 2003). To my knowledge this is the first time that lethal equivalent estimates for total fitness have been reported for individual chromosomes.

My estimate that genomic “homozygotes” of D. melanogaster had near zero total fitness agrees with assertion by Charlesworth and Charlesworth (2010, p.13) that ”a Drosophila individual that is homozygous at all loci effectively has zero fitness.” However, that assertion was made without any computations being reported and no explicit references given, although it was in the context of discussion of the reduced total fitness of chromosomal homozygotes, including the work of Sved and colleagues.

The extremely low fitness of genomic homozygotes is also consistent with the extinction rates in populations inbred by full-sib mating for ~ 18 generations or more in lines from recently caught wild populations of D. melanogaster (F ≥ 0.979). For example, Reed et al. (2003) reported that all 120 full-sib mating lines were extinct by generation 26. Further, Rumball et al. (1994) found that 77% of 120 full-sib lines were extinct by generation 18, despite three pair mating of each line being set up each generation. In these studies there were 26 and 18 generations for purging to occur. Additionally, Brown and Kelly (2020) reported that Mimulus guttatus plants resulting from six generation of self-fertilization (expected F = 0.984) had only 3–5% the total fitness of outbred competitors: in this case, there were six opportunities for natural selection to purge harmful alleles. Their population had a selfing rate of 10% leading to the expectation of a lower mutation load than expected in a random mating species with two sexes and no selfing (such as Drosophila). However, their estimate did not include the effects on progeny of having inbred versus outbred mothers.

My estimate of lethal equivalents for the D. melanogaster species is credible as:

It is greater than the estimate of 2.67 from Latter and Robertson (1962) as expected from their experiment having been done on an old laboratory strain with low genetic diversity and them using a method that underestimated total fitness effects
It lies within the range of lethal equivalent estimate of 3.2 to 18.7 for vertebrates (median 7.5), but is higher than the plant median of 3.5, (Frankham et al. 2017), but given the small number of estimates, the differences are not significant. The trend for median lethal equivalents to be lower for plants than vertebrates or D. melanogaster probably reflects the definition of an outbreeding plant species as having between zero and 20% selfing (Jarne and Auld 2006), such that many will experience more purging than random mating species.

What biases are there in my estimate of lethal equivalents for D. melanogaster? While the total life history is encompassed in the fitness estimates, there is a bias due to the effects on progeny of having an inbred mother versus a non-inbred one not being fully accounted for. For example, in a random mating population containing Cy/+ and +/+ individuals, such maternal inbreeding only affects the +/+ progeny from +/+ mothers, but not +/+ progeny from Cy/+ mothers. This maternal inbreeding effect on progeny is not accounted for in about half of the available estimates of lethal equivalents for total fitness (Frankham et al. 2017). There is possibly a minor bias in the opposite direction, as correcting for the lack of fitness estimates for chromosome 4 homozygotes via an inbreeding coefficient of 0.99 assumes that the mutation load on chromosome 4 euchromatin is similar to the average load for X, 2, and 3 per proportion of the euchromatic genome. However, chromosome 4 is known to have low genetic diversity compared to other autosomes (Frankham 2012), and lower gene density (Leung et al. 2015), so it probably has a lower mutation load per percentage of the euchromatic genome than they do. However, chromosome 4 is so small that any such effect is miniscule. Further, the concept of inbreeding coefficient as the probability of identity by descent (Malécot 1969) does not distinguish between regions of the genome and the original formulation dealt with pedigrees. Since these biases are in opposite directions, and there is no relevant information to correct for them, I do not consider them further.

My estimate of lethal equivalents for total fitness for D. melanogaster assumes multiplicative fitness interactions, but this assumption underlies the whole lethal equivalents concept. Further, the typical regression and point estimates typically come from very narrow ranges of inbreeding levels. For example, estimates are often based primarily on total fitness data of individuals with inbreeding coefficients of zero to 0.25 in animals, and one is even as low as zero to F = 0.125 (Frankham et al. 2017 Table 3.2), yet the B value is an extrapolation to F = 1. In my case, the individual X, 2 and 3 chromosome loci are all subject to F = 1 and compared with non-inbreds (F = 0), thus involving no extrapolation. It is only in combining the chromosomal fitnesses that the multiplicative assumption is involved. Notably, the potential for purging is essentially eliminated in my estimate.

How far can my results be extrapolated to other invertebrates? I expect that the values of genomic homozygosity for fitness and lethal equivalents will be relatively similar in other Drosophila species, as total fitness of autosomal chromosomal homozygotes in D. pseudoobscura (chromosome 2: 5.0 lethal equivalents; Sved and Ayala 1970), D. willistoni (chromosome 2: 4.4 lethal equivalents; Mourão et al. 1972) are of similar order to those reported for D. melanogaster chromosomes in Table 1. However, there are expected to be differences in genomic lethal equivalents related to different relative sizes of X chromosomes, as in some species the X constitutes ~ 20% of the genome and in others ~ 40% of the genome (due to fusion of an autosomal arm to the X) and an approximately two-fold difference in the euchromatic sizes of the chromosomes (Turelli and Begun 1997; Schaeffer et al. 2008). The species with larger euchromatic X chromosomes are expected to have lower mutation loads, but I am unaware of this issue being raised in conservation and evolutionary genetic considerations.

Extrapolation to other Diptera may also be possible. Extensive karyotype work has shown that Diptera have six conserved (syntenic) regions, often referred to as Muller elements A-F which suggest conservation of gene groupings and linkage (Morelli et al. 2022). As shown for D. melanogaster in Fig. 1, five of these are of similar sizes (A = X, B = 2L, C = 2R, D = 3L and E = 3R), and only the F element (the dot fourth chromosomes) is smaller (Gramates et al. 2022). The A-E elements have similar sizes in mitotic chromosomes (Fig. 1), in euchromatic arms in polytene salivary gland chromosomes, and the euchromatic arms have fairly similar DNA in D. melanogaster (Celniker and Rubin 2003).

These six elements are highly conserved genomically in many Dipteran species (Sved et al. 2016). Overall, no new chromosome arms have been created for perhaps a billion generations over the Drosophila and tephritid fruit fly evolutionary lines. This stability at the chromosome level, which appears to extend to all Diptera including mosquitoes, is in stark contrast to other groups such as mammals, birds, fish, and plants, in which chromosome numbers and organization vary enormously among species that have diverged over many fewer generations (Sved et al. 2016). On this basis, I would as a first approximation extend the expectation of similar mutation loads to Diptera with large population sizes akin to those in D. melanogaster. However, other variables may lead to higher or lower levels in specific species, due to factors including population size bottlenecks, active mobile genetic elements and different sized sex chromosomes.

Several methods have been devised to predict mutation loads from genomic data, including GERP, SIFT, and Provean (Bertorelle et al. 2022; Sandell and Sharp 2022). Unfortunately, estimates of mutation load from these are being used quite widely with limited or inappropriate testing of their validity (reviewed by Kyriazis et al. 2022), yielding suspect conclusion (Ralls et al. 2020; Kardos et al. 2021). Since inbreeding depression is greater for total fitness than for its individual components (Frankham et al. 2017), modelling must use mutation load date for total fitness to accurately predict evolutionary outcomes and guide genetic management. Similarly, calibration of genomic estimates must be based on total fitness effects. Field estimates of haploid lethal equivalents for total fitness in vertebrates have a median of 7.5 (Frankham et al. 2017), while Kyraizis et al. (2022) describe calibrations of 1.55 for mammals (based on data for a single fitness component, juvenile survival in captivity), 2.25 for wild vertebrates (based on data for survival to sexual maturity) and their best models assumed lethal equivalents of 3.15. Given that D. melanogaster and several other members of the genus have reference genomes and have been annotated (Misra et al. 2002; Clark et al. 2007), and there are estimates of lethal equivalents for total fitness for chromosomes X, 2 and 3 and the total genome, D. melanogaster offers excellent opportunities to test genomic estimates of mutation load against direct estimates of mutation load for total fitness.

In conclusion, I estimated that genomic homozygotes in D. melanogaster are essentially lethal, and that the species carries 5.4 haploid lethal equivalents of mutation load. Additional estimates of lethal equivalents for total fitness in invertebrates are sorely needed.

Acknowledgements

This work would not have been possible without the pioneering work of John Sved, Francisco Ayala, the late Alan Wilton, Trudy Mackay and their colleagues on estimation of total fitness effects of chromosomal homozygosity. I am grateful to Mark Eldridge and John Sved for helpful comments on the manuscript.

Author contributions I conceived the ideas, prepared the Table based on my computations and wrote the paper.

Funding The author declares that no funds, grants, or other support were received during the preparation of this manuscript.

Data availability I conceived the ideas, prepared the Table based on computations using published data and wrote the paper. All associated data are published or included in the paper.

Conflict of interest The author has no relevant financial or non-financial interest to disclose.

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Effects of genomic homozygosity on total fitness in an invertebrate: lethal equivalent estimates for Drosophila melanogaster

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