The Origin and Evolution of Gamete Dimorphism and the Male-Female Phenomenon

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The origin and evolution of gamete dimorphism and the male-female phenomenon. J Theor Biol

ARTICLE in JOURNAL OF THEORETICAL BIOLOGY · OCTOBER 1972 Impact Factor: 2.3 · DOI: 10.1016/0022-5193(72)90007-0 · Source: PubMed

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Available from: Geoff A. Parker Retrieved on: 22 September 2015 J. theor. Biol. (1972) 36,529-553

G. A. PARKER Department of Zoology, Universitj of Liverpool, Liverpool L69 3BX, England

R. R. BAKER Department of Zoology, University of NewcastIe-upon-Tyne Newcastle NE1 7RU, England

AND V. G. F. SMITH Department of Biological Sciences, Ah& BeUo University, Zanb, Nigeria (Received 14 February 1972) The classical theory for the origin of anisoqamy is that the greate8t number of successful fusions occurs when the gametic material available for the population is divided with a high degas okanisogamy. This assumes that a fkd amount of reserve material is necesky for dmlopment of the zygote and that only disassortative fusions occur (i.e. between small and large &ametes). Assuming (as in previous literatunz) that a gjven gametic mass can be produced in unit time, then individual variations in gamete sizz may arise either from di&ences in the production th$e, or in the number of cell divisions at the time of production. where *te 6tness is in some way related to zygote volume’, relative rtproducti\ie rates can be calculated for a range of variants with dMerent gamete prQductivitie8 (and thcnfore difkent gamete sizm). This model yields eitherdrive for small-producing (where the advantage of high productivity qxeeds that of increased provisioning for the zygote) or drive for large4producing (in the reverse case). However in certain conditions (over park of the range of x where zygote fitness is proportional to volumet) a ,marked disruptive etlbct canbegcneratedinwhichthetwoex-~(largeandsmaugametc production) are favoured. Reasons are given why selection should always lead to the establishment of a stable dimorphism in multicell~ar organisms. When the model is mod&d to include inhexi of gamete siz by simple mcndclian dominance, it is shown that as theTit ‘tial range of variants is imead, the ran& of x (where fitness is prop&tional to volume9 which 530 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH generates stable dimorphism also increases. As high anisogamy is approached, the disadvantageous dominant homozygote is lost leaving two sexes (sperm producers and ovum producers) in a stable 1 : 1 ratio. Stages in the evolution of dissortative fusions are outlined. Though males with sperm which fused only with ova would be favoured throughout, females with assortatively-fusing ova may have been favoured initially. Because of a faster rate of adaptation in sperm than ova, or because of the instability of an isogametic population with assortatively- fusing ova, females face an evolutionary impasse in which the only stable solution is total committment to disassortative fusions. Males are dependent on females and propagate at their expense, rather as in a parasite-host relationship.

1. Introduction Why are gametes dimorphic and why are there two sexes? Though most multicellular organisms have a pronounced anisogamy, the origin of gamete dimorphism has attracted very little attention (see below). Isogamy is common in unicellular species, and hence sexual reproduction does not lead automatically to anisogamy. In multicellular forms, the provision of large amounts of cytoplasmic reserves in the ovum confers advantages on the zygote in its development to adulthood. Though females are now specialized to produce gametes with cytoplasmic reserves, this does not directly explain the origin of gamete dimorphism. Anisogamy may have evolved by disruptive selection from isogamy; or from a situation where a range of gamete sizes were found, but without an obvious isogametic peak. A third and perhaps less likely possibility is that true anisogamy was preceded by the production of gamete-like phage particles (Baker & Parker, in press). The theory presented in the present paper examines the origin of anisogamy by disruptive selection from isogamy or from a population with a range of gamete sizes. The classical theory for the origin of anisogamy dates back to Kalmus (1932), and has recently been examined more rigorously by Scudo (1967). The theory can be summarized as follows. Where there is a fixed amount of reserve material available in a population for gametogenesis, and where the united gametes require a certain quantity of reserve for development of the zygote, the greatest number of successful fusions occurs when the gametic material is divided with a high degree of anisogamy than with isogamy. This assumes that fusions occur only between the two gametic morphs; fusions between like gametes do not occur. However, though Kalmus’ ingenious theory indicates an important advantage associated with anisogamy once evolved (and specialized for fusions only between the two forms of gamete), it does not readily outline the origin and mechanism of evolution of the EVOLUTION OF GAMETE DIHORPHISM 531 system. A possible mechanism of evolution has been suggested by Kalmus & Smith (1960). They envisaged as one possibility a diploid population homo- xygous for gene a (which produces small gametes) in which a dominant gene A arises (producing large gametes). “These gametes which will carry A will thus provide the zygotes with more reserves and thus be advantageous; hence the gene A may be expected to spread through the population. This spread will, however, be checked by the dithculty of union between these large, relatively static gametes, so that the advantage will only remain while there are a sufficient number of small gametes also present. Hence this situation may be expected to lead to an equilibrium in which both dominant and recessive types persist, and most fertile unions are between large and small gametes.” An alternative theory for the origin and evolution of anisogamy is proposed in the present paper.

2. Selective Pressure Acting on#Gamete Size The selective forces determining the optimum sixes for the gametes of a species must be numerous and complex. However, in view of the apparently near universal adoption of dimorphic gamete systems by multicellular organisms it seems reasonable to search for an explanation in terms of the most obvious selective pressures. Two very fundamental pressures immediately appear obvious; both would be related to gamete size and would act in opposition. These are numerical producrioity (i.e. the number of gametes produced in unit time by a given parent) and z$gotefiitness (i.e. a measure of the probability that a zygote will survive to reach adulthood and reproduce, and in the shortest time). There would be a selective advantage in producing the maximum number of gametes, provided that this leads to an increase in the net reproductive rate of a given parent. Productivity would pro ably have the following sort of relationship with the size of gametes pro ! ,uced. Assuming the energy intake of all the adults in the population to be roughly similar, then over unit time the amount of material available for organization into gametes would also be roughly similar. The volume (V) of material available can be subdivided into virtually as many subunits as is possible without cutting down the nuclear material itself. Thus a fairly definite relationship can be predicted between productivity and gamete sir.e (= volume), varying in the series : V/l, V/2, V/3, V4 . . . etc. where the fraction expresses the gamete size and the denominator represents the productivity. Biochemical and energetic arguments can be levied against a perfectly precise relationship of this type; it is not felt that these would make it invalid as an approximation. 532 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH All other things being equal, the maximum selective advantages is to be gained by producing as many gametes as possible without reducing the nuclear material. This would assume that cytoplasmic inheritance is insignifi- cant relative to that conveyed by the chromosomes, so that smaller gametes provide an equal genetic contribution to the zygote as do larger ones. Where V/n approximates to the nuclear size plus the minimum possible cytoplasm, n would represent the most favourable productivity. However, a zygote produced from the fusion of two such gametes may not have high fitness for a multicellular organism. Over a certain range the ability of a zygote to survive, and the speed with which it reaches adulthood, will be increased by having a greater amount of cytoplasm. There would not necessarily be a total drive to produce n gametes if parents producing fewer but larger gametes experienced a compensating advantage because of the greater fitness of their offspring.

3. Sonrce of Variation in Gamete Size It is envisaged that variation in gamete size would arise in two main ways. Firstly, the time taken accumulating protoplasm before dividing it up into gametes may vary. This assumes that a fixed number of cell divisions occur to form the gametes, but that the interval between the production of separate batches varies. Functionally the same thing would occur where gametes, after formation, accumulate protoplasm for varying periods of time (proportional to their size at release). Both could yield continuous variation in gamete size; but the relationship between productivity in unit time and gamete size should remain as outlined in the previous section. A second source of variation, that of the number of cell divisions (d) used in dividing the available protoplasm, should lead to a rather more clearly defined series of variants. For a fixed time between the production of the batches of gametes, the productivity would vary as 2d, and hence the gamete size would vary as V/2d. In the first model, continuous variation is examined. The effects of variation in number of cell divisions is then investigated with the same type of model.

4. The Effects of Size-related Fitness of the Zygote on a Simple, Random-fusion Situation A simple model can be constructed to simulate a primitive, external fertilization system with random fusion where gametes are released into a liquid medium such as sea water. It is assumed that productivity is inherited EVOLUTION OF GAMETE DIMORPHISM 533 and that a range of variants occur (initially in e.qualnumbers) in the population. For simplicity, the model assumesthat all kuiants occur initially at the same frequency, and calculatesonly the relative reproductive rates over the first generation. The parental variants are termed A, B, C, etc. to J, and produce, say, 1,2,3, etc.to 10 gametesrespectively in unit time. If all gametes have an equal probability of fusion, and if fusion occurs in random pairs, then the relative probabilities of fusion of each:possiblepair of gametescan be assessedby direct multiplication, i.e. AA * 1 x 1, AB = 1 x 2 etc. The probabilities can be arranged in the form of a simple symmetrical matrix with A, B, C, etc. arranged along each axis. The model does not include any effect due to size-related mortality before fusion, or to the effect of gamete size and mortality on the probability of encounter and fusion, or to the effect of multiple encounters. Now suppose that fitness of the zygote is independent of the amount of cytoplasm that it contains. The relative net reproductive rates of variants A to J are then equal to the number of gametes each produces (see line U, Fig. 1). Where zygote size is selectively neutral, there would be strong directional selection favouring variants with the highest productivity.

0- ABCDEFGHIJ Fxo. 1. Reproductive rate8 relative to A of a se&s of variants with productivitica in unit timc:A=1,B=2,C=3etc.toJ=10.Forlhe~~gotcfitmssi9umelatedtoit8 volume; for line Y fitams is proportional to volume fv). Curves VP and Ys = fitncaa proportional to volume’ and volun+. 534 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH Instead, suppose that survivorship is directly proportional to the resultant size of the zygote. Zygote size can be estimated roughly as the sum of the sizes of the two fusing gametes. A further matrix (for zygote size) can be constructed which gives an index of the relative fitness of the various zygotes, assuming fitness to be proportional to zygote size. If the size of an A gamete = 1 unit, B would = 05 unit (V/2), c = 0.33 unit (V/3), and so on. Thus zygote AA would have a fitness proportional to 2 units, AB to I.5 units, etc. Relative reproductive rates of the variants, taking into account zygote fitness, can be calculated by multiplying corresponding values from the fusion probability matrix by those in the zygote fitness matrix. The total genetic contribution of each variant to the population after one generation can be determined by summating values, either horizontally or vertically, in the third matrix derived from the multiplication. The convention adopted here is to express these totals (which correspond to relative reproductive rates) as ratios where the variant A has a reproductive rate = 1. This is plotted in Fig. 1 as line V. Again there would be directional selection favouring increased productivity, but much less rigorously than when size is unimportant. For line V, survivorship was assumed purely arbitrarily to be proportional to zygote size. Size could be much more important than this. If zygote volume is weighted as relatively more advantageous by taking fitness as proportional to volume2 and volume3 (Fig. 1, curves V2 and V3), variants with the lowest productivity are favoured and there is a heavy disadvantage sustained by the intermediate variants. However, those with the highest productivity are less disadvantageous than the intermediates, as measured within the present model over the first generation. This disruptive effect is more noticeable in curve V2 than Y3. Though more advantageous than intermediates, the variant with the highest productivity can never exceed the reproductive rate of that with the lowest productivity. This is because it achieves its advantage by gaining the greatest probability of gamete fusion with the largest gametes, which have high fitness as zygotes. What happens if an optimum, rather than maximum sized zygote has the highest fitness? With the above model, the zygote sizes range from 2-O units (AA) to 0.2 units (JJ); the mean size (of all possible sizes from the table) being around 0.8 units. Curves in Fig. 2(a) were used to represent zygote fitness in relation to size, with peaks at O-8 units. (They are two arbitrarily selected distributions.) If values from curve C are used to represent fitness of the different sized zygotes, the relative reproductive rates of the variants would be as shown in curve C, Fig. 2(b). This suggests that there would be an evolutionary drive towards greater productivity; the disparity in fitness between variants is not great enough to counteract the advantage of the variants with higher productivity. If the advantage of size is intensified by EVOLUTION OF GAMETE DIhfORPHISM 535

Zygoteshe (b

01 AECDEFGHIJ FIQ. 2. (a) Curves C and D are two arbitrarily selqcted distributions for zygote size (= volume) in relation to zygote fitness. (b) Reproductive rates relative to A of a series of variants with productivities in unit time: A = 1, B = 2, C = 3, etc., to J = 10. Curve D = fitnessproportional to curve D [Fig. 2(a)]. CurvesC and C = fitnessproportional to curve C [Fig. 2(a)] and curve C?. squaring values from C in Fig. 2(a), the reproductive rates obtained [curve C2, Fig. 2(b)] are similar to those in Fig. 1 far V2, except that the lowest producer (A) in C2 is relatively very disadvantageous since the fitness of its zygotes is relatively lower. Curve C [Fig. 2(a)] is a wide distribution relative to the range of zygote sixes and curve D was selected by way of contrast. When values from curve D are used [curve b Fig. 2(b)], B gametes are especially advantageous (they form zygotes closest to the optimum fitness), but the smallest gametes also experience a small advantage. In summary, variants which have low productivity and which generally form zygotes which are bigger than optimum sustain a high disadvantage. If the optimum sized zygote has a relatively small advantage over the other sizes (which is not great enough to counteract the advantage of high productivity) then there would be directional seleotion for higher productivity. Where the optimum sized zygote has a relatively greater advantage over the 536 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH other sizes, variants which produce the gametes which after fusion most closely approach the optimum sized zygote will reproduce fastest though high producers also experience a (smaller) advantage. As such, the first model (i.e. used for Fig. 1) is essentially the same as the one where there is an optimum sized zygote if one assumes that the lowest producer generally forms zygotes closest to optimum size. Variant A in the second model (Fig. 2) would be selected out fairly fast anyhow, since its gametes are disadvantage- ously large and its productivity lowest.

5. Variance Arising Through the Number of Cell Divisions Perhaps the simplest range of variants in biological terms would be one in which the number of cell divisions (of the material available for gametes) formed the variable factor. This would give a range of productivities 1, 2, 4, 8, etc. In this case, there would be an equal but opposite range of gamete size, each variant’s gametes would be exactly twice as big as the next variant’s which differs by one further cell division. Reproductive rates calculated for variants A to J (varying from 1 to 512 productivity) are plotted in Fig. 3. If zygote fitness is proportional to size, then the variants with the highest productivity experience a relatively enormous advantage (curve v>. Where fitness approaches volume2 of the zygote, the distribution of net relative

ha. 3. Reproductive rates relative to A of a series of cell division variants with productivities in unit time: A = 1, B = 2, C = 4, etc. to J = 516. Curves V, V’ and Y8 = zygote fitnessproportional to volume,volume, and volume9. EVOLUTION OF GAMBTB DIMORPHISM 537 reproductive rates follows a parabola (curve Va) with variant J (the bight producer) experiencing the same reproductive rate as variant A (that having the largest gametes).Where zygote size is relatively more important, as for example when it is proportional to volume’ of the zygote(curve V3), then the variant with the largest gametes “wins” but intermediate variants are highly disadvantageous relative to those with the highest productivity, Thus variance arising through differences in the number of cell divisions at the time of gamete production could lead to rigorous disruptive selection for large and small gamete morphs. The important feature would appear to be the degree of disparity between the productivity of the smallest gamete producer and that of its closest competitors. Where this is small (as for example in the first model where productivity varies only by one between consecutive variants) the disruptive effect is only slight. Where disparity is relatively larger (as with the present model) then the disruptive effect can be very marked. In the first model, a marked disruptive effect can be generated by throwing in a high productivity variant widely different in productivity from its closestcompetitor. In summary, variance arising from either of the sourcesinitially considered could lead to a disruptive advantage in gamete sixesas measuredby genetic contribution over a single generation. The only prerequisites for this effect would (in very general terms) appear to be that zygote sizeis set at a fairly high premium so that fitness declines relatively lsteeplywith decreasingsize, and that the disparity in productivity of the variant with the smallestgametes and its closest competitors is high enough. These two features are related in that the greater the premium on zygote size,the greater the disparity in productivity necessaryto produce a similar disruptive effect. Where zygote sixe is relatively unimportant, a directional drive towards increased productivity might be expected. One aspect which has not been considered is the importance of the initial frequency of the variants, since this affects the probabilities of fusion. So far, all variants have been considered to be present in the population at the same frequency. This was chosen to simulate a random, non-selected situation. However, there would seemto be good grounds for claiming some sort of distribution for the frequencies of the variants in an initially isogametic population. A simple experiment was used to calculate the effects of altering the relative frequencies of the initial variants. $uppose there are just three “cell division” variants (A, B and C!) in the initihl population, with productivities 2, 4 and 8 respectively. If there is a normal distribution of variant frequencies, B will be most common and A and C lessso. Suppose that B is twice as common as A and C. A fusion probability matrix can be drawn up as before but assuming that there will be twice as many B gametes in the 538 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH system. The zygote fitness matrix is calculated as before, and the two tables multiplied to give the numbers of each type surviving to the next generation. Again, summation either horizontally or vertically gives the “genetic gain” of each variant, except that B’s gain is halved in order to assess the relative reproductive rates of a variant of each type. The peak of distribution can be shifted by assuming that A (or C) is twice as common as the other two variants. The results of this experiment are shown in Fig. 4(a, b, c). The three graphs refer to conditions where zygote fitness is proportional to volume, volume2 and volume3 respectively. Lines A, B and C refer in each case to the situation

@A / C l / ‘B

v .HC

I I , (b 1 A 6 C

V V*

FIG. 4. Reproductive rates relative to A of three cell division variants A, B and C. In curves A, B and C, the variants A, Band C respectively occur initially at twice the frequency of the other two variants. Broken curves indicate reproductive rates of A, B and C when the variants occur initially at equal frequencies. In (a) zygote fitness is proportional to volume; in (b) to volum@; and in (c) to volume3. where the population peak occurs at A, B, or C. These can be compared with the broken lines which give values for situations where all three variants have the same initial frequency. Lines B are virtually the same as the broken lines. When A is the most common variant, B and especially C experience a slight advantage relative to A by achieving relatively more fusions with the larger gametes. When C is the most common variant, it tends to fuse with other C gametes more frequently than before, and consequently experience a relative disadvantage. Larger differences from the broken lines can be generated by increasing the disparity in initial frequencies of the variants. Overall, it seems reasonable to claim that the original model is not invalidated because it does not include a distribution of variants. EVOLUTION OF GAMETE DIMORPHISM 539 6. Models Involviag Several SBccesske Genera- Though the models used so far do suggestthat disruptive selection may operate to favour gamete dimorphism under certain conditions, it remains to be shown that over u number qf generurionr intermediate variants die out leaving only the two gametic extremesin stable frequenciesin the population. A problem which immediately arises in any attempt to perform similar calculations over several generations is that of the primitive method of inheritance of gamete production, i.e. what sort of gametesare produced by a zygote resulting from the fusion of two gametes of different sixes?

(A) MODEL 1 One possible system for the inheritance of gametic size in the primitive situation may have been that the gamete sizeis determined by the genesthat the gamete itself contains after meiosis.Thus an AD zygote(formed from the fusion of A sizeand D sizegametes) would give rise to A and D gametesby meiosisfrom an AD cell. In conformity with the flrevious cell division models, the haploid A gamete would not divide further, but the haploid D gamete would divide a further three times, giving eight D gametes to each A gamete. As before, the total gametic massof A would equal that of D, but individual parents would be functionally hermaphroditic, not single sexed. A simple computation with inheritance of this type (starting with equal numbers of zygotesAA, AB, AC, AD, BB, . . . etc. to DD) shows that over a range of zygote fitness (proportional to vx), nes from the largest and smallest gamete-producing variants (A and d are maintained at stable frequencies in the population (Fig. 5); the intermediate variants are deleted. Where zygote fitness is less important than V”*, all variants other than

FIO. 5. F&w&a* stable galotype fkcqmciea in relatih to power x wkc zygote fitness is pmpmticmal to volume+ (V9. The model starts with f+u cell division genes A to D and jmductivlty is detamlncd by the gene carried by the lu@oid gamete. T.B. 35 540 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH homozygous DD are deleted; where fitness is more important than Vze4, only homozygous AA zygotes survive.

(B) MODEL 2 The above model, though theoretically feasible, does not seem relevant to many known mechanisms of gamete size determination. A far more useful model would involve size determination by simple dominance. Suppose that the genes determining productivity lie at a particular locus and that large- producing tends to be dominant over small-producing, or vice versa. An AB zygote, where dominance is of the first type (large dominant) might be expected to produce two gametes in unit time, both size A (exactly as would an AA zygote). However, one of its gametes, though size A, would carry the gene for productivity B. Zygote fitness is determined phenotypically (again as proportional to the sum of the sizes of the two fusing gametes to the power x) whereas the productivity of a given zygote is determined genetically. For simplicity only three genes for productivity (present as alleles) are considered in the model at any one time. For convenience the strictly in- correct convention is adopted whereby dominance is expressed as the first symbol of the zygote (e.g. AB) rather than using upper and lower case lettering (e.g. Aa). The model starts with equal frequencies of the six possible zygotes (AA, AB, AC, BB, BC, CC). Variance arises through the number of cell divisions and there are three genes for productivity (A, B, C; such that AA produces 2, BB produces 4 and CC produces 8 gametes). The result of the computation (over 200 generations) with A dominant over B and C, is that the only surviving zygote is CC where zygote fitness is proportional to less than V1’76; towards V I*” there is a sudden switch so that only CC survives. A similar situation occurs when C is dominant over A and B, but here the transition takes place between Y2”’ and V2’20. Though B genes are never favourable, the model fails to generate gamete dimorphism with A and C surviving together in a stable equilibrium. However, the situation is completely changed by increasing the range of difference between the productivities, in other words by increasing the range of variance in the initial population. If the model is started with genes A, C and E [productivities 2 (AA), 8 (CC), 32 (EE); total range one to five cell divisions] then whether A is dominant over C and E [Fig. 6(a)], or E dominant over A and C [Fig. 7(a)], quite a large range of relative zygote fitness yields stable frequencies of genes for A (large-producing) and E (small- producing). Outside the range of P which yields stable dimorphism, there is drive for small-producing (EE) where zygote size is relatively less important and drive for large-producing (AA) where zygote size is relatively more EVOLUTION OF GAMETE DIMORPHISM 541

Power x (from vx,

ho. 6. percantape 8tRbiC @notypefrcquencia in dation to powerx wherezygote fitness i8 prqmrtiod to volumZ (P). The model8tarta with three cell divisiongenes and the prodwtivity of the zygote is de&mined by simplemend&an dominance where gem8 for lar~gwoduclngare dominantover thosefor small-produding.@ominance scria = large : intemdate : small.)In (a) the threegenea for productkjty are A, C and E (productivities 2,8,32) and in (b) the genesare A, E, J (productivities2, 32,1032). important. A similar, but somewhat contracted, range of stable dimorphism is obtained where there are four cell division variants (A, B, C and 0). In both these models, it is important to note that the intermediate variants (determined by either genes C or B) are selectedout whatever the relation between volume and zygotefitness. These models, with a range of three, four, or five cell divisions indicate that dimorphic gametes could originate in the manner proposed and for a reasonable range of relative fitness provided that the anisogamy ratio (volume of the large gamete divided by that of the small gamete) exceeds between four to eight. What happens where the anisogamy ratio is much higher? A fourth computation involved three genes for productivity A, E and J [productivities 2 (AA), 32 (EE) and 1032(J.; total range one to ten cell divisions]. The results are shown in Figs 6(b) and 7(b). As may be expected, with a wider range the effectsnoted previously are exaggerated.From a model almost naive in its simplicity of assumptions(merely that gamete sizeis controlled by simple dominance, that there is a tide variance, that fusion is 542 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH

.s g! loo- 8 i?i J dcminant w JJ JA 50 - ,-~-:=8-9-*4-e-e -8-e-8-8==8==8=8 AA

-A,- L _ _ I 0 I I.5 2’0- 2.5 3.0 35 Power x (from !4

FIG. 7. Percentage stable genotype frequencies in relation to power x where zygote fitness is proportional to volumti (Vz). The model starts with three cell division genes and the productivity of the zygote is determined by simple mendelian dominance where genes for small-producing are dominant over those for largeproducing. (Dominance series = small : intermediate : large.) In (a) the three genes for productivity are A, C and E (pro- ductivities2,8,32) and in (b) the genesare A, E andJ (productivities2,32,1032).

random, and that zygote fitness is in some way related to zygote volume) it seems remarkable that the following effects are generated. (i) Genes for large- (A) and small-producing (J) stabilize at equilibria for a very wide range of relationship between V” and zygote fitness. Only a small part of the range is shown in Figs 6(b) and 7(b). Stable dimorphism is possible provided that zygote fitness is related to higher relative values than around V1*5. Genes for intermediate productivity are selected out whatever the range of V”. (ii) For much of the range, only two gamete-producing genotypes (two sexes) are common in the population. When genes for large-producing (A) are dominant, these two genotypes are JJ (sperm producers, i.e. males) and AJ (ovum producers, i.e. females). This resembles the common method of sex determination where males are XX and females XY. When genes for small- producing (.I) are dominant, the two genotypes are JA (males) and AA (females)-a comparable condition to one of the other most common forms EVOLUTION OF GAMETE DIMORPHISM 543 of sex determination where the male is XY and the female XX. The dominant homoxygote exists only at a very low frequency in both cases.Where A is dominant, AA is infrequent becauseof the extremely low probability of A-A fusions with a large preponderance of small gametes all carrying J. When J is dominant, J-Jfusions, though common, have a virtually negligible fitnessas zygotes (as do fusions with small A-carrying gametes) and hence do not survive to adulthood. (iii) For much of the range with either alternative for dominance, sperm and ovum producers (males and females) exist in a virtual 1 : 1 ratio. The interesting point is here that previous theories for the stabilization of the sex ratio in panmictic populations [see Fisher, 1930 (summarized by Hamilton, 1967); Kahnus & Smith, 19601have started with the assumptionsof anisogamy, disassortative fusions, and the existence of two sexes (males and females). The present model starts only with a range of gamete-sizeproduct- ion and one of the simplestpossible mechanismsfor its inheritance. It may be argued that the model is inappr+riate since it starts with the improbable equality of initial zygotefrequenci+. This criticism was tested by starting with a 10 : 1 ratio of genesfor intermediate production, so that the initial zygote frequencies were AA = A.! = JJ = 1; EJ = AE = 10; EE = 100. This resemblesan initially isogamete-producing population with a high variance. The stable frequencies of sperm and ovum producers were exactly the sameas in the previous model, though it takes more generations to achieve stability. Thus the disruptive effect noted (in the previous sections)over one generation could lead directly over several generations to the establishmentof stable primary sexual dimorphism (anisogamy, the male-female phenomenon, and a 1 : 1 sexratio) with the assumption only that gamete sizeis controlled by simple dominance. There are several more complicated methods by which gamete size might be inherited; these will not be discussedin detail in the present paper. One method which may be even simpler (or at any rate more primitive) than the one envisaged above could be where inheritance is by incomplete dominance. Dominance is usually considered to evolve (for a summary of present views see Sheppard, 1967) from a less rigorous mechanism. As far as the present model is concerned,individuals with incomplete dominance would fare badly in competition with those with complete don$nana since as heteroxygotes they would produce disadvantageous interme@ate sixed zygotes.As far .aS more complicated me&aGms go, it would seempossible to incorporate the two sexesinto one individual (hermaphroditism) where, for whatewr reasons, it is more advantageous than producing of separate sexes.It is anticipated, however, that when this is done, e total expenditure on sperm 544 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH should equal that on ova (see Fisher, 1930). The present model would therefore still appear valid. Two main questions would seem to remain. Firstly, with a limited range of variants, what leads to the appropriate conditions of zygote fitness (V”) for stable dimorphism? In other words, how is “range adjustment” effected? Secondly, what leads to the adoption of disassortative fusions rather than random fusion ?

7. Range Adjustment Leading to Disruptive Selection for Dimorphic Gametes So far, all that has been claimed from the models is that under certain conditions selection could favour extreme variants in an initial population which differs in the sizes of gametes it produces. Why should these conditions arise? In the present section it is argued that whatever the original condition of zygote fitness relative to zygote size, selection will ultimately result in the establishment of stable anisogamy with a unity ratio of each sex. The models have generated three types of effect-either total drive for increasing gamete size; total drive for decreasing gamete size; or a disruptive drive for a dimorphic gamete system. In no case has a stabilizing effect been detected which would act to favour an isogametic optimum. Consider zygote fitness in relation to size. It is inevitable that as size decreases, a stage will be reached where fitness ultimately falls off suddenly to

Max.

Min. Zygote size -+ Smollneso FIO. 8. The probabk relationship between zygote size and 5tnes.9 in a multicellular organism. Fitness declines very steeply with iwwingsmallnw,andbeyondacertain point zygotes become too small to survive. With increase in size, fitness gradually levels off, so that further increase in size does not yield any increase in fitness. There may even be a decrease in fitness as sin is increased (broken curve). At any point on the curve, the gradknt (Vx) expresses the relationship between zyeote volume* and zygote fitness. For high zygote sizes this approaches VO (or Pf for the broken curve), and for very small zygote sizes this approaches P at the point where increasing smallness becomes lethal. EVOLUTION OF GAMETE DIIiORPHISM 545 nil. This would presumably correspond to zygoteswith virtually no cytoplasm. Conversely there would be a part of the range where increasing size of the zygotedoes not lead to a very great increasein fitness. In fact, it seemslikely that at some point increasing size would become directly disadvantageous. The probable type of relationship between zygotesize and fitnessin Metazoa is plotted in Fig. 8. Supposethat the original population produces isogametes such that the xygotesformed lie within the range where the sizeof the zygote is relatively unimportant (curve 1, Fig. 9). Variants with the highest productivity (and hence smallestgametes) would be favoured and so there would be strong drive towards the production of smaller gametes (curve 2, Fig. 9). This would continue until the zygotesformed entered the range where their siaeis relatively very important. At this stage(curve 3, Fig 9) conditions are set for disruptive selection,and variants with the smallestgametes should be favoured in conjunction with those with the larger ones (curves 4 and 5, Fig. 9 show progressive stages). Suppose that the original population produces zygotesin the range where their size is very important in relation to their fitness (curve 1, Fig. lo), but that the variants for gamete sizeare such that those producing the smallest gametesare most disadvantageous. m this can happen is shown by the model used forlFig. 4(c). It occurswhen the disparity between variants is relatively small and the size of the zygote relatively important.] There would initially be directional selection favouring an increasein gamete sixe(curve 2, Fig. lo), but as the peak shifted towards larger gametes, those variants with the smallest gametes would begin to experiencean advantage.The reason for this could either be that the population shifted into a range where (because of the relatively lesser importance of zygote sire) a narrow range of variants was adequate to give the disruptive

Gametesize + Smallness Fho. 9. Stagea in the evolution of misogamous morphsstarting from aninirlal distribution of hogamete-producing variauts (awe 1). The * tea form zygote8 with fitness proportional to around Yo. ‘Ilxm is drive towards higher roductlvhy,with smallergamete3 (dietribution 2) and as 7iygot8 !liza becomca rclativol7 impomlt for fitacss dhuptiva ~beliartoopaatstofavour~b~tofkrgp~~-~~~morphrina stabla tiequency (ultimately 1 : 1). Distribution 3.4 ssbowprogl-aTaivc~intb8 cstawt of sperm praduccra and stabilization f the ovum prodwcm &modal dllwhtions).-~illtbe~ofspalm zoli cndistribution6)wouldoaW later80 tbatspann-epumhrrionsmaybecomclcthal. 546 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH

Gamete size + Smallness FIG. 10. Stages in the evolution of anisogamous morphs starting from an initial distribution of isogameteproducing variants (curve 1). The isogametes produce zygotes such that their size is very important in relation to fitness, but the range of variance is not adequate to yield disruptive selection for anisogamy. There is at &-st a drive for increased gamete size (curve 2) but this increases the range of variants and allows disruptive selection to occur. The ultimate result is the establishment of stable 1 : 1 frequencies of large- and small-producing morphs @nmdal distribution 3). Further decrease in the size of sperm (broken distribution 4) would occur later so that sperm-sperm fusions may become lethal. effect; or that as the peak shifted this allowed the existing variants with the smallest gametes to experience an advantage, because of their increased disparity. The end result (curve 3, Fig. 10) should stabilize as before with two gamete morphs, one large and one small. Thus whatever the condition of the original population of multicellular organisms, the only stable solution as a result of natural selection appears to be one in which two strongly different gamete size morphs coexist in the population. All calculations used in the models have assumed a rather precise relationship between zygote fitness and volume. This seems improbable where the range of difference of gamete size is very high. It is not a prerequisite of the model that the relationship is as precise as this suggests. A lethal homozygous mutant for small-producing (SS) could spread throughout an isogametic population (ZZ) so long as the fitness of the heterozygote (Z5’)is high enough and the productivity of S’S high enough. This would merely represent an extreme case of the model used for Figs 6(b) and 7(b), where the disadvantageous homozygote is selected against very rigorously.

8. Factors Detemhing the Sizes of the Gamete Morphs It is clear that rather different selective pressures will operate to determine the two gamete sizes. As far as the sperm producers are concerned, selection should favour the maximum number of fusions with the larger gametes. Thus one might predict a total drive towards smallness (and hence greater productivity), the only modification being due to survivorship before fwion. This situation is signified by the broken curves and the arrows in Figs 9 and EVOLUTION OF GAMETE DIMORPHISM 547 10. Maximum fusions would be achieved where the gamete size is such that the productivity multiplied by chances of survival to fusion yield the maximum value. Since there will be few large gametes relative to many small gametes, virtually all of the large gametes may be fused in a fairly short time. Hence selection may favour increasing productivity of the small gametes at high cost in terms of survival, provided that this strategy yields a competitive advantage via initial numerical predominance. It would be expected that the maximum fusions would be achieved by variants having close to the maximum possible productivity, i.e. those releasing virtual “nuclear gametes”. This would be a fair description of the sperm of most animals. For the larger gamete, selection should again favour the size which when fused yields the maximum number of surviving offspring in unit time. If the situation has arisen where large gametes fuse only with small ones (see page 549), the maximum relative net reproductive rate (RR,,3 is achieved when P,i x C( V,i + Vs)f = RR,,,. The optimum productivity of large gametes is represented by P,,,, and (I’,,,+ V,)f the optimum zygote fitness where V,, and V, represent the sizes of the large and the small gametes and power f converts this value for zygote size into an appropriate measure of its relative fitness. C is a positive constant. Thus the optimum size for the larger gamete (V,J is presumably very close to the optimum zygote size (V,, + Vh since the contribution of cytoplasm from the small gamete (V,) will generally be negligible. This description seems compatible with the situation found in the ova of most animals.

9. The Evolution of Disassortative Fusion and Secondary Dimorpbisms Once a difference in reproductive rates is obtainable from a random fusion system, it is likely that selection for non-random fusions would begin to operate. The model suggests that the smaller gametes obtain their advantage by virtue of their fusions with the largest gametes. Because of the relative disadvantage of fusions between two small gametes, sperm producers would be favoured if their sperm fused selectively with large gametes. The zygote fitness in the latter case would be much higher at no extra expense to the sperm producers. Selection would, however, also favour ovum producers whose ova fused selectively with other ova (assortative fusions), since this would yield either fitter zygotes or allow the parental variants an increased productivity for the same zygote fitness. Thus a conflicting situation might be predicted since the favoured variants would produce sperm which fused disassortatively and ova which fused assortatively. How could the present system of disassortative fusion have arisen? 548 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH Selection would act to favour genes in the phenotypes (males or females which yielded maximum propagation of the gamete type that the phenotype carries, irrespective of the gene for productivity that the gamete itself carries. Thus it now seems reasonable to discuss selection on males or females towards establishment of further genetic mechanisms for increasing the propagation rate of their gametes, though the gametes of one sex may differ in their genes for productivity but not in their phenotype. Though sperm-sperm fusions would be highly disadvantageous to sperm producers, ovum-sperm fusions may not be so disadvantageous to the ovum producers-depending on the relationship between size and fitness around the range of ovum size. Moreover, it can be argued that males would have a higher potential rate of adaptation towards disassortative fusions than females could achieve in avoiding them, and toward adopting assortative fusions. The argument can be summarized as follows. The potential source of variation and mutation is proportional to the number of germ cells and therefore differs in the two sexes. An equal number of sperm and ova fuse and so normally the rate of adaptation in the two sexes should be comparable because excess sperm are extraneous to the system. However, sperm mutants which were able to fuse discriminately with gametes that later have high fitness as zygotes would be favoured. This is normally difficult to envisage since the chances that later fitness of the zygote is linked with any recognizable features of a gamete are probably not high. However, gamete size would appear to be a drastic exception to this pre- diction. Gamete size would be a recognizable feature which conveys informa- tion about future fitness. Where sperm are in a competitive situation for fusion with ova, it seems reasonable to argue that sperm producers have more available mutants for sperm-ovum fusions than the ovum producers have to avoid and prevent this. The result might be a greater rate of incorpora- tion of advantageous sperm mutants, in this particular case. These effects (possible stronger selection, more potential variance and competition of sperm for the fertilization of ova) would give a much higher rate of adaptation in sperm than in ova. Thus any move towards assortative fusions on the part of the ovum producers would be quickly offset by counter adaptations in the sperm. Supposing that assortatively fusing ova “won” the adaptive race temporarily, then any sperm producing mutant able to counter the assortative adaptation would quickly drive throughout the population to coexist equally with ovum producers once again. Even if assortatively fusing ova “won” completely with the extinction of the existing sperm producers, the system would not be stable since for the reasons already outlined an isogamete producing population ultimately faces disruptive selection for gamete dimorphism. Once sperm were extinct, the selective advantage in maintaining an anti-sperm selectivity would be lost. It is, however, not necessary to lose EVOLUTION OF GAMETE DIMORPHISM 549 anti-sperm selectivity to allow a return to dimorphic drive since the next sperm producers would evolve by gamete size reduction of one of the existing ovum producers. The only possible way a population would prevent dimorphic drive would be by constant maintenance of a faster rate of counter adaptation to renewed sperm drives-this seems rather against the odds in view of a predictably higher rate of adaptation in sperm than in ova. Ovum producers are forced into an evolutionary impasse--they must adopt the gamete size which gives the maximum reproductive rate as the product of productivity and zygote fitness (see page 547), and since most of their fusion will be with sperm the ovum size must be maintained accordingly large. The relationship between sperm and ova is not dissimilar from the relationship between parasite and host-the parasitic sperm (producers) dependent upon and propagating at the expense of the host ovum (producers). Once this step has occurred, a further stage might be predicted which further commits ova to disassortative fusions with sperm. It is assumed that the initial isogametes would have been motile; this would be necessary to ensure encounter and fusion. Selection would operate differently in a system of dimorphic gametes. Because of the numerical predominance of sperm and selection favouring their fusing disassortatively with ova, ovum producers could afford to lose the motility of their gametes without affecting the time taken to achieve a fusion. This would allow them a greater productivity for the same gamete size and fitness. For sperm producers, however, increased motility would be highly favourable since it would yield gametes which would fare better in competition with other sperm by virtue of increased encounter and ovum penetration possibilities. Thus when ovum-ovum encounters became very rare (a further reason why selection may be less strong against disassortatively fusing ova) and the possible advantage in ovum-ovum fusions relatively small, the optimum strategy for ovum producers may lie in total commitment to disassortative fusions. An overall reduction in biochemical machinery (and a consequent gain in productivity) should result from the loss of ability to fuse with other ova and the specialization towards sperm-ovum fusions. The end point in the evolutionary pathway would seem to be specialixa- tions towards total commitment to disassortative fusions. Many of the adaptations of sperm (e.g. involving vigorous motility and hyaluronidase secretion by the acrosome) can be interpreted in terms of sperm competition (between the sperm of several parental variants) at the ovum cell wall itself. One consequence of obligatory cross fusion would be that many sperm would not fuse since the ova would be vastly outnumbered by the sperm. Recently, Cohen (1969) has proposed that the reason why so many sperm are apparently “wasted” is because only a minute proportion of them may be 550 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH competent and able to effect fertilization. Since sperm producers would be in competition for the limited number of ova, a greater productivity of sperm would, in an external fertilization system (and also often with internal fertilization, Parker, 1970) increase the number of fusions with ova. Sperm excess may not reflect inadequacies at fertilization; rather it may represent an adaptation towards maximization of reproductive success in response to competition between sperm producers for the fertilization of ova.

10. The Sex Ratio Model 2 for inheritance (see page 540) yielded a virtual unity sex ratio without any form of disassortative fusion. It is not envisaged that selection for disassortative fusion would alter this condition. In the model with J dominant over A and E (small dominant) JJ fusions would not occur with disassortative fusion. Though with random fusion they would be the com- monest type of fusion, JJ individuals are selected against because of their low fitness [see Fig. 7(b)] and are therefore unimportant. Disassortative fusion would leave many more sperm in competition for the ova (produced by AA individuals). Sperm producers are JA zygotes which produce A- and J- carrying sperm in equal quantities. These would fuse only with large gametes (all A) and so the sex ratio would here be exactly unity. (AA and JA would have exactly the same fitness as zygotes.) In the model, ovum-ovum fusions occur very infrequently, because of the vast preponderance of sperm and not because of disassortative fusions. Thus to a certain extent the fact that the model yields a unity sex ratio is a reflection of the mechanism of inheritance chosen. It seems likely that were it favourable for individuals to produce a preponderance of one or other sex in their offspring, other mechanisms may be available by which this may be achieved. We believe that the reason why the sex ratio remains stable at around unity is explained for panmictic populations by Fisher’s principle (Fisher, 1930; for an excellent summary see Hamilton, 1967) rather than for the reasons outlined by Kalmus & Smith (1960) which argues from the point of the maximum propagation rate of the population, not that of the individual. Hamilton (1967) has put forward some interesting suggestions as to why some species show modified sex ratios.

11. Sexual Selection and the Evolution of Separate Reproductive Strategies ia the Two Sexes The situation where one sex invests very considerably less than the other in its zygotes (i.e. males less than famales) is one which would lead to fierce intra-sexual competition between the low-investing sex for the limiting EVOLUTION OF GAMETE DIMORPHISM 551 Origin and early evolution of life and sexual reproduction (see Baker & Parker, in press) I t Unicellular eucaryotes Procaryotes

Evolution of .gametes Increased gametic reserves unfavourable t Isogamy I\ i Multicellular Increased gametic reserves eucaryotes - favourable for enhanced zygote fitness f Drive for largeness of gametes, or less likely smallness, thereby increasing the range of variance, t As appropriate range of relationship between zygote fitness and zygote volume is approached, onset of disruptive selection for anisogamy t Stable frequencies of morphs; stabilizing selection for optimum Increasing ovum size but drive for smallness selection on part of sperm producers for disassortative 4 t fusions Two sexes established (sperm producers and ovum producers-males and females); dominant homozygote disappears as anisogamy ratio increases

High anisogamy ratio approached; total commitment to disassortative fusion; adoption of stable 1 : 1 sex ratio 1for the two sexual morphs t Sexual selection and the evolution of separate reproductive strategies for the two sexes 552 G. A. PARKER, R. R. BAKER AND V. G. F. SMITH resource provided by the high-investing sex. Attention has recently been drawn (Trivers, 1972) to the initial disparity of “parental investment” arising through disparity in gamete size, and its importance in precipitating intra- sexual competition (sexual selection) between males. Once sexual selection begins to operate one might predict the optimization of reproductive strategy in males towards achieving the maximum fertilization rate.

12. Unicellular Organisms Though most multicellular organisms have pronounced anisogamy, unicellular organisms are usually isogametic but may produce anisogametes. Increased investment in the form of extra gametic reserves is likely to be very much more favourable on the part of a multicellular parent. Zygote fitness here depends on the speed and survival chances of building up to a much larger and more complex organism. It will be remembered that with Model 2 for inheritance, even with a pronounced anisogamy ratio of 516, zygote fitness must be somewhat more important than proportional to V’, otherwise smallness is favoured. It is much less obvious why increased investment on the part of a unicellular organism would lead to a large increase in zygote fitness. In fact the usual case is that fusion is either solely nuclear or it is followed by reduction in size, rather than the reverse. For organisms where zygote fitness can never approach V’ or more, it might be expected that there would be drive towards gamete smallness. Since in a sense the unicellular organism is a “gametic adult”, then what might be expected is that the stable condition is the smallest possible which, bounded mainly by survivorship before fusion yields the maximum number of surviving zygotes. A re- examination of gamete production in unicellular organisms along these lines might be fruitful.

13. Summary of Predicted Evolutionary Trends The chart outlines the main evolutionary trends envisaged for the origin and evolution of the two sexes. Some of the earlier stages in the evolution of sexual reproduction are considered separately (Baker & Parker, in press). Hermaphroditism has probably evolved several times independently from the primitive situation of two separate sexes. The authors would like to thank Professor A. J. Cain, J. S. Bradley, and Dr B. Charlesworth for their criticisms of the manuscript. We are also indebted to Miss S. Scott who typed it.

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