vol. 155, no. 3 the american naturalit march 2000 The Evolution of Intrapecific Brood Paraitim in Bird and Inect Andrew G. Zink * Department of Ecology and Evolutionary Biology, Cornell Univerity, Ithaca, New York 14853 Submitted December 23, 1998; Accepted October 14, 1999 abtract: Many pecie of bird and inect engage in intrapecific brood paraitim (IBP), when a female lay egg in the net of a conpecific and leave without providing parental care. Thee viiting female may alo act to cooperate with a primary female, taying to provide parental care. Therefore, IBP and cooperative breeding can be conidered extreme on a continuum of parental care provided by a econdary female. When a econdary female abandon a net, he create an aymmetry in parental care between herelf and the hot. While model of aymmetry in reproductive allocation have focued directly on relatedne between female, we lack an appropriate theoretical framework that addree the effect of relatedne on parental care aymmetry. Here, I preent an evolutionarily table trategy (ESS) model that predict the condition under which IBP i favored over cooperation and olitary breeding. Intrapecific brood paraitim i le likely to evolve (relative to cooperation and olitary breeding) a the relatedne between a hot and paraite increae. It can evolve, however, if paraite achieve a high overall fecundity relative to olitary female. Contraint on olitary breeding can further promote IBP under ome circumtance. Cooperation i favored when relatedne i high and reproductive kew i low. Thi model make everal prediction regarding the condition under which IBP may evolve, motivating a variety of experimental approache. Keyword: intrapecific brood paraitim, relatedne, inect, bird, evolutionarily table trategy model. Intrapecific brood paraitim (IBP) occur when a female lay egg in the net of a conpecific and leave without providing parental care. Cliff wallow are known to lay egg in the net of conpecific (Brown 1984), a are American coot (Lyon 1993a, 1993b), with hot female utaining ubtantial cot through the reduction of clutch ize and offpring urvival. In waterfowl alone, there are * E-mail: raz4@cornell.edu. Am. Nat. 2000. Vol. 155, pp. 395 405. 2000 by The Univerity of Chicago. 0003-0147/2000/15503-0008$03.00. All right reerved. 28 pecie exhibiting facultative IBP (Eadie et. al. 1988), and over 20 pecie in which 120% of net are paraitized per population (Rohwer and Freeman 1989). Factor that may elect for IBP in bird include higher fecundity, limitation on neting ite, and reduced cot of parental care for paraitic female (Yom-Tov 1980). Some inect alo exhibit behavior that are very imilar to IBP in bird (Tallamy and Wood 1986; Brockmann 1993). Female lace bug (Tingidae) lay egg in the egg mae of other female, enjoying a higher overall fecundity and fitne relative to primary female (Tallamy and Horton 1990). In addition, many olitary wap and bee lay egg in the net of conpecific, reducing the cot of foraging and net contruction (Field 1992). In contrat to laying egg paraitically, econdary female of ome pecie can be found cooperating with the primary female, haring both reproduction and parental care. Many putatively olitary inect uch a membracid (Eberhard 1986), hield bug (Mappe et. al. 1995), and burying beetle (Eggert and Müller 1992; Scott 1994) can be found reproducing together under certain circumtance. In addition, about 3% of all bird pecie are conidered cooperative breeder, often with ome degree of reproductive aymmetry among female (Vehrencamp 1983; McRae 1996; Arnold and Owen 1998). Recent adaptation of Hamilton theory of incluive fitne (1964) have ued the idea of reproductive kew to make prediction about reproductive allocation among cooperatively breeding female (Vehrencamp 1983; Reeve and Ratniek 1993; Keller and Reeve 1994). Skew theory predict that a dominant female will increaingly monopolize a colony reproduction (high kew) with increaing relatedne between group member. A the relatedne between female decreae, under fixed ecological contraint, ubordinate are given a larger fraction of the reproduction a a taying incentive to remain in the net veru neting independently (Emlen 1982; Vehrencamp 1983; Reeve 1991). Thi prediction ha been upported by recent empirical work (Reeve and Keller 1995; McRae 1996; Reeve et. al. 1998), but deciive tet are till few in number. While reproductive allocation among cooperative
396 The American Naturalit Table 1: Decription of parameter ued in the model Parameter P R K X n v r Decription Number of egg laid by a primary female Number of egg laid in a primary net by a econdary cooperator Number of egg laid in a primary net by a econdary paraite Number of egg laid by a paraite in her olitary net Number of net paraitized by a econdary female Probability that a econdary female will uccefully etablih a net after paraitizing (0 v 1) Average urvival of a brood with two cooperating female divided by the average urvival of brood with a olitary female ( 1 1) Coefficient of genetic relatedne between primary and econdary female Cooperative breeding i favored when there i equitable reproduction (low kew) or when relatedne i high. Thi model generate tetable prediction regarding the condition under which we hould expect to ee the evolution of IBP and cooperative breeding. The Model Conider a econdary female that arrive at the net of a primary female during the hot egg-laying period. Thi female ha three ditinct option: lay egg in the primary female net and leave (paraitim), lay egg and remain at net (cooperation), or found a net of her own. I aume that primary net are already etablihed and are not a limiting reource. I alo aume that the behavior of primary female i fixed in that they remain at the net and do not eject paraite. Appendix A conider the ituation in which primary female control econdary female acce to net. breeder ha received much attention, aymmetry in parental care ha been given le theoretical treatment. Brood paraitim and cooperative breeding can be conidered extreme on a continuum of parental care provided by econdary female that viit a net. Jut a the degree of reproductive kew i determined by the relatedne among cooperating female, we hould expect incluive fitne to affect the degree of parental care provided by a econdary female. Yet we lack an appropriate theoretical framework for predicting how a potential brood paraite will behave a a function of her relatedne to a primary female. After a econdary female ha laid egg, what are the factor that influence her deciion to tay (cooperate) or to leave (paraitize)? One tudy by Emlen and Wrege (1986) found that paraitic female of the white-fronted bee-eater leave the net after paraitizing if they are unrelated to hot female but tay to help out if they are kin. Other reearcher have uggeted that kinhip may actually facilitate the evolution of IBP (Anderon and Erikon 1982; Anderon 1984; McRae and Burke 1996). Thi prediction aume that the cot of being paraitized are alleviated to ome extent when a hot hare many of her gene with the introduced egg. Here, I preent an evolutionarily table trategy (ESS) model of IBP that make prediction about how relatedne affect the evolution of IBP veru cooperation and olitary breeding. Specifically, the model predict that IBP will be le common a the relatedne between a hot and a paraite increae. Intrapecific brood paraitim will be more common, however, a the cot of olitary breeding increae or the fecundity of a potential paraite increae. Table 2: Payoff matrix for behavioral alternative Secondary female behavior Paraitim during Hot Egg Laying Many pecie of bird and inect are known to diplace a hot egg during a paraitic event. In American coot, 54% of paraitic egg are laid during the hot egg-laying period (Lyon 1993b), and hot repond by reducing their clutch ize (Lyon 1998). Female burying beetle that are paraitized rear the ame number of offpring a unparaitized female, thu raiing fewer of their own offpring (Müller et. al. 1990). Other bird and olitary Hymenoptera actually remove hot egg when laying paraitic one (Eickwort 1975; Brown 1984; Field 1992). In thi model I aume that a hot clutch i reduced by the exact number of paraitic egg that are laid in the net and that hot egg are not reduced when egg are laid by a cooperator. Female fitne i defined a the number of offpring reared to maturity. The variable ued in thi model are decribed in table 1. The parameter v repreent the de- creaed probability that a econdary female will uccefully etablih a net after paraitizing (a a reult of late breeding or inferior net ite). The parameter repreent the benefit for brood of cooperating female relative to Solitary breeding Paraitize Cooperate Secondary female fitne P nk vx R Primary female fitne P P K P
Intrapecific Brood Paraitim 397 brood of olitary female (a a reult of increaed protection, proviioning, etc.). Thee variable allow u to contruct fitne value for both the primary and econdary female under each behavioral trategy, a een in table 2. It i poible to et up the incluive fitne function for olitary breeding (W ), paraitim (W p ), and cooperation (W c ) in the form of Hamilton inequality (1964): W=P rnp, (1) W = (nk vx) rn(p K), (2) p W=R r[(n 1)P P]. (3) c Here, the firt term on the right-hand ide of each equation repreent peronal fitne, which i the payoff to econdary female that reult from each form of behavior. Thee term correpond with the firt row of the payoff matrix in table 2. The econd term in each equation repreent the kin component of incluive fitne, which i the peronal fitne for relative affected by the behavior multiplied by the number of relative involved (n) and the relatedne between female (r). Thee term correpond with the econd row of the payoff matrix in table 2. Specifically, r i the coefficient of genetic relatedne between primary and econdary female. For example, iter or mother-daughter would be related by 0.5, firt couin by 0.125, and o on. All three equation decribe the n kin that are affected by each behavior. Thi i why W and W c retain effect on unparaitized kin, which are poitively affected by the econdary female deciion not to paraitize them. It i important to note that equation (1) (3) do not allow for multiple paraitim, in that reident female enjoy an initial full clutch of ize P. It i poible, however, to adapt thee equation to incorporate more than one paraitim event per net. Thi i the ubject of appendix B, where I allow for multiple paraitim a well a unequal paraitim rate for paraitized and unparaitized net. It i now poible to examine the incluive fitne of each trategy relative to the other trategie. For example, what i the incluive fitne payoff for olitary neting veru paraitim? By etting up an inequality with (1) and (2), we can olve for r to get the following condition under which W 1 W : p P 1 vx (which mut be true for the olitary trategy to occur) and that nk 1 P vx (which mut be true for the paraitic trategy to occur). By taking the partial derivative of r with repect to each variable, under thee condition, it i clear that increaing X, K, v, or n caue paraitim to be more favorable. Increaing P, on the other hand, make paraitim le favorable relative to olitary breeding. The tranition from a paraitic to a olitary trategy can be een in figure 1. At the tranition value of r decribed in (4), the fitne value of W p and W are exactly equal, while value of r below or above the quantity expreed in (4) favor a ingle trategy. Thi i the cae for all of the remaining fitne inequalitie that are preented in thi article. Some reader may find it urpriing that increaed contraint on olitary breeding (lower v) will reduce para- itim. Indeed, previou hypothee of IBP have aumed that paraitic female are le ucceful at olitary breeding (Yom-Tov 1980). Thi hypothei eem to apply to ome pecie of bird uch a leer now geee (Lank et. al. 1989) and cavity neter (Eadie et. al. 1998). In thi model, however, I have aumed that a econdary female that chooe the olitary trategy will enjoy the ame ucce a a primary female (clutch ize of P a een in eq. [1]). It i poible to aume that the econdary female will encounter the ame difficultie while neting olitarily that he would encounter when neting a a paraite. Thi approach i jutified if econdary female are of lower quality, le experienced, or late in arriving to the breeding ite. In thi cae, equation (1) can be adapted o that the econdary female olitary clutch of P i multiplied by the probability of neting a a paraite ( v). Thi change equa- tion (4) uch that the value P i replaced by vp. We would then expect paraitim to increae a contraint on olitary neting increae ( v decreae), provided that P 1 X. Con- traint on olitary neting can therefore promote para- P vx r 1 1. (4) nk If the right ide of (4) i between 0 and 1, it mark the tranition from a paraitic trategy to a olitary trategy a relatedne between female increae. I aume that Figure 1: Fitne function howing the tranition from paraitim to olitary trategy with increaing relatedne between hot and potential paraite. Here, P = 10, K =6,n =1,X =5, = 1.2, R =5,and v =1.
398 The American Naturalit R and K to vary independently generate a three-dimenional verion of thi graph (fig. 4). It i clear that, for a given r, cooperation i more likely a R increae and K decreae. Thee relationhip generate tetable prediction about how a econdary female hould behave, againt the background of relatedne, after he ha laid egg in the net of a primary female. Next, what i the payoff for cooperation veru olitary neting? By etting up the inequality Wc 1 W and olving for r we get the following condition: Figure 2: Fitne function howing the tranition from the paraitic to the cooperative trategy with increaing relatedne between hot and potential paraite. Here, P = 10, K =6,n =2,X =8,R =7, = 2, and v = 0.8. itim in econdary female, while contraint on paraite neting can reduce paraitim. I will, however, retain the original form of (1) for the remainder of the model becaue it repreent a more conervative expreion for the evolution of IBP. By etting up the inequality Wc 1 Wp and olving for r, we get the following condition under which cooperation i favored over paraitim: nk vx R r 1. (5) nk P( 1) If the right hand of (5) i between 0 and 1, it mark the tranition from a paraitic trategy to a cooperative trategy a relatedne increae. I aume that vx nk 1 R (in order for paraitim to occur) and that P( 1) 1 vx R (in order for cooperation to occur). The partial derivative of (5) with repect to each variable reveal that, under thee condition, cooperation become more favorable a P and R increae. Paraitim i more favored a v, n, K, and X increae. Increaing will make cooperation more favorable if nk(p R) 1 P(R vx) or le favorable if the revere inequality i true. The tranition from paraitim to cooperation can be een in figure 2. We can ue equation (5) to make prediction about the threhold level of relatedne that i needed for a econdary female to remain at the net and cooperate veru leave (and paraitize). Conider the ituation in which a econdary female ha laid K egg in the net of a primary female and K equal R (the number of egg laid by a econdary cooperator). The threhold value of relatedne needed to keep the econdary female at the net i hown in figure 3, in which value of r above the curve predict that the econdary female will tay and cooperate. Allowing 1 (R/P) r 1. (6) ( 1) It i clear from (6) that cooperation i more favorable a relatedne between female increae. Here, I aume that P 1 R (otherwie cooperation i alway favored). Under thee condition, cooperation i more favorable a P decreae or R increae. Cooperation i alo more favorable a increae if P 1 R (which mut be the cae becaue we aume that P 1 R and 1 1). The value of r marking the tranition from olitary neting to cooperation (eq. [6]) i hown in figure 5. When cooperation occur, R/P i a ratio of the reproductive output of the econdary female relative to the primary female. Thi value of R/P can be viewed a a meaure of the reproductive kew. When reproductive kew i high (primary female lay the majority of the egg), P i much larger than R. When reproductive kew i low (each female lay a ignificant fraction of the egg), P i not a large relative to R. Equation (6) how that reproductive kew mut be low (R/P large) for cooperation to occur at low level of relatedne (r). Rearranging (6) and olving for Figure 3: Plot of the threhold value of relatedne (r) veru the number of egg that a econdary female ha laid in a primary female net. Here, R = K, n =1,X = 8, v = 0.8, = 1.5, and P = 10. Value of r above the curve predict that the econdary female will cooperate, while value below the curve predict that he will abandon the net (paraitize).
Intrapecific Brood Paraitim 399 nk vx P 1 (R/P) 0!!! 1. (8) nk ( 1) Under thee condition we might expect to find population exhibiting all three behavior, depending on the degree of relatedne between female. For a given average r among female in a population, there i alway a bet trategy (fig. 6), but a population may exhibit all three behavior depending on the particular degree of relatedne between a pair of interacting female. Paraitim after Hot Egg Laying Figure 4: Three-dimenional plot of relatedne veru R and K. The urface how the threhold value of r, above which a econdary female i expected to cooperate veru paraitize. Here, n =1,X = 8, v = 0.8, = 1.5, and P = 10. R/P reveal that increaing relatedne allow cooperation even with higher reproductive kew (maller R/P): R 1 r( 1) 1. (7) P Thi reult i conitent with the prediction of kew theory in that a econdary female hould tay to cooperate, even when reproductive kew i high, if he i highly related to the primary female (Reeve and Ratniek 1993). The value of R/P in (7) i analogou to the taying incentive of the traditional kew model, in which a dominant (primary) female give up jut enough reproduction to keep the ubordinate (econdary) female from leaving the net. In thi cae, we would expect the primary female to allow R to increae (or P to decreae) until the minimum value of R/P that atifie (7) i achieved. In each of the cae covered in thi model, an increae in relatedne among interacting female facilitate a tranition from paraitim to cooperation, paraitim to olitary breeding, or olitary breeding to cooperation. The form of the equation confirm that thee tranition are unidirectional, a the denominator of equation (4) (6) are alway poitive. Therefore, tranition of optimal trategie over reaonable value of relatedne can occur in a limited number of way: paraitim to olitary breeding (fig. 1), paraitim to cooperation (fig. 2), or olitary breeding to cooperation (fig. 5). The fourth poibility i that a combination of all of thee tranition will occur (fig. 6). A combination of (4) and (5) decribe the condition under which thi hould occur: In ome bird, paraitic female will lay egg after the primary female ha laid her clutch (Lyon 1993b). In addition, IBP in herbivorou inect doe not eem to affect the clutch ize of a hot (Eberhard 1986; Tallamy and Horton 1990). While each of thee cae allow the primary female to lay an entire clutch, they have the potential to reduce the urvival of the newly enlarged clutch by preading reource over a greater number of offpring. The fitne function of a paraite of thi type can be defined a W = nkq vx rnpq, (9) a where q equal the reduction in urvival becaue of brood expanion or P/(P K ). Egg laid by a paraite after the hot egg laying pread the reource for the original clutch (P) over the newly expanded clutch ( P K). Thi could repreent food proviioning for bird or parental care and defene in ubocial herbivore. It i then intereting to ee which of the two paraitic trategie yield a higher overall fitne. Comparing (2) and (9) reveal that Wp 1 Wa when Figure 5: Fitne function howing the tranition from the olitary to the cooperative trategy with increaing relatedne between hot and potential cooperator. Here, P = 12, R =7,K =6,n =1,X =8, = 1.5, and v = 0.5.
400 The American Naturalit Figure 6: Fitne function howing the tranition from paraitim to olitary to cooperative trategie with increaing relatedne between interacting female. Here, P = 17, K =6,n =2,X =8,R =7, = 1.8, and v = 0.8. K(1 q) 1 r[k P(1 q)]. (10) Subtituting P/(P K) for q give u 1 1 r, which i alway true, and therefore W p i alway greater than W a. We can combine (1) and (9) to get the condition under which W 1 W a: nkq vx P r 1. (11) np(1 q) Here, we mut aume that P np(1 q) 1 nkq vx 1 P for both olitary breeding and paraitim to occur. It i clear that an increae in r or P facilitate the tranition from W a to W. Taking the partial derivative of (11) with repect to each variable reveal that an increae v, n, K, or X ha the oppoite effect, making paraitim more likely. Paraitim i le likely a q decreae if nk vx 1 P, a condition that will alway be atified (auming that nkq vx 1 P and q! 1). Appendix C conider the pe- cial cae in which q 1. A comparion of (3) and (9) reveal the condition under which W 1 W : c a nkq vx R r 1. (12) P[n(1 q) ( 1)] Here, we can ee that an increae in r or P facilitate the tranition from W a to W c, while increaing K, v, or X ha the oppoite effect of making paraitim more likely. The partial derivative of (12) with repect to reveal that cooperation i more likely a increae if nkq vx 1 R[1 n(1 q)]. Paraitim i le likely a q decreae if vx K(n 1) 1 R. Increaing n will alway make paraitim more likely if R 1 vx. There i ome evidence that the urvivorhip of paraitic egg i inherently lower than the urvivorhip of hot egg. Studie of American coot have revealed that egg laid paraitically had one-fourth the urvival rate of egg laid in a paraite own net, a a reult of egg rejection and hatching failure (Lyon 1993a). Including differential urvival of hot and paraite egg doe not change the qualitative reult of the model. In both (4) and (5), the factor of nk in the numerator can be multiplied by u/o, where u i the intrinic rate of urvival for paraite egg and o i the intrinic rate of urvival for hot egg. For paraitic egg that are laid after the hot laying period, we can multiply the factor of nkq in (11) and (12) by u/o. In both cae u/o! 1 make paraitim le favored over olitary breeding or cooperation, a compared to u/o =1. Dicuion The model preented here make everal tetable prediction about the condition under which we can expect to ee the evolution of IBP, cooperation, or olitary breeding. Thee are ummarized a follow. Prediction 1 Intrapecific brood paraitim i more likely to occur in individual, population, or pecie that experience contraint on olitary breeding or when paraite are able to lay a large number of egg paraitically. Secondary female that have difficulty etablihing a olitary net or providing adequate parental care will be more likely to act paraitically. Thee female could arrive at a breeding eaon too late, have difficultie finding a uitable net ite, or have a net detroyed by predator (Yom-Tov 1980; Lyon 1993a). However, if econdary female only experience reduced neting ucce when adopting the paraitic trategy (ee eq. [2]), then a lower value of v will actually promote the olitary trategy. Female are alo more likely to act a paraite if they are able to lay a higher number of total egg through paraitim. Female membracid that lay egg paraitically do actually have more egg in their ovarie than their hot (Eberhard 1984). Studie of bird have revealed that paraite often lay more total egg than nonparaitic female becaue they can lay egg in other net in addition to neting olitarily (Lyon 1993a). For thee paraite, however, olitary neting uually occur after they have laid egg in the net of other female. For example, in American coot, 84% of paraitic egg were laid before a paraite initiated her own net (Lyon 1993b). Prediction 2 When there i IBP, female that paraitize hould be le related to their hot than cooperating or olitary female
Intrapecific Brood Paraitim 401 taken at random from the population. Thi reult ha been een in Emlen and Wrege tudy (1986), where brood paraite were le related to their hot than cooperating female. Thi prediction can be addreed with detailed field experiment coupled with phyical or genetic marker denoting relatedne. In many way, it i the mot intereting and unexpected prediction of the model, contradicting previou peculation that brood paraite will be more related to their hot than individual choen at random (Anderon and Erikon 1982; Anderon 1984; McRae and Burke 1996). Similar to the kew model prediction, the reult i omewhat counterintuitive but can be explained by the incluive fitne of the econdary female. Thi reult alo ugget that relatedne between parent and young directly influence parental invetment, imilar to the optimization model of Winkler (1987) and Wetneat and Sherman (1993). Prediction 3 Cooperative breeding i more likely to occur when econdary female ignificantly contribute to the reproductive output of the net (low kew) or when relatedne between female i high. A een in equation (5), contraint on olitary breeding can facilitate cooperative breeding. Indeed, if v i low enough, a hift from IBP to cooperative breeding depend on a large reproductive output of the econdary female (R) relative to the hot (P). A econdary female may abandon a net (paraitize) if he i unable to lay many egg but will tay if her output i cloer to that of the primary female. Primary female might then allow a econdary female to reproduce in order to entice her to remain at the net. Thi i analogou to the taying incentive decribed in model of reproductive kew. Equation (7) predict that a econdary female will chooe to cooperate, even when her reproductive contribution i low, if he i highly related to the primary female. Thi reult i imilar to kew theory model and experiment howing that reproductive kew increae with relatedne between dominant and ubordinate female (Reeve and Ratniek 1993; McRae 1996; Reeve et. al. 1998). Concluion Thee reult indicate that relatedne ha the potential to affect the evolution and occurrence of IBP. If thi i the cae, we might alo expect to ee the evolution of kin recognition in paraite and hot (Hamilton 1987). The evolution of egg recognition by hot would both increae the ucce of hot offpring and hinder the evolution of IBP (Yamauchi 1993). Further tet of the above prediction could be addreed with the technique of molecular genetic, allowing reearcher to etimate relatedne between hot and paraite (McRae and Burke 1996). In mixed brood, K, R, and P could be etimated with DNA marker or fingerprinting. It i my hope that the prediction of the model preented here will timulate further reearch into the effect of relatedne on the evolution of intrapecific brood paraitim. The main prediction of thi model, that IBP i le likely to evolve a the relatedne between hot and paraite increae, may eem counterintuitive to ome reader. The paradoxical nature of thi reult i reminicent of the prediction of kew theory, in which increaing relatedne between cooperating female reult in greater monopolization of reproduction by the dominant female (higher kew; Reeve and Ratniek 1993). Both approache highlight the uefulne of mathematical model for generating prediction that challenge common aumption. Future model of reproductive allocation that addre variation in parental invetment will continue to enhance our undertanding of the evolution of intrapecific brood paraitim and cooperative breeding. Acknowledgment I am grateful to D. Ardia, M. Geber, H. K. Reeve, M. Waon, and two anonymou reviewer for their inightful comment and uggetion. H. K. Reeve wa particularly helpful and encouraging during all tage of the manucript. J. M. Eadie provided excellent comment on a later draft. The author wa upported by a National Science Foundation graduate reearch fellowhip while working on thi manucript. APPENDIX A Primary Female Can Reject Secondary Female One aumption of thi model i that primary female are unable to repel a econdary female that attempt to paraitize or to cooperate. Here, I relax thi aumption and conider the condition under which a primary female would let a econdary female paraitize her or cooperate with her. Ability of Primary Female to Repel Paraitic Secondary Female The incluive fitne function for a primary female that invite (W i ) or reject (W r ) a econdary female that act a a paraite are a follow:
402 The American Naturalit W=(P K) r(nk vx), i W=P r[(n 1)K v(x K)]. r (A1) (A2) The firt term in the right-hand ide of (A1) and (A2) decribe the peronal component of a primary female incluive fitne, while the econd term decribe the kin component (r time the payoff for the econdary female). The term in (A1) are taken directly from table 2. The kin component of incluive fitne in (A2) aume that the econdary female can lay the K egg (that he doe not lay becaue of rejection) in her olitary net. By combining (A1) and (A2), we get the condition under which W 1 W : i r 1 r 1. (A3) 1 v When the initial aumption that v! 1 i retained, it i clear that under no circumtance will a primary female allow a econdary female to paraitize the net. The reult i the ame if we conider the cae in which the econdary female lay paraitic egg after the primary female ha laid her full clutch. Thi ugget that paraitim exit in nature becaue a reident i unable to defend the net. The widepread abence of defene mechanim in hot remain a mytery but could be explained by negative tradeoff (e.g., rejection of potential cooperator or le time pent foraging), evolutionary time lag, or phylogenetic contraint. primary female will alway invite a econdary cooperator). A cloer examination of (A6), by taking partial derivative with repect to r, reveal that the primary female i more likely to accept a cooperator a P decreae and a R increae. Cooperation i more likely a increae if P 1 R, which mut be true becaue P 1 R and 1 1 (thi i the ame condition found in eq. [6]). Surpriingly, under thee ame condition, a primary female i le likely to invite a econdary cooperator a r increae. Thi i becaue the kin component of her incluive fitne i greater when her kin net olitarily. Combining (6) and (A6) reveal the condition under which both a primary female accept a cooperating econdary female and a econdary female decide to remain and cooperate: 1 P R 1 r 1 m, where m =. (A7) m P( 1) If m! 1 then we hould expect cooperation (over olitary breeding) when equation (6) i atified. If, however, m 1 1and 1/m 1 r, we would expect to ee a primary female invite a econdary female into the net, with the econdary female chooing olitary neting intead (i.e., eq. [6] i not atified). APPENDIX B Ability of Primary Female to Repel Cooperating Secondary Female When doe a primary female decide to invite (W i ) or reject (W r ) a econdary cooperator? The incluive fitne function are a follow: W=P rr, i W=P rp. r (A4) (A5) Equation (A4) and (A5) can be ued to generate the following inequality decribing the condition under which Wi 1 W r: P( 1) r!. (A6) P R Here, it i aumed, a in (6), that P 1 R (otherwie the Multiple Paraitim in Hot Net Equation (1) (3) decribe primary female that have not yet experienced paraitim, in that they tart with a full clutch of ize P. It i poible to adapt thee equation to incorporate more than one paraitim event per net. For example, we can change (1) (3) o that the ize of every hot brood i reduced by an additional K with probability b. In thi cae, I aume that all net have the ame probability of being paraitized. We then get the following erie of equation: W=(P bk ) rn(p bk ), W = (nk vx) rn(p K bk ), p W=R r[(n 1)(P bk ) (P bk )]. c (B1) (B2) (B3) Setting up the inequality W 1 Wp and olving for r reult in the following condition:
Intrapecific Brood Paraitim 403 P vx bk r 1 1. (B4) nk If we compare (B4) with (4), it i clear that multiple paraitim make olitary breeding le favored a econdary female are experiencing paraitim in their own net. Allowing econdary female to remain unparaitized (by adding a value of bk to eq. [B1]) reult in the original inequality, identical to equation (4). Setting up the inequality Wc 1 Wp give u the following condition: nk Xv R r 1. (B5) nk P( 1) bk( 1) A comparion of (B5) and (5) reveal that multiple paraitim make cooperative breeding le favorable relative to paraitim. What if the probability of multiple paraitim i not the ame for all net? It i eay to imagine that paraite prefer to lay egg in unparaitized net, uch that paraitized net are le likely to get paraitized a econd time. Equation (B1) (B3) can be expanded to incorporate paraitim probabilitie that are unique to each type of net: W=(P bk) rn(p bk), W = (nk vx) rn(p K bk), p W=R r[(n 1)(P bk) (P bk)]. c c p (B6) (B7) (B8) Here, b i the probability that a olitary net will get paraitized, b p i the probability that a paraitized net will get paraitized, and b c i the probability that a cooperating net will get paraitized. Examining the inequality W 1 W p and olving for r reveal the following condition: P vx Kb r 1 1. (B9) Kn(1 bp b ) Comparing (B9) with (B4), we can ee that paraitim i more likely if b 1 bp. Setting up the inequality Wc 1 Wp reult in the following condition: nk Xv R r 1. (B10) P( 1) nk(1 bp b ) K(bc b ) Comparing (B10) with (B5), we can ee that paraitim i again more likely if b 1 bp. However, if b 1 bc then par- aitim i le likely. APPENDIX C Paraitim Ha Zero Cot (or I Beneficial) to Hot There may be ome intance in which enlarging a hot brood through paraitim ha no harmful effect on the urvival of the brood. For example, in ome precocial pecie, in which parental care i le important, the cot of paraitim may be negligible for the hot. Here, I aume that clutch ize i not reduced when paraitic egg are laid a there i no reaon for a reident to adjut the ize of a clutch. It i poible to adapt (11) under the condition q=1 to get the following expreion for W 1 W : P 1 nk vx. a (C1) In other word, the kin component of incluive fitne drop out entirely, and a female will behave uch that her fecundity (total egg number) i maximized. We can alo imagine a ituation in which paraitim increae the urvival of a net or a brood. There i ome evidence that lace bug laying paraitic egg on the edge of hot egg mae provide a buffer from predator that can increae the overall urvival of hot egg (Tallamy and Horton 1990). In ant-tended herbivore, larger group of nymph enjoy a higher level of protection from predator (McEvoy 1979). Thi ort of facilitation may occur in ome circumtance, and it change equation (11) to the following expreion for W 1 W, where q 1 1: a nkq vx P r!. (C2) np(1 q) In other word, we hould expect to ee econdary female prefer to paraitize the net of cloe relative. A r increae, we expect to find that paraitim i more likely relative to olitary breeding. I conider thi to be a pecial cae in which the augmentation of a brood will increae the overall urvival of that brood. Literature Cited Anderon, M. 1984. Brood paraitim within pecie. Page 195 228 in C. J. Barnard, ed. Producer and crounger: trategie of exploitation and paraitim. Croom Helm, London. Anderon, M., and M. O. G. Erikon. 1982. Net paraitim in goldeneye Bucephala clangula: ome evolutionary apect. American Naturalit 120:1 16. Arnold, K. E., and I. P. F. Owen. 1998. Cooperative breeding in bird: a comparative tet of the life hitory hy-
404 The American Naturalit pothei. Proceeding of the Royal Society of London B, Biological Science 265:739 745. Brockmann, H. J. 1993. Paraitizing conpecific: comparion between Hymenoptera and bird. Trend in Ecology & Evolution 8:2 4. Brown, C. R. 1984. Laying egg in a neighbor net: benefit and cot of colonial neting in wallow. Science (Wahington, D.C.) 224:518 519. Eadie, J. M., F. P. Kehoe, and T. D. Nudd. 1988. Prehatch and pot-hatch brood amalgamation in North American Anatidae: a review of hypothee. Canadian Journal of Zoology 66:1709 1721. Eadie, J. M., P. W. Sherman, and B. Semel. 1998. Conpecific brood paraitim, population dynamic, and the conervation of cavity-neting bird. Page 306 340 in T. Caro, ed. Behavioral ecology and conervation biology. Oxford Univerity Pre, Oxford. Eberhard, W. G. 1986. Poible mutualim between female of the ubocial membracid Polyglypta dipar (Homoptera). Behavioral Ecology and Sociobiology 19: 447 453. Eggert, A. K., and J. K. Müller. 1992. Joint breeding in female burying beetle. Behavioral Ecology and Sociobiology 31:237 242. Eickwort, G. C. 1975. Gregariou neting of the maon bee Hopliti anthocopoide and the evolution of paraitim and ociality among megachilid bee. Evolution 29:142 150. Emlen, S. T. 1982. The evolution of helping. II. The role of behavioral conflict. American Naturalit 119:40 53. Emlen, S. T., and P. H. Wrege. 1986. Forced copulation and intrapecific paraitim: two cot of ocial living in the white-fronted bee eater. Ethology 71:2 29. Field, J. 1992. Intrapecific paraitim a an alternative reproductive tactic in net-building wap and bee. Biological Review 67:79 126. Hamilton, W. D. 1964. The evolution of ocial behavior. Journal of Theoretical Biology 7:1 52.. 1987. Dicriminating nepotim: expectable, common, overlooked. Page 417 438 in D. J. C. Fletcher and C. D. Michener, ed. Kin recognition in animal. Wiley, Chicheter. Keller, L., and H. K. Reeve. 1994. Partitioning of reproduction in animal ocietie. Trend in Ecology & Evolution 9:98 102. Lank, D. B., E. G. Cooch, and R. F. Rockwell. 1989. Environmental and demographic correlate of intrapecific net paraitim in leer now geee Chen caerulecen caerulecen. Journal of Animal Ecology 58:29 45. Lyon, B. E. 1993a. Conpecific brood paraitim a a flexible reproductive tactic in American coot. Animal Behaviour 46:911 928.. 1993b. Tactic of paraitic American coot: hot choice and the pattern of egg diperion among hot net. Behavioral Ecology and Sociobiology 33:87 100.. 1998. Optimal clutch ize and conpecific brood paraitim. Nature (London) 392:380 383. Mappe, J., A. Kaitala, and R. V. Alatalo. 1995. Joint brood guarding in parent bug an experiment on defene againt predation. Behavioral Ecology and Sociobiology 36:343 347. McEvoy, P. B. 1979. Advantage and diadvantage to group living in treehopper (Homoptera: Membracidae). Micellaneou Publication of the Entomological Society of America 11:1 13. McRae, S. B. 1996. Family value: cot and benefit of communal neting in the moorhen. Animal Behaviour 52:225 245. McRae, S. B., and T. Burke. 1996. Intrapecific brood paraitim in the moorhen: parentage and paraite-hot relationhip determined by DNA fingerprinting. Behavioral Ecology and Sociobiology 38:115 129. Müller, J. K., A.-K. Eggert, and J. Dreel. 1990. Intrapecific brood paraitim in the burying beetle, Necrophoru vepilloide (Coleoptera: Silphidae). Animal Behaviour 40:491 499. Reeve, H. K. 1991. The ocial biology of Polite. Page 99 148 in K. Ro and R. Matthew, ed. The ocial biology of wap. Cornell Univerity Pre, Ithaca, N.Y. Reeve, H. K., and L. Keller. 1995. Partitioning of reproduction in mother-daughter veru ibling aociation: a tet of optimal kew theory. American Naturalit 145: 119 132. Reeve, H. K., and F. L. W. Ratniek. 1993. Queen-queen conflict in polygynou ocietie: mutual tolerance and reproductive kew. Page 45 85 in L. Keller, ed. Queen number and ociality in inect. Oxford Univerity Pre, Oxford. Reeve, H. K., S. T. Emlen, and L. Keller. 1998. Reproductive haring in animal ocietie: reproductive incentive or incomplete control by dominant breeder? Behavioral Ecology 9:267 278. Rohwer, F. C., and S. Freeman. 1989. The ditribution of conpecific net paraitim in bird. Canadian Journal of Zoology 67:239 253. Scott, M. P. 1994. Competition with flie promote communal breeding in the burying beetle, Nicrophoru tomentou. Behavioral Ecology and Sociobiology 34: 367 373 Tallamy, D. W., and L. A. Horton. 1990. Cot and benefit of the egg-dumping alternative in Gargaphia lace bug (Hemiptera: Tingidae). Animal Behaviour 39:352 359. Tallamy, D. W., and T. K. Wood. 1986. Convergence pattern in ubocial inect. Annual Review of Entomology 31:369 390.
Intrapecific Brood Paraitim 405 Vehrencamp, S. L. 1983. Optimal degree of kew in cooperative ocietie. American Zoologit 23:327 335. Wetneat, D. F., and P. W. Sherman. 1993. Parentage and the evolution of parental behavior. Behavioral Ecology 4:66 77. Winkler, D. W. 1987. A general model for parental care. American Naturalit 130:526 543. Yamauchi, A. 1993. Theory of intrapecific net paraitim in bird. Animal Behaviour 46:335 345. Yom-Tov, Y. 1980. Intrapecific net paraitim in bird. Biological Review 55:93 108. Aociate Editor: John A. Byer