- Email: [email protected]
Models of Infanticide: A reply to Hausfater
Short Communications Chapman, M. & Hausfater, G. 1979. The reproductive consequencesof infanticide in langurs: a mathematical model. Behav. Ecol. Sociobiol., 5, 227~40. Glass, G., Holt, R. & Slade, N. 1985. Infanticide as an evolutionarily stable strategy. Anim. Behav., 33, 384391. Hausfater, G. 1984. Infanticide in langurs: strategies, counterstrategiesand parameter values. In: Infanticide: Comparative and Evolutionary Perspectives (Ed. by G. Hausfater & S. Hrdy), pp. 257~82. New York: Aldine/ DeGruyter. Hausfater, G., Aref, S. & Cairns, S. 1982. Infanticide as an alternative male reproductive strategy in langurs: a mathematical model. J. theor. Biol., 94, 391412. Hausfater, G. & Hrdy, S. (Eds) 1984. Infanticide: Comparative and Evolutionary Perspectives. New York: Aldine/DeGruyter. Levins, R. 1966. The strategy of model-building in population biology. Am. Scient., $4, 421431. Vogel, C. &Loch, H. 1984. Reproductive parameters, adult-male replacements, and infanticide among freeranging langurs (Presbytis entellus) at Jodhpur (Rajasthan), India. In: Infanticide: Comparative and Evolutionary Perspectives (Ed. by G. Hausfater & S. Hrdy), pp. 23%256. New York: Aldine/DeGruyter. (Received 1 June 1985; revised 21 August 1985; MS. number." AS-345)
Models of Infanticide: A Reply to Hausfater
In the above note Hausfater (1986) discusses several issues raised by our paper (Glass et al. 1985) . However, his two major points appear to involve the equivalence of our equilibrial solutions and the causes of non-infanticidal populations. The following is intended to comment further on the similarities and differences in our models. Our model was designed as a non-specific, strategic analysis that would allow us to consider a variety of explanations that have been offered for infanticide. It was not intended to analyse a particular infanticidal system in detail. This contrasts with analyses by Hausfater and his co-workers (Chapman & Hausfater 1979; Hausfater etal. 1982; Hausfater 1984) which are tactical models, more closely tailored to examining the details of infanticidal behaviour in a particular species. Obviously, a strategic model cannot subsume the detailed character of a tactical model. Our claim that Hausfater's work could be viewed as a special case of an Evolutionarily Stable Strategy (ESS) arose because, if we limited the range of our parameters, we obtained his equilibrial results but, if we altered the range of our parameters, we obtained other workers' results. When generalizing the predictions of tactical models, it is important to distinguish results that
619
are generally applicable from those that are idiosyncratic features of the organism for which the model was developed. We believe the expression for the equilibrial frequency of infanticidal behaviour derived by Hausfater (1986) and ourselves is an example of the former, while most of the differences, including the persistence of non-infanticidal populations, are because of the latter. In fact, the equilibrium depends on just two general assumptions shared by the models: (1) individual fitnesses are determined by pairwise interactions; and (2) these pairs of individuals are formed randomly from a large population (R. D. Holt, personal communication). Let Wv(P) denote the fitness of an individual with phenotype P when it interacts with an individual using a different phenotype, P', and Wp (P) its fitness when interacting with an individual of its own type. The corresponding fitnesses of the alternative phenotypes are given by Wp(P') and Wv(P'). I f p is the fraction of the population with phenotype P a n d dyads interact randomly, then the average fitness of individuals with pheontype P is W(P) = p Wv(P) + (1 --p) Wv,(P)
(1)
Similarly, the average fitness of individualswith the alternative phenotype p' is W(P') = p We(P') + (1 --p) We,(P')
(2)
Phenotypic fitnesses are frequency-dependent with a linear dependence on p (Glass et al. 1985), regardless of the pairwise fitness values. If the population is to be polymorphic at equilibrium, then all heritable phenotypes must have equal fitnesses (Slatkin 1978). Setting W(P)= W(P')gives an equilibrial frequency for P of P* = (Wv,(P')- Wp,(P))/ (We(P) - Wv(e') + We,(P') - Wp,(P))
(3)
This is the expression as derived by Hausfater (1986). It should be stressed that the logic leading to this expression is general. It is not restricted to infanticide or any other behaviour. For example, equations (1) and (2) are the usual expression for genic fitnesses in randomly mating diploid populations (Crow & Kimura 1970), where the pair of 'individuals' are the alleles at a single locus, and equation (3) describes equilibrial gene frequencies (Crow & Kimura 1970). Thus, the eqnilibrial frequencies predicted by our models are robust if the assumptions are met. The primary difference in our models, which Hausfater discusses, is our explanations for noninfanticidal populations. We both recognize such populations exist, but in Hausfater's models these 'equilibrial' populations are highly susceptible to invasion and are never stable (Hausfater et al.
620
Animal Behaviour, 34, 2
1982). Thus, the mechanisms he proposes for noninfanticidal populations to persist are non-selective. Either restricted gene flow precludes the introduction of infanticidal individuals (Hausfater 1986), or genetic drift eliminates infanticide from polymorphic populations (Hausfater et al. 1982). Non-selective hypotheses certainly need to be considered in evolutionary models (Glass et al. 1985), but to date many, if not most, populations appear to be non-infanticidal. It seems unlikely so many non-infanticidal populations persist for solely non-selective reasons, while infanticidal populations occur because of selection. Rather, we sought to determine if our model would permit non-infanticidal populations to persist. We noted that, when the parameter A2 (/~N--R~N in Hausfater's model), the relative advantage of noninfanticidal behaviour when it is common, was positive, non-infanticidalpopulations could persist through selection. To reconcile our results with Hausfater's, we noted he only allowed A2 to be negative (Chapman & Hausfater 1979; Hausfater et al. 1982; Hausfater 1984). In the formal structure of his model, nothing requires this to be so. Rather, it appears to be an assumption based on the reproductive biology of some langur populations (and some but not all vertebrates) where the loss of offspring speeds a female's return to oestrus. Thus, infanticidal males would have an advantage in non-infanticidalpopulations, other things being equal (e.g. Hausfater 1984). We never stated a negative Az was an error on Hausfater's part, only that it was a restrictive assumption not inherent to the model. We suggested that A2 might be positive in populations of non-infanticidal langurs (and other species) and that these populations might persist because of selective pressures. We proposed this because Hrdy (1977, 1979) had suggested offspring loss had little impact on female oestrus patterns in seasonally breeding langur populations (also Hausfater 1984). If this is true, then A2 would be at least zero and, given the social disruption that often follows infanticide (Hrdy 1979; Hausfater 1984), it might actually be disadvantageous to be infanticidal under such circumstances. Thus, our point was that a selective explanation ought to be considered along with non-selective hypotheses when trying to account for non-infanticidal populations. Regardless of this, the value of Az is an empirical question open to testing (Glass et al. 1985). The nature of our model also led us to consider some additional circumstances not addressed by Hausfater et al. (1982). Among these was a historydependent explanation of infanticide. With alternative stable states (history-dependent equilibria) it
is possible that infanticide can be maintained in one population, by selection, while, in another population, strictly non-infanticidal behaviour can persist, through selection, even if the populations inhabit identical physical environments. This provides another mechanism for the persistence of non-infanticidal behaviour. Strategic and tactical models both have their limitations. Strategic models can rarely achieve the detail incorporated into tactical models, while tactical models may incorporate aspects of a particular behaviour in one population that obscures its relationship to behaviour in other populations or species. However, they can both be used as checks on one another to increase our understanding of infanticide. I would like to thank G. Hausfater for the stimulating note, C.T. Snowdon for the opportunity to discuss it, and R. D. Holt for the derivation of (3). J,E. Childs and G.W. Korch read earlier drafts of this paper. GREGORY E. GLASS Immunology and Infectious Diseases, The Johns Hopkins University, 615 N. Wolfe St, Baltimore, AID 21205, U.S.A.
References Chapman, M. & Hausfater, G. 1979. The reproductive consequencesof infanticide in langurs: a mathematical model. Behav. Ecol. Sociobiol., 5, 22%240. Crow, J. F. & Kimura, M. 1970. An Introduction to Population Genetics Theory. New York: Harper & Row. Glass, G. E., Holt, R. D. & Slade, N. A. 1985. Infanticide as an evolutionarily stable strategy. AnOn. Behav., 33, 384-391. Hausfater, G. 1984. Infanticide in langurs: strategies, counterstrategies and parameter values.In: Infanticide." Comparative and Evolutionary Perspectives (Ed. by G. Hausfater & S. Hrdy), pp. 257-282. New York: Aldine/ DeGruyter. Hausfater, G. 1986. Convergent models: evidence of a robust theory of infanticide. Anim. Behav., 34, 617619. Hausfater, G., Aref, S. & Cairns, S. J. 1982.Infanticide as an alternative male reproductive strategy in langurs: a mathematical model, or. theor. BioL, 94, 391-412. Hrdy, S, B. 1977. The Langurs of Abu." Female and Male Strategies of Reproduction. Cambridge, Massachusetts: Harvard University Press. Hrdy, S, B. 1979. Infanticide among animals: a review, classification,and examination of the implications for the reproductive strategies of females. Ethol. Sociobiol., 1, 13-40.
Short Communications Slatkin, M. 1978. On the equilibration of fitnesses by natural selection. Am. Nat., 112, 845-859. (Received 25 September 1985; revised 3 October 1985; MS, number. AS-357)
Importance of Female Behaviour in the Dawn Chorus
A strong peak of song in the early morning is a very c o m m o n feature o f the daily routines of passerines in spring. Recent explanations for this dawn chorus suggest that the early morning may be a good time to sing due to better sound transmission (Henwood & Fabrick 1979), a lower cost of not foraging and a higher risk of intrusion by males seeking territories at dawn (Kacelnik & Krebs 1983). This paper considers the effect of the behaviour of females on the dawn chorus. In great tits (Parus major), this peak of song at dawn does not occur in March despite much singing throughout the day (Hinde 1952) but, from about 3 weeks before egg-laying until early May when most clutches are complete, song occurs between the male waking time and the first emergence of the female from her roost-hole (male and female roost apart). After the female emerges, the pair copulate and male singing drops to a low level. Hence the duration of the dawn chorus is related to the time o f female emergence. This is demonstrated by the positive correlation between the duration of male song (in min, including pauses if less than 15 s) in the first 80 min of the day (measured from civil twilight) and the time of female emergence, which varied from 18 to 75 min after twilight (r=0.851, P < 0.01, N = 8 pairs using mean values from up to four days for each pair). This relationship could be due to both male singing and female emergence being controlled by the same environmental cue, e.g. light intensity. Alternatively the female's emergence and mating may terminate the dawn chorus. To separate these alternatives, female emergence time was manipulated experimentally. The experiment was carried out in Marley Plantation, Oxfordshire in April 1985. Five pairs of great tits, all of which were nest-building or laying eggs in nest-boxes, were watched for three consecutive days each. On day 1 and day 3 normal female emergence time and the duration of male song were recorded from a hide. On day 2 the nest-box entrance was blocked with an inconspicuous, foam plug put in position the previous evening after the female had gone in to roost. The plug was attached to a string and could be removed quietly by pulling the string from inside the hide. The plug was
621
removed, allowing the female to fly out, 15 rain after her emergence time on day 1. Neither males nor females showed signs of alarm during the experiment. The results (Table I) show that delaying the emergence and mating of a female leads to more singing by her mate. Results are presented relative to the normal female emergence time oI each pair (see Table I). Table Ia shows that, before normal female emergence time, there was no significant difference in the amount males sang between days. Table Ib shows that the time the male spent singing in the 20 min after normal female emergence time was typically low or zero on the two control days (mean 0.65 rain) but was significantly higher on day 2 (mean 7.50 rain) when females were emerging 15 min later. On day 2 there was less song in the extra 15 rain when the female was 'blocked in' than in the preceding 15 min (mear difference 1.20 min), but not significantly less (Wilcoxon matched-pairs signed-ranks test: P > 0.1). Hence the female's behaviour controls the duration o f the dawn chorus. This song may be directed at the female tc stimulate her to copulate or may be a 'keep out signal to other males or, most likely, serves botl" functions. There is evidence from correlation, between traits of young and neighbouring male~ (Alatalo et al. 1984) and the mate guarding beha viour of males (Gowaty 1981) that cuckoldry is Table I. Minutes of song (a) before and (b) in the 20 min after normal* female emergence time Pair no.:
l
2
3
4
5
Mean
(a) Before normal female emergence time Day 1 12-5 36.5 14.0 34.0 25-5 24.5 Day2 18.5 30.5 21.0 32.0 17.0 23.8 Day3 20.0 36.0 20-0 29-5 24.5 26.0 Two-way Anova: Pair, F = 12.13; df=4,8; P<0.01 Day, F=0.41; df= 2,8; Ns (b) After normal female emergence time Day 1 2.0 0.0 0.0 0.0 0.0 Day 2 8.5 11.0 5.5 7.5 5.0 Day 3 2.5 0.0 1-5 0-0 0.5 Two-way Anova: Pair, F = 1.37; dr=4,8; Ns Day, F=33.70; df= 2,8; P < 0-001
0.4 7.5 0.9
* For each pair, normal female emergence time on day 1 and day 3 is actual female emergence time i.e. (a) when the female is in her box and (b) when she is out. On day 2 'normal' time is the mean times of day 1 and day 3 i.e. the time the female might have been expected to leave her box had she not been blocked in.
Models of Infanticide: A Reply to Hausfater
In the above note Hausfater (1986) discusses several issues raised by our paper (Glass et al. 1985) . However, his two major points appear to involve the equivalence of our equilibrial solutions and the causes of non-infanticidal populations. The following is intended to comment further on the similarities and differences in our models. Our model was designed as a non-specific, strategic analysis that would allow us to consider a variety of explanations that have been offered for infanticide. It was not intended to analyse a particular infanticidal system in detail. This contrasts with analyses by Hausfater and his co-workers (Chapman & Hausfater 1979; Hausfater etal. 1982; Hausfater 1984) which are tactical models, more closely tailored to examining the details of infanticidal behaviour in a particular species. Obviously, a strategic model cannot subsume the detailed character of a tactical model. Our claim that Hausfater's work could be viewed as a special case of an Evolutionarily Stable Strategy (ESS) arose because, if we limited the range of our parameters, we obtained his equilibrial results but, if we altered the range of our parameters, we obtained other workers' results. When generalizing the predictions of tactical models, it is important to distinguish results that
619
are generally applicable from those that are idiosyncratic features of the organism for which the model was developed. We believe the expression for the equilibrial frequency of infanticidal behaviour derived by Hausfater (1986) and ourselves is an example of the former, while most of the differences, including the persistence of non-infanticidal populations, are because of the latter. In fact, the equilibrium depends on just two general assumptions shared by the models: (1) individual fitnesses are determined by pairwise interactions; and (2) these pairs of individuals are formed randomly from a large population (R. D. Holt, personal communication). Let Wv(P) denote the fitness of an individual with phenotype P when it interacts with an individual using a different phenotype, P', and Wp (P) its fitness when interacting with an individual of its own type. The corresponding fitnesses of the alternative phenotypes are given by Wp(P') and Wv(P'). I f p is the fraction of the population with phenotype P a n d dyads interact randomly, then the average fitness of individuals with pheontype P is W(P) = p Wv(P) + (1 --p) Wv,(P)
(1)
Similarly, the average fitness of individualswith the alternative phenotype p' is W(P') = p We(P') + (1 --p) We,(P')
(2)
Phenotypic fitnesses are frequency-dependent with a linear dependence on p (Glass et al. 1985), regardless of the pairwise fitness values. If the population is to be polymorphic at equilibrium, then all heritable phenotypes must have equal fitnesses (Slatkin 1978). Setting W(P)= W(P')gives an equilibrial frequency for P of P* = (Wv,(P')- Wp,(P))/ (We(P) - Wv(e') + We,(P') - Wp,(P))
(3)
This is the expression as derived by Hausfater (1986). It should be stressed that the logic leading to this expression is general. It is not restricted to infanticide or any other behaviour. For example, equations (1) and (2) are the usual expression for genic fitnesses in randomly mating diploid populations (Crow & Kimura 1970), where the pair of 'individuals' are the alleles at a single locus, and equation (3) describes equilibrial gene frequencies (Crow & Kimura 1970). Thus, the eqnilibrial frequencies predicted by our models are robust if the assumptions are met. The primary difference in our models, which Hausfater discusses, is our explanations for noninfanticidal populations. We both recognize such populations exist, but in Hausfater's models these 'equilibrial' populations are highly susceptible to invasion and are never stable (Hausfater et al.
620
Animal Behaviour, 34, 2
1982). Thus, the mechanisms he proposes for noninfanticidal populations to persist are non-selective. Either restricted gene flow precludes the introduction of infanticidal individuals (Hausfater 1986), or genetic drift eliminates infanticide from polymorphic populations (Hausfater et al. 1982). Non-selective hypotheses certainly need to be considered in evolutionary models (Glass et al. 1985), but to date many, if not most, populations appear to be non-infanticidal. It seems unlikely so many non-infanticidal populations persist for solely non-selective reasons, while infanticidal populations occur because of selection. Rather, we sought to determine if our model would permit non-infanticidal populations to persist. We noted that, when the parameter A2 (/~N--R~N in Hausfater's model), the relative advantage of noninfanticidal behaviour when it is common, was positive, non-infanticidalpopulations could persist through selection. To reconcile our results with Hausfater's, we noted he only allowed A2 to be negative (Chapman & Hausfater 1979; Hausfater et al. 1982; Hausfater 1984). In the formal structure of his model, nothing requires this to be so. Rather, it appears to be an assumption based on the reproductive biology of some langur populations (and some but not all vertebrates) where the loss of offspring speeds a female's return to oestrus. Thus, infanticidal males would have an advantage in non-infanticidalpopulations, other things being equal (e.g. Hausfater 1984). We never stated a negative Az was an error on Hausfater's part, only that it was a restrictive assumption not inherent to the model. We suggested that A2 might be positive in populations of non-infanticidal langurs (and other species) and that these populations might persist because of selective pressures. We proposed this because Hrdy (1977, 1979) had suggested offspring loss had little impact on female oestrus patterns in seasonally breeding langur populations (also Hausfater 1984). If this is true, then A2 would be at least zero and, given the social disruption that often follows infanticide (Hrdy 1979; Hausfater 1984), it might actually be disadvantageous to be infanticidal under such circumstances. Thus, our point was that a selective explanation ought to be considered along with non-selective hypotheses when trying to account for non-infanticidal populations. Regardless of this, the value of Az is an empirical question open to testing (Glass et al. 1985). The nature of our model also led us to consider some additional circumstances not addressed by Hausfater et al. (1982). Among these was a historydependent explanation of infanticide. With alternative stable states (history-dependent equilibria) it
is possible that infanticide can be maintained in one population, by selection, while, in another population, strictly non-infanticidal behaviour can persist, through selection, even if the populations inhabit identical physical environments. This provides another mechanism for the persistence of non-infanticidal behaviour. Strategic and tactical models both have their limitations. Strategic models can rarely achieve the detail incorporated into tactical models, while tactical models may incorporate aspects of a particular behaviour in one population that obscures its relationship to behaviour in other populations or species. However, they can both be used as checks on one another to increase our understanding of infanticide. I would like to thank G. Hausfater for the stimulating note, C.T. Snowdon for the opportunity to discuss it, and R. D. Holt for the derivation of (3). J,E. Childs and G.W. Korch read earlier drafts of this paper. GREGORY E. GLASS Immunology and Infectious Diseases, The Johns Hopkins University, 615 N. Wolfe St, Baltimore, AID 21205, U.S.A.
References Chapman, M. & Hausfater, G. 1979. The reproductive consequencesof infanticide in langurs: a mathematical model. Behav. Ecol. Sociobiol., 5, 22%240. Crow, J. F. & Kimura, M. 1970. An Introduction to Population Genetics Theory. New York: Harper & Row. Glass, G. E., Holt, R. D. & Slade, N. A. 1985. Infanticide as an evolutionarily stable strategy. AnOn. Behav., 33, 384-391. Hausfater, G. 1984. Infanticide in langurs: strategies, counterstrategies and parameter values.In: Infanticide." Comparative and Evolutionary Perspectives (Ed. by G. Hausfater & S. Hrdy), pp. 257-282. New York: Aldine/ DeGruyter. Hausfater, G. 1986. Convergent models: evidence of a robust theory of infanticide. Anim. Behav., 34, 617619. Hausfater, G., Aref, S. & Cairns, S. J. 1982.Infanticide as an alternative male reproductive strategy in langurs: a mathematical model, or. theor. BioL, 94, 391-412. Hrdy, S, B. 1977. The Langurs of Abu." Female and Male Strategies of Reproduction. Cambridge, Massachusetts: Harvard University Press. Hrdy, S, B. 1979. Infanticide among animals: a review, classification,and examination of the implications for the reproductive strategies of females. Ethol. Sociobiol., 1, 13-40.
Short Communications Slatkin, M. 1978. On the equilibration of fitnesses by natural selection. Am. Nat., 112, 845-859. (Received 25 September 1985; revised 3 October 1985; MS, number. AS-357)
Importance of Female Behaviour in the Dawn Chorus
A strong peak of song in the early morning is a very c o m m o n feature o f the daily routines of passerines in spring. Recent explanations for this dawn chorus suggest that the early morning may be a good time to sing due to better sound transmission (Henwood & Fabrick 1979), a lower cost of not foraging and a higher risk of intrusion by males seeking territories at dawn (Kacelnik & Krebs 1983). This paper considers the effect of the behaviour of females on the dawn chorus. In great tits (Parus major), this peak of song at dawn does not occur in March despite much singing throughout the day (Hinde 1952) but, from about 3 weeks before egg-laying until early May when most clutches are complete, song occurs between the male waking time and the first emergence of the female from her roost-hole (male and female roost apart). After the female emerges, the pair copulate and male singing drops to a low level. Hence the duration of the dawn chorus is related to the time o f female emergence. This is demonstrated by the positive correlation between the duration of male song (in min, including pauses if less than 15 s) in the first 80 min of the day (measured from civil twilight) and the time of female emergence, which varied from 18 to 75 min after twilight (r=0.851, P < 0.01, N = 8 pairs using mean values from up to four days for each pair). This relationship could be due to both male singing and female emergence being controlled by the same environmental cue, e.g. light intensity. Alternatively the female's emergence and mating may terminate the dawn chorus. To separate these alternatives, female emergence time was manipulated experimentally. The experiment was carried out in Marley Plantation, Oxfordshire in April 1985. Five pairs of great tits, all of which were nest-building or laying eggs in nest-boxes, were watched for three consecutive days each. On day 1 and day 3 normal female emergence time and the duration of male song were recorded from a hide. On day 2 the nest-box entrance was blocked with an inconspicuous, foam plug put in position the previous evening after the female had gone in to roost. The plug was attached to a string and could be removed quietly by pulling the string from inside the hide. The plug was
621
removed, allowing the female to fly out, 15 rain after her emergence time on day 1. Neither males nor females showed signs of alarm during the experiment. The results (Table I) show that delaying the emergence and mating of a female leads to more singing by her mate. Results are presented relative to the normal female emergence time oI each pair (see Table I). Table Ia shows that, before normal female emergence time, there was no significant difference in the amount males sang between days. Table Ib shows that the time the male spent singing in the 20 min after normal female emergence time was typically low or zero on the two control days (mean 0.65 rain) but was significantly higher on day 2 (mean 7.50 rain) when females were emerging 15 min later. On day 2 there was less song in the extra 15 rain when the female was 'blocked in' than in the preceding 15 min (mear difference 1.20 min), but not significantly less (Wilcoxon matched-pairs signed-ranks test: P > 0.1). Hence the female's behaviour controls the duration o f the dawn chorus. This song may be directed at the female tc stimulate her to copulate or may be a 'keep out signal to other males or, most likely, serves botl" functions. There is evidence from correlation, between traits of young and neighbouring male~ (Alatalo et al. 1984) and the mate guarding beha viour of males (Gowaty 1981) that cuckoldry is Table I. Minutes of song (a) before and (b) in the 20 min after normal* female emergence time Pair no.:
l
2
3
4
5
Mean
(a) Before normal female emergence time Day 1 12-5 36.5 14.0 34.0 25-5 24.5 Day2 18.5 30.5 21.0 32.0 17.0 23.8 Day3 20.0 36.0 20-0 29-5 24.5 26.0 Two-way Anova: Pair, F = 12.13; df=4,8; P<0.01 Day, F=0.41; df= 2,8; Ns (b) After normal female emergence time Day 1 2.0 0.0 0.0 0.0 0.0 Day 2 8.5 11.0 5.5 7.5 5.0 Day 3 2.5 0.0 1-5 0-0 0.5 Two-way Anova: Pair, F = 1.37; dr=4,8; Ns Day, F=33.70; df= 2,8; P < 0-001
0.4 7.5 0.9
* For each pair, normal female emergence time on day 1 and day 3 is actual female emergence time i.e. (a) when the female is in her box and (b) when she is out. On day 2 'normal' time is the mean times of day 1 and day 3 i.e. the time the female might have been expected to leave her box had she not been blocked in.