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This article was downloaded by: [Florida Atlantic University]On: 10 November 2014, At: 10:54Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Journal of Natural HistoryPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tnah20
Pairing, oviposition and developmentin two sibling species of phoreticmites (Acari: Mesostigmata:Parasitidae: Poecilochirus spp.)associated with burying beetles(Coleoptera: Silphidae: Nicrophorusspp.)H.H. Schwarz a c & M.G. Walzl ba Universität Bielefeld, BIO VII , Universitätsstr. 25, D-33615,Bielefeld, Germanyb Institute für Zoologie , Universität Wien , Althanstr. 14,A-1090, Wien, Austriac ETH Zürich, Experimentelle Oekologie , ETH Zentrum NW ,CH-8092, Zürich, SwitzerlandPublished online: 17 Feb 2007.
To cite this article: H.H. Schwarz & M.G. Walzl (1996) Pairing, oviposition and developmentin two sibling species of phoretic mites (Acari: Mesostigmata: Parasitidae: Poecilochirus spp.)associated with burying beetles (Coleoptera: Silphidae: Nicrophorus spp.), Journal of NaturalHistory, 30:9, 1337-1348, DOI: 10.1080/00222939600771251
To link to this article: http://dx.doi.org/10.1080/00222939600771251
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JOURNAL oF NATURALHISTORY, 1996, 30, 1337-1348
Pairing, oviposition and development in two sibling species of phoretic mites (Acari: Mesostigmata: Parasitidae: Poecilochirus spp.) associated with burying beetles (Coleoptera: Silphidae: Nicrophorus spp. )
H. H. S C H W A R Z * t and M. G. WALZL:~
~f Universiti~t Bielefeld, BIO VII, Universitiitsstr. 25, D-33615, Bielefeld, Germany
:~ Universitiit Wien, Institute fiir Zoologie, Althanstr. 14, A-1090 Wien, Austria
(Accepted 6 September 1995)
The Poecilochirus carabi species complex consists of several morphologically similar but reproductively-isolated mite species, which reproduce in the brood chambers of burying beetles. In this study, we examine pairing behaviour, oviposition rates and development times of two species of the P. carabi complex that occur sympatrically on German burying beetles. The two species are referred to as 'species P-vs' and 'species P-vo' because species descriptions have not yet been completed.
We analysed the pairing behaviour of the two sibling species by measuring the durations of four behavioural sequences. In species P-vo, pairing lasted about three times longer than in species P-vs. This difference in pairing duration was caused by differences in the time spent in the venter-to-venter mating position and in the time the pairs stayed together after mating. In the absence of conspecifics, adults of the two sibling species formed heterospecific pairs. The heterospecific pairs needed longer than monospecific pairs before they adopted the mating position. None of them produced offspring. In breeding experiments at 15 and 20°C, females of both mite species laid about 200 eggs. Daily egg production varied from pleak values of 30 to 50 eggs day -1 at the beginning of oviposition to one egg day at the end of a females' life. At both temperatures, females in species P-vs deposited their eggs faster and their offspring reached the phoretic deuter- onymphal stage earlier than in species P-vo. We discuss pairing duration and egg- laying rates of species P-vs and P-vo in relation to data available in the literature for other mesostigmatic mite species, and discuss possible reasons for the differences in reproductive biology between the two sibling species.
KEYWORDS: Poecilochirus, sibling species, mating behaviour, oviposition, develop- ment time, phoresy, Nicrophorus.
Introduction The Poecilochirus carabi species complex (Mesostigmata: Parasitidae) consists o f
several morphological ly similar but reproductively-isolated mite species, which are associated with burying beetles o f the genus Nicrophorus (Coleoptera: Silphidae)
*Present address: ETH Ziirich, Experimentelle Oekologie, ETH Zentrum NW, CH-8092 Ziirich, Switzerland.
0022-2933/96 $12"00 © 1996 Taylor & Francis Ltd.
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1338 H.H. Schwarz and M. G. Walzl
(Mfiller and Schwarz, 1990; Brown and Wilson, 1992). The deuteronymphs (the last pre-adult stage) of these mite species disperse phoretically on the adult beetles. They stay active during transport and participate in their carrier's meals (Neumann, 1943; Springett, 1968). Their development, however, is inhibited; usually, they do not moult into adults as long as their carrier does not reproduce.
Burying beetles reproduce on small vertebrate carcasses, which they bury in subterranean brood chambers (Trumbo, 1991). In most cases, a brood chamber is occupied by a single beetle pair, which cares for its brood until larval development is complete. The deuteronymphs of the P. carabi complex that arrive on the beetle pair disembark when their hosts bury the carcass. They moult into adults within a few hours, which then reproduce in close vicinity to the beetle brood (Korn, 1982a, 1983). The adult, larval and protonymphal stages of the mites are not phoretic. They are free-dwelling in the beetles' brood chamber, where they live on the carcass and its associated microfauna (Korn, 1982b, 1983; Wilson and Knollenberg, 1987). Because they can only disperse from the brood chamber by attaching to a beetle, the mites of the new generation have to reach the phoretic deuteronymphal stage before the beetles depart. This is usually the case at the end of larval development of the beetle progeny. The parent beetles then terminate brood care and take-offin search of a new carcass, and their larvae leave the brood chamber to pupate singly in the surrounding soil (Pukowski, 1933; Springett, 1968; Schwarz and Mfiller, 1992).
Poecilochirus carabi G. et R. Canestrini 1882 has long been regarded as a single species, although Vitzthum (1930) found variation in deuteronymph morphology and established P. necrophori Vitzthum 1930. However, the morphological criteria he used to discriminate between P. carabi and P. necrophori were proven to be arbitrary (Hyatt, 1980; Korn, 1982c). Later, using choice experiments, Mfiller and Schwarz (1990) found that mites deriving from the two beetle species Nicrophorus vespilloides Herbst 1783 and N. vespillo (Linnaeus 1758) preferred different host species, and that mites differing in host preference did not reproduce with each other. Diagnostic differences in atlozyme patterns confirmed that P. carabi consists of at least two reproductively-isolated species (Schwarz et al., 1991). Schwarz (in press) showed that deuteronymphs of the two-mite species also occur on other European Nicrophorus species; they usually use different beetle species for transport, but mites of both species may co-occur on the same beetle in some cases. Following the terminology introduced by Mfiller and Schwarz (1990) the two-mite species are referred to here as 'species P-vs' and 'species P-vo' because species descriptions have not yet been completed.
Because previous authors examining the ecology of the mites associated with European burying beetles did not recognize P. carabi as a species complex (Neumann, 1948; Belozerov, 1957; Springett, 1968; Korn, 1982a, b, c, 1983), not much is known about the respective life histories of species P-vs and P-vo. Mfiller and Schwarz (1990) found in laboratory cultures that the first deuteronymphs of species P-vs always emerged before those of P-vo, indicating that the mites differ in development time. In this paper we focus on the reproductive behaviour of the two sibling species. We analyse different behavioural sequences during the pairing process, assess egg-laying rates and longevity of the females, and measure the time required from oviposition to deuteronymph emergence.
Materials and methods The mites we used in this study derived from beetles of the two host species N.
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Reproductive behaviour of mites 1339
vespilloides and N. vespillo, which we caught near Bielefeld, Germany, in the summer of 1991. Because it is impossible to discriminate between deuteronymphs of species P- vs and those of P-vo by morphological characters, we used their differential host preferences to separate them by choice experiments as described in Schwarz et al. (1991). Choice experiments have been repeatedly used to successfully discriminate between the two sibling species (Mfiller and Schwarz, 1990; Schwarz et al., 1991; Schwarz and Mfiller, 1992). After separation of the two species, we kept the deuteronymphs on beetles of their preferred host species at 20°C and a light : dark cycle of 18 : 6 h, until we used them for the experiments.
Pairing behaviour In this text, we define 'pairing duration' as the whole period a mite pair stays in
direct contact, from initial pair formation until the moment of disengagement (Crespi, 1989). 'Mating' only refers to the sequence within the pairing process in which the male adopts the 'venter-to-venter mating position', hanging from the venter of the female by clasping her legs IV with his spurred legs II (Fig. 1). This is the typical position in which the male of tocospermic Mesostigmata produces the spermato- phore, takes it up with one of his chelicerae and transfers it into the spermatheca of the female (Evans, 1992).
To obtain unmated adults for the pairing experiments, we removed about 100 conspecific deuteronymphs from their carriers and put them into a plastic container (100 x 100 x 60mm) that contained 10mm of moist peat and a piece of pig's liver. The container was stored in the dark at 20°C. The deuteronymphs fed on the liver and
FIG. 1. A male (M) and a female (F) of species P-vs (Poecilochirus carabi species complex) in the venter-to-venter mating position. The chelicerae of the male are inserted into the female's
genital orifice. Scale bar 250 #m.
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1340 H.H. Schwarz and M. G. Walzl
grew rapidly. After 8 to 16 h they reached adult size, and the male deuteronymphs could be easily distinguished from the larger female nymphs. We sexed the deuter- onymphs by body size and put them singly into small plastic boxes (50 x 30 x 16mm) containing peat and liver, where they completed their development and moulted into adults.
Pairing experiments started within 4 h of the adult moult. At the start of each experiment, we put one male and one female into a plastic arena (50 x 30 x 16mm) lined with moist filter paper. We observed the mites continuously with a stereo microscope (magnification 16x). In parasitid mites, pairings are usually initiated by the male mounting the female's back. Then he moves to her venter and adopts the actual mating position (Evans, 1992). We quantified pairing behaviour by measuring: (1) time until first contact; (2) duration of initial back-riding; (3) duration of the venter-to-venter mating position; and (4) duration of time the pairs remained in direct contact after abandoning the mating position. To compare the measurements taken for the two species we used Mann-Whitney U-tests. To hold the group-wide type I error rate to at most a = 5%, we applied the sequential Bonferroni technique for the k = 4 U-tests (Rice, 1989). In total, we observed the behaviour of 19 pairs of species P-vs and 22 pairs of species P-vo. Additionally, we formed 20 heterospecific pairs. For half of these pairings we used males of species P-vs, for the other half we used P-vo males.
Female longevity, egg-laying behaviour, and offspring development To establish the number of eggs laid female-1 day-l, we put single pairs of newly
hatched male and female mites into plastic breeding boxes (50 x 30 × 16mm) provided with peat and a small piece of liver and stored them in the dark. Until the death of the female, we transferred each mite pair into a new breeding box every 24 h. Because the females buried their eggs in the substrate and attached little soil particles to them, it was not possible to assess egg numbers by counting the eggs in the breeding boxes directly. Therefore, after the removal of the adult mites, we stored each breeding box in the dark until their offspring emerged and grew to the deuteronym- phal stage. Then we estimated the number of eggs laid day -1 by counting the number of deuteronymphs emerging per breeding box. We calculated the development time of the mite offspring as the difference between the date of egg-laying and the date of deuteronymph emergence. Because life history parameters in arthropods are strongly influenced by temperature (Roff, 1992), we undertook this experiment at 15°C and again at 20°C.
For statistical analysis, we calculated Two-Way Anovas using mite species and temperature as categorical variables for the following dependent variables: (1) longevity of females; (2) number of eggs produced; (3) time between adult moult of the female and the day on which she deposited 50% of her eggs; and (4) average development time of offspring, from the egg to the deuteronymphal stage. The last variable we calculated as the grand mean of the single means assessed for the offspring of each female. To hold the group-wide type I error rate to at most a = 5%, we applied the Bonferroni technique for the k = 4 tests (Rice, 1989).
Results Pairing behaviour
In both species P-vs and P-vo all monospecific mite pairs tested established direct
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Reproduct ive behaviour o f mites 1341
Table 1. Pair formation and pairing behaviour in species P-vs and P-vo, two sibling species of the Poecilochirus carabi complex. Arithmetic mean, standard deviation (SD), and range of different behavioural sequences are given in seconds.
Species P-vs (n = 19) Species P-vo (n = 22) Behavioural Significancet
sequence Mean SD Range Mean SD Range U-test
(1) time until first contact 40.4 44.3 5-155 21"5 18'9 2-66 P = 0.099
(2) initial back-riding 4.8 5-1 1-17 4.3 3-2 2-16 P = 0.325
(3) first mating position 39"1 5"8 29-51 138-2 102"6 44-519 P < 0-000001~
(4) remaining time before separation 28-8 35'6 0-159 88.2 70.6 6-295 P = 0.00006~
total pairing duration (2-4) 72.7 39'1 35-213 230.7 127"0 74-643
~'Control over table-wide type I error was obtained using the sequential Bonferroni technique (Rice, 1989).
$Indicates significance at a group-wide 5% level.
Table 2. Pair formation and pairing behaviour in interspecific matings between species P-vs and species P-vo. Arithmetic mean, standard deviation (SD), and range of different behavioural sequences are given in seconds.
P-vs male x P-vo female (n = 8)
P-vo male x P-vs female (n = 6)
Behavioural Significance sequence Mean SD Range Mean SD Range U-test
(1) time until first contact 95"8 65.2 21-192 115.0 70-8 36-224 P = 0.61
(2) initial back-riding 7'5 9-0 2-28 17.7 19"7 3-57 P = 0.10
(3) first mating position 72.4 88-2 18-288 85.8 86-7 13-245 P = 0.79
(4) remaining time before separation 30-5 44"5 4-129 30'3 37-5 1-102 P = 0.74
total pairing duration (2-4) 110'4 91"6 24-304 133"8 83'8 43-277
contact and mated. Pair format ion usually started within 1 min o f the male being introduced into the test arena (Table 1). In all cases, the male initiated pairing by mount ing the back of the female, staying there for t - 17 s before adopt ing the venter- to-venter mat ing position.
The two sibling species differed greatly in the length of time the pairs spent in the mating position (Table 1). Pairs o f species P-vo, on average, remained in this position more than three times longer than pairs of P-vs. Additionally, the variation in the duration o f the mating position in species P-vo was much greater than in P-vs. During mating, P-vo males were very active and stroked the sides and the back of the females with their legs, I, I I I and IV, whereas in most cases P-vs males only vibrated their first legs.
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ta~
4
~
Tab
le 3
. L
onge
vity
and
egg
-pro
duct
ion
of fe
mal
es, a
nd m
ean
deve
lopm
ent t
ime
of o
ffsp
ring
(egg
dep
osit
ion
to d
eute
rony
mph
em
erge
nce)
in s
peci
es P
-vs
and
P-v
o at
15
and
20°C
. G
iven
are
the
ari
thm
etic
mea
ns a
nd t
he s
tand
ard
devi
atio
ns (
in b
rack
ets)
.
T =
15
°C
T =
20°
C
Spec
ies
P-v
s Sp
ecie
s P
-vo
Spec
ies
P-vs
Sp
ecie
s P
-vo
n=
9
n=
10
n
=6
n
=9
AN
OV
A P
roba
bili
ties
t
Spec
ies
Tem
p.
Spec
. x
Tem
p.
~z
Fem
ale
long
evit
y (d
ays)
* 11
.8 (
1.4)
12
-1 (
1'4)
7.
5 (1
-2)
9.6
(1.4
) 0.
232
0"00
45
0.32
7 N
umbe
r of
egg
s 21
7"6
(73"
1)
186"
4 (5
6'2)
20
2 (3
5"9)
25
3 (5
9-.3
) 0"
636
0"22
8 0-
057
Tim
e a
fem
ale
need
s to
ovi
posi
t 50
% o
f he
r eg
gs (
days
) 5-
3 (0
.9)
5-8
(0'8
) 3.
2 (0
-5)
4.3
(0"5
) 0.
0045
<
0.00
01~
0" 1
86
Mea
n de
velo
pmen
t ti
me
of o
ffsp
ring
(da
ys)
9.7
(0.2
) 10
-3 (0
'5)
5.9
(0'3
) 6.
4 (0
.2)
< 0-
0001
~
< 0-
0001
~ 0.
359
tCon
trol
ove
r ta
ble-
wid
e ty
pe I
err
or r
ates
was
obt
aine
d us
ing
the
Bon
ferr
oni
tech
niqu
e (R
ice,
198
9).
:~In
dica
tes
sign
ific
ance
at
a ta
ble-
wid
e 5%
lev
el.
*Dat
a w
ere
log-
tran
sfor
med
for
ana
lysi
s to
red
uce
the
corr
elat
ion
betw
en m
ean
and
vari
ance
.
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Reproductive behaviour of mites 1343
FI~. 2
a) 60-
"O
-~ so g
40 "6
3o
10
t ¢ ~ 0 n t~ _
0 1 2 3 4 5 6 7 8 9 " I I 1 1 1 I 6 0 - b)
~q
"6 $
..iCl E E
O}
@ >
5 0 -
40 -
30 -
20 -
10-
0 1 2 3 4 5 6 7 8 9 1 1 1 1 1
Days after adult moult
Average number of eggs day -1 produced by females of species P-vs (black columns) and species P-vo (hatched columns) at (a) 20°C and (b) 15°C.
After having abandoned the mating position, males of species P-vs returned only briefly to the back of the females before they left and started wandering around in the test arena. If male and female met again, they did not attempt to re-establish direct contact; they either ignored each other, or they reacted negatively and ran away in different directions. Males of species P-vo, in contrast, stayed with the females considerably longer after mating (Table 1). They spent most of the remaining time before pair separation on the females' backs, still manipulating them with their legs I and pedipalps. Fourteen of the 22 P-vo males briefly returned to the venter of the female during this period, 7 of them repeatedly.
Only 14 of the 20 heterospecific mite pairs established direct contact. These displayed the same pairing sequences as the monospecific pairs, including the venter- to-venter mating position. Whether P-vs males paired with P-vo females or vice versa had no significant influence on the pairing behaviour (Table 2). On average, pair formation between mites of different species started after 104 s (all heterospecific pairings pooled, SD = 65.7 s, n = 14), considerably later than in monospecific pairings (Table 1). Correspondingly, the initial back-riding phase on average lasted more than twice as long (mean = 11-8 s, SD = 14.8 s, n = 14) as in the monospecific pairings. The duration of the mating position (mean = 78 s, SD = 84"4 s, n = 14) and the time the pairs remained together after mating (mean = 30.4s, SD = 40-1s, n = 14) was very variable, lying within the range measured for monospecific pairings.
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1344 H.H. Schwarz and M. G. Walzl
None of the heterospecific pairs produced offspring, although some of the females were seen laying eggs.
Female longevity, egg-laying behaviour, and offspring development Longevity and total egg production did not differ between females of species P-vs
and females of species P-vo (Table 3). However, P-vs females deposited their eggs in a shorter length of time and their offspring reached the deuteronymphal stage earlier than was the case for P-vo females.
Females of both species lived longer at 15 ° than at 20°C (Table 3). Offspring development in both species was about 1.6x slower at 15 than at 20°C. Total egg production did not vary with temperature, but at 15°C the females took longer to deposit their eggs. This was partly because oviposition started later at the lower temperature (Fig. 2).
Daily egg-laying rates increased rapidly in species P-vs, reaching maximum values at days 2 and 4 after adult moult at 20 and at 15°C, respectively (Fig. 2). This increase in the rate of egg production at the beginning of oviposition was less rapid in species P-vo. At 20°C, the females reached maximal oviposition rates on day 4. At 15°C no distinct maximum was obvious; the females produced average egg numbers of 23 to 24 eggs per day between days 3 and 7.
Most females continued egg-laying until 1 or 2 days before they died. Females of species P-vs, on average, ceased egg-laying 1-5 and 2 days before dying at 20 and 15°C, respectively. Females of species P-vo terminated egg-laying 1"8 and 1'7 days before dying.
Discussion In the two sibling species of the Poecilochirus carabi complex examined here,
pairing behaviour followed the pattern typical for tocospermic mesostigmatic mites (Evans, 1992). The respective pairing durations lie within ranges reported for phoretic Parasitidae (Rapp, 1959; Costa, 1964; Korn, 1982a) and are short when compared with those of other mesostigmatic mites, in which pairings often last longer than 30min (Bhattacharyya, 1962; Faasch, 1967; Compton and Krantz, 1978; Yasui, 1988; Takahashi and Chant, 1993; Woyke, 1994; Ruf, in press). Significant differences in pairing behaviour between species P-vs and P-vo were obvious in the time that the pairs remained in the venter-to-venter mating position and in the length of time the pairs stayed together after mating. Korn (1982a), who did not discriminate between the two sibling species and probably examined mixed samples, reported that the males transferred either one or two spermatophores during one pairing. Therefore, the difference in mating duration between species P-vs and P-vo may reflect a difference in the number of spermatophores transferred, as was demonstrated for two phytoseiid mite species (Amano and Chant, 1978). However, currently we cannot exclude alternative hypotheses, such as sperm competition (Suter and Parkhill, 1990).
In our experiments adults of species P-vs and P-vo formed heterospecific pairs when no conspecifics were present. In contrast to the monospecific pairings where all the mites mated, only 14 out of 20 heterospecific pairs established permanent contact and adopted the mating position. Furthermore, the heterospecific pairs needed longer until pair formation, and the initial back-riding phase, which is considered to be important for olfactory mate recognition (Korn, 1982a; Hoy and Cave, 1988), was prolonged. These results indicate that at least a weak mechanism for species-specific mate recognition exists. A similar case was reported for four sympatric phytoseiid
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Reproductive behaviour of mites 1345
mite species, where behavioural differences in mating behaviour exist but are not sufficient to exclude heterospecific matings totally (Takahashi and Chant, 1993). In the case of the P. carabi sibling species, strong pre-mating isolating mechanisms may not be necessary because differential host specificity already reduces the probability of interspecific encounters (Schwarz, in press). Colwell (1986) suggested that differential host preferences may have been the primary mechanism for reducing gene flow between several species of hummingbird flower mites.
At the two temperatures used in our experiments, females of both species produced approximately 200 eggs. This is considerably more than has been reported for females of other mesotigmatic mites, where egg numbers vary between 20 and 100 (Hunter and Rosario, 1988; Yasui 1988; Walter and Ikonen, 1989; Murphy and Sardar, 1991; Sabelis, 1991; Athias-Binche, 1994), and even in phoretic Parasitidae rarely exceed 100 eggs per female (Costa, 1969; Richards and Richards, 1976; Wise et aI., 1988). Because female longevity in species P-vs and P-vo was also relatively short and most females stopped egg-laying some days before dying, the daily oviposition rates were extraordinarily high. Considering the relative size of the eggs (egg diameter of 0.3mm compared to a female idiosoma length of about l '5mm (Korn, 1982c)), the high oviposition rates only seem possible because the females have access to virtually unlimited resources of protein-rich food: during egg-laying they feed on the carcass and prey on nematodes, mites and insect eggs that are available in the brood chamber of their host (Korn, 1982 a,b, 1983; Beninger, 1993).
The high egg-laying rates and the short longevity of the mite females can be explained by the fact that they are semelparous and have to reproduce within the short period between the construction of the beetles' brood chamber and the dispersal of the beetles. Burying bettles usually abandon their brood chamber within 10-18 days after its construction (Trumbo, 1991; Brown and Wilson, 1992). Schwarz and Mfiller (1992) showed that in Nicrophorus vespilloides the beetles usually disperse before day 12 at 20°C. Because the mite offspring need 5 6 days to develop into the phoretic deuteronymphal stage, there is strong selection for females that produce as many of their eggs as soon as possible. High-reproductive rates in turn are likely to incur physiological costs and hence may reduce the longevity of an individual (Roff, 1992). This is supported by the observations of Korn (1982a), who reported that in Poecilochirus spp. unmated adults live longer than mated ones. The necessity to disperse from the brood chamber on the beetles also means that there is selection for short offspring development. Accordingly, the development times in species P-vs and P-vo are shorter than in many other mesostigmatic mite species at comparable temperatures (Bhattacharyya, 1962; Richards and Richards, 1976; Walter and Ikonen, 1989; Murphy and Sardar, 1991; Sabelis, 1991; Athias-Binche, 1994).
Although both species have high oviposition rates and short development times, we found significant differences between species P-vs and P-vo in these life history parameters. This corresponds to the differences in the time of deuteronymph emergence observed by M~ller and Schwarz (1990). It was suggested that differential development times of the mites represented adaptations to differences in brood care behaviour or development time between the respective host species (Mfiller and Schwarz, 1990; Brown and Wilson, 1992). Pukowski (1933) suggests that N. vespillo, the main host of species P-vo (Schwarz, in press), differs in brood care behaviour from the other German species of burying beetle. However, the brood care behaviour of all four German host species must be examined under controlled conditions before it
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can be decided to what extent the timing of reproduction and development in the two sibling species is affected by the duration of brood care in the repsective host species.
Acknowledgements We are grateful to Christiane Strietzel for her help with the pairing experiments.
Many thanks also to Anne Baker, Stelta Koulianos and Nathan Rank for their helpful comments on the manuscript.
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