Age structure - the relative numbers of eggs, immatures and adults - in populations of the house dust mites Dermatophagoidespteronyssinus and Euroglyphus ...
Experimental & Applied Acarology, 16 (1992) 49-74
49
Elsevier Science Publishers B.V., Amsterdam A C A R I 634
Age structure and dynamics of house dust mite populations M.J. Colloff
Department of Zoology, University of Glasgow, Glasgow, UK
ABSTRACT Colloff, M.J., 1992. Age structure and dynamics of house dust mite populations. Exp. Appl. Acarol., 16: 49-74. Age structure - the relative numbers of eggs, immatures and adults - in populations of the house dust mites Dermatophagoidespteronyssinus and Euroglyphus maynei was investigated in four sequential monthly samples taken from mattresses in each of eight homes in Glasgow, Scotland. Additionally, age structure ofD. pteronyssinus was determined in samples taken bimonthly for 6 months from nine quadrats of a double mattress. It was found that although age structure varied considerably with time, for D. pteronyssinus in different homes the most common structure was one in which immatures were dominant, then eggs and then adults (31% of samples). Immatures or eggs were dominant in 75% of samples. For E. maynei the age structure was quite different: the most common structure was one in which adults were dominant, then immatures and then eggs (69% of samples). In different quadrats of a double mattress, mean age structure of D. pteronyssinus underwent a shift towards higher proportions of immatures and then eggs during the sampling period, which reflected the increase in population density detected during this period. Life and fecundity tables were constructed for D. pteronyssinus and E. maynei using previouslyavailable in vitro data on fecundity and survivorship rates and hypothetical values based on means derived from a number of studies. From the tables the stable age distributions were calculated and compared with the age structures of the natural populations. It was found that mean age structure of natural populations of D. pteronyssinus was fairly close to the predicted stable age distribution, but those of E. maynei indicated the populations were in decline during the sampling period, a fact confirmed by abundance data. The concept that the rate of increase of house dust mite populations can be estimated by determining age structure of mites isolated from dust samples was explored using the hypothetical population parameters ofD. pteronyssinus. It was predicted that quite large differences in fecundity and mortality would not drastically alter the proportions of eggs, immatures and adults in stable populations. Eggs as components of the house dust mite population are considered seriously for the first time. Those ofD. pteronyssinus and E. maynei were identified and differentiated by allometry. It is stressed that for D. pteronyssinus, during the sampling period, half or more of the mites in a dust sample may be represented as eggs, and to ignore them is to deliberately make a less accurate estimate of population density than could be otherwise achieved.
Correspondence to (present address): M.J. Colloff, Scottish Parasite Diagnostic Laboratory, Department of Bacteriology, Stobhill Hospital, Glasgow G21 3UW, Scotland, UK.
0168-8162/92/$05.00
9 1992 Elsevier Science Publishers B.V. All rights reserved.
50
M.J. COLLOFF
INTRODUCTION
The subject of house dust mite population dynamics has not received a great deal of attention from researchers. This is surprising considering that the control of house dust mites entails effecting drastic intervention on two of the most basic population parameters, age-specific birth and death rates, and that seasonal fluctuation in population density is the underlying cause of seasonal increases in house dust mite allergen exposure suffered by people with house dust mite hypersensitivity. Indeed, one cannot hope to explain the seasonal dynamics of allergen production without an appreciation of house dust mite population dynamics, simply because population growth is an expression of the population productivity, i.e. biomass, and part of that productivity includes the production of allergens. Previous investigations of age structure and population dynamics have concentrated on seasonal fluctuations in population density in relation to the proportions of the immature stages and adults (Dusb~ibek, 1975; Arlian et al., 1983 ). However, neither of these studies included data on the proportion of the population that was represented by eggs. Age structure of the population, for the purposes of the present paper, refers (more correctly) to 'stage structure': the relative numbers of the different stages of the life-cycle that constitute the population. House dust mite populations are comprised of eggs, larvae, protonymphs, tritonymphs and adult males and females. If the relative proportions of these components fluctuate significantly with time, the age structure of the population is said to be unstable. An unstable age structure is indicative of a population in which growth is somehow interrupted or suppressed, since a population growing geometrically will develop a stable age distribution (Lotka, 1922). Examples of populations that may have unstable age distributions are those that are colonising new habitats or retreating from old ones, or those for which periods of growth alternate with periods of decline caused by external limiting factors. By way of contrast, a stable age distribution implies that the population has become established in its habitat, that external conditions affecting birth and death rates are relatively constant and favourable and that there has been no human intervention by way of attempts at eradication. This scenario contains the assumption that emigration and immigration are minor factors influencing seasonal house dust mite population dynamics, for which there is some evidence (reviewed by Colloff, 1991c). What practical use can the study of age structure of house dust mite populations have for mite control? The mortality-risk of each stage in the population is different, and in general, egg-specific mortality may be assumed to have less effect on the success of control measures than immature- or adultspecific mortality because the duration of the egg is much shorter than that of the other stages and its mortality risk is thus lower. Egg-specific mortality,
AGE STRUCTUREAND DYNAMICSOF HOUSE DUST MITE POPULATIONS
51
however, is a very important factor influencing the recovery of mite populations following acaricide treatment, as is the proportion of the population that is at the egg stage. In order to be effective an acaricide needs to be capable of killing all stages. Some that are currently available commercially have no direct toxicity to eggs, e.g. Natamycin, although some mortality may be achieved by the mechanical clogging of the pores in the shell (de Saint GeorgesGridelet, 1987). If all stages except eggs were killed during a given eradication treatment, then the rate of recolonization of the treated area would be more rapid than if the acaricide was an efficient ovicide. The concept of differences in stage-specific mortality implies that two mite populations of identical density could have radically different chances of surviving control methods that were selective for a particular stage, or stages, if one population had a higher proportion of that stage, or those stages, than the other. It is known that proportions of different stages show seasonal variation (Arlian et al., 1983 ). Is there then an optimal mite control season for some acaricides, and can it be predicted from the analysis of age structure of the mite populations? The aim of the present paper is to explore some of these issues by describing the fluctuations in age structure of populations of Dermatophagoidespteronyssinus and Euroglyphus maynei in homes in Glasgow, Scotland. Additionally, because there has been so little research on population dynamics of house dust mites other than studies of seasonal variation in density, some calculations of basic life-history parameters of the two species were made, based on data on D. pteronyssinus presented by Arlian et al. (1990) and on E. maynei by Taylor (1975). Life and fecundity tables for the two species were constructed and compared, and the stable age distributions of the populations that were described by the life and fecundity tables were calculated and compared with the age structure of the natural populations. ANALYSIS OF AGE S T R U C T U R E OF N A T U R A L P O P U L A T I O N S
Experimental methods To examine age structure of house dust mite populations in different homes, dust samples were taken on four occasions, one month apart, from mattresses in homes in Glasgow between January and May, 1985. An area of 0.25 m 2 was sampled in 1 min using a portable vacuum pump and dust trap. Sampling, mite extraction and preparation techniques have been described previously (Colloff, 1987a, 1989 ). Mites were assessed as 'damaged' or 'intact' as a means of determining whether they were dead or alive at the time of sampling. Determination of the immature stages was done using the key of Mumcouglu (1976). The eggs of D. pteronyssinus and E. maynei were easily visible in dust samples suspended in lactic acid: they are elongated, cylindri-
52
M.J. COLLOFF
cal, and stain heavily when lignin pink is added to the suspension. The identity of eggs was determined allometrically: mean length and breadth of eggs of D. pteronyssinus ( +_standard deviation) is 151 _+9 • 59 + 5 #m and of E. maynei is 122 + 9 X 55 +_6/tin (Colloff, 1991 a). This method is quite accurate only about 7% of eggs overlap the size ranges of the two species - and pyroglyphid mite eggs are the only items of these sizes and shapes likely to be encountered in house dust. The eggs of acarid and glycyphagid mites are much more rounded than those of pyroglyphids. It should be noted here that in dust samples from Glaswegian mattresses, D. pteronyssinus and E. maynei are the two most frequent and abundant species. Dermatophagoides farinae and D. m icroceras are so rare as to be absent for practical purposes (Colloff, 1987a). In regions where multispecies Dermatophagoides populations exist, e.g. Continental Europe, allometry of eggs will not discriminate the different Dermatophagoides species. To examine age structure of house dust mite populations in different areas within one bed, dust samples were taken bimonthly from a 15-year-old double mattress that had been marked out into nine 0.24-m 2 quadrats (Colloff, 1988 ). Each quadrat was sampled for 1 min. -
Results House dust mite populations in different homes Only homes in which live mites of all stages were detected were included in the analysis, and complete data on age structure of populations ofD. pteronyssinus and E. maynei are available from eight homes for each species. No home yielded complete data on age structure of both species. For simplicity, data are expressed as the relative abundances (expressed as percentages of total live mites) of three groups only: eggs, immatures (larvae, protonymphs and tritonymphs combined) and adults. From Figs. 1 and 2 it is clear that age structure can vary considerably from month to month and that in no home is age structure consistent over the sampling period. For D. pteronyssinus the most common form of curve is that in which relative abundance follows the sequence: immatures>eggs>adults (type 4; Table 1 ). Immatures or eggs were numerically dominant in 75% of samples. By way of contrast, for E. maynei the most common curve followed the sequence: adults > immatures > eggs (type 1; Table 1 ). Immatures and eggs dominated numerically in only 19% of samples. Thus the age structures of natural populations of the two species during the sampling period was entirely opposite: in D. pteronyssinus populations, young stages predominated whereas in E. maynei populations, older stages did. Over the 3-month sampling period, mean monthly age structure ofD. pteronyssinus and E. maynei within different homes showed only slight variation
AGE STRUCTURE AND DYNAMICS OF HOUSE DUST MITE POPULATIONS
53
"6
~N
A 0 10
100
40
0 10
40
IO0
duration
• duration
~ ,o] / l: " U /
/~.S
-.
0 10 40 • duration
too
0 10 40 7, d u r a t i o n
too
0 10
100
0 10
100
40
7, duration
40
x duration
./1_.
o
.~-
8
,o /LZ ~,ol/U< / ~. immatures > eggs 2. Adults > eggs > immatures 3. Immatures > adults > eggs 4. Immatures > eggs > adults 5. Eggs > adults > immatures 6. Eggs > immatures > adults
E. maynei Homes (n=32)
Homes (n=32)
0
7
22
1
1
4
9 13 7 6
6 10 3 5
2 1 2 1
TABLE 2 Mean age structure (relative abundances, expressed as percentages) and type of age structure of eggs (E), immatures (1) and adults (A) of Dermatophagoides pteronyssinus within nine quadrats of a double mattress on four bimonthly sampling occasions and ofEuroglyphus maynei and D. pteronyssinus on four monthly sampling occasions in mattresses in eight different homes Sampling occasion
D. pteronyssinus
E. maynei
Mattress (n = 9)
1 2 3 4
Homes (n = 8 )
E
I
A
Type
22 28 44 40
61 58 26 34
17 14 30 26
4 4 5 6
23 24 33 29
Homes (n = 8)
I
A
Type
E
I
A
Type
43 49 36 46
34 27 31 25
3 3 4 4
9 21 22 18
26 33 27 28
65 46 51 54
1 1 1 1
(Table 2). For D. pteronyssinus, on sampling occasions 1 and 2, age structure followed a type-3 sequence while on the latter two occasions it followed a type-4 sequence. For E. maynei it followed a type-1 sequence on every sampling occasion.
House dust mite populations in different parts of a mattress Age structure of D. pteronyssinus populations within nine quadrats of a double mattress over a 6-month period is shown in Fig. 3. The structure is more consistent than that ofD. pteronyssinus in mattresses in different homes; there was only one sample (quadrat 2C, m o n t h 4) in which adults were numerically dominant. Immatures were dominant in 61% of samples, eggs in 36% (Table 1 ).
56
M.J. COLLOFF
A
B
~~~ . x ~ ,
t ~a
,o
~,o ~>.,' 0 10
40 duration
O 10
..
2 g ~o]1~ \ ' ~ . .
O 10 40 V. d u r a t i o n
6
100
100
100
0 10 40 • duration
100
"\.
.-.-\,
2,.f'o~
~,,o/
40 ~ duration
./.-~. , ol,,'-u~/'.,/w ~,oI! J/x. x,~oo,-t ~o
/~\.~_
.,'-'-~.
o~/j
J~\ , ,oj~'-,v-->.,/xz t 60
:Z:,--" ~:~>.~04oo-"
100
0 10 40 V~d u r a t i o n
~
C
0 10 40 ~ duration
~.o
2/0~ ,*
~ 2o]1 U / U \ /
E I A 0 1(] 40 7=d u r a t i o n
100
~ . . . . 0 10 40 7, d u r a t i o n
s 0 100
~ 100
0 10 40 • duration
100
Fig. 3. Fluctuations in age structure of populations of Dermatophagoidespteronyssinusin nine 0.24-m2 quadrats of a double bed over a 6-month period. Rows 1, 2 and 3 refer to the top, middle and bottom of the mattress; columns A, B and C to the right-hand side, middle and lefthand side. Rest of legend as for Fig. 1.
Age structure o f some adjacent quadrats had identical sequential patterns during certain periods (e.g. in quadrats 3A, 3B and 3C during the first 4 months; adults are of higher numerical dominance in quadrats of row 1 than elsewhere) b u t in no two quadrats was the sequence of types of age structure identical over the entire period. An examination of the mean bimonthly variation in age structure of D. pteronyssinus (Table 2) showed there was a distinct shift from a type-4 sequence on sampling occasions 1 and 2 to a type 5 during the 4th m o n t h and a type 6 during the 6th. This shift, towards a d o m i n a n c e of eggs during the latter two months reflects the increased population density o f D . pteronyssinus that was detected during this period (data not shown).
57
AGE STRUCTURE AND DYNAMICS OF HOUSE DUST MITE POPULATIONS
REPRODUCTION AND SURVIVORSHIP
Construction of life and fecundity tables To the author's knowledge, life and fecundity tables for any pyroglyphid species have not been published previously. It seems there is sufficient data contained in only two studies to construct them. In the case ofD. pteronyssinus, Arlian et al. (1990) provided data on the total number of eggs laid per day by a cohort of 58 females and the daily mortality of that cohort at 23 oC, 75% RH (their fig. 3 ), but no data on mortality of immature stages or eggs. From this, adult female survivorship and the numbers of female eggs laid per adult female per day were calculated by graphical interpretation by the present author and used to construct the life and fecundity table (Appendix 1f). For E. maynei, Taylor ( 1975 ) provided data on survivorship of all stages in the life-cycle (Fig. 4) (not just adult females) at five combinations of temperature and humidity. In the present study, to make survivorship data of E. maynei comparable with that of D. pteronyssinus, survivorship values for each day of adulthood were expressed 1.0
|
[] O
25C 60% RH
+ 25C 75% RH D 25C 80% RH
0.8
& 30C 75% RH O 3OC80% RH
H
0.6
e~ to
,>
0.4
~0
&
~
~
30C 8O%RH 25C 80% RH
0.2
~30C 75% RH 0,0 10
20
30
40
Days
Fig. 4. Mean age-specific survivorship ofEuroglyphus maynei at five different combinations of temperature and humidity. Lines of best fit were estimated by eye. Drawn from original data presented by Taylor (1975).
58
M.J. COLLOFF
as a proportion of 1.0. Taylor ( 1975 ) did not detail the total numbers of eggs laid per day by his cohorts of females, only the total number laid per female during her entire oviposition period. Estimates of the former were made by the present author by graphical interpretation as follows: data on the total number of eggs laid by each female during her oviposition period were plotted against the duration of the oviposition period. To obtain a line of best fit from what is naturally a curvilinear relationship - the numbers of eggs laid per day decreases with time - regression analysis was done using log~o-transformed values of oviposition periods (Fig. 5 ). From the lines of best fit, numbers of female eggs laid per female per day were calculated. Life and fecundity tables of E. maynei are presented in Appendix 1a-e. Both D. pteronyssinus and E. maynei have equal sex ratios, thus the number of female eggs laid per female per day is half of the total eggs laid per female per day. The columns in the life and fertility tables and the parameters derived from them are as follows (cf. Birch, 1948): x is the age interval in days, also called the pivotal age. 3 5 -
+ A
O 25C 60% RH
30-
+
13 25C80% RH
E 25-
& 30C 75% RH
$ r
25C 75% RH
9
30C 80% RH
20
r 15"
..Q E r.
10'
~0
s.
I-0
i
0
10
i
~
20
30
i
40
t
50
Days Fig. 5. Cumulative age-specific oviposition rates of Euroglyphus maynei kept at five different combinations of temperature and humidity. Lines of best fit were derived from regression analysis using log~o-transformed values of oviposition periods. Drawn from original data presented by Taylor ( 1975 ).
AGE STRUCTURE AND DYNAMICS OF HOUSE DUST MITE POPULATIONS
59
lx is the age-specific survival rate (survivorship); the proportion of adult females alive in age interval x. lx, is the proportion of females alive in the age interval x calculated from day 1 of adulthood (thus the last day of the tritonymph stage has a value of 1, since 'day 1' refers here to the end of the day, not the beginning). mx is the number of female eggs produced per surviving adult female per day at time x. It is half the total number of eggs laid per female per day: equal sex ratios of eggs are assumed. l~mx is the number of female eggs produced per original adult female in the cohort per day at time x. xl~rnx is the total realised fecundity. Ro is the net reproduction; the average number of female offspring produced per adult female during its lifetime. In other words, it is the number of times a population will multiply in each generation:
Ro = Elxrnx
( 1)
T is the mean generation time: the average age of parenthood. The approximation used here is obtained by dividing the sum of the total realised fecundity by Ro:
Zxl~m~ T-
Ro
(2)
rm is the intrinsic rate of natural increase of the population and is calculated as follows: rm-
log I e Ro T
(3)
2 is the finite rate of increase, the number of times the population multiplies in a unit of time, calculated as the natural antilog, of the intrinsic rate of increase: 2 = e rm
(4)
Doubling time is the time in days it would take for a population, at a given value of 2, to double in numbers. It is calculated as: 1
2-1
(5)
Results From the graphical representations of the life and fecundity data of E. maynei and D. pteronyssinus (Fig. 6a-f), it is clear that mean longevity of D.
M.J.COLLOFF
60
Ix
'
0.5 6
Ix
15
23
I"
.
33
mx
0.5
60% RH
25~
57
1.0
1.0
mx
75% RH
25~ 5
ix
12
C 1.0 1~ 0.5
~
~ 5
d Ix 1.0 0.5
18
4
26
45
~ ,
1.5 mx 1.0
13
20
27
48
1.s i ,,
11
19
1.0 0.5
26
1.0 ~
~
4
f
10
mx
75% RH 30~
45
1.0 Ix 0.5 ]
80% RH 25~
0.5
mx
80% RH 30~
0.5
17 22
39 ~
0t
Ix 0.5
1
.
5
0mxToRH 05
i 8
19
i 26
34
23~
65
Days
Fig. 6. (a-e) Comparative rates 0f reproduction (rnx) and survivorship (lx) of Euroglyphus rnaynei at five different combinations of temperature and humidity. From data presented by Taylor ( 1975 ). (f) Reproduction and adult su rvivorship (tx,) of Dermatophagoidespteronyssinus at 23~ 75% RH. Redrawn from original data presented by Aflian et al. (1990). Numbers on x axis are the mean durations of eggs, larvae, protonymphs, tritonymphs and adult females, in that order. Dotted line represents last day before adulthood; survival rate of adults given by l~,.
pteronyssinus was g r e a t e r t h a n t h a t o f E . maynei a n d t h a t a l t h o u g h its m a x i m u m mx v a l u e (1.72 f e m a l e e g g s / f e m a l e / d a y ) was slightly l o w e r t h a n the highest o f E. maynei (1.78 at 3 0 ~ 75% R H ) , high f e c u n d i t y rates were m a i n t a i n e d f o r a m u c h l o n g e r p e r i o d . Dermatophagoides pteronyssinus h a d
AGE STRUCTURE AND DYNAMICS OF HOUSE DUST MITE POPULATIONS
61
17 days on which rex> 1, whereas the equivalent durations for E. maynei were: 2 days at 25~ 60% RH; 3 days at 25~ 75% RH; 0 days at 25~ 80% RH; 2 days at 30~ 75% RH; and 2 days at 30~ 80% RH. Adult survivorship (lx,) of D. pteronyssinus during the period of highest fecundity remained very high when compared with that ofE. maynei: no adult female D. pteronyssinus died for the first 11 days. By way of contrast, maximum survivorship of adult E. maynei on day 11 was 0.73 (at 30~ 80% RH). In other words, the net reproductive rate (Ro) of D. pteronyssinus is greater because adult females produce a relatively high number of eggs over a longer period during which mortality is relatively low. Mortality only starts to increase noticeably after fecundity has slowed (Fig. 6f). With E. maynei, the relatively short period of maximum fecundity coincided with periods of relatively rapid female mortality, leading to low values of R0. It has to be said that this situation is in part an artifact of the different ways that lx, has been calculated for the two species. It is likely, for example, that were 56 pairs of newly-moulted female E. maynei to be removed from cultures and placed with males, as was done with D. pteronyssinus in the study by Arlian et al. (1990), that survivorship would be higher over the first few days than if it was calculated as a function of survivorship of all stages from age x = 0, as it was in the present study. Similarly, the method used herein to calculate age-specific fecundity of E. maynei gives nowhere near as accurate an estimate as that used by Arlian et al. (1990). Additionally, the growth of E. maynei populations had been retarded by the experimental procedures used by Taylor (1975 ). This is indicated by the very high mortality rates among the eggs and immatures (Fig. 6a-e), which was responsible for the computation of a negative value Ofrm for those mites kept at 30~ 75% RH, and also by the fact that Hart and Fain (1988) and Hart (pers. commun., 1991 ) reported much higher fecundity of E. maynei - a mean of 84 eggs laid per female in 60 days at 25 ~ 75% RH. Table 3 shows that high mortality during egg and immature stages has the effect of reducing the value of R0, rm and 2, and increasing doubling time very considerably. In the case of E. maynei at 30~ 75% RH, Ro is < 1, giving a negative value of rm, indicating that the population is declining in numbers. For D. pteronyssinus, the finite rate of increase (2) is higher and the doubling time ( 13.3 days) more rapid than the shortest doubling time for E. maynei (16.4 days at 25~ 75% RH). This is in accordance with reports in the literature (reviewed by Colloff, 1991b ) that in general D. pteronyssinus has a shorter life-cycle duration, occurs more frequently and in higher densities than E. maynei. STABLE AGE DISTRIBUTION
Having constructed life and fecundity tables it is possible to calculate the age distribution of the population. This gives an estimate of the proportion of
62
M.J. COLLOFF
TABLE 3 Summary of values of demographic parameters of Euroglyphus maynei (upper figures calculated using Ix,, lower figures calculated using lx) and Derma tophagoides pteronyssinus (calculated using Ix, ) Population parameters
Ro
T
Doubling time (days)
rm
.~
E. maynei 25~
30~
60% RH
6.97 1.18
44.05 44.04
0.044 0.0038
1.045 1.0038
22.2 263.2
75% RH
7.55 2.41
34.48 34.65
0.059 0.0254
1.061 1.0257
16.4 38.9
80% RH
4.18 1.32
36.50 36.60
0.039 0.0076
1.04 1.0076
25.0 131.6
75% RH
6.25 0.56
33.80 33.78
80% RH
4,82 1.80
30.44 29.95
30.87
47.6
0.054 -0.018
1.056 0.983
18.0 -
0.052 0.0197
1.053 1.0199
18.9 50.3
0.072
1.075
13.3
D. pteronyssinus 23~
75% RH
individuals in each age class in a growing population in which age structure has become stabilised. This is of relevance to the present study because it shows how close the age structure of a natural population is to the stable age distribution, thus giving an indication of the rate of growth of the natural population. This implies that the rate of increase can be estimated if the age structure of the population is known. In theory this is true, but whether a reliable estimate of the rate of increase of a population could be obtained by determining age structure in a single sample is a different matter. In practical terms, it tells us whether the natural population is 'obeying' the pattern of population growth predicted for it from the life and fecundity table. If so, then this implies that the constraints on population growth imposed by the environment are of negligible effect and if not, that constraints are noticeably retarding population growth.
Calculation of the stable age distribution ofE. maynei Methods of computation are given by Birch (1948) and Andrewartha and Birch ( 1954, pp. 43-45 ). The following formulae were used: Lx is the stationary age distribution, calculated as: Lx -
l~+lx+l 2
(6)
Px is the proportion of individuals aged between x and x + 1 in the stable population:
AGESTRUCTUREANDDYNAMICSOFHOUSEDUSTMITEPOPULATIONS m
a
Ix
2.o
1.0 -
1.0
0.5"
0.5
6
b i X
~
1.0
0.5
12
1B
~ 6
12
25
63
mx
66
2.0 1.5 '
mx
1.0
0.5
18
1
25
66 Days
Fig. 7. (a,b) Reproduction (mx) and survivorship (Ix) rates of two hypothetical populations of
Dermatophagoidespteronyssinus.(a) has an lx value of 50% by the last day of mean adult duration and an mx range from 2.0 max. to 1.0 min. (b) has an lxvalue of 20% by the last day of mean adult duration and an mx range from 1.0 to 3.5.
Px=flLxe -rm(x+1)
(7)
1/fl= ~ Lxe -rm~x+l)
(8)
x=O
where x = m to m + 1 is the last age group in the life table age distribution. The s u m m e d values o f L~e -rm~+l) for age group x to x + 1 can be expressed as a percentage of 1~ft. To calculate the stable age distribution, age-specific survivorship of all stages in the life cycle is required (lx). These data are not available for D. pteronyssinus at present so, in order to examine what the stable age distribution o f D. pteronyssinus would be like, two life and fecundity tables were constructed using an hypothetical population of D. pteronyssinus with a m e a n longevity, derived from the means o f the values in Table 5, o f 66 days. Two sets of hypothetical l~ values were used; one with 50% survivorship by day 66, the other with 20% survivorship, and also two sets of hypothetical mx values; one with a m a x i m u m o f 2.0 by day 6 o f adulthood (pre-oviposition period o f 3 days) which declined to 1.0 by day 40 and one with mx max. o f 1.0, declining to 0.5 (Fig. 7a,b).
Results A s u m m a r y of the age structure o f E. rnaynei in stable populations, expressed as stages, at five combinations o f temperature and humidity is given
64
MJ. COLLOFF
TABLE4 Estimated stable age distributions and type of distribution (expressed as percentage relative abundance of eggs, immatures and adults) of Euroglyphus maynei at different temperatures and humidities, and of two hypothetical populations of D. pteronyssinus Temperature (~
Humidity (%RH)
% relative abundance
Type
Eggs
Immatures
Adults
36 37 29 . 31
49 51 53
15 12 18
4 4 4
51
18
4
47 49
10 14
4 4
Euroglyphus maynei 25
60 75 80 75 80
30
.
.
.
Dermatophagoides pteronyssinus l~50 mx 2.0 /~.20 m~ 1.0
o;_ 6o. 40
43 37
.b?
d
a
:
E 0 10
I
.
,,.. 2 O A 55
100
duration Fig. 8. Stable age distribution of the E. maynei population at 30~ different values ofrm: a=0.02; b=0.0002; c= - 0 . 0 2 ; d = -0.05.
80% RH, computed with
in Table 4. They all correspond to type-4 age structures, the most common age structure of the natural populations ofD. pteronyssinus and very different from those found in the natural populations ofE. maynei (Tables 1 and 2), which have an age structure indicative of a decline in the natural populations over the sampling period. This was confirmed by the data on numerical abundance of E. maynei (data not shown). The bottom part of Table 4 shows the stable age distributions of D. pteronyssinus based on the two sets of hypothetical lx and mx values. It is interesting that there is a relatively small difference (6%) in the percentage of eggs between the two populations, considering that one has half the maximum fecundity and more than twice the maximum mortality of the other. These hypothetical stable age distributions do actually resemble the age structures found in the natural populations: they are both of type 4.
65
AGE S T R U C T U R E AND DYNAMICS O F H O U S E D U S T MITE P O P U L A T I O N S
. ~
9 n~
0
0 o t'N
I
