So far I have published or placed on the internet three papers.  Here are links to papers two and three and the entirety of paper one.  The editors of the first paper, published in African Entomology is difficult to find on the internet, have kindly allowed me to share it at will, so here it is after papers two and three.

Paper two: Kinship governs fertility with pre- and post-zygotic mechanisms mediated by match of methylation patterns

Paper three: Folic Acid Reduces Drosophila melanogaster Fertility at Clinically Significant Dilution

Paper one:
Fluctuation of fertility with number in a real insect population and a
virtual population
M.L. Herbert1* & M.G. Lewis2
1Volunteer Department, Pinellas County Health Department, 205 Dr M.L. King Street North, Saint Petersburg,
Florida 33701, U.S.A.
2Clinical Pathology, USF College of Medicine, 12901 Bruce B. Downs Blvd, MDC 2, Tampa, Florida 33612, U.S.A.
and Sun Pathology, PA, 6501, Pasadena Avenue North, Saint Petersburg, Florida 33710, U.S.A.
Real fruit fly fertility increases with average consanguinity thus decreasing with population
size in a pattern that is modelled successfully with a virtual population. This invites the
deliberate manipulation of wild insect populations for the control of vectors of human
Key words: fruit fly, Drosophila melanogaster, disease vector, mosquito, malaria, dengue,
population control, insect control, pesticide, gene pool size.
Population growth rate in animals is related to
population size so it would be helpful if this effect
could be used in the control of insect populations.
Insect-borne diseases are a serious health issue,
and insects can be killed by such things as insecticides
but this typically results in a population
larger than ever. Our captive population of
Drosophila melanogaster showed a cyclic rise and
fall not consistent with a simple equilibration process
and that could be duplicated with a computer
program. There is an opportunity for empirical exploitation
of this and it could serve as an experimental
model for elucidating the mechanism.
It has been established that in wild populations,
the growth rate of the population is largely determined
by population size (Sibley et al. 2005).Asimilar
pattern is seen in humans (Helgason et al. 2008)
or can be inferred in humans (Diamond 2002) and
during mouse plagues (Singleton & Krebs 2007)
because of a similar time course of the population
We reasoned that if this effect was robust and
widespread that it could be used to manage wild
insect populations. We were motivated by the
thought that insect-borne human diseases are
important and that any means that might be used
to control the insect numbers might have desirable
results for human health. Accordingly, laboratory
fruit flies were raised in a large cage and their
population size was followed. We found that the
time course of the population size was predictable
enough to invite such a management attempt.
Since the effect can be demonstrated in the laboratory
the opportunity exists to work out the cause
of the connection between population size and
thus average consanguinity on the one hand and
fertility on the other.
We suspected a pre-zygotic epigenetic mechanism,
one that happens before the ovum is fertilized
since sperm have been shown to recognize
kin sperm (Fisher & Hoekstra 2010) and thus
might well recognize related ova. In the event
there is evidence for a post-zygotic mechanism so
the distinction remains equivocal.
Our starting material consisted of 16 lines of
commercially available laboratory fruit flies that
had been raised in isolation from each other for
their value in having distinctive phenotypic traits.
These traits were not of interest to us, but the fact
that they had been isolated from each other permitted
us to establish an outbred population. The
chosen lines were designated by the supplier as
wild type, bar, scalloped, vermilion, white, white
miniature forked, yellow, black, cinnabar, sepia,
white apterous, white vestigal, dumpy, lobe, scarlet
and ebony and designated by us as A to P, respectively.
Sexes were separated, and crosses were made in
four sequential generations by the scheme A × B,
B × C, C × D …P × A. Then we bred AB × CD,
BC×DE, CD×DE…NO×PA. The next generation
African Entomology 21(1): 119–125 (2013)
*Author for correspondence. E-mail:
MNO. This resulted in 16 lines, ABCDEFGHIJK
initial generations were raised in standard laboratory
vials on commercially available fruit fly
medium with water and yeast.
When the crosses had been completed, the vials
were placed open in a cage of sheer fabric over a
wood and hardware cloth frame. Light mittens
were sewn into the fabric. A pass-through was
placed with one door opening into the cage and
one outside. Observation windows were included.
The system was plumbed for vacuum so that the
cage could be vacuumed or the pass-through
flushed of insects. This plumbing did not prove
The dimensions of the cage were 89 cm high
56 cm wide × 152 cm long. The pass-through
measured 32 cm high × 30 cmwide × 55 cmlong.
There were 8 shelves suspended in the cage
measuring 54 cm × 47 cm. Counts were taken on
two areas of observation window each measuring
13 cm × 12.5 cm. Bottles in the cage measured
5 cm × 5 cm × approximately 11 cm and were
initially filled with four ounce measures of culture
medium and five ounce-measures of water with
about 32 grains of yeast. When the vials were
placed, four culture bottles were placed with
them. To these four more were added daily. After
one week the vials were removed. Each day all the
bottles were moved. Bottles that were 28 days old
were removed. Counts were made at about 08:00
everymorning before the flies had been disturbed.
For 10 days counts were also made after the flies
had been disturbed.
Each month two of the bottles being removed
were emptied and for two days allowed to accumulate
flies that had eclosed. These were then
collected and kept until they had produced
maggots to verify their fertility. Then they were
taken for histological study. One of the bottles was
treated with isopropyl alcohol and kept. Twice,
from 23 August to 26 October 2009 and from 1 November
2009 to 12 May 2010, supplementary food
was given in the form of a dish with six ouncemeasures
of medium and eight of water. This
supplement was replaced weekly. A bowl of the
foam vial stoppers soaked in water was always
present in the cage and was changed as needed.
The room temperature and humidity were
controlled. Illumination was through windows
with blinds drawn so that direct sunlight did not
enter. The room lights were rarely turned on
except when the observations and bottle changes
were being made. The original lines were maintained
in vials on a table in the same room and
none of the original lines died out.
Ten days of counting before the flies were disturbed
totalled 401 flies. The same 10 days of
counting after the flies were disturbed totalled
1024 flies. The interior area of the cage was
54 048 cm2. The counting areas together had an
area of 326 cm2. They constituted one part in
165.8 of the available surfaces excluding the
shelves, which remained essentially vacant except
for the edges. The proportion of flies that were
present initially was one part in 2.554 of those on
the windows after they had been disturbed. Some
flies remained in bottles after the disturbance;
these were not taken into account. Flies avoided
the pass-through possibly because bottles being
removed were tapped on the pass-through to
clear them of flies. Flies tended to accumulate on
the edges of the shelves. Some remained in the air,
particularly after they had been disturbed. It was
not deemed feasible to increase the accuracy of the
census by taking these flies into account. So the
best estimate of the actual number of flies would
be reached by multiplying the raw counts by the
correction for window size, the correction for flies
remaining in bottles and dividing by seven days of
pooled counts, or by multiplying raw pooled
counts by 24.
No evident effect was seen on the counts that
could be attributed to the supplementary feeding,
seasonal changes, the weather over a week or the
few occasions when dead flies were vacuumed
For histology, collections of intact Drosophila
were received in 10 % neutral buffered formalin
for fixation. They were then processed in a standard
method using an automated processor for
embedding in paraffin. Sections were cut at 5 μm
approximately. Multiple levels were placed upon
glass microscopic slides and cover slipped in the
usual fashion. The sections were stained with
haematoxylin and eosin prior to examination
under a Leica™ compound microscope.
To better understand the process, a computer
program was constructed using C++ language
that created a virtual population with fertility
120 African Entomology Vol. 21, No. 1, 2013
decreasing with decreasing consanguinity and
increasing population size using both a pre-zygotic
mechanism and a post-zygotic mechanism.
Parameters for the post-zygotic mechanism were a
single simulation that lasted 1000 generations of
which only the first 79 are shown. There were 100
in the population at the outset with a maximum of
1000 each generation. Each pair could have up to
100 offspring. There were 100 sites subject to
changes affecting post-zygotic fertility with a
change rate of 2100 per site per 100 000 generations
with a loss of 2100 one thousandth of an offspring
per unit of mismatch.
Runs were done with the same program using
only the pre-zygotic mechanism. Parameters for
the pre-zygotic mechanism were a single simulation
that lasted up to 1000 generations. There were
100 in the population at the outset with a maximum
of 100 each generation and then on repeat
simulation 1000 each generation. Each pair could
have up to 100 offspring. There were 100 sites
affecting pre-zygotic fertility with a change rate of
5000 per site per 100 000 generations with a loss of
500 one thousandths of an offspring per unit of
Further runs were done employing both the
pre-zygotic mechanism and post-zygotic mechanism
at the same time. Parameters for the combined
mechanism were a single simulation lasting
up to 1000 generations. There were 1001 in the
population at the outset with a maximum of 1000
each generation and on repeat simulation 50 each
generation. Each pair could have up to 100 offspring.
There were 100 sites affecting pre-zygotic
fertility with a change rate of 500 per site per
100 000 generations with a loss of 500 one thousandths
of an offspring per unit of mismatch.
There were 100 sites affecting post-zygotic fertility
with a change rate of 2100 per site per 100 000
generations with a loss of 2100 one thousandths
of an offspring per unit of mismatch.
Two years of daily counts were obtained on our
captive fruit fly population. Daily counts were
pooled on a weekly basis and the resulting population
changes graphed in Fig. 1.
There is a short series of peaks in which the
peaks are successively lower in linear fashion and
the valleys are successively lower in linear fashion
with the peaks skewed to the left. Then the population
size becomes less predictable.
When our computer program that created a
virtual population with fertility decreasing with
decreasing consanguinity and increasing population
size using a post-zygotic mechanism was run,
the results shown in Fig. 2 were obtained.
In the initial stage of growth, the real population
started after four generations of outbreeding. In
the virtual population initial growth started from
what was a virtual clone with all members
optimized for maximum fertility so, as would be
expected, the initial growth of the virtual population
rose disproportionately high. Then there was
a short series of peaks, each peak lower than the
last and each valley lower than the last in linear
fashion and the peaks skewed to the left. Then the
Herbert & Lewis: Fluctuation of fertility with number in virtual and real insect populations 121

Fig. 1. Raw counts pooling both windows for two weeks. The vertical axis is the accumulated counts. The horizontal
axis is time. Counts started on 7 July 2008 and continued to 11 July 2010.
population size began to wander. This was true for
both the real population and of the virtual population.
This matched closely the pattern observed in
the experiment, so we have evidence for a simple
mechanism producing post-zygotic infertility and
need invoke nothing further. That is not to say that
this elegant match will happen every time either
in the virtual world or the real world. Specifically
in the simulation the decline in the valley heights
was not consistent. The numbers are higher and
the statistics are better in the experimental model
both with regards to population size and presumably
at the molecular level. Still it is only one
history. Possibly a repeat attempt would be different.
Oneobvious hypothesis is that the population in
each case is undergoing adampedoscillation seeking
equilibrium. But this is not possible because
that would require the peaks to fall, which they do,
but also that the valleys must rise, which they do
The same pattern using a simulation with a
pre-zygotic mechanism was not obtained. Rather
the pattern was as in Fig. 3.


122 African Entomology Vol. 21, No. 1, 2013

Fig. 2. A single run of a computer program modeling a population affected by post-zygotic infertility increasing with
decreasing consanguinity and increasing population size.

Fig. 3. A single run of a computer program modelling a population affected by pre-zygotic infertility increasing with
decreasing consanguinity and increasing population size.
Under these conditions the population survived
for 1000 generations when it was limited to 100
individuals. However when the population was
permitted to rise as in Fig. 3, it grew, declined,
appeared to be stabilizing and then abruptly
collapsed. This does not reflect the behaviour or
the fruit fly population nor do we know of any
data in the real world reflecting such a time course.
When the two effects were combined, the time
course is shown in Fig. 4.





With this many processes going on the noise
level rises. In fact the population limited to 50 only
survived for 80 generations while the population
of 1000 died out in fewer than 30. Even given the
noise it can be seen that the time course is different
from the pure pre-zygotic mechanism and the
pure post-zygotic mechanism. The population
rises, falls and rises again before collapsing.
In the histological examination, multiple adult
Drosophila were examined on each slide. Many of
these flies were cut at different planes of section
and at different angles; however, it was readily
apparent that the gonadal tissue in both males and
females could be easily identified and roughly
correlated in terms of quantity from one to three.
There were easily identifiable spermatozoa in
the males, and easily identifiable ova and active
oogenesis in the females.
Although there appears to be some variation in
the quantitative aspects of both oogenesis and
spermatogenesis, in none of the samples was there
a complete absence of either. Although some
specimens did appear to have more activity than
others, it is doubtful if this had any statistical
When collections were compared during rapid
population growth with collections during rapid
population decline, no correlation was found with
the activity of either spermatogenesis in the male
or oogenesis in the female or any other phenotypic
Therefore, it is concluded from this part of the
study that sterility, at least as measured by histological
appearance, does not fluctuate or correlate
in fluctuation with the population studies described
It was not known at the outset whether the cage
would be sufficiently large to accommodate a
population large enough to show the effect of the
published relationship between population size
and fertility. In the event, it appears to have been
adequate although a larger population would
have been interesting.
The fly population rises exponentially at first but
then falls and the cycle repeats for a total of four
cycles. Then the population appears to stabilize
relatively but continues to wander. Thus we
confirm what is already known (Sibley et al. 2005)
and conclude that fluctuation of the population is
not regulated by available resources under the
experimental conditions. The cycles last about
Herbert & Lewis: Fluctuation of fertility with number in virtual and real insect populations 123
Fig. 4. A single run of a computer program modelling a population affected by pre-zygotic and post-zygotic infertility
increasing with decreasing consanguinity and increasing population size.
20 weeks. Assuming that it takes a fruit fly two
weeks to mature and that it survives and is fertile
for another four weeks, the average generation
time is four weeks. That implies that a cycle runs its
course in only five generations. This is far too fast
forDNAmutations to be important (Haag-Liautard
et al. 2008). We surmise that there is some
epigenetic effect at work, some mechanism that
regulates genes rather than changes in the genes
themselves; epigenetic changes can be much
faster (Petronis 2010). Besides, it cannot be due to a
simple matter of interacting genes. The population
had been crossed in 16 different ways so every
gene had already had the opportunity to react
with every other gene.
The fact that the first four cycles of about four
generations each reach a lower maximum and fall
to a lower nadir suggests that this is not simply a
matter of the population equilibrating to the level
the environment could support. In that case the
peaks should be falling and the valleys rising
(Nicholson 1957).
Although there was never a shortage of food
or space for the adults, it was evident that the
maggots were quite crowded. Furthermore when
a vial was exposed in the cage briefly a few
maggots appeared and then the pupae eclosed at
the expected time over a period of two days. But
when a vial was placed in the cage where it was
exposed to many flies longer and then watched,
pupae continued to eclose for several days longer
suggesting that crowding delayed the development
of the maggots. This was a possible confounding
It would be of interest to follow the time course
of an isolated population of some different animal
to see whether the same phenomenon is manifested.
The time course of a population in Long
House Valley in the American southwest was
followed by counting the number of habitations
that were occupied each year according to radiocarbon
dating of the remains of their fires (Diamond
2002). The number of occupied dwellings tracked
closely with tree ring width, and Diamond quite
reasonably suggested that rainfall was determining
the carrying capacity of the valley. If we take
the opposite view, namely that the farmers were
cultivating the trees so as to meet their needs, the
human population changes may be due to a
similar mechanism to the one seen in the flies.
Early on the population is low. Eventually it rises
exponentially, falls, rises again and then falls to
zero. The time course from takeoff to the last
dwelling falling vacant is about 300 years or
roughly 150 years per cycle. If we assume that
humans start having children at about 20 and stop
at about 40, that would mean a 30-year generation
time or five generations per cycle. So although the
profile of the curve is different, the basic cycle time
is similar.
In the Long House Valley experience the second
peak is higher than the first and does not appear to
last as long. The peaks of the insect data are
skewed toward the left and the peaks of the
mammalian data are, if anything, skewed toward
the right. Still the time course is close enough to
encourage us to think that the five-generation
pattern is widespread in nature and will be found
in other insects.
Returning to mammals, regular counts of the
number of mice present during and between
mouse plagues in Australia and New Zealand
have been done and recorded (Singleton & Krebs
2007). Usually the plague is reflected in a single
population spike. Occasionally there is a double
spike, lower than the single spikes, with the
double spike following much the same pattern as
that seen in Long House valley. This lends further
support to the impression that the same process is
The data reported in a study done in Iceland
(Helgason et al. 2008), one done in Denmark
(Labouriau & Amorim 2008) and studies done in
animals (Sibley et al. 2005) all tend to show the same
pattern of consanguinity and fertility. Fertility
is low when consanguinity is high, rises as consanguinity
decreases and then falls and tends to
level off as consanguinity continues to fall. There is
thus a single peak.We knew from previous study
that roughly the same single peak occurs both
with the pre-zygotic mechanism and the postzygotic
mechanism. However the time course of a
population is different from a static relationship
between consanguinity and fertility. A more
complex curve is seen when the two mechanisms
are runtogether aswehaveshownabove. It is thus
possible to suggest that the relationship between
consanguinity and fertility in mice and humans is
mediated by a combination of both mechanisms.
The fruit fly study needs to be replicated, not
only because it suggests an approach to a fundamental
law of zoology but because it is so cheap
and easy. Ideally a better way of taking a fly census
should be found and a maggot census would be
124 African Entomology Vol. 21, No. 1, 2013
most helpful, possibly using MRI scanning. We
eagerly look forward to a demonstration of the
probable epigenetic cause. There might, of course,
be a better animal model to work with.
The fact that the computer model gives an excellent
match with reality supports the position
that the population fluctuations are indeed due to
consanguinity and population size rather than
some spurious factor.
As is evident, the computer simulation is less
elegant than the real data. Furthermore our lack of
visible somatic alteration by histology suggests a
pre-zygotic mechanism but the computer simulation
only succeeded in matching data when a
post-zygotic mechanism was used. Thus whether
the real mechanism is pre- or post-zygotic or a
combination remains equivocal for us at this time
but we lean toward a pure post-zygotic mechanism
in fruit flies.
As for our initial hope of managing insects that
carry human disease, assuming that the results
also hold in a target insect species, it does appear
that it might be possible to exploit the effect. After
insecticide spraying an insect population generally
rises to higher than it was before (Nicholson
1954). We see that this is to be expected, that this
rise is temporary and that the timing of a repeated
treatment could be chosen on a rational basis such
as treatment when the population was least fertile
and perhaps afford relative sparing of non-target
populations with different generation times. Or
one might consider using ultraviolet light to lure
mosquitoes into travelling over long distances to
reduce their consanguinity and fertility.
This study was funded by the authors. There is
no conflict of interest on the part of the authors.
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Accepted 12 October 2012
Herbert & Lewis: Fluctuation of fertility with number in virtual and real insect populations 125

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