Biological Journal of the Linnean Society (1996), 58: 75-84. With 3 figures
Evenness and species number in some moth
populations
L. M. COOK AND C. S. GRAHAM
The Manchesb Museum, Universig of Manchester, Oxford Road, Manchsb M13 9PL
Received 16january 1995, acceptedfor publuation 17 May 1995
More than 300 samples of Macrolepidoptera have been collected over 24 years at a site in southern
England on field courses run for university students. The samples were taken in mercury vapour light
traps. They show that numbers have fluctuated markedly between periods of high abundance and
periods of low abundance. Species richness in the samples is strongly affected by abundance. Evenness
of distribution of numbers between species is higher in samples from woodland than in samples collected
over grass, and higher earlier than later in the season. For a series of samples from the same population,
MacArthur’s overlapping niche and the broken stick resource apportionment models predict a weakly
positive regression of the evenness J of a sample on species number, whereas the sequential breakage
model predicts a negative regression. The latter implies the highest level of competitive interaction
within the moth communities sampled. We find that the data agree with the sequential breakage model,
rather than the other two. A weak positive regression was expected in view of the trapping method used
but was not found. The fit of the sequential breakage model also implies that species abundance is log
normally distributed, which it may be for many reasons. It is argued nevertheless that such comparisons
may be of use for detecting competitive interaction, and that it is important to do so in order to judge
the validity of predictions about effects of environmental change or human interference on the structure
of communities.
01996 The Linnean Society of London
ADDITIONAL KEY WORDS: -Lepidoptera diversity - resource apportionment - competition.
~
CONTENTS
Introduction . . . . . .
Material and methods . . .
Collecting and scoring .
Methods of measurement
Results . . . . . . . .
Temporal changes . .
Diversity results . . .
Discussion . . . . . . .
Acknowledgements . . . .
References . . . . . . .
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LNTRODUCTION
Field courses for students from Manchester University biology courses have been
run at Woodchester Park Field Centre since 1967 (Baker, 1985). Almost from the
0024-4066/96/050075
+ 10 $lS.OO/O
75
01996 The Linnean Society of London
76
L. M. COOK AND C. S. GRAHAM
start, moth samples have been taken using mercury vapour light traps. The purpose
of these was to provide material to help students to think about the problems
involved in measuring diversity in field data. The data set is now long enough for it
to be interesting to examine whether patterns are apparent in the full sequence, and
to use the results for analytical study. It is hoped to show that data collected in a
comparatively inexpert manner by different sets of investigators in different years can
nevertheless provide useful information about population changes and diversity.
MATERIAL AND METHODS
Collecting and scoring
The site of this work is the Woodchester Park Field Centre, situated in a wooded
valley in the Cotswold hills in south Gloucestershire (Askew & Yalden, 1985; Baker,
1985). One series of field courses had provided data for a period of 2 weeks at the
end of June and the beginning of July from 1969 to 1992 inclusive. Between 1976
and 1985 a second course was run for two weeks from the middle to the end of July.
Samples were taken using light traps with either a mains-powered 125W mercuryvapour bulb or a 12 V ultraviolet fluorescent tube (see Baker, 1985, for description).
Collection usually took place on 1 to 2 days, with 2 to 4 traps operating at a time.
Sometimes no more than one sample was taken during a two-week course, but in
other years many such samples were collected and sometimes there were longer
sequences. The majority of collections were made in traps situated on lawns, but
others come from traps set in mixed deciduous wood or occasionally in a larch stand,
situated 0.5 km or less from the grass samples. Scoring of the moths was carried out
using the illustrations in standard identification handbooks (usually South, 1961 and
later, Skinner, 1984). On occasion some individuals are likely to have been
misidentified, so that the total number of species recorded may be inflated, while in
some groups, notably the Eupithciu species, distinct taxa have been lumped. The
same members of staff have been available to assist with identification throughout the
period, so that, although the taxonomy is not perfect, it is likely to give a reasonable
indication of the diversity of species encountered.
Methods
of measurement
Measures of diversity have been calculated for each catch, using Shannon’s Index
H and the Evenness J (see Pielou, 1975, Magurran, 1988). These are, respectively,
H = -Zpiln pi and J = H / l n S, where pi is the frequency of the Ith species and S is
the number of species recorded. Together they provide excellent support for
discussion of the issues involved in assessing community diversity, but it is not
apparent at first sight what exactly they tell us. The index H increases with S, so has
only limited use for comparing samples of varying sizes. J is the value of H as a
fraction of the maximum it can attain for the observed S, so it is a standardized
quantity. However, in this case it is not clear that it should be expected to be constant
as S changes. Despite yet again covering some old ground it is therefore worth
attempting to assess the value of the measures used.
Two approaches to the problem of assessing diversity have been used, the
EVENNESS IN MOTH POPULATIONS
77
statistical and the resource apportionment approach (Pielou, 1975). The first of these
can be most readily appreciated by considering the sample to represent a distribution
of number of species on number of individuals per species (speciesabundance), while
the second is represented as rank order of individuals per species. Various
mathematical models have been fitted to the species abundance distribution, starting
with the negative binomial and moving through the log-series and the geometric
series to segments of the log normal curve (e.g. see Williams, 1964; Preston, 1962;
Taylor, Kempton & Woiwood, 1976; May, 1975, 1981 and reviewed by Pielou,
1975; Wolda, 1983; Magurran, 1988). Despite the advocacy of the log-series by
many workers (e.g. Kempton & Taylor, 1974; Taylor et al., 1976) and the use of its
parameter a as a diversity index (e.g. recently by Robinson & Tuck, 1993), all of
these models seem to have restricted biological interpretation except perhaps the lognormal. Agreement with the log-normal pattern may simply reflect the fact that
many independent factors, having broadly multiplicative effects, are involved in
generating the distribution (MacArthur, 1960; May, 1975, 1981). If this is all that is
being detected it does not tell us anything of great interest about samples from a
particular community.
On the face of it, resource apportionment models are more encouraging. They are
based on consideration of the way coexisting species might divide resource amongst
themselves. MacArthur (1957, 1960) described two, now called the Overlapping
Niche (ON)and the Broken Stick (BS) models. In the first of these, resources are not
limiting to the number of species which can be present. Each species has an
abundance independent of the other abundances, which is a random portion of a
similar amount of resource as is available to the next species. In the second (BS)
model, there is a limited total amount of resource which is partitioned at random into
as many segments as there are species. The two models lead to Merent expectations
of rank order of numbers of individuals per species, for which there are explicit
expressions (MacArthur, 1957; Pielou & Arnason, 1965). There is a third possibility
which should be considered in the context, namely the Sequential Breakage (SB)
model (Pielou, 1975). In this case, the total finite resource is partitioned successively
into as many components as there are species, each species taking a random portion
of the resource of a preceding species chosen at random from those available. Again,
an expected distribution of rank order can be obtained, this time by averaging series
of simulations.
The SB and BS models have been thought of respectively as representing
sequential or simultaneous occupancy of the available resource space. Alternatively,
they may be considered to represent development of communities where the
competitive interaction depends on taxonomic similarity as compared to one where
the chance of a new species interacting is proportional to the abundance of the
established species with which it interacts.
For each sample of data collected the observed rank order can be compared with
these expectations. Agreement with SB would seem to imply presence of competitive
interactions in generating the distribution, agreement with BS or O N suggests
progressively less evidence of competition. In any attempt to find out whether one
model fits better than another, each comparison is essentially a single data point, the
question being the pattern to which they tend to converge. In our analysis of the
moth data we have therefore obtained the single values H or 3 for the observed
sequence from each sample to compare with the H or 3 values from the models for
the same total number of individuals and number of species. It turns out that J varies
L. M.COOK AND C . S. GRAHAM
78
Figure 1. Relation of evenness3 to species number Sfor three resource apportionmentmodels. From top
to bottom the curves represent the overlapping niche (ON), broken stick (BS) and sequential breakage
(SB) models. SB is obtained as a moving average of the means of 100 simulated suns at each Svalue; the
others are calculated explicitly.
with S in a characteristically different way for the SB model than for the other two
(Fig. 1). Whereas for low S all three start from aJvalue of between 0.8 and 0.9 (0.8 1 1
for BS and SB, 0.881 for ON), BS and ON then rise with increasing S to a level of
about 0.88 and 0.94 respectively, while SB drops to just under 0.6. Thus, SB implies
lower 3 values than the other two models. In practice, this may not be as useful as
it looks because J will tend to be inflated by the effect of having integer numbers in
place of low frequencies in some of the classes in finite samples. A more important
result is that the slope of3 on S is negative for the SB model, zero or positive for the
other two.
Another useful feature of this approach is that the expected change in J can be
guessed for situations where data are mixed. If two samples are taken from the same
population and combined, the J values for the mixture should tend to the same value
as the J values for the individual samples. If the samples come from taxonomically
different populations, however, the J for the mixture may be higher than for the
individual samples. In some circumstances this allows predictions about homogeneity
of samples to be tested. For example, Cook, Cameron & Lace (1990) found that
mixed samples of endemic and non-endemic species of snails in an island fauna show
higher 3values than samples containing endemics alone or the endemic component
of the mixed samples.
RESULTS
Taporal changes
A summary of the data on catch size and number of species is given in Figure 2.
Total number of individuals caught per sample (n) are represented on the scale on
the left and are shown by circles on the graph. The irregular line is the cumulative
number of species caught, represented by the scale on the right. The period during
which a second, later field course was run in addition to the first is indicated. Vertical
EVENNESS IN MOTH POPULATIONS
79
Figure 2. Collections of Macrolepidoptera made at Woodchester Park Field Centre, Gloucestershueover
a 24 year period. Total numbers of individuals caught in light trap samples and cumulative number of
species recorded. For further details see text.
lines separate years; the distance between them is simply dictated by the number of
collections made that year.
There is large fluctuation in abundance from year to year. The period up to 1976
generally produced large numbers of individuals, with samples of over 1000. A
period of poor collecting followed until 1982, when abundance again increased. By
1985 numbers had again dropped. Factors, presumably associated with weather
conditions, have operated over a time scale of a few years to change average catches
by a factor of 10.
The discovery curve of new species probably reflects these changes. At first there
was a rapid increase in new species recorded. This levelled off by about 1978.
Another increase commenced in 1982 and the curve may now again be levelling off.
This pattern is not due to changes in technique or personnel. Since the emergence
times of Lepidoptera in the British climate are highly seasonal and number of species
present increases through the first half of the year, the addition of the later collecting
period might be expected to increase the number of species. Any such effect is hardly
noticeable, however. The most likely interpretation of the cumulative species curve
is that rare species come to the traps in seasons of high numerical abundance and are
missing when numbers are lower. The pattern of entry of new species therefore
reflects the pattern of relative abundance in the community from which the samples
are taken.
Diversity results
The total data set consists of 3 15 samples. Figure 3 shows the relation of H to S
and J to S for the full set. The mean number of species per sample was 29.7 and the
mean 3 value 0.765. A downward trend of 3 with S is clearly apparent in both
graphs. F o r 3 on S the regression b = -0.0022 is significant (t = 4.85, P < 0.001).
This result is not a consequence of the index chosen; equivalent associations with S
are also seen if we use the Berger-Parker Index, Simpson’s Index or the log-series a
L. M. COOK AND C. S. GRAHAM
80
J
0.5
0
58
8
lm
0.0
Figure 3. Relation of diversity indexes to number of species (4 per sample for all samples. (a) Relation
of diversity H to S, @) relation of evenness J to S. In (a) the upper curve shows the maximum value H
can attain, represented by J = 1. Curves below this are isoclines of lower values of3.
as measures of diversity. IfJ is recalculated as (H-Hmd/(ZnS- H,,), the regression
is still negative with a mean J of 0.752, although it is no longer significant
(b = -0.0080, t = 1.05, n.s.) because of low values attained in some populations with
very few species (Hminis the minimum possible value of H for a sample, given Nand
4. Overall, therefore, when the data are compared with a resource apportionment
model they accord with the SB assumptions, rather than those of BS or ON.
In making the above comparison we have treated all samples as if coming from the
same population. Further subdivision can be made, however, into those collections
made on the earlier course, and those made on the later course. They can also be
divided into those collected on grass and those in woodland. Table 1 shows mean 3
values for the four categories. There is greater dominance (lower3 in the samples
collected from over grass than for woodland samples in both collecting periods. This
suggests that the populations being sampled are different. There is also a greater
dominance in the later samples than in samples taken earlier in the season. This may
be because emergence of the adults is highly seasonal, with peak species richness in
mid to late summer. The earlier catches therefore contain more species whose
emergence period is incomplete. Combining the data leads to an increase inJ when
samples from woodland and grass are combined. When early and late samples are
combined the combined values lie between the individual values. The implication is
TABLE
1. Mean values of J given for different categories of sample. Values for the &testand
probablilities are given for comparison between pairs. Significance test were carried out on
arcsin transformed values of square root of]
Woodland
Grass
t
Combined
Early samples
Late samples
0.740
0.715
0.661
0.643
1.63(n.s.)
1.94(n.s.)
0.776
0.742
t
0.67(n.s.)
0.51 (n.s.)
Combined
0.729
0.656
2.72(<0.01)
2.18(<0.05)
0.765
EVENNESS IN MOTH POPULATIONS
81
that woodland and grass sites are sampling different faunas, while early and late
sessions are not.
DISCUSSION
A notable feature of the sequence of moth trap samples is the temporal fluctuation
in numbers. Collections made within Werent five-year periods during the time of
the survey would give very different pictures of the fauna of the area, both in terms
of numbers of individuals present and of taxonomic composition of the samples. This
observation is important in connection with programmes designed to monitor the
effect of man-made environmental changes on the fauna.
Comparison of sample data with expectations for regressions ofJ on S suggests a
way of testing hypotheses about factors generating sample distributions. The results
examined favour the SB (sequential breakage) model over the others. The mean
values ofJ are similar to those of the SB model, although somewhat higher, perhaps
because of the effect of discontinuity on the lower frequencies in the distributions.
The SB model, based on rank order, is equivalent to a log-normal distribution of
species abundance (Pielou, 1975). The fit to this defined model may therefore
indicate no more than that there is a general underlying tendency for such data to
form long-normal distributions (May, 1975, 1981). Starting from species abundance
distributions, Holloway (1977) also found that moth samples were fitted satisfactorily
by log-normal distributions. The matter is worth pursuing, however, because not all
experimental data give this distribution and there is a particular reason why moth
trap data might not do so.
The expected relation ofJ to S under different model assumptions which we show
here was also derived by Glasser (1989). He tested data on marine organisms
colonizing flat surfaces. The simultaneity assumed for the broken stick (BS) model
might be expected to apply with this kind of data, and he found that the BS model
fitted better than SB.
With moth sampling it might be expected that the samples are taken from a
community occupying a limited area, within which the competitive assumptions of
SB would apply. However, this depends on the mode of action of the mercury
vapour light trap. Baker (1985) has argued persuasively that the traps work because
the moths at risk of being caught are migrating. When doing so they use lunar or
astronomical cues which are temporally confused with the trap light if the insect is
sufficiently close to the trap (Baker & Sadovy, 1978).Many moth species are known
to migrate over long distances (Baker, 1978), and these include species which are
common in our samples. Baker (1985) likens the process to recording some of the
traffic travelling in one direction along a motorway, rather than to sampling from a
community. If this is the mechanism at work then the moths caught come not from
the vicinity of the traps but from other places further afield, different species from
different places. Although abundance of each may be constrained, they are not
subject to common constraints such as would lead to an interaction that could be
picked up by examining relative abundance. Given the three models considered, the
prediction is that the O N or BS models should fit better than SB. They do not. Either
the model testing procedure is so weak as to be useless or the action of the traps, or
of the moths they catch, are not as described. The results of Glasser (1989)show that
data sometimes match the less constraining models. Moth trap catches sometimes do,
82
L. M. COOK AND C. S. GRAHAM
too. While this paper was being prepared some data of DrJohn Willott from mercury
vapour traps set in tropical dipterocarp forest canopy in Sabah were examined for
the relation ofJ to S. In a total of 79 samples the mean number of species per sample
was 53.3 and the mean3 was 0.9 19. The regression ofJ on Swas 0,0001,which was
not significantly different from zero (t = 0.272). These results provide a very good
match to ON or BS and contrast with those from Woodchester Park (where the
equivalent figures were S = 29.7, J = 0.765 and b = -0.0022).
The difference in pattern between catches on grass and in woodland suggest that
the communities in these two habitat types in close proximity are different. However,
this may be explained by arguing that different species have different favoured flight
paths (cf. Majerus et al., 1994). Kearns & Majerus (1987) and Jones, Majerus &
Timmins (1993),using mercury vapour moth traps, have shown that in polymorphic
species the morph frequencies may differ between coniferous and deciduous
woodland sites close to each other, which could indicate that separate populations
are being sampled.
The question discussed here continues to be of interest because we still do not
know how important competition is in defining communities. Many tropical biota,
such as tropical rain forest plant species, have very high species diversity. If
interspecific competition plays little part in determining success, the average number
of individuals in a community could be set by speciation and migration, balanced by
extinction, the gain and loss processes being essentially random. Hubbell (1979) and
Hubbell & Foster (1986) have considered models in which there is a large random
element of this type. Presumably, the expectation should be that the abundance
patterns tend to ON or BS patterns. The situation is analogous to consideration in
population genetics of the number of alleles present as a result of mutation in a
population of given size (e.g. see Gale, 1990). As the population size goes up the
probability of loss declines, the number of coexisting alleles increases and the
evenness of frequency increases. On the other hand, Tilman (1994) and Tilman &
Pacala (1993) have shown that if it is assumed that there is a trade-off between
competitive ability and dispersive ability, a reasonable assumption for sessile species
such as tropical rain forest plants, then in theory there is no limit to the number of
species which can coexist in a deterministic fashion. Theirs is a modern,
metapopulation approach to visualizing community structure. In practice, finite area
and stochastic environmental fluctuations will set an upper limit, but the system
envisaged is a stable one driven by competitive interaction. Using T h a n ’ s (1994)
equations with randomly chosen mortality and dispersal coefficients we can estimate
relative frequencies of species at or near equilibrium and calculate the associated 3
values. With different assumptions we get slightly different results, but the mean 3
values come to between 0.55 and 0.7, not the values of about 0.9 which would be
expected on a random recruitment and loss model. Values obtained are affected by
the cut-off point chosen to decide whether a species at very low frequency should in
fact be assume;d to have gone extinct. J is lowered if the cut-off point is lowered,
which is equivalent to saying that J decreases with increase in number of species
included. Using T h a n ’ s model we therefore also predict a negative regression o f 3
on S, something which can be tested in sample data. A simple competition model for
multi-species interaction with random interference coefficients has been used by
Godfray, Cook & Hassell (1992).This also produces a negative regression when the
cut-off point is low and the range of coefficients is set to produce an average J value
of about 0.8. Which type of model is more likely to be applicable is clearly of
EVENNESS IN MOTH POPULATIONS
83
importance in considering effects of destruction of forest and of continued future
maintenance of diversity. Current models which predict effects of habitat destruction
(e.g. Nee & May, 1992; Tilman et al., 1994) depend for their usefulness on the
correctness of the assumptions about the nature of interactions.
ACKNOWLEDGEMENTS
We thank the Kelly family for their hospitality at Woodchester Park Field Centre
over many years and Drs R.R. Askew, R.R. Baker and D.W. Yalden for many
identifications, comments and permission to use the data. This paper was written at
the Danum Valley Field Centre, Sabah, Malaysia, supported by the Royal Society.
We are grateful to the Management Committee and Dr J. Witlott for facilities
provided there.
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