Bio/. Jb. Dodonaea, 44, 1976, 210-2 16.
ON THE RELATIVE ABUNDANCE
OF NATURAL POPULATIONS
by
C. HEIP
ABSTRACT.
-The constant and similar statistical variability shown by various
aquatic populations is postulated to be a result of competition for space. When
competition for space occurs, numbers of species should form a series of abundance
in which two adjacent species differ by a factor which at closest packing is 1.27.
This hypothesis is tested by comparing different communities where competition
for space is expected to occur (marine phytoplankton) or not (brackish water
copepods).
The variability v of biological populations, defined as the ratio of the
standard deviation 0to the mean m as calculated from the number of individuals in samples from those populations, will tend to a constant value
l/ii when density increases ; in this a is the slope of the linear regression
between the variancejmean ratio Vlm and the mean m (HEIP, 1975). This
is true when the relationship between VJm and m is indeed linear and this is
the case for many populations which are distributed in patches or aggregations and whose spatial patterns may be described by contagious distributions. The value of v which is approached when density increases (or the
sample gets larger) is remarkably constant and similar for otherwise very
different populations. In this paper I will explore a possible explanation for
this phenomenon.
Values of the variability of different aquatic populations were obtained or
calculated from literature and are summarized in table 1.
Table 1
Variability of different populations and communities
Oceanic zooplankton
Near-shore phytoplankton
Estuarine phytoplankton
Macrobenthos St. E24
(<
St. E2
((
St. E6
<<
St. C5
Hydrobia spp. (2)
Bivalvia
Polychaeta
Oligochaeta
Benthic Foraminifera
Source
FRONTIER(1972)
PLATTef al. (1970)
MCALICE(1 970)
GAGE& GEEKIE(1973)
Podon polyphernoides
Meioben thos, Nematoda
Meiobenthos, Copepoda
Meiobenthos, brackish water
It is obvious that in most cases v has a value around 0.25-0.30 ; exceptions
are in part explained by low values of m (the Foraminifera-data) or a large
heterogeneity of the station. This great resemblance between the variability
of widely differing populations points to a general mechanism underlying it.
MAY (1973) studied the case of a one-dimensional resource spectrum
sustaining a series of species, each having a preferred position in the spectrum and a characteristic variance around this mean position, described by
some utilization function. MAY (LC.) proved that in a stochastic environment there is an effective limit to niche overlap consistent with long term
stability of the system ; this limit to the species packing parameter p,
defined as the difference between the mean positions of adjacent species on
the resource spectrum, is roughly equal to the width of the utilization function. May's result is robust, being rather insensitive to the details of the
mathematical model.
When we consider space as a resource, the width of the utilization func-,
tion is given by the standard deviation of the number of individuals in
the population (utilization of space meaning simply being there). The largest degree of niche overlap (the closest possible packing of species) should
equal this standard deviation, that is, the numbers of two adjacent species R1
and R2 will differ by some value which at closest packing will be R2 - Rl
=s=vRl, or X2/Rl=v+ 1.
-
The value v = 0.27 gives k2 = 1.27 XI, or in general the numbers of adjacent species will differ by a constant ratio of 1.27 ; stated otherwise, the
relative abundance of species in a community will form a geometric series
with a ratio which approaches the limit 1 + v when competition for space
drives the species to their closest packing. This limit is the same for different communities because space as a resource is experienced similarly by
different populations, and evidence from aquatic communities suggests it to
lay between 1.25 and 1.30.
I will now investigate two communities, one where competition for space
is not expected to be important and one where it is. HEIP & ENGELS(in
press) concluded that competition for space is very unlikely between species
of copepods inhabiting the benthos of a brackish water habitat, called
Dievengat and situated in northern Belgium (see HEIP, 1973 for a description).
Table 2
Ratio of the series of relative abundances of copepod species from brackish water
(after HEIP, unpublished). Ratios were calculated as arithmetic mean of the ratios of
abundances of successive species. Mean abundances over three months, adults.
Ratio
Density of dominant
species (per 100 cm2)
Total density
(per 100 cm2)
1970
Jan-Mar
Apr-Jun
Jul-Sep
Oct-Dec
I971
Jan-Mar
Apr-Jun
Jul-Sep
Oct-Dec
1972
Jan-Mar
Apr-Jun
Jul-Sep
Oct-Dec
When mean densities over periods of three months are compared (table 2) the
following trends are apparent : the ratio of the series fluctuates widely but
on the average it is larger in winter than in summer and on the whole it is
significantly larger when there are more individuals, either from the
dominating species (correlation r = 0.625) o r totally (correlation r = 0.5 13).
The mean value is 4.98 ; this is considerably higher than the limit value of
1.27 which is to be expected when competition for space is extreme. The
conclusion should be that there is no competition between these species, as
in fact was expected.
Table 3
Mean monthly abundance over fourteen years and ratio between successive
species, calculated as the arithmetic mean, from phytoplankton of the Irish sea.
Data from JOHNSTONE
et al. (1924).
Month
Jan
Feb
Mar
A P ~
May
Jun
Jul
Aug
S ~ P
Oct
Nov
Dec
Density
ind. per haul
51753
89552
715277
5727630
11680414
6635047
897829
29639
736533
459857
181782
56222
Ratio
A community where competition is a dominant factor regulating abundance
of species is the marine phytoplankton. JOHNSTONE,
SCOTT& CHADWICK
(1924) published a remarkable series of values of abundances from monthly
samples taken during fourteen years in the Irish Sea. Although they listed
only 20 species, and their ratios will be too high, the mean monthly abundances of these species over these fourteen years provide us with a unique
series of data. From table 3, where these values are given, it is clear that the
ratio follows a cycle with lowest values in early spring and autumn, i.e. a
cycle with roughly the inverse characteristics as the cycle of abundance itself. There is no significant correlation between ratio and abundance
( r = 0.3091, but the correlation becomes significant ( r = 0.600) when the
ratio is compared with density one month earlier. It therefore seems that
competition for food (nutrients) precedes competition for space.
Table 4
Ratio of the series of relative abundances of phytoplankton species. Data from
Lours & CLARYSSE
(1 971).
ratio
Whole region (1968) :
Whole region (1969) :
Zone 1
Zone 2
Zone 3
Zone 4
Zone 5
Zone 6
Zone 7
Zone 8
1.29
1.23
2.62
1.48
1.56
1.37
1.32
1.24
1.28
2.28
density
(cellslliter)
15412
2338 1
23359
675 1
6708
9112
9674
9333
14578
5523 1
LOUIS & CLARYSSE
(197 1) published extensive tables of abundance of
phytoplankton species in the North Sea and the North Atlantic between
Scotland and Iceland. I calculated the arithmetic mean of the ratios between
successive species. From table 4 it is clear that calculated ratios are in good
agreement with expected values close to 1.27. Values are higher, suggesting
reduced competition, in zones 1 and 8, which are situated on the Icelandic
shelf and along the Belgian coast. In these regions nutrient concentrations
are higher than in the open sea, and so is the total abundance of phytoplankton. As id the previous cases, a higher abundance corresponds to a
higher ratio (r = 0.699).
The fact that the ratio of the series is higher when abundance is higher
can only be explained by assuming interdependence between space and
other dimensions of the niche. This might very well be true, as food abundance or predatory activities will certainly contain spatial components.
Moreover, when competition segregates species, food appears to be more
important than space. When food (or nutrients) is becoming more abundant, competition for space is relaxed too in spite of higher abundances of
species. It seems that species might first compete for food and when packing
is closest along this dimension, competition for space will take over.
In conclusion, the constant and similar variability shown by many
aquatic communities is postulated to be a result of the utilization of space as
a resource ; the number of individuals of different species in these communities will be determined by the simple fact that individuals occupy space
and that, if stability is to exist, the occupation of space prevents equality of
numbers of different species. This may be the general explanation underlying phenomena as the relationship between the number of species and the
surface area of islands and the logarithmic and lognormal distribution of individuals among species.
I acknowledge a grant from the Belgian National Foundation for Scientific Research.
B o s c ~ ,H. F. & W. ROWLAND
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Rijksuniversiteit Gent.
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