Freshwater Biology (1986) 16,161-173
A regression technique for the estimation of epiphytic
invertebrate populations*
JOHN A. DOWNING D6partement de Sciences Biologiques, University de Montreal,
Montreal, Quebec, Canada
SUMMARY. 1. A regression method is proposed for the estimation of
populations of epiphytic invertebrates. Small samples of macrophytes
and attached animals are taken by gentle enclosure. Regression analysis
is used to relate the number of animals collected to the macrophyte
species composition and biomass in these small samples. These rela
tionships estimate the number of organisms of each taxon per unit mass
of each macrophyte species. Areal population density is estimated by
multiplication of macrophyte mass-specific invertebrate density by
standing macrophyte biomass.
2. The regression method yields population density estimates several
times greater than the best of current methods for several fauna.
Differences are most pronounced for active organisms such as water
mites, amphipods, cladocerans, copepods, lepidopterans, ostracods, and
trichopterans.
3. Precision levels obtained using the regression method are compara
ble to other techniques. The regression technique automatically pro
vides estimates of macrophyte species-specific colonization density and
the abundance of organisms swimming among macrophytes in littoral
areas.
Introduction
Macrophyte dwelling invertebrates are impor
Recent articles have emphasized the ecological
importance of the freshwater epiphytic inverte
brate fauna while pointing out the paucity of
accurate, cost-effective population estimation
techniques (Kajak, 1971; Downing, 1984).
Widuto, 1975; Howard-Williams & Lenton,
1975; Lim & Fernando, 1978), constitute a
major source of food for fish and waterfowl
This is a joint publication of the Groupe d'Ecoloeie des Eaux douces of I'Universite de Montreal,
and the McGill University Limnology Research
Centre.
tant consumers of materials and energy in
lakes (Pieczyriska, 1973; Guziur, Lossow &
(Gascon & Leggett, 1977; Keast & Harker,
1977; Menzie, 1979, 1980; Kiorboe, 1980;
Laughlin & Werner, 1980; Baltz & Moyle,
1982), and are implicated in the management
of populations of many adult terrestrial insects
(e.g. Davies, 1984). Population estimates of
Correspondence: Dr John A. Downing. Depart
ment de Sciences Biologiques, Universite de Mon
epiphytic invertebrates are notoriously variable
Canada H3C 3J7.
degree
treal, C.P. 6128, Succursale lA\ Montreal. Quebec,
11
(Pieczynska, 1973; Downing, 1984). The high
of
spatial
heterogeneity
found
in
161
162
John A. Downing
macrophyte dwelling invertebrates stems from
their non-uniform distribution on macrophytes
which are themselves patchily distributed
(Forel, 1904; Davies, 1970; Sheldon & Boylen,
1978; Wong & Clark, 1979). Sampling costs are
necessarily high, because aggregated organisms
yield large sampling variances, and numerous
replicate samples must be taken in order to
increase sampling precision to acceptable levels.
Although epiphytic invertebrates are thought to
be ecologically important, few attempts have
been made to improve sampling techniques or
lower costs.
Epiphytic invertebates are usually sampled
using quadrat clipping, box samplers, scoops,
grabs, and nets. A problem with these sam
plers is that animals can be shaken or fright
ened from the macrophytes during collection
(Downing & Cyr, 1985). Ideally, animals
should be enclosed and collected without dis
ruption and the density of organisms on plants
and the density of macrophytes per unit lake
bottom should be estimated separately (Menzie, 1980). Small samples of invertebrates
could then be used to reveal quanitative rela
tionships between animal numbers and plant
weights, and large samples of macrophytes
could then be used to yield low-error estimates
of animal numbers per unit area. Such twostage sampling is called ratio or regression
population estimation (Cochran, 1977).
Cochran (1977) suggests that where a vari
able (Y) such as invertebrate numbers is corre
lated with a second variable (X) such as
macrophyte biomass, sampling precision may
be improved through
the
use of ratio
or
regression estimators. Where one wishes to
estimate the population mean Y (e.g. inverte
brates), and the population mean X (e.g.
macrophyte biomass) can be estimated with
high
precision, a measure of macrophyte
biomass (*,), is obtained for each small sample
of invertebrates (y(). The regression method
can be used to estimate Y if the relationship
between y, and jc, is linear. In this case, the
linear relationship between the y, and ,t, is
established:
y=a+bx
(1)
and the regression population estimate (Y) is
calculated:
Y=a+bX
(2)
where X is the macrophyte biomass estimated
by separate sampling, and a and b are taken
from equation (1). Cochran points out that the
regression estimate can lower sampling costs in
many cases where a correlated variable fa) is
much less costly to estimate than the variable
of interest (y,).
The number of macrophyte dwelling inverte
brates per unit lake bottom is correlated with
macrophyte abundance and this relationship is
approximately linear (Biochino & Biochino,
1980). In addition, the estimation of macrophyte
biomass costs about one-tenth that of estimates
of epiphytic invertebrate abundance (Downing
& Cyr, 1985). Thus, the regression population
estimation technique holds promise for use in
estimating epifauna populations.
The purpose of this research was to combine
gentle collection of epiphytic invertebrates
with a regression population estimation tech
nique to produce population estimates of high
precision and accuracy. This article presents
this technique and compares it to methods
currently in use by aquatic ecologists.
Materials and Methods
The regression method for epiphytic
invertebrates
Application of the regression population
estimation technique to littoral invertebrates is
simple. A rigid enclosure (Fig. 1) can be used
to take small samples of macrophytes and
invertebrates. These boxes enclose even
mobile organisms without disruption (Down
ing, 1981), and are of constant volume permit
ting correction for collection of organisms
swimming among the plants (cf. Campbell.
Clark & Kosinski, 1982). The number of
invertebrates per unit macrophyte biomass is
then estimated by least squares regression
analysis. Quadrat samples of macrophytes are
taken to estimate macrophyte biomass per unit
area, and these figures are multiplied by in
vertebrate densities per unit macrophyte to
yield estimated invertebrate density per unit
area.
In our trials, replicate samples (« = 12-21)
were taken at random points along each side of
a 50 m cord stretched at uniform depth in a
weed-bed. The plastic box (Fig. 1) was gently
closed around the
macrophytes,
the unen-
Sampling epiphytic invertebrates
163
analysis (Draper & Smith, 1981; Prepas, 1984).
Least-squares regression was chosen because
error involved in jc, is small, consisting only of
drying and weighing errors.
•i—hinges
One of these
equations must be fitted for each invertebrate
taxon under investigation. The coefficient a
estimates the number of organisms collected
when Og of macrophytes are enclosed, thus a
neoprene
sampling
port
estimates the average number of organisms of
an invertebrate taxon that were unassociated
with aquatic macrophytes.
outlet tube
The estimate of average number of epiphytic
invertebrates m~2 could then be calculated:
(3)
Y=bX
where X is the average macrophyte biomass
m~2. Because macrophyte biomass error dis
FIG. 1. Transparent plastic box for the enclosure
and collection of macrophyte dwelling invertebrates.
The chamber encloses macrophytes which are sealed
from the exterior by 7x7 mm strips of closed-pore
neoprene. The inside dimensions are 30 x 20 x 10 cm
(6 litre volume). The box is constructed from 7 mm
Plexiglas™.
tributions can be asymmetrical (Davies, 1970;
Sheldon & Boylen,
1978; Wong & Clark,
1979), the error distribution of Y should be
reproduced directly through calculation of the
products of b and each individual quadrat
estimate of macrophyte density (e.g. ^-bx^.
As the number of macrophyte samples be
comes large, however, macrophyte biomass
closed stems were cut, and the sample re
frequency distributions should perform like
turned to the boat. Samples were sealed in
plastic bags and kept cold for transport to the
laboratory. The organisms were removed from
the macrophyte surface by gentle washing with
a jet of 100/im filtered lake water. Sample
volumes were reduced using a large (21 cm
diam.) filter funnel (Likens & Gilbert, 1970)
made with 100/«n nylon mesh. Samples were
preserved in 80% ethanol. All organisms of
major taxonomic groups in each sample were
counted at 16x magnification. Macrophytes
collected in these samples were sorted to
species, air-dried, dried to constant weight
(60°C, 48h), and weighed (±10mg). Quadrat
normal distributions and skewness of error
samples (991 cm2) were taken at the same time
estimation might therefore function poorly by
to estimate the standing biomass of macrophytes
per unit lake bottom area. These samples were
sorted, dried, and weighed as above to yield
estimates of total biomass and biomass of
relating numbers of organisms to total mac
individual macrophyte species (g dry wt m~2).
The regression estimate of the number of
organisms per unit biomass of macrophytes
was calculated as b in equation (1), where y,
and Xj are the numbers of organisms and
biomasses of macrophytes (sum of all species)
in individual small box samples, and a and b
are constants fitted by least squares regression
distributions
should
be
reduced
(Scheffe\
1959). The mean and variance of phytofaunal
population densities could then be calculated
as the product of two means (i.e. equation (3);
see Colquhoun, 1971; p. 40).
Some authors suggest that species of mac
rophytes have differing amounts of habitable
area
per
unit
macrophyte
biomass
or
are
differentially colonized for other reasons (e.g.
Entz,
1947; Sebestye"n, 1948; Smyly,
1952,
1957; Smirnov, 1963; Quade, 1969; Pieczynska,
1973;
Biochino
Soszka,
&
1975a,
Biochino,
b;
Macan,
1980).
1977;
Regression
rophyte biomass, alone. Thus, analyses em
ploying
all
available
information
on
mac
rophyte species composition were performed
for comparative purposes. I have fitted multi
ple regression equations as:
ti+b2x2i+-
(4)
where *,,-*,, are biomasses of / species of
macrophytes in the i samples, and br-b) are j
fitted regression coefficients. Regression equa
tions were fitted by stepwise forward selection
164
John A. Downing
(Hocking, 1976). Inclusion of variables was
halted when inclusion of the next variables
would have resulted in a partial F-value that
was statistically insignificant (P>0.05) or an
The substrate was sandy clay to clayey allu
increased residual mean square. Apart from
the usual assumptions of parametric statistics,
this analysis made only the assumption that
macrophyte species characteristics (e.g. area/
weight ratios, toxicity, leaf articulation, etc.)
did not differ between macrophytes collected
in boxes and by quadrats. As long as there are
no strong correlations among the Xjit the re
gression coefficients (bx-bj) represent esti
The regression population estimation tech
nique was applied by performing both bivariate (equation 1) and multiple regressions
(equation 4) for each taxon of epiphytic in
vertebrate as functions of total macrophyte
mates of number of a taxonomic group of
values were
invertebrates per unit mass of each particular
biomass estimates obtained through the collec
species of macrophyte (Gujarati, 1978). If
there are strong correlations between estimates
of macrophyte abundance in invertebrate sam
ples, then the analysis may ignore the effect of
tion of quadrat samples, to yield estimated
one of the correlated macrophyte species. The
actually collected in replicate quadrat samples.
intercept a estimates the number of organisms
of each taxon, on average, that were collected
in the 6-litre sample but were not associated
with the macrophytes. The estimate of average
number of epiphytic invertebrates m~2 (analo
gous to equation (3)) could then be calculated:
Y=blXl+b2X2~-+t>A
(5)
where Xj is the average biomass m"2 of
vium (I-IV) and mud and clay (V). Median
standing macrophyte biomass ranged from 41
to 55 g dry wt m~2.
biomass or macrophyte species biomasses in
box samples. This analysis yielded estimates of
number of invertebrates of each taxon per unit
dry
weight
of
macrophyte
multiplied
by
species.
These
the macrophyte
number of organisms of each taxon for each
replicate quadrat sample. These values were
compared with the number of organisms
Comparison with quadrat sampling
The regression population estimation tech
nique was compared with the quadrat harvest
method of estimating phytofaunal populations
(e.g. Soszka, 1975a; Mackey, 1976) on four
occasions (trials I, II, IV and V). Quadrat
harvest estimates were the most accurate ex
macrophyte species /. Again, due to the skew-
isting methods compared by Downing & Cyr
ness
(1985). In quadrat harvest samples, SCUBA
divers clipped macrophytes from randomly
of
error
distributions
of
macrophyte
biomass estimates, the error distribution of
invertebrate density was calculated as the sums
placed quadrats using grass shears, and plant
of the products of the statistically significant b,
and animal material was gently placed into
and the biomasses of individual species of
macrophytes in quadrat samples X^ (e.g.
backwashed into plastic bags using a jet of
yi=biXii+b2X2i+.. ,+bjXji.
AH insignificant
(jP>0.05) regression coefficients (bj) were set to
zero.
The regression technique was evaluated five
60x50cm 100//m mesh bags. Samples were
100//m filtered lake water. Samples were kept
cold for transport to the laboratory where they
were
separated,
rinsed,
reduced,
preserved
and counted as above. The technique yielding
times (trials I-V) during the summer of 1982.
the
Trials I-IV (13, 22, 23 July and 5 August) were
judged the most accurate because both the
carried out at lm depth near Cove Island of
highest
population estimates
should
be
regression and quadrat harvest methods are
Lake Memphremagog (Quebec-Vermont; 45°
passive
O'N, 72° L7'W), while trial V (10 August) was
tween regression and quadrat samples were
made using the Wilcoxon test (Conover, 1980).
performed at lm depth in Holbrook Bay of
the same lake. The macrophyte beds were
composed of Cabomba caroliniana (Gray),
Elodea canadensis (Michx.), Myriophylhtm
spicatum (L.), Najas sp., Potamogeton filifor-
(Downing,
1984).
Comparisons be
Relative precision and cost
The relative precision of regression popula
mis (Pers.), P. gramineus (L.), P. richardsonii
tion estimates were assessed by comparison
((Benn.)Rydb.),
americana
with variances obtained using other techniques
(Michx.) (nomenclature after Fassett, 1940).
at the same sites. Downing & Cyr (1986) have
and
Vallisneria
Sampling epiphytic invertebrates
found that the variance (s2; on a m2 basis) of
sets of replicate samples obtained from Lake
Memphremagog using quadrat clipping, or the
Gerking, Macan, Minto or KUG samplers,
follows the function:
(6)
where y is the mean density of a phytofaunal
taxon (number m~2) and A is the area (cm2)
covered by the phytofaunal sampler (/?2=0.94,
TABLE 1. Proportion of correlation coefficients that
were statistically significant (P<0.05) for bivariate
conelations between total macrophyte biomass and
number of invertebrates (r) and for multivariate
correlations between macrophyte species biomasses
and number of invertebrates (R) collected in small
box samples, n indicates the number of calculable
correlations. Data are presented for trials I-V.
'Misc.' gastropods are those not belonging to the
other gastropod taxa, and species 'L' is a distinct yet
unidentified gastropod species.
Proportion of n trials
significant (P<0.05)
n=497). If the regression technique yields sets
of estimates following the same variance func
tion as other techniques (i.e. having the same
precision), then the residuals in log10 form (i.e.
i°gio ^-logio $2) for sets of regression popula
tion estimates, should sum to zero. Significance
of departures of regression population estimates
from equation (6) were made using a Mest
(Prepas, 1984).
The three major costs in sampling the phyto-
fauna are the time spent in (1) collection, (2)
laboratory processing and preservation, and
(3) counting of epiphytic invertebrate samples.
Divers and laboratory workers measured the
time spent on each stage of sampling using a
waterproof chronograph.
Bivariate
Multiple
Taxon
n
(r)
(R)
Acari
Amphipoda
Chironomidae
Cladocera
Alona sp.
Camptocercus sp.
Eurycercus sp.
Sida crystallina
(Muller)
5
5
5
0.8
0.6
0.6
1.0
0.8
1.0
2
5
1
5
0.5
0.6
1.0
0.4
Copepoda
Cyclopoids
Harpacticoids
5
Ephemeroptera
5
0.4
0.25
0.2
0.6
0.25
0.6
0.4
1.0
0.0
0.4
0.4
0.8
0.5
0.4
0.8
1.0
1.0
0.8
0.8
1.0
0.0
0.25
Trichoptera
5
5
2
5
5
5
2
5
4
5
2
4
5
5
2
4
0.4
0.0
0.0
0.2
0.6
0.0
0.0
1.0
0.0
0.5
0.6
0.8
0.0
0.5
Total organisms
5
0.8
1.0
Gastropoda
Ancylidae
Bulimidae
Lymnaea
Results and Discussion
Regression estimation
The regression population estimation tech
nique works well for most epiphytic taxa,
especally those with highest population levels.
Bivariate regressions (equation 1) of number
of individuals as functions of total macrophyte
biomass were statistically significant (P<0.05)
in 44% of the cases examined (Table 1). The
average coefficient of determination (r2) was
0.27. Correlations were much stronger when
macrophyte species abundances were consi
dered individually (equation 4; Table 1). This
lends weight to the idea that aspects of macrophytes other than crude biomass determine
the suitability of macrophyte substrates. More
than 73% of multiple regressions of numerical
abundance as
functions of individual
plant
species biomasses were statistically significant
(P<0.05). The average R2 nearly doubled
(0.50) over that found for bivariate regres
165
Misc.
Physidae
Planorbidae
Species 'L'
Hirudinae
Hydra sp.
Lepidoptera
Megaloptera
Nematoda
Oligochaeta
Ostracoda
Platyhelminthes
4
1.0
0.8
1.0
0.6
1.0
0.8
linear functions such as equations (1) and (4)
leave no systematic lack of fit in the data.
Most organisms collected by this method
were associated with the macrophytes. More
than 80% of intercepts of multiple regression
equations (a; equation 4) were not significantly
different from zero (P>0.05; Table 2), indicat
ing that in most cases none of the phytofaunal
organisms were found swimming among the
macrophytes. Only 12% of estimated a-values
sions. Analysis of the residuals from bivariate
represented densities of >1 organism litre"1
and multiple linear regressions suggests that
(i.e. a>6).
166
John A. Downing
TABLE 2. Intercepts (a) and standard errors of intercepts of multiple regression equations fitted as in
equation (4). These intercept values estimate the number of organisms of each taxon that were statistically
unassociated with the macrophytes (animals 6litres"1). (-Tests show whether intercepts are significantly
different from zero (*P<0.05 and **P<0.01). Dashed lines indicate that either no data were collected for the
taxon, or that no statistically significant multiple regression equation could be generated.
Intercepts (a) (and standard errors of intercepts) for multiple regressions
Taxon
Tr.II
Tr.I
Acari
0.1 (0.3)
Amphipoda
-1.9(1.0)
Chironomidae
4.7 (3.5)
Tr.III
5.8(3.6)
-0.4 (0.3)
35.0(24.5)
Tr.IV
-2.2 (8.5)
0.5 (0.4)
4.0 (44.6)
Tr.V
1.7 (2.8)
-0.4 (2.8)
-1.4(0.7)
83.1 (29.3)*
-27.9(37.8)
60.3 (42.3)
-24.7 (147.9)
—
VluUUvvi U
Alona sp.
Camptocercus sp.
Eurycercus sp.
Sida crystallina
(Miiller)
0.3 (0.3)
—
—
—
0.6 (48.4)
Copepoda
Cyclopoids
Harpacticoids
70.0 (79.6)
Ephemeroptera
Gastropoda
-0.1 (0.0)
Ancylidae
0.9(1.0)
-1.3(5.0)
—
1.7(0.7)*
Misc.
Physidae
Planorbidae
Species 'L'
Hirudinae
Hydra sp.
Lepidoptera
Nematoda
Oligochaeta
Ostracoda
Trichoptera
-1.6(1.8)
Total organisms
42.3 (46.9)
0.0 (0.2)
0.1 (2.5)
-0.1(0.2)
-1.3(1.0)
1.0(1.4)
0.0 (0.2)
—
1.7(0.8)*
—
4.8 (4.6)
-0.3 (0.4)
—
-22.1 (10.6)
0.1 (0.1)
—
-1.7(1.1)
—
—
1.6(0.5)*
14.1(4.8)*
—
974.0 (208.6)*
158.7 (135.7)
—
—
-1.2(1.3)
0.4 (0.2)*
6.4 (9.6)
62.4(157.1)
—
2.7(2.9)
—
99.1(24.4)**
620.6(166.0)**
—
0.7 (0.5)
10.5 (3.4)*
42.0 (28.8)
1.5(0.6)
—
-0.1 (0.5)
-4.5 (6.9)
-4.1 (4.5)
23.1(8.1)*
-0.3(0.1
50.4(21.8)*
-3.5 (7.4)
-1.5(2.3)
—
-0.8 (0.4)
-2.2 (0.9)*
—
—
-1.0(0.9)
5.4 (4.0)
—
—
0.0(0.1)
—
46.4(61.3)
0.0(0.1)
-0.2 (0.7)
0.3 (0.4)
0.4 (0.6)
—
-1.3(1.8)
0.1 (0.5)
0.5 (0.6)
6.1 (6.2)
—
49.0 (13.6)* *
0.9 (0.3)*
-0.3 (0.2)
—
—
—
11.9(22.9)
—
—
—
—
—
—
—
Lymnaea
10.6 (43.2)
-7.7(12.4)
117.1(45.4)*
—
Bulimidae
0.5(1.3)
47.0 (24.9)
-0.3 (0.6)
68.3 (380.9)
TABLE 3. The number of invertebrate taxa for which macrophyte species
yielded significant (P<0.05) partial regression coefficients for predicting the
number of invertebrates collected in box samples (see equation 4). The number
of taxa for which significant (P<0.05) multiple regressions were calculated
were: Trial 1=16, 11=17, 111=13, IV=19, and V=18. Data on the partial
significance of total macrophyte biomass are not shown.
No. of significant coefficients
Macrophyte species
Tr.I
Tr.II
Tr.III
Tr.IV
Cabomba caroliniana (Gray)
Elodea canadensis (Michx.)
Myriophyllum spicatum (L.)
Najas sp.
Potamogeton filiformis (Pers.)
P. gramineus (L.)
P. richardsonii ((Benn.)Rydb.)
Vallisneria americana (Michx.)
0
4
0
4
2
1
8
4
4
0
1
0
1
6
9
8
0
0
6
0
0
0
0
2
1
3
5
1
The importance of various macrophyte spe
cies for colonization by epiphytic invertebrates,
1
Tr.V
1
5
4
0
0
1
0
6
3
1
1
macrophyte species (Table 3), varied markedly
among trials. No consistent ecological pattern
measured by the relative frequency of partial
as
significance
example, in some trials, broad leaved mac-
of
the
ft,
(equation
4)
for
yet
seems
apparent
in
these
data.
For
Sampling epiphytic invertebrates
rophytes
(e.g.
Potamogeton
richardsonii
((Benn.)Rydb.)) were good predictors of the
abundance of many invertebrate taxa (trial I),
while in other cases macrophytes with finely
divided leaves (e.g. Myriophyllum spicatum
(L.)) were most important (trial III). There
was no significant covariation (P<0J05) be
tween the estimated relative standing biomass
of macrophyte species and their relative value
as
predictors
of
invertebrate
abundance
(Downing, unpubl.).
Example application of the regression technique
Although regression population estimation is
simple to apply, it involves more mathematics
than traditional techniques, thus I provide a
worked example. The appendix contains data
on the number of chironomids found in
twenty-one small box samples, as well as the
biomass of macrophyte of each species from
which they were removed. Fig. 2(a) shows the
bivariate relationship between the number of
chironomids in these samples (Yc) and the
summed biomass of macrophytes in these sam
ples (Xb). The linear relationship (r=0.42;
P=0.057), analogous to equation (1) is:
Yc=S5+99Xb
500
Suich & Derringer, 1977). When biomass of all
macrophyte species are considered in a stepwise fashion, the relationship is much clearer.
Three species of macrophyte yielded signifi
cant partial F-values (Table 4). The resulting
relationship (/?=0.89; P<gO.OOl), analogous to
300
o
8
£
200
I
100
equation (4), is:
^=35+536^+396^+1549*^
0-5
1-0
1-5
2-0
2-5
500 h
400
Z
300
I
200
1
100
(8)
where Xp, Xet Xcb are the species-specific
biomasses (in box samples) of Potamogeton
richardsonii
((Benn.)Rydb.),
Elodea
canadensis (Michx.), and Cabomba caroliniana
(Gray), respectively. This equation yields a
much better fit to the observed data (Fig. 2b).
Macrophyle dry mass (g)
£
(7)
This relationship has little predictive value (see
400
S
167
TABLE 4. Analysis of variance table for regression
(equation 8) of number of chironomid larvae in small
box samples as a function of the dry mass (g) of
Potamogeton richardsonii (Xp), Elodea canadensis
(Xe) and Cabomba caroliniana (Xcb). Partial F-values
(F) are calculated as the increase in model SS when
the variable in question is entered into the multiple
regression as the last variable. F is a measure of the
variation in Yc accounted for by each independent
variable. The probability of obtaining any of these For
100
200
300
400
500
Observed number of chironomids
FIG. 2. (A) Relationship between the number of
chironomids and the total biomass (g dry wt) of
macrophytes collected in small box samples. The line
is equation (7). (B) Relationship between the num
ber of chironomids collected in small box samples,
and the number of chironomids predicted consider
ing biomasses of all species of macrophytes (equa
tion 8). The line indicates a 1:1 correspondence.
Data were collected in trial II.
F values by chance is <0.01. 'SEb is the standard
error of the estimated regression coefficient listed in
equation (8).
Source of variation
df
SS
F
R2
Model (equation 8)
Error
3
17
20
335,920
86,946
422,866
21.9
0.79
Independent variable
SEb
F
xf
74.5
107.4
462.2
52
Total
Xcb
14
11
168
The
John A. Downing
regression
coefficients
estimate
macrophyte species. These chironomid abund
the
average number of chironomids g~l dry wt of
ance estimates are contained in column 6 of
each macrophyte species. These coefficients
Table 5. Also listed are the number of chirono
have small standard errors (14-30%; Table 4).
mids collected from these quadrat samples
The regression coefficients show that chirono
using the standard quadrat clipping method
mids were most dense on the surface of finely
articulated Cabomba caroliniana (1549 anim.
(Y'c). The values are of the same order of mag
nitude and although the regression population
estimation technique yields higher population
estimates in six out of nine possible compari
sons, a Wilcoxon matched-pairs, ranked-signs
test (Conover, 1980) shows that this difference
g~l), and relatively less abundant on Pota
mogeton richardsonii (536 anim. g"1), and
Elodea canadensis (397 anim. g"1). The ba
lance of macrophyte species yielded insignifi
cant (P>0.05) regression coefficients and thus
had little statistical effect on the number of
chironomids collected. A /-test shows that the
intercept (34.99) is not significantly different
from zero (r=1.43; n=21; P>0.05) and thus
the number of chironomids unassociated with
is not statistically significant (P>0.05).
Comparison with the quadrat harvest method
Analogous comparison of the quadrat clip
ping
and
regression
population
estimation
the macrophyte was insignificant.
Calculation of the number of chironomids
methods were made for twenty-three taxa in
per unit lake bottom can be made by multi
quadrat estimates were made for the same
plying the estimated number of organisms per
sampling units (e.g. columns 6 and 7 of Table
unit macrophyte by estimates of the standing
5), a Wilcoxon ranked-signs test could be used
trials I, II, IV and V. Because regression and
biomass of macrophytes per unit lake bottom
to make simultaneous comparisons of all trials.
(i.e. (anim. g-1)x(g m"2)=anim. m~2). Esti
Table 6 shows the results of these analyses.
mates of anim. g"1 for different macrophyte
The regression and quadrat clipping methods
species can be read from equation (8) while
Table 5 shows macrophyte biomass determined
yielded equal number of relatively non-motile
by random sampling with «=lO square quad
rats (991cm2). Regression estimates of the
todes and oligochaetes. The regression popula
organisms such as gastropods, leeches, nema-
tion estimation method yielded significantly
abundance of organisms contained within each
higher estimates (P<0.05) of active organisms
of these quadrats (Y3) are made:
such as water mites, amphipods, chironomids,
cladocerans, cyclopoid copepods, lepidopter-
ans. ostracods and trichopterans (Table 6).
The quadrat clipping method only yielded
where XL X'e, and X'cb are areal biomasses of
TABLE 5. Estimates of standing macrophyte biomass (g dry wt
quadrat"1) made using ten randomly placed quadrats (991cm2).
Shown are the summed biomass of all macrophyte species (X'b), the
species-specific biomasses of Elodea canadensis (Michx.) (X'e),
Potamogeton richardsonii ((Benn.)Rydb.) (X'p)t and Cabomba caro
liniana (Gray) (X'cb), the number of chironomid larvae within the
quadrat estimated using the multiple regression method (Yc; equa
tion 9), and the number collected from each quadrat using the
standard quadrat clipping method (Y'c).
Quadrat
X'b
X't
K
X'cb
Yc
Y'c
6
23
29
4.30
4.05
3.39
2.99
3.39
5.03
5.29
3.82
4.44
4.14
1.51
0.60
0.22
0.33
0.56
1.73
1.51
0.19
0.50
0.22
0.00
0.09
0.00
0.00
0.00
0.04
0.00
0.00
0.13
0.00
0.00
741
237
86
367
291
686
598
281
200
89
466
34
40
56
60
80
97
98
0.00
0.00
0.44
0.00
0.00
0.00
0.00
0.00
0.00
259
187
143
184
(lost)
295
142
189
286
Sampling epiphytic invertebrates
169
TABLE 6. Results of Wiicoxon matched-pairs comparisons
(Conover, 1980) of population estimates made using the
regression and quadrat clipping techniques. Shown are the
number of paired comparisons (n), the Wiicoxon test-statistic
(Z), and the probability that the two population estimation
techniques tend to yield the same estimates. '+' indicates that
the regression technique yielded higher estimates,'-' indicates
that quadrat clipping yielded higher estimates, while 'ns'
indicates no significant difference (P<0.05).
Taxon
n
Z
P
Sign.
Acari
Amphipoda
Chironomidae
31
25
31
-2.028
-3.996
-3.351
0.043
<0.001
+
0.001
+
19
21
-3.284
-2.798
-3.942
<0.001
0.005
<0.001
+
16
-3.702
-1.348
-0.345
<0.001
0.178
0.730
Oligochaeta
Ostracoda
Platyhelminthes
Trichoptera
31
31
9
31
31
31
21
19
31
6
22
31
12
6
-2.612
-1.225
-0.913
-1.230
-0.314
-0.137
-1.836
-2.722
-2.692
-0.447
-0.834
-4.184
-3.059
-2.201
0.009
0.221
0.361
0.129
0.754
0.891
0.066
0.006
0.007
0.655
0.404
<0.001
0.002
0.028
Total organisms
31
-3.645
<0.001
+
Cladocera
Alona sp.
Camptocercus sp.
Sida crystallina
(Muller)
Copepoda
Cydopoids
Harpacticoids
Ephemeroptera
25
21
6
+
+
+
ns
ns
Gastropoda
Ancylidae
Bulimidae
Lymnaea
Misc.
Physidae
Planorbidae
Hirudinae
Hydra sp.
Lepidoptera
Nematoda
higher estimates of population density in one
out of twenty-three taxa (Hydra sp.). Because
regression population estimation yields higher
estimates of population densities of many taxa,
it also yields significantly (P<0.001) higher
estimates of total numbers of organisms per
unit area (Table 6).
The
regression
population
estimation
estimates
that
method
are
yields
substantially
higher than those obtained by quadrat clip
+
ns
ns
ns
ns
ns
ns
-
+
ns
ns
+
+
+
+
mobile organisms dwelling on the surfaces of
macrophytes.
Precision
The relative precision of regression popula
tion estimates of the phytofauna was assessed
by comparison to a variance function derived
for other sampling devices at the same sites.
The mean number of chironomids m~2 esti
ping. The ratios of the median estimates for
mated using the regression method can be
taxa
were
calculated by multiplying each value in column
found between techniques (Table 6) are shown
in Fig. 3. The median population density
estimated by the regression technique was
6 of Table 5 by 10,000/991, then averaging
in
which
significant
differences
more than two-fold that estimated by quadrat
clipping in 65% of these comparisons. The
median
ratio was 3. The quadrat clipping
technique often underestimates the number of
these
products (mean=3608 m~2; s=2398;
n=l0). The standard deviation (s) agrees quite
well with that predicted from equation (6)
(£=1516M=991).
Overall agreement of observed and pre
dicted variances can be assessed by analysis of
170
John A. Downing
®
123456789
5
f 3
2
Ralio of medians
FIG. 3. Frequency histogram of ratios of median
population densities estimated using the regression
technique and the quadrat clipping technique. A
ratio of 2 indicates that the regression technique
yields a median 2 times that estimated using quadrat
clipping. Ratios were only calculated where a signifi
cant difference was found between techniques
(Table 6). Data are taken from trials I, II, IV and V.
Four observations were >9 and are not plotted
(n=38 taxon-trial combinations).
I
0
123456789
log,0 Observed variance
FIG. 4. Relationship between the variance of repli
cate regression estimates of epiphytic invertebrate
populations and variances predicted from equation
(6). The line indicates a 1:1 correspondence. Two
observations are hidden behind plotted points.
the residuals (observed s2-predicted s2). If the
regression population estimation method yields
similar precision to that of traditional methods,
then
the
average
departure
of
observed
variances from predictions from equation (6)
should not be significantly different from zero.
Because equation (6) is fitted in logarithmic
form,
the
residuals
are
calculated:
log,0 ^2-logio s2. Downing & Cyr (1985) found
that the mean and variance of residuals for all
samplers were 0 and 0.166 (w=497), respec
tively. The mean and variance of such re
siduals found here for regression estimations
were 0.0174 and 0.270 (n=66). A /-test for a
difference between these two groups of mean
residuals (Prepas,
1984) yields 7=0.95. and
indicates no significant difference (P>0.05).
Fig. 4 shows that observed variances using the
regression technique correspond directly to
predicted from equation (6). After
Downing & Cyr (1985), the number of repli
cate quadrat samples of macrophytes (n)
needed to attain a specified precision (y?=SE/
y) can be predicted:
these
/i=67.76)7,1-0.360,4-(1.435..-2
(10)
where all other variables are as in equation
(6). This equation shows that the requisite
number of replicate samples increases with
decreased population density, decreased sam
pler area, and increased precision (i.e. de
creased p). Improvement of precision levels
can be made by increasing the number of
quadrat samples of macrophytes. This is most
efficiently done by taking large numbers of
small (<500cm2) macrophyte biomass samples
(e.g. Green, 1979; John el «/., 1980).
Relative sampling cost
Unfortunately,
regression
estimation
was
more costly than quadrat clipping (Table 7).
The cost saving suggested by Cochran (1977)
was not realized simply because macrophyte
spatial variability was too great. On the other
hand, the regression technique loses fewer
organisms, and yields valuable information on
macrophyte species-specific colonization by in
vertebrates. Precision levels of regression esti
mates could be improved very inexpensively by
increasing the number of quadrat samples of
macrophytes. A regression method employing
gentle entrapment of invertebrates should be
used where mobile phytofauna are being stu
died. The quadrat clipping method leads to
biased population estimates for many taxa.
Sampling epiphytic invertebrates
171
TABLE 7. Time (min) required for collection, processing, and counting of
samples taken with the regression and quadrat clipping techniques in trials
I-V. Collection time for regression samples includes time needed for the
collection of both box samples and quadrat macrophyte samples. Processing
time is the time needed to rinse animals from plants and preserve samples.
'nr' and 'n ' are the number of box samples and quadrat samples taken in
each trial.
Collection
Trial
T
II
III
IV
V
nr
17
7,1
13
12
12
10
9
8
6
6
Processing
Counting
Reg.
Quad.
Reg.
Quad.
Reg.
Quad.
145
134
98
103
107
64
73
31
41
55
127
137
155
126
92
98
471
2158
1323
304
1097
1217
537
654
177
101
107
85
615
1298
Acknowledgments
Downing J.A. (1981) In situ foraging responses of
three species of littoral cladocerans. Ecological
I gratefully acknowledge the financial support
of the Canadian National Sportsmen's Fund,
the National Science and Engineering Re
Downing J.A. (1984) Sampling the benthos of stand
ing waters. A Manual on Methods for the Assess
ment of Secondary Productivity in Fresh Waters
search Council of Canada, and the Minister of
Education of the Province of Quebec (FCAR).
Thanks especially to H61ene Cyr for patient
field and microscope work, and T. Briza, M.
Downing and L. L'Heureux for help in the
Monographs, 51, 85-103.
(Eds J. A. Downing and F. H. Rigler), IBP
of Cladocera associated with shallow water mac-
Handbook No. 17, 2nd edn, pp. 87-130. Blackwell Scientific Publications, Oxford.
Downing J.A. & Cyr H. (1985) The quantitative
estimation of epiphytic invertebrate populations.
Canadian Journal of Fisheries and Aquatic Scien
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Draper N. & Smith H. (1981) Applied Regression
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Entz B. (1947) Qualitative and quantitative studies
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Fassett N.C. (1940) A Manual of Aquatic Plants.
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Forel F.-A. (1904) Le Liman, Monographic Limnologique. Tome troisieme. Slatkine Reprints
(1969), Geneva.
Gascon D. & Leggett W.C. (1977) Distribution,
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Fisheries Research Board of Canada, 34, 1105-
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Cochran W.G. (1977) Sampling Techniques, 2nd edn.
Green R.H. (1979) Sampling Design and Statistical
construction of sampling devices. Two anony
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Sampling epiphytic invertebrates
Appendix
°Raw data used in the worked example
Data on the abundance of chironomid larvae (Yc), and dry masses (g) of the sum of
"*°all species (Xb) and each individual species (X,) of macrophytes collected in box samples
^taken in trial II. Macrophyte dry massses are listed for Cabomba caroliniana (Gray)
(Xcb), Elodea canadensis (Michx.) (Xe), Myriophyllum spicatum (L.) (Xm), Najas sp.
(Xn), P. gramineus (L.) (Xpg), P. richardsonii ((Benn.)Rydb.) (Xp), and Vallisneria
americana (Michx.) (Xv). A dry mass of 0.005g indicates that the species was present
but below the limit of detection of our balance.
Sample
Yc
xb
Xcb
xe
xm
xn
Xpg
*p
xv
0.16
0.77
0.63
0.65
0.36
0.00
1.16
0.24
0.07
0.10
129
2.41
76
0.63
1.12
0.79
1.51
0.99
0.22
0.35
0.02
0.09
0.06
0.18
0.05
0.14
0.01
0.00
0.00
0.005
0.24
0.08
0.06
0.20
0.00
0.04
0.43
0.00
0.15
69
73
75
83
86
88
89
0.00
0.26
0.01
0.61
0.005
0.01
0.11
0.04
0.00
0.00
0.22
0.00
0.06
0.32
0.005
0.005
0.005
0.00
0.30
0.01
0.005
0.00
0.00
0.01
0.02
0.00
67
0.00
0.00
0.00
0.00
0.00
0.13
0.10
0.00
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.07
0.00
51
54
62
18
365
391
287
181
501
121
232
9
18
119
137
115
0.18
1.64
1.54
1.51
0.66
0.60
1.58
0.67
0.07
0.16
0.60
0.49
0.00
0.23
0.00
0.19
0.00
0.005
0.00
0.11
0.10
0.01
0.00
no.
2
13
14
16
19
25
30
32
43
47
452
71
174
173
45
58
1.22
0.00
0.00
0.00
0.18
0.00
0.00
0.00
0.02
0.29
0.02
0.16
0.00
0.16
0.00
0.00
0.04
0.00
0.03
0.13
0.17
0.02
0.01
0.01
0.04
0.05
0.00
0.13
0.21
0.05
0.005
0.00
0.83
0.00
0.24
0.32
0.00
0.37
0.00
0.01
0.00
0.00
0.11
0.10
0.14
0.61
0.00
0.00
0.19
0.08
0.00
0.11
0.09
0.84
1.45
0.47
0.26
0.24
0.91
0.51
0.14
0.11
173