Statement
Population density is population size in relation to some unit of space. It is generally assayed and expressed as the number of in- dividuals, or the population biomass, per unit area or volume- for example, 200 trees per acre, 5 million diatoms per cubic meter of water, or 200 pounds of fish per acre of water surface. Some- times it is important to distinguish between crude density-the number (or biomass) per unit total space, and specific or eco·
logical density 0 -the numher (or biomass) per unit of habitat space (available area or volume that can actually be colonized by the population). Often it is more important to know whethe:
a population is changing (increasing or decreasing) in size at any one moment. Also, population size often changes so rapiuly (es- pecially among lower plant and animal taxonomic g):oups) or is so difficult to measure accurately (perhaps bec.'1use of the large size of the area to be censused or because of the irregular distribu- tion of individuals) that density per unit space has little meaning.
In such cases, indices of relative abundance are useful; these may be "time-relative," as, for example, the number of birds seen per
• Also caller! economic density by Elton (1933).
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §2 151
hour, or they may be percentages of various kinds, such as the percentage of sample plots occupied by a species of plant.
Explanation
In undertaking a study of a population, density would often be the first population attribute to receive attention. It might be said that natural history becomes ecology when "how many" as well as "what kinds" are considered. The effect which a population exerts on the community and the ecosystem depends not only on what kind of organism is involved but also on how many-in other words, on population density. Thus, one crow in a 100-acre corn·
field would have little effect on the ultimate yield and cause the farmer no concern, hut 1,000 crows per 100 acres would be some- thing else!
As with some of the other population attributes, population density is quj~e variable. However, it is by no means infinitely variable; thel'(~ are definite upper and lower limits to species population sizes that are observed in nature or that theoretically could exist for any length of time. Thus, a large area of forest might show an average of 10 birds per hectare and 2,000 soil arthropods per square meter, but there would never be as many as 2,000 birds per square meter or as few as 10 artlu-opods per hectare! As has been brought out in Chapters 3 and 4, the upper limit of density is determined by the energy flow (productivity) in the ecosystem, the trophic level to which the organism belongs and the size and rate of metabolism of the organism. The lower limit may not be so well defined, but in stable ecosystems, at least, homeostatic mechanisms operate to keep density of the common or dominant organisms within rather definite limits.
Within these broad limits, density will vary according to interac- tion with other species (competition) and action of physical limit- ing factors.
In Figure 40 the range of denSity reported for common mam- mals is shown. Density (expressed as biomass per hectare) is that of the species within its normal geographical range, in its pre- ferred habitat (i.e., ecological density) and under conditions where man or other "outside" forces are not unduly restrictive.
Species are arranged in the chart according to trophic level, and within the four levels according to individual size. We see that while denSity of mammals as a class may range over nearly five orders of magnitude, the range for any given species or trophic
152 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS; CR. 6
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Figure 40. TIle range of population density (as biomass per hectare) of various species of mammals as reported from preferred habitat of the species in localities where man is not unduly restrictive. Species are arranged accorn- ing to trophic levels and according to individual size within the four levels to illustrate the linlits imposed by truphic position and size of organism on the expected standing crop. (Graph prepared from data collected by Mohr ( 1940) plus results of later studies.)
group is much less. The influence of trophic level is, of course, striking, and the effect of size is also indicated since larger mam- mals in each level tend to maintain a larger biomass than the small mammals. The point to emphasize is that the first order of population control is the energy flow- physical factor complex;
the second order of control involves the subject matter of this and the subsequent two chapters.
When the size of individuals in the population is relatively uni- form, density expressed in terms of number of individuals is quite satisfactory as a measure. On the other hand, when individual size is variable, as is true of fish, trees, or mixed populations gen- erally, some sort of biomass measure may be more satisfactory as a measure of density. Live (or wet) weight, dry weight, volume, and carbon or nitrogen weight can be used as a measure of bio- mass density. Special measures and terms are used for speCial groups. With trees, for example, the population can be divided into size classes and the number in each detennined, or the 'oasal area" could be calculated. Basal area is the sum total of cross sec- tion area of h'ee trunks (determined from measurements of
ORGANIZATION AT THE SPECmS POPULATION LEVEL: §2 1 S3
"d.b.h.," or "diameter breast high"). Foresters, of course, deter- mine "board feet" or other measures of the commercially usable part of the tree. These and many others are density measures as we have broadly defined the concept, since they express in some manner the size of the "standing crop" per unit area.
One of the greatest difficulties in measuring and expressing density arises from the fact that individuals in populations are often unevenly distributed in space, i.e., show a "clumped" dis- tribution (see Figure 62). Therefore, care must be exercised in choice of size and number of samples used to determine denSity.
This problem is discussed in detail in Sections 13 to 15 of this chapter.
As was indicated in the statement at the beginning of this sec- tion, relative abundance is often a useful measure when denSity cannot be determined. The terms "abundant," "common," "rare,"
etc., are common, and are most useful when tied to something that is measured or estimated in a manner that makes comparison meaningful. Such population "indices," as might be imagined, are widely used not only with rapidly changing populations but with populations of larger animals and terrestrial plants, where it is imperative that a measure applicable to large areas be obtained without excessive expenditure of time and money. Percentage in- dices are widely used in the study of vegetation, and speCially defined teIIDS have come into general use, for example: Frequency
= per cent of sample plots in which the species occms. Abun- dance
=
per cent of individuals in a sample. Cover=
per cent of ground surface covered as determined by projection of areal parts.Other such indices are discussed in Chapter 11. One should be careful not to confuse indices of relative abundance with true denSity, which is always in terms of a definite amount of space.
Relating the indices of relative ablmdance to actual abundance on an area basis is an important job that generally is yet to be done.
Many different techniques for measuring population density have been tried, and methodology comprises an important field of research in itself. There would be little point in going into detail on methods here, because the man in the field will generally find that he will first have to review the original literature applying to his situation and then develop modifications and improvements of existing methods to fit his specific case. It can be pOinted out, however, that methods fall into several broad categories: (1)
154 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: CH. 6 total counts, sometimes possible with large or conspicuous organ- isms or with those which aggregate into colonies; (2) sampling methods (involving plots, quadrats, transects, Or sampling de- vices of various sorts), by necessity often the most widely used (see Sections 13 to 15); (3) marking-recapture methods (for ani- mals ), in which a sample of population is captured, marked, and released, and proportion of marked individuals in a later sample used to determine total populations 0 (with . proper precautions and a knowledge of life history and population attributes this can be a very good method); (4) indirect methods, involving "Signs";
hunting, fishing, and trapping take; food or oxygen consumption, etc.
Examples
Samples of observed range in densities of selected populations (and various units of measurement) listed in Table 11 illustrate many of the pOints discussed and give some idea of the order of magnitude to be expected in dealing with different kinds of organ- isms. Also, some examples of relative abundance indices are given. These data are largely self-explanatory; only a few spot comments need be made. Example 1-3 illustrates "specific den- sity," which is more meaningful than "crude density" in cases where the habitat of the organism in question is specialized or suf- ficiently well known to be delimited from unsuitable areas. Ex- ample II -2 illustrates the tendency (by no means universal) for mixed populations to be larger in areas of mixed habitat; this is because there are generally more niches available in mixed habitat than in an equal area comprising uniform habitats. Examples II-I and 3 call attention to the tremendous number of organisms that exist in soil and water. (See also Tables 21, 22 in Chapter 11.) Example III provides another illustration of operation of food chain and ecological pyramid principles. Bass and other game fish are higher on the pyramid than "rough fish," and biomass density is correspondingly less. Example V illustrates how denSity in terms of individuals alone may be misleading when individual size varies greatly.
In the case of measures of relative abundance, it is highly de-
o If 100 individuals were marked and released and 10 out of a second sample of 100 were found to be marked, then population would be figured as follows: 100/P = 10/100, or P = 1000.
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §2 155
sirable to have more than one "index" applicable to the same population as shown in example VI-2, where combination of two indices gives a better picture of the relative importance of species in a grassland than does either index alone. Experimentation with various combinations of indices is an active field of interest at the present time. When seasonal or annual changes are being in- vestigated, it is also desirable to have more than one measure of relative abundance, as illustrated by VI-3. One is inclined to put more confidence in such measures of relative abundance if sev- eral indices all show the same trend.
All in all, the subject of numbers is a fascinating one. The ex- amples shown in Table 11, it is hoped, will whet the appetite of the reader for further explorations in this direction.
Table ·11. Examples of population densities, their variation in time, and different units of measurement
I. Species populations, individuals per unit area; with indication of variation in density found in long-range intensive studies in restricted geographical areas: 1. Loblolly pine (Pinus taeda), Piedmont, North Carolina (data from OOS!-
ing, 1942).
Age of stand in years Density, trees per 100 m.2
11 27
22 18
31 15 2. Dob-white quail, fall population density in two regions.
34 12
42 12
75 S
Wisconsin; at edge of Southem Georgia estates;
range, unfavorable win- favorable climate (Data ter climate (Data from from Stoddard, 1932)
Errington, 1945) Observed range
of denSity over 2.7 to 9.6 20 to 100
a period of years per 100 acres per 100 acres 3. Specific denSity, knapweed gallfiy (Urophora iaceatla), at Madingley,
England, peak season (July-August); number per sqllare meter of Imap- weed (data from Varley, 1947).
Adult flies emerging Larvae forming galls
1934 43
1935 6.9 147.6 II. Mixed populations, individuals per unit area or volume:
1936 2.0 28.0
1. Zooplankton (mostly copepods), various stations in western Atlantic from Tortugas to Long Island Sound (data from Riley, 1939).
380 to 224,000 per cubic meter water
2. Breeding birds in three biotic communities, Uniteo States (data from Hickey, 1943, Appendix B).
156 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: CH. 6
Table 11 (continued)
C cnnmunity
Grasslands (Central U. S.) Maple-beech and oak-
Number areas censusecl
11 hickory forests (Eastern U. S.) Diversified man-made
]0 habitats (campuses, estates,
and parks) (East and
Pacinc Coast, U. S.) 11
Population density, adults per 100 acres Allerage Extremes
144 20- 591
465 232- 634
827 140-2,020 3. Macroscopic soil invertcbrates. TreeJease Woods, Urbana, Illinois. samples
at all seasons over a period of 6 years (data from Shelford. 1951).
50 to 2,200 per square meter III. Mixed populations, biomass per unit area:
Fish in artificial pOl1d~ in Illinois (data from Thompson and Bennett, 1939). Fish groups arranged in approximat"e order of food chain relations with "rough fish" occupying the lowest trophic level and "game fish" the highest.
Fish in pound.s per acre Pond Pond Pond No.1 No.2 No.3 Game and pan fish (bass, bluegi1ls, etc.) 232 46 9 Catfish (bullheads and channel cats) 0 40 62 Forage fish (shiners, gizzard shad, etc.) 0 236 3 Rough fish (suckers, c~rp, etc.) 0 87 1,143
Totals 232 409 1,217
IV. Comparison of individual and biomass denSity where size of organism un- dergoes pronounced change with age:
Fingerling sockeye salmon in a British Columbia lake. The salmon hatch in streams and in April enter the lake, where they remain until mature.
Note that betwocn May and October the fish grew rapidly in size, with the result that biomass increascd thrce times, even though the number of fish was greatly reduced. From October to the next April very little growth occurred, and continued death of fish reduced the total biomass.
(Data from Ricker and Forester, 1948.)
Individuals, thousands in the lake Biomass, metric tons in the lake
May 4,000 1.0 V. Estimates of total population size of large areas:
Oct-ober 500
3.3
April 250 2.0
1. World population of the gannet (Sula bass(Jna), a large sea bird which nests in a few densely populated colonies on northern Atlantic shores of North America and Europe (data from Fisher and Vevers, 1944).
Date Total number breeding indiViduals 1834
1894 (after considerable persecution by man) 1939 (following protection by man)
334,000 106,000 165,600±9,500
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §3
Table 11. (continued)
157
2. Estimated number of pronghorn antelope on approximately 50,000 square miles of the desert plains region at junction of California, Nevada, Oregon, and Idaho, determined by aerial censuses made from slow, low- flying planes. Number in large herds determined from enlarged aerial photographs. (Data from Springer, 1950.)
Total in 1949 , , , , , , . , , '. 29,940 VI. Example of indices of relative abundance:
1. Colombia (South America) jungle mosquitoes, See Figure 52 (page 191). 2. Relative importance of species of grasses and forbs in a Texas grassland
(data from Dyksterhuis, 1946).
Cooert/.mes Species Cover (%) Frequency (%) frequency
And.opogon scoparius 64.66 100 64.66
Pcrennial Forbs 8,2] 100 8,21
Bouteloua curtiper~dula 8,11 100 8,11
Sorghllstrum nutllllS 5.12 83 4,25
STJorobolus asper 2.10 92 1.93
Bouteloua hirsuta 2.50 67 1.68
Annual forbs 2.30 50 1.15
Andropogoll furcatus 2,20 50 1.10
Stipa leucotriclw 0.70 42 0.29
3. Relative abundance of mourning doves, as determined by two different seasonal inJices, in southeastern states (unpublished data, U. S, Fish and Wildlife Service, noted with permission).
Statement
Breeding season index, Average num- ber doves calling per 20-milc samplc route (3 minute listening station each
1950
mile in early morning) 15,65 ± 1.02 Fall index. Doves killed by hunters,
number per gun hour 1.44
3. Basic concepts regarding rates
1951
21.20± 1.03 1.55
Since a population is a changing entity, we are interested not only in its size and composition at anyone moment, but also in how it is changing. A number of important population character- istics are concerned with rates. A rate is always obtained by divid- ing the change by the period of time elapsed during the change;
it is the rapidity with which something changes with time. Thus, the number of miles traveled by a car per hour is the speed rate, and the number of births per year is the birth rate. The "per"
means "divided by." For example, the growth rate of a population is the number of organisms added to the population per time and
158 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: CH. 6
80 en a
« z
;:60
o J:
l-
N
i ~40
wIf) w 020 z
3 6 9 12
TIME IN WEEKS
15 Ie
Figure 41. A population growth curve (upper) and growth rate curve (lower) for two bee colonies in the same apiary. A-Italian bees; B-Cyprian bees. (Redrawn from Bodenhein)er, 1937.)
is obtained by diViding the population increase by the time elapsed.
If time is plotted on the horizontal axis (x-axis, or abscissa) and the number of organisms on the vertical axis (y-axis, or or- dinate) of a graph, a population growth curve is obtained. In Figure 41, growth curves for colonies of two kinds of honeybees raised in the same apiary are shown. Also, the approximate growth rate at weekly intervals is plotted against time. Note that growth rate increases and decreases as the slope of the growth curve in- creases and decreases. Population B's growth rate is conSiderably less than A's during the first eight weeks or so, but eventually population B grows as rapidly as A. Not only do population growth curves provide a means of summarizing time phenomena, but the type of curve may give hints as to the underlying processes con- trolling population changes. Certain types of processes give char- acteristic types of population curves. As we shall see in Section 8, S-shaped growth curves and "humped-backed" growth rate curves are often characteristic of populations in the pioneer stage.
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §3 159 For convenience, it is customary to abbreviate "the change in"
something by writing the symbol t.. (delta) in front of the letter representing the thing changing. Thus, if N represents the nwnber of organisms and t the time, then:
t..N = the change in the number of organisms.
AN = the average rate of change in the number of organisms per At (divided by, or with respect to) time. This is the growth
rate.
AN or AN = the average rate of change in the number of
~ N M organisms per time per organism (the growth rate ,N divided by the average number of organisms dur-
ing the period of time). This is often called the per cent growth rate or the specific growth rate.
Often we are interested not only in the average rate over a period of time but in the theoretical instantaneous rate at par- ticular times; in other words, the rate of change when t..t ap.
proaches zerO. In the language of calculus, which is the branch o~
mathematics dealing (in part) with the study of rates, the letter d (for derivative) replaces the t.. when instantaneous rates are being considered. In this case the above notations become:
~i'i = the rate of change in the number of organisms per time at a t particular instant.
dN
~
= the rate of change in the number of organjsms per time per individual at a particular instant.In terms of the growth curve the slope (straight line tangent) at any point is the growth rate.
For the purposes of this book and for the usual purposes of measurement in ecology, the calculus notation is not necessary.
Calculus formulations are mainly used in ecology in theoretical mathematical derivations by which the quantitative consequences of various assumptions are computed. In this and the next chapter we are interested in using simple mathematical models to illus- trate principles and provide a more precise meaning to terms and concepts, leaving the derivation of models for advanced studies.
For this reaSOn we shall use the t..NIt..t notation. The dNldt nota- tion can be substituted in any of the models, and this would be necessary in many types of actual mathematical manipulations.
Example
Suppose a population of 50 protozoa in a pool is increasing by