Vaccari D.A., Strom P.F., Alleman J.E. Environmental Biology for Engineers and Scientists

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Using equation (14.10), the sensitivity would be expressed as

¼ 0:3367P

0:09

¼ 0:264 mg=mg

This indicates that a 1- mg/L increase in phosphorus would be expected to produce a

0.264-mg/L increase in chlorophyll a.

14.3.2 Resources and Environmental Conditions

The chemical resources include oxygen, CO

and water as well as other macronutrients

and micronutrients. Ot her resources are light and habitat. The latter includes substrate,

shade or sun, shelter, territory and space. Resources can also interact with environmental

conditions. Some of the most important environmental conditions are temperature, humid-

ity, pH, soil, salinity, ﬁre, wind, and photoperiod.

The nutrients most often limiting are nitrogen and phosphorus. The ratio N/P in most

biomass is about 16 : 1. In aquatic systems it is about 28 : 1. If phosphorus is supplemen-

ted, cyanobacter will ﬁx nitrogen to bring the ratio back to nominal values. Therefore,

phosphorus is the usual limiting nutrient. Cyanobacter are not abundant in marine envir-

onments. Thus, nitrogen may become limiting in saline systems. In the open ocean the

micronutrient iron has been shown to be a limiting nutrient. Other micronutrient limita-

tions may be signiﬁcant in algal succession in lakes (see below).

The highest temperature that any organisms are known to tolerate is microorganisms at



C. Among animals, some ﬁsh and insects can go up to 50



C. Some organisms are

known to perform better under temperature variations than at any particular constant tem-

perature. Plants that use the C

photosynthesis outproduce the C

plants at high tempera-

tures and light intensities. Th ey also conserve water better. Conversely, the C

plants are

more competitive under cooler, low-light conditions. The fraction of wild grasses that use

the C

pathway varies along the Atla ntic coast of North America, starting from 80% in

Florida, 48% in the Carolinas, 34% in the mid-Atlantic region, 23% in New England, to

12% in the northern Maritime Provinces of Canada.

Water is, of course, one of the key determinants of the type of ecosystem that will exist

in a terrestrial environment. A rough classiﬁcation based on amount of precipitation can

be made as follows:

0 to 25 cm/yr Desert

25 to 75 cm/yr Grassland or open woodland

75 to 125 cm/yr Dry forest

125 cm/yr or more Rain forest

Humidity affects water balance and cooling in p lants and animals. As humidity falls

below saturation, water is lost by evapotranspiration. Evapotranspiration is needed by

plants to help them transport nutrients from the roots to the leaves. Too-low humidity

can cause plant stomates to close to limit water loss. This prevents oxygen from diffusing

out and CO

in, favoring photorespiration in C

plants. High humidity, on the other hand,

both limits nutrient transport and encourages growth of plant diseases.

Many terrestrial ecosy stems are adapted to peri odic ﬁres. Foresters have learned that

too aggressive suppression of ﬁres has resu lted in shifts in population as less ﬁre-resistant

468 ECOLOGY: THE GLOBAL VIEW OF LIFE

species outcompete the adapted natives. Wind can be a factor in dispersal of seeds, pollen,

and insects. As a climatic factor it can affect survival of a species in harsh conditions.

Pressure may be a factor only in the ocean, where it can reach 1000 atm. Pressure of

that magnitude can affect the conformation and function of enzymes; organisms adapted

to the deep ocean have evolved unique enzymes for that condition.

Photoperiod has a signiﬁcant effect on the behavior of plants and animals. The best

known example is that the ﬂowering of many plants is controlled by the length of the

day. Many physiological responses of animals are also tied to day length. Birds molt,

migrate, and breed in response to day length. Insect eggs are stimulated to go into a rest-

ing stage by long days, so they will not hatch until the following spring, even if tempera-

ture and other factors are favorable.

14.3.3 Tolerated Range of Factors

Each species can tolerate a range within each factor. More precisely, their favorable range

of factors can be deﬁned as a region of the vector space deﬁned by all the factors. Deter-

mining this space is very difﬁcult. Laboratory tests can be misleading. The marine hydra

Cordylophora caspa was found in the laboratory to have an optimal growth rate at 16

parts per thousand salinity. However, the species is never found at that salinity in nature,

only at much lower levels. Evidently, some other factor in nature is limiting its distribu-

tion to only a part of the salinity range that it tolerates. Field and laboratory experiments

are both needed to understand a species’ range.

(

)

012345

Rainfall (inches)

Temperature (deg F)

European

Optimum

Missouri

Montana

(

)

55 65 75 85 95

Relative Humidity (%)

Temperature (deg C)

Optimum

1932

1927

Figure 14.12 Temperature-moisture climograph. (a) The successful introduction of the Hungarian

partridge to Montana, the unsuccessful introduction to Missouri, compared to average conditions in

its native breeding range in Europe. (b) Conditions in Tel Aviv, Israel showing conditions favoring

an outbreak of the Mediterranean fruit ﬂy in 1927. (Redrawn from Odum, 1983; original from

Twomey, 1936.)

FACTORS THAT CONTROL POPULATIONS 469

An example of the combined effect of variables can be seen in Figure 14.12. The plot

shows a temperature–moisture climographs, a phase-plane plot of temperature and

rainfall. The numbers around each polyg on indicate month of the year. The plot shows

three climographs. One represents average conditions in the region of Europe where

the Hungarian partridge naturally breeds. The other two are for the states of Montana

and Missouri, where attempts were made to introduce the partridge. The introduction

was successful in Montana but failed in Missouri.

The natural range of an organism can be examined to determine which levels of which

factors are associated with the boundaries of the range. However, it is thought that differ-

ent factors may operate within a range. In fact, it h as been demonst rated that individuals

near the edge of a geographic range may differ genetically from those in the center. The

genetic variation may be due to natural selection, which in this context is called factor

compensation. Thus, organisms living in the warm er region of a species range might no t

be able to tolerate the colder climate that other more adapted individuals of the same spe-

cies can. The locally adapted populations are called ecotypes. For example, the jellyﬁsh

Aurelia aurita has a southern population that cannot swim outside the temperature range

11 to 36



C. A northern population is sharply limited to between 0 and 28



C. Altho ugh

they are the same species, subpopulations have evolved to ﬂourish over different tempera-

ture ranges.

A species is often limited by geographic factors such as mountain ranges or oceans,

which in turn limit their dispersal. If transplanted outside their normal range, they repro-

duce and spread. This is seen most clearly in the many cases where humans introduced

foreign species to an area, sometimes deliberately and sometimes inadvertently. Often,

these species become nuisances and displace native species. Examples include the

gypsy ﬂy, the chestnut blight, and the starling in the United States, and the rabbit and

the cane toad in Australia.

14.3.4 Species Interactions

Finally, a major factor that can limit the spread of a species is their interactions with other

species. Within the ranges favorable to an organism, it is the interactions with other spe-

cies that seem to dominate its distribution and abundance. Species interactions can be

classiﬁed as beneﬁcial, detrimental, or neutral in their effects on each of the interacting

species. Note that a species that beneﬁts from anot her may also become dependent on it.

Thus, its range may be limited by the range of the species it depend s on. A variety of

major interaction types and subtypes have been identiﬁed (Table 14.5). We will give

examples of several.

Competition arises when two species attempt to exploit the same resources. When the

negative effect is due to the fact that one species’ use of the resource reduces its avail-

ability to the other, it is called resource competition.Ininterference competition, one

species has a more direct effect on the other’s ability to compete for a resource. It may do

so by chasing it away or by producing a chemical that inhibits competing species. Che-

mical inhibition of competitors is also called allelopathy. For example, sage plants (Sal-

via leucophylla) produce gaseous terpenes, which adsorb onto the soil near the plant and

inhibit germination of seedlings. Some species of sponge produce a toxin that acts on

other sponge species.

470 ECOLOGY: THE GLOBAL VIEW OF LIFE

Predator–prey relationships result in the death of the prey. Most carnivorous organ-

isms are predators (can you think of exceptions?). We usually think of this category in

terms of animals that chase, catch, and eat other animals, but animals such as the blue

whale simply seine the water for shrimp, small ﬁsh, and so on. In the microbial world,

rotifers and stalked ciliates ﬁlter smaller organisms from the water. Populations of preda-

tor and prey oft en exhibit an out-of-phase oscillation. When the prey population increases,

the predator population follows as its resource increases. This results in a drop in the prey

population, followed a short time later by a drop in the predator population. This relation-

ship is explored mathematically in Section 10.4.1.

Parasitism is distinguished from predation because the parasite is usually much smal-

ler than its host, and the host will usually survive the interaction, although it may be

harmed. Infectious disease falls into this category, although it is sometimes classiﬁed

separately. Herbivores may are also be classiﬁed as separate þ/ categories. Here we con-

sider them to be predators if they kill the plant, or as parasites if they eat only part and the

plant survives.

An example of predation involves the prickly pear cactus, which overran pastures and

rangelands after it was introduced to Australia. The cactus moth was brought in from

South America. Its caterpillar feeds on the cactus’s new shoots, literally ‘‘nipping it in

the bud’’. In a few years the cactus was no longer a problem. It wasn’t eradicated, though,

because the cactus could spread faster than the moth, although it would be followed soon

after. It is interesting that it is difﬁcult to ﬁnd the moth in cactus stands either in Australia

or its native South America. Its signiﬁcant role might never have been discovered if not

for the Australian experiment.

Predator–prey and parasitic relationships have resulted in what’s been called an evolu-

tionary ‘‘arms race’’ as hosts evolve ever better defenses and predators and parasites

evolve to overcome them. Defensive tactics include escape, camouﬂage, body armor,

and chemical defenses. Poisonous animals often have conspicuous coloration to warn

potential predators away. Other species may mimic poisonous ones. Plants have been par-

ticularly adept at developing chemical defenses. They may be toxic or just noxious. Oaks

and many other plants produce tannins, which complex with digestive enzymes of insects,

TABLE 14.5 Types of Two-Population Interactions

Interaction Type Species 1 Species 2

Neutralism 0 0 No effect of either population on the other

Interference competition Each species inhibits the other directly

Resource competition Inhibition only when a resource is in short supply

Amensalism  0 One species is at disadvantage, other not affected

Commensalism þ 0 One species beneﬁts, other not affected

Parasitism þA parasite is usually smaller than the host, and the

host usually survives

Predation þA predator is usually larger than the prey, and the

prey does not survive

Protocooperation þþFavorable to both, but not obligatory

Mutualism þþFavorable to both, and is obligatory

0, no signiﬁcant effect on that species; , a detrimental effect; þ, a beneﬁcial effect.

Source: Odum (1987).

FACTORS THAT CONTROL POPULATIONS

471

rendering oak leaves nonnutritious. Nicotine from tobacco plants is a nerve toxin. Pyre-

thrum is an insecticide that is extracted from the chrysanthemum plant.

Insects obtain food from ﬂowers while pollinating them. Lichens are an association

between a fungus and a ﬂower; neither can live without the other. Bacteria in mammalian

intestinal tracts are beneﬁcial to the host. This is especially true for ruminants, animals

such as cows who depend on bacteria to digest cellulose in their feed. Seed-eating birds

help disperse seeds while obtaining food. Another term for mutualism is symbiosis or

synergy. An example of mutualism that we have already met is the mycorrhyzal fungus

(described in Section 10.7.4). This is a form of mutualism called syntrophy, in which two

species provide some nutritional requirement for each other. Syntrophy is common among

bacteria.

Pioneer communities such as are found in newly cleared areas tend to have more nega-

tive interactions. Negative interactions tend to be less common in well-developed commu-

nities. Even in laboratory predator–prey experiments, the population oscillations dampen

as time goes on. Three-way interactions may also occur. An example is the scavenger–

predator–prey relationship. The scavenger is a carnivore that eats remains of food killed

by other animals.

14.4 POPULATION S AND COMMUNITIES

Now we focus on the aggregate behavior of groups of individuals of one kind—species

and groups of species—communities. The discussion here will emphasize animal popula-

tions, although much of this applies to other kingdoms as well. The questions we address

include: How will a given population change? Will it increase or stay the same? How high

can it go? How can we compare the number of species in one ecosystem with those of

similar ecosystems? How can we measure the effect of pollution on species distribution

and abundance? How does the abundance of organisms of a species depend on such fac-

tors as the geographical extent of its range, its trophic level, or its physical size? How does

a community change in response to environmental inﬂuences such as seasonal changes or

natural disasters?

14.4.1 Growth Models: Temporal Structure of Populations

Here we look with some depth at the methods that have been developed to predict changes

in populations as they grow, use resources, compete, and feed on each other. This is one of

the most active areas of ecology and is a prime example of the importance of mathematics

to biol ogy. For the most part, we deal with population as a continuous variable. The result-

ing models are in the form of differential equations. Similar models can be developed for

populations that change in discrete steps, such as annually. This would result in difference

equations instead.

Vital Statistics and the Life Table The size of a population will increase if the natality

(rate of production of new organisms by birth, hatching, division, etc.) plus immigration

(rate at which individuals join the population from outside) exceeds the sum of mortality

(rate of death) and emigration (rate at which individuals leave the population). These four

parameters determine the rate of change of a population. We focus on natality and mor-

tality as the intrinsic determinants of growth.

472 ECOLOGY: THE GLOBAL VIEW OF LIFE

For a given environmental situation, the average natality and mortality both depend on

the age of the organism. Natality is usually zero for an initial period. Some organisms may

then produce young at a ﬁxed rate for their entire lives. Others, such as humans, are cap-

able of bearing young only during a range of ages of the females. Some organisms, such

as salmon, produce young only once in their lives, just before dying. The rate at which

individuals in a given age group, x, produce young is called the fecundity or fertility, and

is denoted b

Mortality also depends on age. The age-speciﬁc rate is denoted q

. Although each

population is unique, three basic types of mortality vs. age relationships are noted:

Type I: fairly low and constant mortality over most of the life span, followed by

increasing mortality with age. Humans follow this pattern.

Type II: constant mortality regardless of age. This is typical of birds.

Type III: high mortality among juveniles, followed by fairly low and constant mortality

for the rest of the life span. This is typical of ﬁshes and many lower animals such as

zooplankton, which produce huge numbers of young, few of which survive to

adulthood.

Species that go through several discrete stages, such as insects, may exhibit multiple pla-

teaus of mortality in their lifetimes.

Mortality can be measured by following a group of individuals born in the same age

group through their life span, until all have died. The life span is divided into age groups.

The number that survive to enter each age group x, denoted n

. A table of the values of n

called a life table, shows the age structure of the population. Table 14.6 is a life table for a

population with a ﬁve-year life span. (Immigration and emigration are neglected.) The

mortality is denoted q

. Note that the midpoint of the age groups is used for calculations,

so calculations for all organisms of age 0 to 1 are based on age 0.5.

This is called a cohort life table. It is based on a single group that goes through the age

groups together. It is often difﬁcult to follow a cohort for life. Instead, it is approximated

by a synoptic, or static, life table. If the population is at steady state, the two will be iden-

tical. A steady-state condition means that natality equals total mortality and that none of

the age groups is changing in size. A cohort life table can be used to compute the mor-

tality as the fraction that die in each age group:

 n

iþ1

ð14:11Þ

The information n

, q

, and b

from the life table can be used to compute several things

of interest, such as the steady-state age distribution changes in population and age

TABLE 14.6 Life Table for a Hypothetical Type I Population

i Midpoint Age, x

Number, n

Natality, b

Mortality, q

0 0.5 1000 0.000 0.200

1 1.5 800 0.450 0.100

2 2.5 720 0.500 0.100

3 3.5 648 0.500 0.300

4 4.5 454 0.000 1.000

POPULATIONS AND COMMUNITIES 473

distribution when given a starting distribution and the intrinsic rate of increase of the

population.

The steady-state age distribution is easily computed from mortality. A basis population

must be assumed for the ﬁrst age group, such as the number 1000 used for n

in Table 14.6.

Then successive age group populations are computed by rearranging equation (14.11):

iþ1

¼ n

ð1  q

Þð14:12Þ

The age distribution is often presented as a histogram, as in Figure 14.13. This can be

compared to a steady-state life table histogram. Populations with relatively large numbers

of young and of individuals of offspring-producing age will tend to be increasing.

To compute unsteady-state changes, the mortality is simply applied to each age group

at time step j to ﬁnd the population entering the next age group:

iþ1; j þ1

¼ n

i; j

ð1  q

Þð14:13Þ

The population of the ﬁrst age group is obtained from the nata lity of each population, b

0; jþ1

i¼0

i; j

ð14:14Þ

Table 14.7 shows several generations that result based on the given starting population

distribution and the life table in Table 14.6. Figure 14.14 is a plot of the total population

over 45 generations of the organism.

Note the ‘‘baby boom’’ caused by the large number of young in the starting population.

Eventually, the oscillations die out as the population assumes a stable age distribution.

This approximates the steady state because natality exceeds mortality and the population

is growing. Note that the population distribution at 45 days is still not at steady state. In

fact, steady state is never reached. This population is growing exponentially, because birth

exceeds mortality.

When the oscillations die out, the total population, N, increases in a constant propor-

tion, l, or geometrical ly, with each gener ation:

l ¼

tþ1

ð14:15Þ

¼ N

ð14:16Þ

where N

is the total population at time t and N

is the initial population. If population

growth can be assumed to be continuous, growth can be described by the familiar ﬁrst-

order growth equation giving the rate of increase as being proportional to the current

population:

¼ rN ð14:17Þ

where r is called the intrinsic rate of increase. This is a the rate of increase normalized

by the population (dN/dt)/N. The case of equation (14.17) in which r has a constant value

is the exponential growth rate model.

474 ECOLOGY: THE GLOBAL VIEW OF LIFE

Figure 14.13 Population histogram for three different growth scenarios. Kenya represents a

country with a high growth rate, 2.5% per year. The U.S. growth rate is moderate, 1.0% per year.

Italy is a country with a low growth rate, 0.3% per year, which is expected to begin to decline over

the next several decades. Each bar represents a cohort of ﬁve years of age. (From U.S. Census

Bureau, 2004.)

POPULATIONS AND COMMUNITIES 475

Models based on differential equations such as this one are more appropriate to popu-

lations that breed continuously, with overlapping generations. On the other hand, equatio n

(14.16) is better suited to species that breed at ﬁxed intervals, once per season. The solu-

tion to equation (14.17), given an initial total population of N

, is the exponential relation-

ship

¼ N

ð14:18Þ

and by comparing (14.16) and (14.18), we obtain

r ¼ ln l ð14:19Þ

The values of l and r computed by equations (14.15) and (14.19) do not require age

distribution information to predict growth—only data on total population and the assump-

tion that the population distribution is stable. Examples of these calculations are given in

Table 14.7. Notice that they vary widely until stability emerges.

TABLE 14.7 Population Distribution Changes Based on Life Table from Table 14.6

i 1 2345 44 45

0 1000 51 410 419 490 719 729

1 100 800 40 328 335 567 575

2 10 90 720 36 295 503 510

3 1 9 81 648 33 446 452

4 0 1 6 57 454 308 312

Total 1111 950 1257 1487 1606 2541 2578

l 0.855 1.323 1.183 1.080 0.807 1.015

rðtÞ0.156 0.280 0.168 0.077  0.214 0.015

Each column represents one generation; each of rows 2 through 6 represents an age group.

500

1000

1500

2000

2500

0 5 10 15 20 25 30 35

Generation

Population

Figure 14.14 Predicted total population changes based on life table in Table 14.6.

476

ECOLOGY: THE GLOBAL VIEW OF LIFE

An interesting parameter that can be computed from r is the doubling time, t

ln 2

0:693

ð14:20Þ

The values of r and l could also be estimated directly from mortality and natality with-

out having to simulate the population changes. Two intermediate values must ﬁrst be com-

puted: the net reproductive rate, R

, which is the average number of offspring produced

per individual over a generation; and the mean length of a generation, G, which is the

average time between the birth of an offspring and that of its parents:

i ¼0

ð14:21Þ

where l

¼ n

is the age distribution norm alized to the ﬁrst age group:

G ¼

i ¼0

ð14:22Þ

r ¼

ln R

ð14:23Þ

For the data from Table 14.6, we have R

¼ 1:044, G ¼ 2:47, and r ¼ 0:0175 per unit

time, for a doubling time t

¼ 39:6 time units.

All populations are capable of exponential or geometric growth if favorable environ-

mental conditions are maintained. However, this kind of growth is truly ‘‘explosive.’’ Dar-

win gave an example of the elephant, which he predicted could grow from two individuals

to 19 million over 750 years. This corresponds to a mere r ¼ 0:021 per year, or a doubling

time of 33 years. He also pointed out that although many parasites have a high intrinsic

rate of increase, they are nevertheless rare. Clearly, the growth models described earlier

need to take into account factors that limit growth, such as limiting factors, competition,

and predation. These are the subjects of the next sections.

Single Species: The Logistic Equation A simpl e strategy to place a limit on the expo-

nential growth of equation (14.17) is to have r decrease as N increases. A simple way to

do this is to have it decrease linearly from a maximum speciﬁc growth rate , r

, when N

is zero, down to zero when N increases to a particular level, K:

r ¼ r

K  N

ð14:24Þ

Since the rate goes to zero as N goes to K, the population cannot increase beyond K

(except by immigration). Thus, K, called the carrying capacity, reﬂects the inherent abil-

ity of the ecosystem to support the population. Both K and r

can vary with environmental

conditions; for example, they might decrease in time of drought. When the rate equation

(14.24) is substituted into the growth equation (14.17), we get the important model of

population growth in the presence of a limiting factor, called the logistic equation:

¼ r

K  N

ð14:25Þ

POPULATIONS AND COMMUNITIES 477