Ecology – Biology 3500
POPULATION ECOLOGY UNIT Dr. Adams
Chapter 11: Population Growth
Geometric/Exponential population growth -- not possible for any length of time due to
limiting factors. However, for short periods of time populations do have tremendous
capacity for increase (under very favorable conditions).
See Covid virus growth rates (pg. 239) -- I'll use the Georgia DPH site data
Geometric growth -- pulsed growth (discrete generations), where successive generations
differ in #'s by a constant ratio. For what organisms can we see this, at least temporarily?
Examples: Annual plants, insects with distinct broods (broods cannot overlap)
Exponential growth -- continuous (not pulsed). Nt = N0ert (will discuss in lab)
When is exponential growth possible? (Re)Colonization of areas with little competition
and abundant resources for a SHORT period of time
Examples: Scots Pine (Pinus sylvestris) in Great Britain in the last postglacial
Whooping Crane populations after near extinction
Eurasian Collared Doves in G.B. (remember Chapter 10) -- in this example, however,
population growth slowed (below exponential predictions) within fifteen years of
Logistic Population Growth
If start with low numbers and favorable conditions, population will grow for a while but
then reach environmental limits (the carrying capacity -- K) so that growth will slow
and then stop, resulting in a sigmoidal (S-shaped) growth curve (see Fig.11.8).
Examples: see Figs. 11.9 - 11.12.
So, r (rate of growth) is, of course, dependent on births and deaths; indeed, r = (b - d)
where b = natality (# of births) and d = mortality (# of deaths), and growth at
a particular moment would be (b - d)N = rN. But clearly r is not a constant, and
depends on the number of individuals already there and how close the number is to K.
As such, the logistic growth formula takes this into account:
where dN/dt = change in numbers through time; rmax = intrinsic (maximum) rate of increase
The formula: dN/dt = rmax N ((K-N)/K) = rmax N (1 - N/K) = rN
So, at any given time, r = rmax (1 - N/K); this is the realized per capita rate of increase,
which, as should be obvious, is dependent on population size; r = rmax only when popula-
tion size is small and rapidly growing; r approaches 0 as pop. nears K; if r<0 then the pop.
will be declining in numbers. Another way of saying this is: if N<K, r will be >0 and
the pop. grows; when N=K, r = 0; and if N>K, r<0 and the pop. declines.
How can N>K you ask? Because, technically, K is not a constant either; conditions
can be very good for a while, N increases, but then with worsening conditions suddenly
N exceeds what K was previously. Can lead to "boom-and-bust" growth curves.
Limits to Population Growth
Density-dependent and Density-independent limiting factors
We've already indicated that r is density-dependent; i.e., the rate of growth depends on
the current density of individuals in the population and nearness to K.
There are numerous factors that affect r in this way, called density-dependent factors:
most are biotic -- competition (for resources), predation, mating, disease, parasitism, etc.
However, there are also a number of factors which may affect pop. growth and size
independent of density; these are, of course, called density-independent factors:
these tend to be the abiotic factors -- weather events, fire, flood, hard freeze, and
castastropic events (volcanic eruption, earthquake, etc.), though these factors do not
ALWAYS act independent of density.
An example: Rainfall, Cactus Finches (Geospiza scandens and conirostris) and Cactus
Finches eat from the prickly pear cactus (Opuntia helleri): nectar and pollen from mature
flowers; eat pollen by opening flower buds during dry season; eating seeds and seed
coatings; and insects from the pads/under bark. Cactus gets pollinated and seeds
dispersed, but finches can damage/destroy up to 78% of the flowers. In times of too
little water (drought) finches may damage so many flowers that fruit production is
tremendously suppressed and new plant growth is almost non-existent. During time of
too much water (El Niño years), cactus may be inundated (develop osmotic problems)
and overgrown by fast growing opportunistic other plants. So both biotic and abiotic
factors are influencing BOTH the cactus and the finches in terms of survival.
Human Age distribution curves -- structure and growth in different parts of the worlds
Chapter 12: Life Histories
Be sure to read the "nice" redwood/mayfly story at the beginning of the chapter; it captures
the essence of the term "life history", and how life histories are tremendously different from
species to species. Life history refers to characteristics that shape the life of an organism --
size, lifespan, age at first reproduction, number of reproductive efforts, number of offspring per
effort, etc. Clearly, VASTLY different life histories have been selected for in different
species over the history of life on the planet.
Offspring number vs. size
There is clearly, because of limiting factors (resource/energy availability), a trade-off
between number and size of offspring. Those that produce larger offspring also produce fewer;
those that produce smaller offspring can produce more (assuming all other aspects are equal,
such as size of the female producing the offspring). Resources must be allocated among all
needs, which restrains the amount that can be put into offspring to a finite, limited amount.
Egg size/number in fish: the Darter example
Obviously, darter species that are larger can (and do) produce more eggs; they could
conceivably produce larger eggs, but that trend is not seen here.
It is also true, however, that the Darters that do lay larger eggs produce proportionally
fewer eggs (adjusted for size of the fish)
What is also interesting, however, is that there is more gene flow between populations
where female lay more numerous smaller eggs than between populations of species
that produce fewer, larger eggs. What does this mean? Smaller fish (at hatching)
are more susceptible to downstream drift; larger fish immediately begin feeding and
are less likely to drift.
Seed size/number in plants
Size range: from 2 millionths of a gram for some orchids up to 27 kg for giant coconut
Similar trade-offs between size and number of seeds produced are seen in a wide
variety of plants. However, seed size (and number) may be tied in with a number of
other traits in the plants, such as . . .
growth form: graminoids (grass-like), forbs (herbaceous), woody plants, & climbers
seed size smallest in graminoids, order of magnitude larger in woody/climbers
dispersal strategy: smallest to largest in the following categories
unassisted, wind, adhesive, ant-dispersed, vertebrate-dispersed, hoarded.
benefits of smaller size? more produced, quickly dispersed into disturbed plots
benefits of larger size? increased seedling-size (head start in growth), increased
recruitment (more likely to establish a new plant in an existing ecosystem);
typical of understory trees that need to get a head start in gap (treefall) situations;
large seeds allow longer dormancy in seed banks
Adult Survival and Reproductive Allocation
Age at first reproduction and survival rate are strongly correlated, with species that have
low probability of survival beginning reproduction earlier and investing more resources into a
large reproductive effort; the opposite is generally true for species with higher survivability.
See examples in book (and online). Even within species, age a first reproduction and repro-
ductive effort may vary among different populations, with higher survivorship as adults
being correlated with lower individual reproductive efforts (though total number of eggs
produced across several reproductive efforts could be collectively greater). WHY
would smaller individual reproductive efforts make sense under these circumstances?
Life History Classification
K-strategist vs. r-strategists
K-strategists are so-called because they attempt to maintain relatively stable pop.
levels at or near K, the carrying capacity of the environment. Likely to be most strongly
selected for in stable environments, at least as far as the species involved is concerned.
(Remember, due to different tolerances and resource needs, what is stable to one species
may not be stable to others).
r-strategists are so-called because they attempt to maximize r, the rate of increase;
they reproduce rapidly when conditions are favorable. Particularly selected for in species
colonizing new or disturbed habitats (rapid reproduction enables rapid colonization)
(Expected) Lifespan relatively long relatively short
Development slow rapid
Time to age of first reproduction longer shorter
Adult Size large small
# of potential reproductive efforts many (iteroparity) few (semelparity)
# of offspring per reproductive effort few many
Parental care common uncommon
Survivorship curves type I common type III common
Age structure most young survive to few young survive; largest
reproductive age age class is pre-reproductive
Growth curves Logistic (S-shaped) "boom and bust"
Utilization of resources optimal maximal
Competitive ability Highly selected not highly selected
Habitat relatively stable relatively unstable
Factors influencing pop growth density-dependent density-independent
Mating systems (see parental care) Promiscuity uncommon Monogamy unlikely
Examples are obvious and you should recognize organisms that have characteristics
of one or the other. For instance, in mammals: mice vs. elephants.
However, there are species which show characteristics of both, in other words, these
categories, though convenient, are not applicable to a number of organisms with other life
histories. For example, most trees produce many offspring and few survive, but the
expected lifespan of an individual that does survive is incredibly long, and they have
potentially a huge number of reproductive efforts. What about a similar animal example?
For these organisms that don't neatly fit into K vs. r strategists, ecologists have
proposed alternative classifications.
Plant Life Histories:
Ruderal vs. stress-tolerant vs. competitive (Grime, 1977 & 1979)
disturbance and stress (which limits growth of plant parts) are important here
For instance, drought is an obvious stressor
Ruderals: do well in highly disturbed (but low stress) habitats, indeed may count on
disturbance to remove other competitors and their biomass. These are "weedy"
plants -- early to sprout, fast to grow, and produce large numbers of seeds (for
dispersal into newly disturbed habitats). Among plants these would be r-strategists.
Stress-tolerant: adapted to higher stress (but lower disturbance) habitats, though any
habitat could be high stress for SOME plants. Typified by evergreen, slow-
growing, nutrient/carbon conservers; usually (but not always) adept at exploiting
temporarily favorable conditions. Cacti would be classic stress-tolerant plants.
Competitive plants: do best in low stress and low disturbance (relatively stable)
habitats. These plants may outcompete many other plants when resources are
continuously available, and end up in stiff competition with plants with a similar
strategy. Many trees fit this category.
Even with this classification, there will be intermediate life strategies
Opportunistic, Equilibrium, and Periodic life histories: Winemiller and Rose, for fish
Uses three life history characteristics for the comparison:
survivorship among juveniles (lx), number of offspring produced (mx), and
age at maturity (generation time) (T)
The opportunistic strategy emphasizes early age at maturity, and production of
a number of eggs (even though lx may be low); the idea being that rapid
development & production of numbers of juveniles allows opportunistic
colonization of temporarily open habitats
The equilibrium strategy emphasizes later maturity, high juvenile survivorship,
and low numbers of offspring (sound familiar?). Similar to a K-strategist.
The periodic strategy emphasizes later maturity, with high numbers of offspring, but
lower juvenile survivorship -- this would be similar to the competitive category in
Grime's classification (certain trees). Allows these organisms to hang around and in
those periods when conditions ARE favorable for growth, more offspring survive.
The reason why none of the three
classifications proposed seems to fit all species
well is because the different investigators have compared different groups of organisms
and emphasized different life history characteristics.