Population Regulation There are many limiting factors in nature that regulate the growth of populations



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Population Regulation

  • There are many limiting factors in nature that regulate the growth of populations

  • Limiting factors can act from outside the population - extrinsic limiting factors - can be physical (abiotic) factors:

  • Sunlight

  • Water

  • Nutrients

  • Food

  • Resources

  • Limiting factors can act from outside the population - extrinsic limiting factors - can be biotic (living) factors:

  • Competition

  • Predation

  • Symbiosis

  • The pioneering ecologist Charles Elton proposed that equilibrium in nature resulted mainly from a balance of interactive forces, especially competition and predation

  • Elton also proposed that food supply was a critical limiting factor for most species

  • Limiting factors can also act from inside the population - intrinsic limiting factors

  • Changes in reproductive physiology

  • Changes in behavior

  • Most populations are regulated by a combination of limiting factors - they never reach their full reproductive potential

  • Limiting factors can act in proportion to how dense the population has become - density-dependent limiting factors

  • Limiting factors can have the same effect regardless of how dense the population has become (forest fires, tidal waves) - density-independent limiting factors

  • These limiting factors act as a feedback loop to keep populations in equilibrium with their environment

  • Are these limiting factors extrinsic or intrinsic, density dependent or independent?

  • Forest fires

  • Food

  • Diseases or parasites

  • Predators

  • Density-dependent regulation can be subtle

  • Populations can still regulate themselves with respect to density, even when their resources are unlimited

  • John B. Calhoun’s classic experiments in the 1950’s with Norway rats have some serious implications for human populations

  • Calhoun determined the level of population density at which rats started to show signs of stress, then let the populations grow to twice that density

  • He provided a rat utopia, with unlimited food, water, and nesting materials

  • Everything except more elbow room…

  • Rats are great mothers, build comfortable nests, carry their babies away from danger by the scruff of the neck, just like momma cats

  • Male rats have a stable pecking order, rarely bother the females or young

  • As densities increased, Calhoun observed a gradual breakdown in maternal care

  • Females stopped building nests

  • Females scattered or abandoned their infants, leaving them to be killed and eaten by other rats

  • As densities increased, Calhoun observed a gradual breakdown in male behavior

  • Males became socially catatonic, withdrawn

  • Males fought more often, became hyperaggressive

  • As densities increased, Calhoun observed a gradual breakdown in male behavior

  • Males became cannibalistic

  • Males showed homosexual behavior

  • When the experiment was complete, Calhoun analyzed the rats’ brains

  • Found gross changes in the adrenal cortex, a center for production of several key hormones driving aggressive and reproductive behavior

  • Later trials found evidence of brain changes at relatively low levels of overcrowding

  • These same brain mechanisms are found in our own brains

  • Will we end up like Calhoun’s rats??

  • In lab populations of fruit flies, as # of flies per bottle increases:

  • mortality increases

  • fecundity decreases (average number of offspring produced per female per breeding season or age interval)

  • Many birds have long lives, during which their reproductive success can be quite high

  • But for various reasons this potential is never realized

  • There are many limiting factors in nature that work together to limit birds from reaching their full reproductive potential

  • To better understand the way populations are regulated, we must understand the way they grow

  • the person who first described the pattern of population growth was a young man who went by the name of Bob…

  • Thomas Robert Malthus - born in 1766 near Guilford England (Albury Parish, Surrey)

  • Second son of seven children

  • Godfathers were Jean Jacques Rousseau, David Hume - dad was a bit radical…

  • Borne with a speech impediment - hare lip and cleft palate

  • Lived a quiet life, with his parents, who called him Bob…

  • May have gotten his inspiration from his father, arguing over social philosophy

  • Utopian schemes were all the rage

  • Utopian philosophers felt that nature had much to teach us

  • Social evolution followed natural evolution, nations could evolve into utopias

  • Dad was a “free thinker”, believed that the utopians were correct

  • Malthus disagreed…

  • Home schooled, later taught by radical social philosopher Gilbert Wakefield, at a school called the Dissenting Academy

  • Very liberal education…

  • Teacher jailed for seditious libel in 1799

  • Malthus studied theology at Cambridge 1776 to 1782 , was ordained into the Church of England in 1788

  • Was a good student, popular with his peers, “often a source of infinite delight and pleasantry to his companions…wont to set the table in a roar.”

  • Eventually moved a few miles down the road from his parents, as curate of Okewood Chapel

  • 1804, age of 39, married his first cousin Harriet (age 28…hmmm), had 3 children (moderate for the times)

  • Access to parish registers of births and deaths, gave him statistical data on the growth of the local population, which was booming

  • Everyone read the Essay or talked about it

  • Malthus wrote to counteract arguments that social progress could be achieved through a better understanding of nature

  • Malthus agreed that nature had a lot to say

  • But what nature really had to tell us was not very pleasant

  • Nature demonstrates that progress is only possible with enormous suffering and sacrifice of life

  • Wars, famines, plagues…these were nature’s way of balancing the books on the excess human population

  • Malthus thought that the “passion between the sexes” was too instinctual to be reasonably controlled or restrained

  • Besides, sex was supposed to feel good!

  • Sexual passion was part of the divine plan behind nature, “be fruitful and multiply”

  • Malthus did not object to the exercise of passion, but to the lack of sexual moderation among the lower classes

  • We were just too damned fruitful…

  • Was a 32 year old bachelor, still living with his parents when he wrote his famous essay

  • Basic argument was entirely mathematical

  • Population would increase geometrically, but resources could only increase arithmetically

  • Over time, this would lead to a growing gap between too many people and too few resources

  • Out of this gap came what Malthus called “the struggle for existence”

  • Ideas were a major influence on Darwin, who reasoned that what was true of humanity must also apply to other animals as well - a struggle for existence

  • The struggle for existence would inevitably lead to widespread starvation and suffering

  • This was also part of the divine plan

  • Creator aimed to prevent laziness and immoderation among the lower classes

  • If you didn’t work, or had too many children, you deserved to starve

  • Views were controversial, but widely accepted

  • Won over William Paley (Natural Theology)

  • Malthus said exactly what many powerful industrialists wanted to hear - justified their faith in laissez-faire capitalism

  • Misery was what the poor deserved for being so prolific

  • It was unnatural for the government to provide welfare support the lower classes

  • Besides which, welfare breeds dependency

  • Not quite a right wing bogeyman

  • Wanted to eliminate the British welfare system, but only by weaning the poor off welfare, into fruitful labor - workfare!

  • And you thought Bill Clinton invented it…

  • First “Poor Law” dates to Elizabethan times (1601)

  • British welfare system was the first modern welfare state

  • Poor Law Amendment of 1834 significantly reduced welfare, Malthus still influential

  • Was Malthus correct?

  • Do populations grow geometrically?

  • In order to answer this question, we’ll have to make a few assumptions

  • Seasonal breeders - annual breeding season, like deer, birds, plants…

  • No limits to growth

  • No immigration or emigration

  • R = replacement rate, number of offspring left behind by each adult female

  • At time t, population size N = Nt

  • At time t = 0, population size N = N0

  • What is the population size N1 at the end of the first breeding season?

  • N1 = R * N0

  • What is the population size N2 at the end of the second breeding season?

  • N2 = R * N1

  • N2 = R * (R * N0) = R2 * N0

  • What is the population size N3 at the end of the third breeding season?

  • N3 = R * N2

  • N3 = R * R * (R * N0)

  • N3 = R3 * N0

  • What is the population size Nt at time = t ?

  • Nt = Rt * N0

  • This is the classic J-shaped curve of exponential growth, predicted for seasonal breeders with no limits to growth

  • Exponential growth does occur in nature, as in this graph of the White Ibis population in Louisiana

  • Additional food resources during the breeding season, provided by crawfish farm ponds, has allowed this population to grow exponentially

  • Several other colonial wading bird populations in Louisiana, like those of the Great Egret and the Snowy Egret, show a very similar pattern

  • But humans aren’t seasonal breeders…

  • Humans (like bacteria) breed continuously - every night is date night, all over the world…

  • Exponential model

  • Continuous breeders - like bacteria, humans…

  • No limits to growth

  • Must call upon the mighty powers of calculus to solve this one!

  • Births and deaths occur all the time

  • At any given time, the rate of population growth will equal the difference between births and deaths at that moment

  • b = birth rate, d = death rate

  • r = instantaneous growth rate (or intrinsic rate of natural increase)

  • r = b - d

  • What is the change in population size vs the change in time?

  • dn/dt = N * (b - d) = r * N

  • Solving this equation for any time t:

Nt = N0 * e rt

  • So Malthus was right after all

  • Populations that breed continuously will grow in an exponential fashion

  • Same basic J shape, now smooth and continuous

  • What assumption in these two models is totally unrealistic?

  • Nature has limits - unlimited growth in nature is exceptional

  • Need a third (and final) model

  • Logistic model assumes

  • Continuous breeders - like bacteria, humans…

  • Growth is limited

  • How can we represent limits to growth?

  • Any given habitat can only support a finite number of organisms

  • Let’s call this the carrying capacity

  • K = carrying capacity

  • How can we work this variable into our growth equation?

  • dn/dt = N * (b - d) = r * N

= r * N * [ (K-N) / N ]

= r * N * [ 1- (N / K )]

  • r-selected organisms (colonizers) have a strategy that depends on rapid and continuous breeding, with little limit to growth

  • K-selected organisms (stable) have a strategy governed by the carrying capacity of their species in a given environment

  • We can observe this S- shaped growth curve in the laboratory, by putting bacteria into a nutrient broth

  • The growth of the cattle egret population in Louisiana shows a logistic pattern

  • Cattle egrets follow cows around, catch bugs

  • Limited number of cows to follow

  • Little r is proportional to big R

  • You can estimate r by using field data to calculate R for a given population

  • Geometric model

  • Seasonal breeders

  • No limits to growth


  • Exponential model

  • Continuous breeders

  • No limits to growth


  • Logistic model

  • Continuous breeders - like bacteria, humans…

  • Limits to growth (K)



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