BIOL 4120

Principles of Ecology

Phil Ganter

320 Harned Hall

963-5782

      An immature bug on a eucalyptus leaf.

Lecture 11 Intraspecific Population Regulation

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Overview - Link to Course Objectives

Logistic Growth

In the equation for exponential growth, the rate of population increase simply increases with N

  • Not very realistic, as all populations with an r greater than 0 would increase to infinity given infinite time
  • Logistic growth is one way to limit the population size

Logistic growth is based on the idea of a Carrying Capacity (K) for any environment, a population size:

  • Above which the population decreases
  • Below which the population increases
  • When the population size is at the carrying capacity, then no growth occurs
  • If K is the carrying capacity in the environment (expressed in numbers of individuals of a species) then
  • produces a sigmoid curve
  • hits an equilibrium value
    • stable equilibrium because the population returns to it from any other population size, given time
  • logistic growth model:
    • is a continuous model (notice that what is predicted above is the growth rate, not the size of the population
      • there is an equation, based on the logistic above, for predicting population size, but we will not use it here and so I will not present it except in the additional materials available at Modeling Density-Dependent Growth
    • is useful because it is conceptually straightforward, although it does not accurately predict the growth of many natural populations
    • assumes that:

      1. the change in dN/dt with a change in N is a hyperbola with a maximum (which means it is a dome and not a valley - see graph above) at K/2
        • A graph of r*(K-N)/K versus N is a straight line which means that r is multiplied by an ever smaller fraction, until the product of r and (K-N)/K hits 0
        • The graph above shows that the rate of population change (dN/dt) increases with N less than K/2 but at a decreasing rate (it constantly increases in exponential growth) until it hits a maximum at K/2 and begins to decline after until it reaches 0 at K
        • this makes sense as the population should stop growing when it reaches its carrying capacity, K
            • for animals with complex life histories and mating systems, the assumption of is not always met
            • social systems which entail some individuals not breeding when they could obviously violate this assumption
      2. there are no lags in the timing of the change in dN/dt with any change in N
        • lags are common when life histories are complex, as in holometabolous insects
            • larvae live in different environment and a change in larval density may not have an effect on egg-laying until after they pupate and become adults
      3. constant K (constant environment over space and time)
        • K is likely to change over both space and time
      4. constant r (all individuals equally fit)
        • often only a portion of a population breed, the rest may be helpers or may not have access to enough resources to breed
      5. no migration
        • dispersal can be important, even keeping a population from going extinct when the net replacement rate is below 1
  • Time lags introduce oscillatory behavior into these models
    • populations can cycle between small and large values, with even intermediate levels possible
    • With lags, nonlinear relationships between dN/dt and N, and/or large r values, the models can become chaotic

For more on the logistic, including a derivation and some problems, go to Modeling Density-Dependent Growth

Density-Dependence vs. Density Independence and Regulation

Populations fluctuate in size and you can always find an average population size if you have measured the population size at two or more times.

  • A question that immediately arises about the average is whether or not the population is regulated
  • Regulation in terms of populations means that there is some population size that represents a turning point in terms of population growth (called a set point)
    • In regulated populations, the growth rate of the population tends to be negative when the population size is greater than the set point and positive when the population size is smaller than the set point.
      • This means that the population grows to the set point when it is below it and declines to the set point when it is above it.
    • In Unregulated populations, there is no relationship between population growth and population size or, if there is a relationship, the relationship will not result in the population size being stabilized

What mechanisms might regulate populations?  Ecologists have a general answer for this question.

  • Density Dependent influences change strength according to the density of individuals
    • to regulate, the relationship between the factor and population size must reduce population growth as density increases
      • This will be a positive relationship for a factor that affects mortality (mortality rate increases as population increases)
      • This will be a negative relationship for a factor that affects natality (birth rate decreases as population increases)
    • intraspecific competition is a good example of DD effects
    • Logistic is a DD model because the population growth rate (dN/dt) is positive below K and negative above K
  • Density Independent influences have no relation to the density of individuals
    • It is best to think of these two things as opposite ends of a continuum, as many factors are not strongly influenced by density, but are weakly density dependent or are density dependent only over a particular range of densities
    • DI effects often arise when population growth rate is influenced by the abiotic portion of an organism's environment
    • Do not think that all environmental effects are always DI
      • If cold weather kills off an insect, cold winters kill more than warm winters and, described like this, you would expect the mortality caused by temperature to be density-independent, since the proportion of the insects killed in the winter is not related to population size, only temperature
      • This effect may have a DD aspect if we add some more information.  If the insects that find Refugia (safe places) are those that survive cold weather and there are only a limited number of places that provide refuge, when the population size is small all find refuge and few die but, when the population size is large not all fit into the refugia, a larger proportion of the population will die.
      • This is a DD effect because, although cold kills, places in refugia are the limited resource that interacts with density

Remember that density-dependent effects can be seen in both mortality rates and in birth rates!

Intraspecific Competition

Competition occurs when a resource is in limited supply such that not all organisms that need it will obtain all that they need (no limitation, no competition!)

If the organisms competing are all members of the same population, it is Intraspecific Competition

Competition occurs in two general ways:

Scramble (Resource) competition

  • No need for individuals to interact directly, as each takes from a common resource
  • Each competitor affects all other competitors by reducing the amount of resource available to others
  • Schoener divided this into:
    • Exploitative -- consumption of the same food item or abiotic resource
    • Preemptive -- taking space on a surface needed for living (rocks for mussels, land for plants, etc.)

Interference (Contest) competition

  • Competitors interact directly, outcome of one contest need not affect any other competitors
  • Competition for territory
  • Inhibitory chemicals
  • Contests for individual resource items (crocs and lions!)

More Mechanisms of Density-Dependent Regulation

Density dependent effects can be seen in many aspects of life history

Density-Dependent Dispersal

  • Rather than die or fail to reproduce, organisms often leave
  • Density-dependent dispersal has the potential to be an important regulatory mechanism
  • Has not often been detected in natural situations

Social Behavior

  • Some animals live in Social Groups, where individuals interact and cooperate in obtaining food and in reproduction
  • Social groups are often Kin Groups of related individuals
  • Group size often responds to the availability of resources, such that there are many small reproducing groups when resources are plentiful and fewer reproducing groups when resources are scarce

Territoriality

  • Animals have Home Ranges, areas they use in a year's activity
  • In some cases, ranges are defended from incursion of other competitors and they become Territories
  • Territories represent a division of resources and may determine  reproductive success

Plant Mechanisms

  • Just a note on competition from the viewpoint of a plant
  • Plants compete with immediate neighbors for
    • Sunlight (shading is a competitive mechanism)
    • Soil Minerals (plants may secrete chemicals that inhibit the growth of other plant's roots and, in that manner, secure access to resources)
  • Sessile animals (sponges, corals, etc.) may compete in ways similar to the ways in which plants compete

Terms

Logistic Growth, Carrying Capacity (K), Regulation, Density Dependent, Density Independent, Abiotic, Refugia, Intraspecific Competition, Scramble (Resource) competition, Interference (Contest) competition, Density-Dependent Dispersal, Social Behavior, Territoriality

Last updated March 2, 2007