Lecture 25:
Population dynamics I

• Population regulation

.   effects of population density on death rate or fecundity of plants
.   without density-dependent effects on mortality or fecundity population regulation is not possible
:   a population growth rate < 1 leads to extinction
:   a population growth rate > 1 leads to explosion
:   without density-regulated mortality or fecundity a population growth rate of exactly one is infinitely improbable
.   density effects in natural population may be
:   unmeasurable small in populations that have normally low densities
:   absent for most of the time if the population undergo regularly disasters reducing the population density
    but at least some density-dependence at some times is necessary to prevent populations from exploding.
.   density regulation
:   direct (intra-specific competition)
:   indirect (herbivores, seed predators, pathogens; see chapter 13); has a longer negative feedback loop than in
    direct regulation, and therefore tends to be less effective in population regulation


 

•  Effects of intra-specific competition (the empirical evidence)

.   plant fecundity (also see fig. 12.13c in the book)

(Vulpia fasiculata; after Watkinson & Harper, 1978)
 
.   mortality (also see fig. 12.13b in the book)
(Glycine soja; after Yoda et al., 1963)
 
   (also, notice the time aspect: The negative effects of density become more pronounced with time)
 
 
• How strong effects of plant density do we need to effectively regulate a population?

.   density regulation:
:   under-compensating
.:  relatively weak density-dependence
.:  stable equilibrium (monotonous convergence)
.:  most plant populations show undercompensating density-dependence
:   over-compensating
.:  strong density-dependence
.:  stable equilibrium (oscillatory convergence), cycles, and even chaos are possible
.:  overcompensating density-dependence is rare (the figure above shows over-compensation at high
    densities after 61 and 93 days)
 

 
• Self-thinning and the '-3/2 power law'

.   Empirical relation between log-plant weight and log-plant density often shows a linear relation
    with a slope of approximately -3/2  (see Fig. 12.14, p.382 in the book)
.   This is a consequence of packing a number of individuals of a given size in a given area:
 

 
.   A given surface area can contain either a large number of plants (N) with a small projected area (A) or a fewer
    number of plants with a large projected area (see figure above) such that if all the space is filled up, then the product
    AN  will be approximately constant.
.   The projected area (A) will be approximately proportional to the plant's weight (W) to the power 2/3.
    (Check this out for your self with a cube if you don't believe it.)
 
.   Dynamic aspect of self-thinning:
:   The -3/2 line gives the relation between log-plant eight and log-plant density when no space remains
    unoccupied.
:   In the region below the line there is still unoccupied empty space; Plants in a population starting below the line
    will grow upward  (red line in graph below) until the -3/2-line has been reached; Once on the line, occasional
    deaths of plants reduces the plant density and creates new space that allows the remaining plants to increase in
    size. In this way, as the time proceeds, the population moves up along the -3/2-line.
:   the region above the line remains unreachable.