BIOS 6150: Ecology - Western Michigan Universityhomepages.wmich.edu/~malcolm/BIOS6150-Ecology/Lectures/6150… · BIOS 6150: Ecology - Dr. S. Malcolm. Week 3: Intraspecific Competition

BIOS 6150: Ecology - Dr. S. Malcolm. Week 3: Intraspecific Competition Slide - 1

BIOS 6150: Ecology Dr. Stephen Malcolm, Department of Biological Sciences •  Week 3: Intraspecific Competition. •  Lecture summary:

• Definition. • Characteristics. •  Scramble & contest. • Density dependence •  k-values • Discrete & continuous

models


2. Competition:

•  Interactive process. •  Product of combined demand for resources. •  Leads to competition among individuals,

either: •  intraspecifically or, •  interspecifically.

•  Results in a negative outcome for all competitors.


3. Definition of Competition:

•  “competition is an interaction between individuals, brought about by a shared requirement for a resource [in limited supply], and leading to a reduction in the survivorship, growth and/or reproduction of at least some of the competing individuals concerned” (Begon et al., 2006, p. 132) •  The ultimate effect of competition on an individual is a

decreased fitness contribution to the next generation (fewer offspring) compared with what would have happened had there been no competitors.


4. Four characteristics of intraspecific competition:

•  (1) Decrease in fitness: •  The ultimate effect of competition is a decrease in the fitness of all

interactants (thus it is a “-,-” interaction): •  Often via decreased survivorship or fecundity. •  Fitness reduction must be measurable to conclude that competition occurred.

•  (2) Limited supply of resources: •  The resource for which individuals compete must be in limited supply.

•  (3) Reciprocity: •  Even if the detectable competition is either mostly one-sided, or

balanced, it must be reciprocal and have a negative impact on both interactants (symmetrical and asymmetrical).

•  (4) Density dependence: •  The probability of an individual being adversely affected increases with

increasing competitor density (in contrast to density independent effects).


5. Extremes of intraspecific competition:

•  Scramble (exploitation) and contest (interference) competition were first described as simplistic extremes by Nicholson (1954) in Australia. •  Mortality (% or kcompetition due to competition) or

survivorship is plotted against logarithm of initial density to show degree of density dependence.


6. Scramble & Contest Competition:

•  Scramble competition: •  Nicholson described scramble competition for dungflies

competing for the limited resources of cow feces. •  Each member gathers a constant amount of resource at all densities.

Thus at high density there is insufficient resource and the whole population dies (slope b = ∞).

•  Contest competition: •  Where individuals of the population interfere or contest with

each others abilities to harvest resources, some survive. •  Exact density-dependent compensation is thus described by a

mortality slope b = 1. •  Figs. 5.1 & 5.2 from Begon et al. (2006) to show both kinds and

negative effects of competition in single species populations.


7. Density dependence:

•  Competition also increases with population density when mortality may increase or survivorship may decrease (Fig. 5.2). •  The nature of density dependence can also

change with increasing density from: •  density independence, through, •  undercompensating density dependence, to, •  exactly compensating density dependence, to, •  overcompensating density dependence

(Figs 5.3, 5.4 & 6.5).


8. Density dependence (continued):

•  So intensities of both kinds of intraspecific competition increase with population density and change from density independence to density dependence. •  Thus density dependent birth and mortality rates lead to

the regulation of population size at a stable equilibrium where births = deaths.

•  This is the carrying capacity (K) at the population size sustainable by available resources as shown in Figs. 5.7 & 5.8.

•  Density dependent population regulation generates the sigmoidal or S-shaped curve characteristic of intraspecific competition (see Fig 5.11).


9. Density dependent growth:

•  In addition to effects on numbers, competition also negatively influences growth: •  This in turn influences numbers through reduced per capita

reproductive output.

•  Rates of growth and rates of development can be reduced as shown in Figs 6.14 & 5.12: •  But the total population biomass can remain the same, despite

individuals being smaller: •  The “law of constant final yield” (exact compensation)

•  Reproductive allocation can also shift with changing resource availability (Figs. 6.16 & 5.15): •  Within genets, tiller growth was less variable and more regulated

than the genets themselves.


10. k-values and density dependent mortality:

•  k-values of mortality due to competition can define competition according to the slope b of the relationship (Fig. 5.16) of kcompetition plotted against the logarithm of initial density (density before the effects of competition).

•  b = 0 density independence. •  b < 1 undercompensating density dependence. •  b = 1 (contest) exact density dependent compensation. •  b > 1 overcompensating density dependence •  b = ∞ (scramble) overcompensating density dependence

•  see Fig. 2-3 from Hassell (1976) of scramble and contest competition. •  k-mortality is shown in Fig 5.16 & k-fecundity in Fig. 6.20.


11. Discrete breeding season model of intraspecific competition:

•  Using: •  R net reproductive rate •  Nt population size at time t •  Nt+1 population size at time t+1

•  In the absence of competition, the model describes population increase simply as:

•  Nt+1 = NtR and •  Nt = NoRt

•  This gives the exponential population growth across discrete

generations as in Fig. 5.18.


12. Carrying capacity, limited resources and the effect of competition:

•  At high density when the ratio of Nt/Nt+1 = 1 this is by definition the carrying capacity K.

•  So in the presence of competition, the population rises to K as shown in Fig. 5.18. •  according to:

•  Nt+1 = NtR/1+(aNt) •  where a = (R-1)/K

•  so the unrealistic R in the first equation is now replaced by the more realistic R/(1 + aNt)

•  as a and Nt increase so does the effect of competition and R is decreased.


13. Density dependence of the model:

•  The k-value for mortality due to competition is thus the difference between log NtR and log NtR/(1+aNt) and plotting these k values against log10Nt (Fig. 5.20) shows that the model exactly compensates with a slope b = 1.


14. Incorporation of variable density dependence with b:

•  A more realistic model of competition that incorporates a range of competitive regulation was derived by Maynard Smith & Slatkin (1973) in which they simply added the slope b of the k-value plotted against log initial density:

•  Nt+1 = NtR/1+(aNt)b --- equation 5.18 (p.148) •  in which b is the slope of mortality (k) against

population size (log10Nt) and, •  a substitutes for (R-1)/K as before

(see Figs. 5.21 & 6.26 for real data). •  Also generates realistic ranges of population

fluctuations (Fig. 5.22).


15. Continuous breeding - the logistic equation:

•  The model above was for discrete time steps described by a “difference” equation.

•  For continuously breeding populations (birth and death continuous) we need a continuous form of the model using a “differential” equation. •  So for exponential population increase the rate of population

increase is dN/dt and this speed of change is described in the absence of competition by:

•  dN/dt = rN •  where r is the intrinsic rate of natural increase which is lnR or lnRo/T

•  So the continuous equivalent to Fig. 5.18 is shown in Fig. 5.23 and this is the differential form of the difference equation Nt = NoRt


16. Logistic limitation to a carrying capacity:

•  The differential form of Nt+1 = NtR/1+(aNt) in Fig 5.18 is given by:

dN/dt = rN((K - N)/K) •  This is the famous logistic equation. •  This shows that exponential increase is

decreased to K by the logistic term (K - N)/K


17. Asymmetrical competition:

•  Large vs small Impatiens in a woodland (Fig. 5.26): •  Small plants did not grow and so the asymmetry

increased with time. •  Root vs shoot competition in morning glory

Fig. 5.27 (Weiner expt.): •  Root competition for nutrients resulted in most

biomass reduction, but shoot competition for light generated most size inequality and increase in asymmetry.


Figure 5.1: Intraspecific competition among cave beetles for cave cricket eggs (a) scramble or exploitation, (b) contest or interference.


Figure 5.2: Survivorship of red deer on the island of Rhum declines with lower birth rate and increased density.


Figure 5.3:

Density dependent mortality in flour beetles changes from (1) density independence, to (2) undercompensating density dependence, to (3) overcompensating density dependence.


Figure 5.4: Exact compensation in trout fry.


Figure 6.5 (3rd ed.): Density dependent mortality in soybeans leading to overcompensation with time.


Figure 5.7: Density dependent birth and mortality rates.


Figure 5.8:

Differences between births and deaths (a), generate recruitment (b), and population increase to a carrying capacity (c).


Figure 5.11:

Examples of S-shaped population increase for (a) Rhizopertha beetles on wheat, (b) wildebeest after a rinderpest outbreak, and (c)

willows after myxomatosis killed rabbit herbivores.


Figure 6.14 (3rd ed.):

Effects of density on growth rate and size in (a) Rana tigrina frogs and (b) reindeer.


Figure 5.12: Effects of intraspecific competition on growth and final biomass of populations of the limpet Patella cochlear.


Figure 6.16 (3rd ed. – see Fig. 5.14, 4th ed.):

“Constant final yield” of plants sown at a range of densities for (a) subterranean clover, (b, c) the dune annual Vulpia fasciculata.


Figure 5.15: Intraspecific competition in rye grass regulates the number of modules (tillers).


Figure 5.16:

k-values to describe variable density dependent mortality in (a) a dune annual, (b) almond moth, (c) fruit fly, and (d) the moth Plodia interpunctella.


Figure 2.3: (Hassell, 1976)


Figure 6.20, 3rd ed., see Fig. 5.17, 4th ed.):

k-values to describe density dependent reductions in fecundity in (a) limpets, (b) cabbage root fly, (c) grass mirid, and (d) plantain.


Figure 5.18: Difference equation model to describe population increase in species with discrete generations.

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Figure 5.21: Different intensities of intraspecific competition incorporated in equation 6.19.


Figure 6.26 (3rd ed.):

Equation 5.18 fitted to data for different beetle species in the laboratory (a, b, c & e), and winter moths in the field (d).


Figure 5.22: Range of population fluctuations for (a) values of b and R and (b) population size against time, generated by equation 6.19.


Figure 5.23: Exponential and sigmoidal models of population increase against time for continuous breeding - the logistic model of population growth.


Figure 5.26:

Asymmetric competition in the woodland plant Impatiens pallida in SE Pennsylvania.


Figure 5.27: Root vs shoot competition in morning glory vines, Ipomoea tricolor.

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BIOS 6150: Ecology - Western Michigan Universityhomepages.wmich.edu/~malcolm/BIOS6150-Ecology/Lectures/6150… · BIOS 6150: Ecology - Dr. S. Malcolm. Week 3: Intraspecific Competition