2. Competition - Western Michigan...

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Dr. S. Malcolm BIOS 3010: Ecology Lecture 5: slide 1

BIOS 3010: Ecology Lecture 5: Processes: Intraspecific competition

•  Lecture summary: – Competition definition. – Extremes of

intraspecific competition.

– Density dependence. – Discrete breeding

model. – Continuous breeding

model.


2. Competition: •  An interactive process that is a product of combined demand for

resources that results in competition among individuals either intraspecifically or interspecifically and a negative outcome for all competitors.

•  Thus competition can be defined as: •  "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., 1996).

–  Thus the ultimate effect of competition on an individual is a decreased contribution to the next generation compared with the outcome in the absence of competition.


3. Two kinds of intraspecific competition: •  Two kinds of intraspecific competition which

represent extremes of a continuum: – exploitation or scramble:

•  interact indirectly via direct resource use. •  e.g. flies on a cow pat, or plants competing for light, or

resource depletion zones - RDZs –  interference or contest:

•  interact directly via indirect resource use •  e.g. territoriality, or fighting for females, or use of

allelochemicals and space as a resource) –  Figs. 5.1 & 5.2 show both kinds and negative effects of

competition in single species populations.

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4. Density dependence:

•  Competition increases with density (Fig. 5.2). •  Density dependence can vary with increasing

density (Figs 5.3, 5.4, 6.5), from – density independence, through – undercompensating density dependence, to – exactly compensating density dependence, to – overcompensating density dependence.

•  so the intensity of both kinds of intraspecific competition increase with population density and change from density independence to density dependence.


5. Density dependence & carrying capacity:

•  Density dependent birth and mortality rates lead to the regulation of population size at a stable equilibrium: –  the carrying capacity (K) – at the population size sustainable by available

resources as shown in Figs. 5.7 & 5.8 – generates the sigmoidal or S-shaped curve

characteristic of intraspecific competition (Fig. 5.11).


6. Density dependent growth:

•  In addition to effects on numbers, competition negatively influences growth: –  Which 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. 5.14 & 5.15): –  Within genets, tiller growth can be less variable and more

regulated than the genets themselves.

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7. k-values and density dependent mortality: •  Use of k-values of mortality due to competition can define

competition according to the slope b of the relationship of k-values plotted against the logarithm of initial density (before the effects of competition) (Fig. 5.16). –  b = 0: density independence –  b < 1: undercompensating density dependence –  b = 1: exact density dependent compensation

(contest competition) –  b > 1: overcompensating density dependence –  b = ∞: overcompensating density dependence

(scramble competition) •  see Fig. 2.3 from Hassell (1976) of scramble & contest •  k-mortality is shown in Fig 5.16 & k-fecundity in Fig. 5.17


8. Discrete breeding season model of intraspecific competition:

•  Using the net reproductive rate (R) and population sizes of Nt (at time t) and Nt+1 (at time t+1), in the absence of competiton, the model describes population increase simply as: Nt+1 = Nt R and,

Nt = NoRt

•  this describes exponential population growth

across discrete generations as in Fig. 5.18.


9. Discrete breeding and competitive limitation to a carrying capacity:

•  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)

•  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.

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10. Density dependence of the model:

•  The k-value is thus the difference between logNtR and logNtR/(1 + aNt).

•  Plotting these values shows that the model exactly compensates (Fig. 5.20).

–  A more realistic model of competition that incorporates a range of competitive regulation was derived by Hassell (1975) (not Maynard Smith & Slatkin, 1973) in which he simply added the slope of the k-value plotted against log initial density:

Nt+1 = NtR/1+(aNt)b –  in which b is the slope of population size (log10Nt) against mortality (k)

and a substitutes for (R-1)/K as before (see Figs. 5.21 & 6.26 for fit to real data).


11. Continuous breeding - exponential growth:

•  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.

•  For exponential population increase the rate of population increase is dN/dt and this speed of change is described by: dN/dt = rN

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

– 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


12. Continuous breeding, carrying capacity & the logistic equation:

•  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 (Fig. 5.23)

•  Shows that exponential increase is decreased to carrying capacity (K) by the logistic term (K - N)/K

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Figure 5.1: Intraspecific competition among cave beetles eating cricket eggs (a) exploitation, (b) interference


Figure 5.2: Red deer population size, birth weight and survivorship


Figure 5.3: Density dependent mortality in flour beetles (1 = density independent, 2 = undercompensating mortality, 3 = overcompensating mortality)

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Figure 5.4: Density & mortality in trout fry


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


Figure 5.7: Density dependent birth & mortality - equilibrium at carrying capacity (K)

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Figure 5.8: ‘n’-shaped recruitment and carrying capacity (K)


Figure 5.11: S-shaped population increase in beetles, wildebeeste & willows after rabbit death


Figure 6.14 (3rd ed.): Effects of density on growth rate & size in frogs and reindeer.

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Figure 5.12: Intraspecific competition in limpets with density


Figure 5.14: “Constant final yield” of plants at different densities


Figure 5.15: Intraspecific competition and regulation of module number in rye grass

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Figure 2.3 (Hassell, 1976)

(Exploitation) (Interference)


Figure 5.16: k-values and density dependent mortality

(a) dune annual (b) almond moth (c) fruit fly (d) Plodia moth


Figure 5.17: k-values and density dependent mortality

(a) limpet (b) cabbage root fly (c) grass mirid (d) plantain

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Figure 5.18: Discrete model of population increase with time - exponential and sigmoidal


Figure 5.20: Slopes (b = 1) of k against log density for exact compensation


Figure 5.21: Variable slopes (b) for k mortality due to competition against log density

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Figure 6.26 (3rd ed.): Discrete model fit to data for 4 beetle species (a, b, c, e) and the winter moth (d)


Figure 5.23: Continuous model of exponential and sigmoidal population increase

2. Competition - Western Michigan...

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