Biology 20C - Fall 1998

Biology 20C - Fall 1998

ECOLOGY AND EVOLUTIONARY BIOLOGY

Lecture 22 - Realized Growth; LHC Evolution

REALIZED vs. POTENTIAL GROWTH

The exponential model is the basis for a family of models that become increasingly realistic as they include more environmental factors and interactions with other organisms. As each new component is added, realized (observed) growth declines increasingly from the potential shape, rate, and maximum density predicted from the physiological "optimum fundamental niche".

1. Potential Unlimited Growth: The Exponential describes "J-shaped" growth at a constant rate in an infinite environment. Under ideal conditions, it describes the theoretical maximum, physiological growth potential for that population in any environment:

dN/dt

= r_maxN

2. Observable Unlimited Growth: Realized constant exponential growth rates ( r ) are environment-specific and observed r is almost always < r_max

dN/dt

= rN

3. Intra-Specific Competition: The Logistic is the simplest model of growth in a finite environment. It describes "S-shaped" (sigmoidal) growth until N is stabilized at the carrying capacity ( K ) of the environment by density-dependent, intra-specific competition for a finite resource:

dN/dt

= rN (K -N)/K

4. Inter-Specific Competition: Lotka-Volterra Inter-Specific Competition Models extend the logistic model to 2 (or more) species competing for the same resource:

	dN₁/dt	= r₁N₁ (K₁ -N₁ - a N₂)/K₁	a converts N₂ into numbers of N₁ exerting same competitive effect
	dN₂/dt	= r₂N₂ (K₂ -N₂ - b N₁)/K₂	b converts N₂ into numbers of N₁ exerting same competitive effect

5. Predation: Lotka-Volterra Predator-Prey Models extend the exponential model to include density-dependent effects of predators, herbivores, parasites, pathogens etc on their prey or host.

	Each Species in Isolation
Prey	dN/dt	= (+) r_NN	positive exponential growth to infinity
Predator	dN/dt	= (-) r_PP	negative exponential decline to extinction

	Both Species Together		NP = Probability of predator encountering prey
Prey	dN/dt	= (+) r_NN -q NP	q converts encounters into kills
Predator	dN/dt	= (-) r_PP + g NP	g converts encounters into meals and numbers of baby predators produced from that meal

6. Disturbances: Effects of density-independent stochastic (random) factors (e.g. storms, frosts, fire) are superimposed on the interactions above, further limiting realized growth. Deviations from smooth curves (e.g. overshoots, undershoots, cycles, damped oscillations, fluctuations, crashes) become increasingly marked as other species and factors are included.

EVOLUTION OF LIFE HISTORY CHARACTERISTICS

r- and K-Selection Models

These models were the first comprehensive attempt to explain how LHC evolve. These models are based on observations that many LHC tend to co-occur; and that different sets of LHC seemed to be correlated with the predominant kind of population growth (exponential or logistic) in a particular species. r-Selection and K-Selection represent end-points along a continuum. The arguments for them are presented as a series of contrasts.

	r-Selected	K-Selected
Habitat Properties:
Variation	Unstable	Stable
Predictability	Unpredictable	Predictable
Disturbances	Common	Rare

Typical Population Densities:
Variation	Highly variable	Constant N
Usual N	Unpredictable but << K	At or near K
Extinctions	Common	Rare

Population Growth:
Observed growth rates	r is variable: high + ; 0 ; high -	r at or near 0
Limitation	Density-independent by disturbances	Density-dependent competition for resources
Pattern	Exponential	Logistic

Life History Characteristics:
Body size	Small	Large
Physiology	Conformers	Regulators è Homeostatic
Development	Rapid	Slow
Longevity	Often very short	Often very prolonged
Average mortality rate	High	Low
Survivorship l_x	Type III or Type III è Type I	Type I or II
Fecundity b_x	Semelparous	Iteroparous
Generations	Non-overlapping	Overlapping
Generations/"season"	One to many	Less than one
Age of first reproduction	Early	Late
Clutch size	Many	Few or 1
Egg or birth size	Small	Large
Post-reproductive life	None	May be prolonged
Parental care	None	Often extensive

Selection Strategies:	Opportunistic	Equilibrium
Timing	When r is strongly positive	When r = 0 (at K)
	Whenever conditions are favorable	Largely independent of external conditions
Labels	"Big Bang"	(maximize persistence)