Life history tradeoffs.
• Reproductive female red deer on Scottish island have lower survival rates than non-reproductive females of same age
•Adult kestrels (sparrow hawks) have better survival if their broods are artificially reduced, and poorer survival if the broods are artificially enlarged. Fig 52.6, Campbell 6 Fig. 52.7, Campbell 7
Demography and Population Dynamics
November 17 2006 Announcements • we’re now 1 lecture behind; I hope to catch up next time
by combining two lectures on species interactions • No class Friday Dec. 8. Review session scheduled for Monday Dec. 11, 6-7:30 pm 2050 VLSB–come with questions
See Fig 52.5 Campbell 6
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Population biology
• Demography: study of how the vital rate of individuals (birth, death, growth) affect structure and dynamics of populations • Population: group of potentially interbreeding individuals (same species, co-occur in time and space) – Properties of populations: • Density: number of individuals per area or volume • Size structure: proportion of individuals in various size categories • Age distribution: proportion of individuals in various age categories 3 • Sex ratio: number Males: number Females
Life Tables
• Life (and reproductive) table—summary of age (or size) specific rates of survival and fecundity (progeny per individual) • Constructed by following cohort: a group of individuals of the same age, from birth until they all die (or by other methods that approximate this ideal approach) .
The Essay on Student Exploration: Rabbit Population By Season
Vocabulary: carrying capacity, density-dependent limiting factor, density-independent limiting factor, limiting factor, population, population density Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. Suppose you had a pet rabbit. What would the rabbit need to stay alive and healthy? Pet rabbits need food, fresh water, a clean living space, and shelter from the elements in order to ...
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Cohort life table (assume all are reproductive): ax – number surviving at time x lx – proportion original cohort alive at time x mx – fecundity of individual at age x lx mx – number of progeny contributed per original individual at time x
•Survivorship curve: proportion of numbers in a cohort still alive at age X. (Fig. 52.3, Campbell)
1000 Number of survivors
Type II. Squirrels, birds Type I. Humans
Basic Reproductive Rate Ro = ! lx mx Ro is sum of progeny produced per original individual at the end of the cohort’s life. If Ro > 1, population grows.
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100
Type III. Trees, oysters, insects, fish
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0
50 % of maximum life span
100
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Population growth (N = number of individuals)
“N = Births – Deaths (population closed to migration) “BIDE” equation:
dN/dt = b N – d N = (b – d) N = r N ! N(t) = N(0) ert
(e = 2.71828… = base natural logarithm)
” N = Births + Immigration – Deaths – Emigration (open pop.) “N / ” t = rate of change dN/dt = rate of change over very small time interval
b = per capita birth rate (number of births/(N – time) = time-1) if N = 1000 and there were 34 births in a year, b = 0.034 year -1 d = per capita death rate (deaths / number-time) = time-1) if N = 1000 and there were 16 deaths in a year, d = 0.016 year -1
If r > 0, population grows exponentially. If r
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dN/dt = b N – d N = (b – d) N = r N (closed population) 7
r = b – d = per capita rate of population growth (time
-1
)
Huge effect of age of first reproduction on population size in an expanding population
The Term Paper on Population Growth Rate Inindia
... of the world, females of a general population have lower death rates than males." Indeed, except for the ... the real problem is the lack of sufficient numbers of dedicated women physicians who are willing to ... who adhere to religious strictures against artificial birth control, but the major Indian religions have ... work in rural areas and spend some time in pre-insertion and post-insertion follow- ...
B = 2, N(4) = 16 B = 3, N(4) = 9 B = 8, N(4) = 8
Human Population Explosion
Billions of people:
1650 – 0.5 1850 – 1 1930 – 2 1975 – 4 2000 – 6
Years
A=1
A=2
A=4
B = brood size N(t) = population size at time t A = age at 1st reproduction
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Exponential growth in duck weed…
Campbell, Fig. 52.13–density dependence in per capita birth and death rates (due to intraspecific (within species) competition
(mutually adverse interaction))
Time 4
Time 5 What keeps the world from being smothered in elephants, E. coli, or us? 11
Per capita = per individual birth or death rates
Time 1
Time 2
Time 3
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*r describes population growth at low density, K describes density at which population stops growing.
Campbell, Fig. 52.11 K = carrying capacity of environment for a given population K depends on both the environment and the organism in question (how efficiently it can use 14 resources)
Numbers in Population
K
“Logistic equation”: dN/dt = rN [(K-N)/K] 0 Time
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r* vs K* selected life history traits • r-selected traits • K-selected traits
– Short life span – Small size – High predator vulnerability – Weak competitor – Good disperser – Many small offspring – Early reproduction – Long life span – Large size – Low vulnerability to predators – Strong competitor – Slower disperser – Fewer but better provisioned offspring – Late reproduction overshoot
Territoriality can produce this type of population growth
Density independent factors?
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Campbell, Fig. 52.11
K = carrying capacity of population in a given environment Negative feedback: system responds to change by reversing direction (stabilizing)
Change in limiting factor
e.g. speed limit, versus regulation by enforcement of minimum and maximum speed
N Period of looser regulation Time
Positive feedback—system responds to change by changing 17 more in same direction (destabilizing, e.g. exponential growth)
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Analogy: speed limit (60 mph) regulated strictly (55-65) or loosely (50-70).
Fast speed (high population growth rate (r)), oversteering (strong density-dependent feedback), or time lags in feedbacks (distracted drivers) all can destabilize population growth. N Time
The Essay on The Growth Of Rats
Problem Statement: When a ship sails across the ocean two rats are on board. A female and male are then left on a deserted island during late December. This island soon becomes the rats’ home. The number of offsprings that might be produced from this pair in a year should be estimated. One should make these assumptions when executing the problem. ❏ Every litter produces six young rats, and three ...
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Source: United Nations, World Population Prospects, The 1998 Revision; and estimates by the Population Reference Bureau
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Demographic transition, change from Zero Population Growth (ZPG) due to high death rate to ZPG due to low birth rate
Age structure of population reflects age-specific birth and death rates
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Huge effect of age of first reproduction on population size in an expanding population
B = 2, N(4) = 16 B = 3, N(4) = 9 B = 8, N(4) = 8
Fig. 52.23 Campbell: Ecological footprint: Estimate of land and water area needed to produce all resources a nation consumes, and to absorb all the waste it generates
Years
A=1
A=2
A=4
B = brood size N(t) = population size at time t A = age at 1st reproduction
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