Population Regulation

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• Population Regulation
• J-shaped vs Sigmoidal Population
  GrowthLatitudinal Gradients in Avian Clutch Size
  
• Daylength Hypothesis Prey Diversity
  Hypothesis Spring Bloom or Competition
  Hypothesis Nest Predation Hypothesis
  (Skutch) Hazards of Migration HypothesisEvolutio
  n of Senescence
• Recession of time of expression of the overt
  effects of a detrimental allele
• Precession of time of expression of the effects
  of a
• beneficial allelle

Lecture 15 12 October 2018
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Equilibrium, Opportunistic and Fugitive
Species Correlates of Density-independent vs
Density-dependent selection Correlates of r- and
K-Selection Winemillers 3D Life history Model,
Bet Hedging Change in Population Density vs
Density Lemmings, Voles, and Snowshoe Hares 4 and
10 year wildlife population cycles
3
Decaying Exponential
Pearl-Verhulst Logistic Equation
(
(
K N K K

(
N K
(

1
4
Verhulst-Pearl Logistic Equation dN/dt rN
rN (N/K) rN (rN2)/K dN/dt rN 1
(N/K) rN (K N)/K dN/dt 0 when (K
N)/K 0 (K N)/K 0 when N K dN/dt
rN (1 N/K) rN (r/K)N2
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Inhibitory effect of each individual on its own
population growth is 1/K
rN

V
ra rmax rmax
/
(
K)N
V
V
N
rN
V
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bN
V
rN

dN
V
rN
V
dN
V
bN
N
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Derivation of the VerhulstPearl Logistic
Equation 1 At equilibrium, birth rate must
equal death rate, bN dN bN b0 x N
dN d0 y N b0 x N d0
y N Substituting K for N at equilibrium and r
for b0 d0 r (x y) K or
K r/(x y)
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bN
V
rN

dN
V
rN
V
dN
V
bN
N
r/(xy)
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Derivation of the Logistic Equation 2 Derivation
of the VerhulstPearl logistic equation is easy.
Write an equation for population growth using
the actual rate of increase rN
dN/dt rN N (bN dN) N
Substitute the equations for bN and dN into
this equation dN/dt
(b0 xN) (d0 yN) N
Rearrange terms,
dN/dt (b0 d0 ) (x y)N) N
Substituting r for (b d)
and, from before, r/K for (x y), multiplying
through by N, and rearranging terms,
dN/dt rN
(r/K)N2
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Density Dependence versus Density Independence
Dramatic Fish Kills, Illustrating
Density-Independent Mortality ____________________
_______________________________


Commercial Catch Percent
Locality Before After Decline ________________
___________________________________ Matagorda 16,
919 1,089 93.6 Aransas 55,224 2,552
95.4 Laguna Madre 12,016 149
92.6 _____________________________________________
______ Note These fish kills resulted from
severe cold weather on the Texas Gulf Coast in
the winter of 1940.
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Fugitive Species
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Some of the Correlates of r- and K-Selection
____________________________________
__________________________________________________
_


r-selection K-selection
_________________________________________________
_______________________________________


Climate Variable and unpredictable
uncertain Fairly constant or predictable more
certain Mortality Often catastrophic,
nondirected, More directed, density
dependent density independent
Survivorship Often Type III Usually Types I
and II Population size Variable in time,
nonequil- Fairly constant in time, ibrium
usually well below equilibrium at or
near carrying capacity of envi- carrying
capacity of the ronment unsaturated
com- environment saturated munities or
portions thereof communities no
recolon- ecologic vacuums recolon- ization
necessary ization each year Intra- and
inter- Variable, often lax Usually
keen specific competition Selection favors 1.
Rapid development 1. Slower development 2.
High maximal rate of 2. Greater competitive
ability increase, rmax 3. Early
reproduction 3. Delayed reproduction 4. Small
body size 4. Larger body size 5. Single
reproduction 5. Repeated reproduction 6. Many
small offspring 6. Fewer, larger progeny Length
of life Short, usually less than a year Longer,
usually more than a year Leads
to Productivity Efficiency Stage in
succession Early Late, climax _________________
_________________________________________________
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Mola mola
Dr. Kirk Winemiller Texas A M. Univ.
Sturgeon
Gambusia
Sharks, skates, and Rays
Mosquito Fish
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o
o
o
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Sequoia Tree
Dr. Kirk Winemiller Texas A M. Univ.
Dandelion
Cocoa Nut Tree
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Population Regulation Ovenbird example
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Frequencies of Positive and Negative Correlations
Between Percentage Change in Density and
Population Density for a Variety of Populations
in Different Taxa ________________________________
__________________________ Numbers of
Populations in Various Categories Positive
Positive Negative Negative
Negative Taxon (Plt.05) (Not sig.) (Not sig.)
(Plt.10) (P lt .05) Total
_________________________________________________
_________

Inverts 0 0 0
0 4 4 Insects 0 0 7
1 7 15 Fish 0 1 2
0 4 7 Reptiles 0 0 0
5 19 24 Birds 0 2 32
16 43 93 Mammals 1 0 4
1 13 19 Totals 1 3 45
23 90 162 _____________________________________
______________________ Homo sapiens
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http//www.commondreams.org/view/2011/03/07-0
Microtus
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Hudson Bay Company
Notice apparent 10-year periodicity
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Hudson Bay Company
Hudson's Bay was incorporated on 2 May 1670, with
a royal charter from King Charles II. The charter
granted the company a monopoly over the region
drained by all rivers and streams flowing into
Hudson Bay in northern Canada. The area gained
the name "Rupert's Land" after Prince Rupert,
the first governor of the company appointed by
the King. This drainage basin of Hudson Bay
constitutes 1.5 million square miles, comprising
over one-third of the area of modern-day Canada
and stretches into the present-day north-central
United States. The specific boundaries were
unknown at the time. Rupert's Land would
eventually become Canada's largest land
"purchase" in the 19th century.
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Population Cycles

• Sunspot Hypothesis
• Time Lags
• Stress Phenomena Hypothesis
• Predator-Prey Oscillations
• Epidemiology-Parasite Load Hypothesis
• Food Quantity Hypothesis
• Nutrient Recovery
• Other Food Quality Hypotheses
• Genetic Control Hypothesis

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Sunspot Hypothesis (Sinclair et al. 1993. Am.
Nat.) 10 year cycle embedded within 30-50 year
periods Maunder minimum 1645-1715 Three periods
of high sunspot maxima 1751-1787 1838-1870
1948-1993 Canadian Government Hare survey
1931-1948 Hare cycle synchronized across North
America Yukon 5 km strip, tree growth rings (N
368 trees) One tree germinated in 1675 (gt300
years old) Hares prefer palatable shrubs, but
will eat spruce leaving dark tree ring marks
Anthony Sinclair
Charles J Krebs
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CH4
C
C02
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Other Food Quality Hypotheses Microtus
palatability ltgt toxic (Freeland
1974) Snowshoe
hares Plant chemical defenses against
herbivory
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Chittys Genetic Control Hypothesis
Could optimal reproductive tactics be involved in
driving population cycles?
Dennis Chitty
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http//www.commondreams.org/view/2011/03/07-0
Microtus
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Chapter 10 Social Behavior Hermits must
have lower fitness than social individuals Clumpe
d, random, or dispersed (variance/mean
ratio) mobility motility vagility (sedentary
sessile organisms) Use of Space Philopatry F
luid versus Viscous Populations Individual
Distance, Daily Movements Home
Range Territoriality (economic
defendability) Resource in short
supply Feeding Territories Nesting
Territories Mating Territories
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V
Net Benefit
V
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Sexual Reproduction Monoecious versus
Diecious Evolution of Sex gt Anisogamy Diploidy
as a fail-safe mechanism Costs of Sexual
Reproduction (halves heritability!) Facultative
Sexuality Protandry -- Protogyny (Social
control) Parthenogenesis (unisexual
species) Possible advantages of sexual
reproduction include two parents can raise
twice as many progeny mix genes with desirable
genes (enhances fitness) reduced sibling
competition heterozygosity biparental origin
of many unisexual species
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Sex Ratio Proportion of Males Primary,
Secondary, Tertiary, Quaternary Why have
males? Fishers theory equal investment in the
two sexes
Ronald A. Fisher
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Comparison of the Contribution to Future
Generations of Various Families in Case a in
Populations with Different Sex Ratios ____________
__________________________________________________
____ Case a Number of Males Number of
Females __________________________________________
________________________ Initial
population 100 100 Family A 4
0 Family C 2 2 Subsequent
population (sum) 106 102 CA 4/106
0.03773 CC 2/106 2/102 0.03846 (family C
has a higher reproductive success) _______________
__________________________________________________
_ Note The contribution of family x is
designated Cx.
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__________________________________________________
_________________________ Case b Number of
Males Number of Females _________________________
__________________________________________________
_ Initial population 100 100 Family A
2 0 Family B 1
2 Subsequent population (sum) 103 102 CA
2/103 0.01942 CB 1/103 2/102 0.02932
(family B is more successful) Initial
population 100 100 Family B 1
2 Family C 0 4 Subsequent
population (sum) 101 106 CB 1/101 2/106
0.02877 CC 4/106 0.03773 (family C is more
successful than family B) Natural selection will
favor families with an excess of females until
the population reaches its equilibrium sex ratio
(below). Initial population 100 200 Family
B 1 2 Family C 0
4 Subsequent population (sum) 101 206 C
B 1/101 2/206 0.001971 CC 4/206
0.01942 (family B now has the advantage) _________
__________________________________________________
__________________ Note The contribution of
family x is designated Cx.
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Differential Mortality of the sexes during the
period of parental care.
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Differential Mortality of the sexes during the
period of parental care
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Sexual Selection Mating Preferences
Certainty of Maternity, uncertainty of
paternity Competition for the best mates
of the opposite sex Sex that invests the
most is the most choosy about mates
Jealousy, Desertion, Cuckoldry Epigamic
selection (intersexual, between the
sexes) Battle of the sexes Natural selection
produces a correlation between male genetic
quality and female preference Sexy son
phenomenon (females cannot afford to mate with
males that are not attractive to other females)
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Sexual Selection Mating
Preferences
Drosophila subobscura
Inbred versus outbred male flies differed in
viable sperm counts. Females mated to inbred
males laid an average of only 264 eggs, whereas
females mated to outbred males laid 1134 fertile
eggs. Within an hour, virgin females exposed to
outbred males mated 90 of the time but only 50
of those exposed to inbred males mated during the
first hour. Female side-step dance courtship
display.
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Sexual Selection Mating Preferences Mate
Choice Experiments
Columba livia
Blue Check Blue Bar Ash Red
gt
gt
Nancy Burley Nancy Moran
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Sexual Selection Mating Preferences Sex
that invests the most is the most choosy about
mates Competition for the best mates of the
opposite sex Jealousy, Desertion,
Cuckoldry Certainty of Maternity, Uncertainty of
Paternity Epigamic selection (intersexual,
between the sexes) Battle of the
sexes Natural selection produces a correlation
between male genetic quality and female
preference Sexy son phenomenon (females cannot
afford to mate with males that are not
attractive to other females)
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Sexual Selection Mating Preferences Sex
that invests the most is the most choosy about
mates Competition for the best mates of the
opposite sex Jealousy, Desertion,
Cuckoldry Certainty of Maternity, Uncertainty of
Paternity Epigamic selection (intersexual,
between the sexes) Battle of the
sexes Natural selection produces a correlation
between male genetic quality and female
preference Sexy son phenomenon (females cannot
afford to mate with males that are not
attractive to other females)
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Sexual Selection Mating Preferences Sex
that invests the most is the most choosy about
mates Competition for the best mates of the
opposite sex Jealousy, Desertion,
Cuckoldry Certainty of Maternity, uncertainty of
paternity Epigamic selection (intersexual,
between the sexes) Battle of the
sexes Natural selection produces a correlation
between male genetic quality and female
preference Sexy son phenomenon (females cannot
afford to mate with males that are not
attractive to other females)
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Mating Systems
Promiscuity Monogamy
Polygamy Polygyny Polyandry
Polygyny threshold minimal difference in male
territory quality that is sufficient
to favor bigamous matings by females
Long-billed Marsh Wren
Jared Verner
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Jacana, Lily Pad Walker --
Polyandry Polygyny threshold minimal
difference in male territory quality that
is sufficient to favor bigamous matings by
females
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b Polygyny threshold
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etzel
puted to be
morphic
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Male Peacock, a victim of female mating preference
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Leks Runaway Sexual Selection
(Fisher) Handicap Hypothesis (Zahavi) Sensory
Exploitation Hypothesis (Ryan) Alternative
mating tactics Internal versus External
Fertilization Satellite males Ecological Sexual
Dimorphisms Bower birds Ratites
Bushland tinamou
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Burley, N.T. R. Symanski. 1998. "A taste for
the beautiful" latent aesthetic mate
preferences for white crests in two species of
Australian grassfinches. The American Naturalist
152 792 - 802
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Sage Grouse Lek
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Sage Grouse Female
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Male Reproductive Succes in Sage Grouse
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Geographic Range of Sage Grouse
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Atwater Prairie Chicken
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Prairie Chicken
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Refuge
Atwater Prairie Chicken National Refuge
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Female releases unfertilized eggs (ova) into
water first. Then, male releases sperm (full of
spermatozoa) over them. If female abandons, male
is placed in a cruel bind
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Amplexus in frogs
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Rhea Paternal Care
Emu
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Kiwi
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Cassowary
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Tinamou
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Moa
New Zealands Extinct Moa
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Ostrich Male Parental Care
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Emu Male Parental Care
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Dinosaur fossils suggest that male parental care
could be ancestral in birdsIf so, ratites could
have retained the ancestral stateAnd, if so,
then female care and biparental care would be
derived conditions
A male of the medium-sized predatory dinosaur
Troodon (North America late Cretaceous) brooding
a large clutch of eggs. Female archosaurs extract
substantial amounts of calcium and phosphorus
from their skeletal tissues during egg formation.
Histologic examination of cross sections of bones
(femur, tibia, and a metatarsal bone) from an
adult Troodon found in direct contact with an egg
clutch revealed little evidence of bone
remodeling or bone resorption, suggesting that
the bones were those of a male. Fossilized
remains of Troodon and two other types of
dinosaurs found with large clutches of eggs
suggest that males, and not females, protected
and incubated eggs laid by perhaps several
females (Credit Bill Parsons)
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16
9
20
11
14
15
1
4
7
3
11
5
6
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Red-eyed Vireo
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Four Possible Situations Involving an
Individuals Behavior and Its Influence on a
Neighbor _________________________________________
_________________________ Neighbor(s) Gain
Neighbor(s) Lose ___________________________
_______________________________________
Individual Gains Pseudo-altruistic behavior
Selfish behavior (kin selection)
(selected for) _________________________
_________________________________________
Individual Loses True altruistic behavior
Mutually disadvanta- (counterselected)
geous behavior
(counterselected) ________________________________
_________________________________
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W. D. Hamilton (1964) Kin
Selection Inclusive Fitness
Hamiltons rule r n b c gt 0 r
coefficient of relatedness n number of
relatives that benefit b benefit received
by each recipient c cost suffered by
donor r n b gt c Adaptive
Geometry of a Selfish Herd
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W. D. Hamilton (1964) Died 7 March 2000
Malarial Hemorhagic Fever I
will leave a sum in my last will for my body
to be carried to Brazil and to these forests.
It will be laid out in a manner secure
against the possums and the vultures just as
we make our
chickens secure and this great Coprophanaeus
beetle will bury me. They will enter, will
bury, will live on my flesh and in the shape
of their children and mine, I will escape death.
No worm for me nor sordid fly,I will buzz in the
dusk like a huge bumble bee. I will be many, buzz
even as a swarm of motorbikes, be borne, body by
flying body out into the Brazilian wilderness
beneath the stars, lofted under those beautiful
and unfused elytra which we will all hold over
our backs. So finally I too will shine like a
violet ground beetle under a stone.
W. D. Hamilton (born 1 August 1936, died 7 March
2000, age 63)
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Adaptive Geometry of a Selfish Herd
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Eusocial Insects Hymenoptera (thin
wings) Ants, bees, wasps, hornets
Workers are all females Haplodiploidly Isopte
ra (same wings) Termites (castes consist of
both sexes) Endosymbionts Parental
manipulation Cyclic inbreeding
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Inclusive fitness should be understood within a
multilevel selection approach, as a nested
hierarchy extending from genes, to individuals,
to kin, and finally to even larger groups.
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White-Fronted Bee Eaters, Kenya (Emlen and
Wrege, Cornell)
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Peter Wrege

Steve Emlen
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Helpers at the Nest in White-Fronted Bee Eaters
in Kenya _________________________________________
_________________________ Breeders r Number
of Cases Cases ________________________________
__________________________________ Father x
Mother 0.5 78 44.8 Father x
Stepmother 0.25 17 9.8 Mother x
Stepfather 0.25 16 9.2 Son x
Nonrelative 0.25 18 10.3 Brother x
Nonrelative 0.25 12 6.9 Grandfather
x Grandmother 0.25 5 2.9 Half
brother x Nonrelative 0.13 3
1.7 Uncle x Nonrelative 0.13 2
1.1 Grandmother x Nonrelative 0.13 1
0.6 Grandson x Nonrelative 0.13 1
0.6 Great grandfather x Nonrelative 0.13
1 0.6 Nonrelative x Nonrelative 0.0
20 11.5 Total 174 100.0 ____________
__________________________________________________
____ r coefficient of relatedness.
S. T. Emlen and P. Wrege, Cornell