Parent-offspring conflict

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Parent-offspring conflict A parent would
maximize its fitness by producing as
many surviving offspring as possible (and
considering both current and future reproductive
value) but the offspring is best served (in the
selfish sense) by being given more resources, and
having what is available divided up among as few
offspring as possible. Think about this and
consider whats happening between a plant parent
and the offspring (seeds, fruits, nuts, ) its
producing simultaneously. What control does a
parent have? What might an offspring do to get a
larger share of resources?
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Readings for lectures today and Tuesday Chapter
13 pages 256-8 (today) Chapter 14 pages 269-273,
283-289 (today) Chapter 14 remainder
(Tuesday) A preliminary form of Tuesdays
lecture is posted with todays lecture, since you
will need it to answer some of the problems for
next weeks lab. It will (almost certainly) be
modified before Tuesday.
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Populations Population can be defined in two
ways to serve the needs of ecology... One is
ecological in context A population is
comprised of individuals of a single species that
occupy the same general area, rely on the same
resources, have a high likelihood of
interacting with one another, and are influenced
by similar environmental factors.
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The second is genetic in context, but also
important in ecology A population is a group of
individuals living in close enough proximity to
have both the potential to interbreed
(conspecifics) and a reasonable likelihood of
that occurring.
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A population has properties some are
characteristics that can be assessed in
individuals, and some have meaning only for the
population as a unit. Individual properties a
life history (how long it takes to mature, how
frequently they reproduce, how many young in a
litter, how old it is when it dies, ), its size,
Group properties population size, birth rate,
death rate, age distribution, r, dispersion,
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In ecology we are interested in distribution and
abundance. They depend on a combination of
individual and group properties. Considered
together, they constitute the populations
structure First, lets consider distribution.
While there is a continuum of distribution
types, there are 3 categories named to represent
major patterns. They are 1) random 2) regular
(sometimes called overdispersed or
uniform 3) clumped
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1) randomly example trees of any single species
in a tropical forest
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2) overdispersed (or regularly spaced)
examples penguins establishing territories
(why?) tilapia (a tropical lake fish)on
nesting territories creosote
bushes spaced out by chemical interaction
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3) clumped - higher densities where
environmental conditions (temperature,
light, food, water) are better. This
indicates the environment is heterogeneous (and
frequently patchy). - this is the most
common pattern, especially when
populations are viewed from a larger scale
perspective.
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Young-of-the-year perch, forming schools in
western Lake Erie represents which type of
distribution?

1. random
2. regular
3. clumped
4. None of these

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The second area of interest is abundance. We are
interested not just in how many there are, but
also in the dynamics of the population. How does
the size of the population change over
time? There are, once more, a continuum of
possibilities that are categorized by two end
points Density-independent growth
and Density-dependent growth The first models
to consider are density-independent
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In assessing abundance and its dynamics, there
are four major factors B births (or birth
rate) I immigrants (or immigration rate) D
deaths (or death rate E emigrants (or
emigration rate) The basic equation (a discrete
time model) Nt1 Nt B I - D - E Studies
of population dynamics are investigations of
one or more of these parameters. Some are harder
to quantify than others. Many population models
assume that I E, and drop them from the
models.
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Another simplifying approach in many studies is
to assume that over long (ecological) time
periods B I D E If this werent the
case, wed either be overrun with species that
were growing or seeing a much larger rate of
natural extinction for species that were
declining. In this initial view, we know when
populations will grow whenever B I gt D
E and that populations will decline when B I
lt D E
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We can readily consider a discrete time model of
density- Independent population dynamics
Consider a population that starts at time T.
What is its size at time T1? At the start, size
is N(T) One time unit later, the size is
N(T1) N(T1) N(T) B - D I E or,
assuming I E, and converting B and D to per
head rates N(T1)/N(T) ? (B
D)/N(T) the simplifying symbol ? is the
difference between birth and death rates (number
per head per generation usually or some other
time interval)
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The population size at T 1 (one generation
later) is N(T 1) ? N(T) Now, what will
the population size be at T2? N(T2)
?N(T1) ?(?N(T)) ?2N(T) and at t generations
in the future
N(Tt) ?tN(T) we normally set the starting
time at T0, so that this reads N(t) ?t
N(0) This is the equation describing geometric or
exponential growth.
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The time unit used is usually the generation time
for an organism under study that fits the
discrete model, and since there is no indication
of any density effect in reducing the number of
births or increasing the number of deaths, we are
modeling density-independent growth. A parallel
model for continuous growth uses the change in
size over a time interval (the difference
between the number of births and the number of
deaths. ?N/ ?t bN - dN b and d are per
capita birth and death rates, and (b - d)
r. The result is the familiar equations
dN/dt rN Nt N0ert
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There are important assumptions in these models
of density-independent growth - r (or ?), the
per capita growth rate, is a constant - a
population growing exponentially is not
limited by resources - all individuals have
identical life histories - we can ignore
complications due to mating, thus we
effectively assume reproduction is asexual
(the easiest way is to assume the population is
comprised of parthenogenetic females)
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Other things (beyond assumptions) we recognize
about exponential growth - limits to
exponential growth are set by abiotic factors,
e.g. weather - the same proportion of population
affected by changes in abiotic conditions,
whatever its size or density - slope of
growth curve (rate of growth) increases as
population grows, even though the per capita
rate is constant. The slope is determined by both
r (or ?), which we assume is constant, and N,
the current size of the population, which
is increasing
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How about some examples Discrete exponential
growth If N(0) 1000 and the population doubles
each generation, (? 2), what is the
population after 5 generations? N(5) ?5 (1000)
32,000 Continuous exponential growth If r
0.2 insects/insect/week and N(0) 500, how many
insects are there after 20 weeks? N(20) 500
ert 500 e(0.2)(20) 500 e4 27,000
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Typically, small-sized organisms have high values
of r. One reason is that small organisms have a
short generation time. Here are a few values for
r scaled per day Species r Paramecium 1.3
Flour beetle 0.12 Rattus 0.015 Dog 0.009 H
omo sapiens 0.0003
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The critical problem for models of exponential
growth is Lack of realism Natural
populations are limited by physical and
biological features of their environments. These
limiting factors prevent exponential growth from
continuing for long periods of time. You have
seen in Populus simulations a number of different
patterns population growth may take. Real
populations may show much more complicated
patterns than the simple models display.
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Here are real data for heron populations in
England, re-drawn after Stafford (1971) -
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The herons are a useful example that limits to
growth are usually evident. Population size
varies, but never reaches or exceeds 5000
birds. Models that have a maximum population
size, designated by K, also called the carrying
capacity, are density-dependent, or logistic
models. Heres what the growth curve looks like
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The model tells you what to expect about growth
by comparing the current N with the value of K
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The logistic model must account for the level of
saturation of the environment with individuals
in the population. For example, if K 100, and
there are currently 50 individuals in a
population, we would say that the environment was
half saturated with members of this population.
(N/K 50/100 50) At N 80, the environment
is 80 saturated. More important than a value
for saturation, as N grows closer to K, the rate
of growth within this population should slow.
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The result of recognizing a carrying capacity,
and that growth should slow as the population
size increases, is the logistic model
or, re-arranging
This is the logistic equation developed by
Verhulst and rediscovered by Pearl and Reed
around 1920.
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This familiar form is the continuous growth
model. There is a parallel, discrete form for
the logistic. Once more, it calculates the
population size for a time one unit later (N.B.
not one generation later)
Both the discrete and continuous logistic growth
models can be integrated, and the integral is
what is usually plotted to give the sigmoid
curve. Its not an easy integration. Heres the
result for the continuous model
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The assumptions of the logistic model 1. r and K
are constants, invariant as the population grows
this determines that the effect of
increasing number on declining growth rate
is linear. 2. the population has a stable age
structure (constant proportions of each age
group in the population). 3. all individuals in
the population have identical life histories
this generally happens only when the
individuals are genetically identical. This
assumption pretty much eliminates sexual
reproduction as a mode for this simple
model. 4. there are no time lags in the response
of growth rate to density. Implications?
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Which of the following is not an assumption of
the logistic model for population growth?

1. The population is in a stable age distribution
2. Individuals in the population have the same
   schedules for survival and reproduction
3. Both r and K are constant
4. Limits to population size are set by abiotic
   factors

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Assumption 1 tells us the per head growth rate
declines from r when the population begins to 0
when the population reaches K. From the equation
When N 0, the per head growth rate is r. When
N K, then the per head growth rate is r r 0.
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Assumption 2 When a population has a stable age
structure (or distribution), the distribution is
called a SAD. The proportion of the total
population in each age class remains constant. As
an example, imagine a population of mice
comprised of 20 young mice just weaned, 10
sub-adult mice (like teenagers), and 5 adult
reproducing mice. If the mice were in a stable
age distribution, then when the population had
doubled in size we would find 40 young, 20
sub-adults, and 10 reproductive adults.
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• Assumption 4
• No time lags means that there is no time
  interval between the occurrence of an event and
  its effect on population size or dynamics.
• Violations of this assumption
• gestation time lag an organism is conceived by
  parents, but its appearance as a separate
  individual to be counted in the population is
  delayed by the gestation period.
• maturation time lag the model equation assumes
  that all countable individuals in a population
  contribute to growth. Frequently there is a
  more-or-less extended period of development
  before reproduction begins.