(c) 2001 w.h. freeman and company chapter 15: temporal and spatial dynamics of populations robert e....
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(c) 2001 W.H. Freeman and Company
Chapter 15: Temporal and Spatial Dynamics of Populations
Robert E. RicklefsThe Economy of Nature, Fifth Edition
(c) 2001 W.H. Freeman and Company
Chapter Opener
(c) 2001 W.H. Freeman and Company
(c) 2001 W.H. Freeman and Company
Some populations exhibit regular fluctuations.
Charles Elton first called attention to regular population cycles in 1924: such cycles were known to earlier
naturalists, but Elton brought the matter more widely to the attention of biologists
Elton also called attention to parallel fluctuations in populations of predators and their prey
(c) 2001 W.H. Freeman and Company
Evidence for Cycles in Natural Populations
Records of the Hudson’s Bay Company yield important data on fluctuations of animals trapped in northern Canada: data for the snowshoe hare雪兔 (prey) and the
lynx猞猁 (predator) have been particularly useful thousand-fold fluctuations are evident in these
records
Records of gyrfalcons毛隼 exported from Iceland in the mid-eighteenth century also provide evidence for dramatic natural population fluctuations.
(c) 2001 W.H. Freeman and Company
Figure 15.1
(c) 2001 W.H. Freeman and Company
Figure 15.2
(c) 2001 W.H. Freeman and Company
(c) 2001 W.H. Freeman and Company
Fluctuations in Populations
Populations are driven by density-dependent factors toward equilibrium numbers.
However, populations also fluctuate about such equilibria平衡 because: populations respond to changes in
environmental conditions:direct effects of temperature, moisture, etc.indirect environmental effects (on food supply, for
example)
populations may be inherently unstable
(c) 2001 W.H. Freeman and Company
Fluctuations of Fragmented Populations
Dynamics of individual subpopulations vary from one another: ecological conditions vary from place to place subpopulations are isolated to some degree
and behave partly independently
Changes in a subdivided population are the sum of changes in its subpopulations: subdivided populations thus have unique
properties
(c) 2001 W.H. Freeman and Company
Fluctuation is the rule for natural populations.
Tasmanian sheep and Lake Erie伊利湖 phytoplankton both exhibit different degrees of variability in population size: the sheep population is inherently stable:
sheep are large and have greater capacity for homeostasis
the sheep population consists of many overlapping generations
phytoplankton populations are inherently unstable:phytoplankton have reduced capacity for homeostatic内稳
态 regulationpopulations turn over rapidly
(c) 2001 W.H. Freeman and Company
Figure 15.3
(c) 2001 W.H. Freeman and Company
Figure 15.4
(c) 2001 W.H. Freeman and Company
Periodic cycles may or may not coincide for many species.
Populations of similar species may not exhibit synchrony同步 in their fluctuations: four moth飞蛾 species feeding on the same
plant materials in a German forest showed little synchrony in population fluctuations
4-5 year population cycles of small mammals in northern Finland were regular and synchronized across species
(c) 2001 W.H. Freeman and Company
Figure 15.5
(c) 2001 W.H. Freeman and Company
Temporal variation affects the age structure of populations.
Sizes of different age classes provide a history of past population changes: a good year for spawning and recruitment may
result in a cohort同龄群 that dominates progressively older classes for years to come
The age structure in stands of forest trees may reflect differences in recruitment patterns: some species (such as pine) recruit well only after
a disturbance other species (such as beech山毛榉 ) are shade-
tolerant and recruit almost continuously
(c) 2001 W.H. Freeman and Company
Figure 15.7
(c) 2001 W.H. Freeman and Company
Figure 15.8
毒芹
(c) 2001 W.H. Freeman and Company
Population cycles result from time delays.
A paradox: environmental fluctuations occur
randomly:frequencies of intervals between peaks in
tree-ring width are distributed randomly
populations of many species cycle in a non-random fashion:frequencies of intervals between population
peaks in red fox are distributed non-randomly
(c) 2001 W.H. Freeman and Company
Figure 15.9
(c) 2001 W.H. Freeman and Company
Figure 15.10
(c) 2001 W.H. Freeman and Company
A Mechanism for Population Cycles?
Populations acquire “momentum动力” when high birth rates at low densities cause the populations to overshoot their carrying capacities.
Populations then overcompensate with low survival rates and fall well below their carrying capacities.
The main intrinsic causes of population cycling are time delays时滞 in the responses of birth and death rates to environmental change.
(c) 2001 W.H. Freeman and Company
Time Delays and Oscillations震荡 : Discrete-Time Models
Discrete-time models of population dynamics have a built-in time delay: response of population to conditions at one
time is not expressed until the next time interval
continuous readjustment再调整 to changing conditions is not possible
population will thus oscillate as it continually over- and undershoots its carrying capacity
(c) 2001 W.H. Freeman and Company
Oscillation Patterns - Discrete Models
Populations with discrete growth can exhibit one of three patterns: r0 small:
population approaches K and stabilizes
r0 exceeds 1 but is less than 2:population exhibits damped oscillations
r0 exceeds 2:population may exhibit limit cycles or (for
high r0) chaos混乱
(c) 2001 W.H. Freeman and Company
Figure 15.11
(c) 2001 W.H. Freeman and Company
Time Delays and Oscillations: Continuous-Time ModelsContinuous-time models have no
built-in time delays: time delays result from the developmental
period that separates reproductive episodes between generations
a population thus responds to its density at some time in the past, rather than the present
the explicit time delay term added to the logistic equation is tau (t)
(c) 2001 W.H. Freeman and Company
Oscillation Patterns - Continuous Models
Populations with continuous growth can exhibit one of three patterns, depending on the product of r and τ: rτ < e-1 (about 0.37):
population approaches K and stabilizes
rτ < π/2 (about 1.6):population exhibits damped oscillations
rτ > π/2:population exhibits limits cycles, with period 4τ -
5τ
(c) 2001 W.H. Freeman and Company
Cycles in Laboratory Populations
Water fleas, Daphnia, can be induced to cycle: at higher temperature (25oC), Daphnia magna
exhibits oscillations:period of oscillation is 60 days, suggesting a time delay of
12-15 daysthis is explained as follows: when the population
approaches high density, reproduction ceases; the population declines, leaving mostly senescent individuals; a new cycle requires recruitment of young, fecund individuals
at lower temperature (18oC), the population fails to cycle, because of little or no time delay of responses
(c) 2001 W.H. Freeman and Company
Figure 15.12
(c) 2001 W.H. Freeman and Company
Storage can promote time delays.
The water flea Daphnia galeata盔形溞stores lipid droplets and can transfer
these to offspring: stored energy introduces a delay in response to
reduced food supplies at high densities Daphnia galeata exhibits pronounced limit
cycles with a period of 15-20 days another water flea, Bosmina longirostris, stores
smaller amount of lipids and does not exhibit oscillations under similar conditions
(c) 2001 W.H. Freeman and Company
Figure 15.13
(c) 2001 W.H. Freeman and Company
Figure 15.14
(c) 2001 W.H. Freeman and Company
Overview of Cyclic BehaviorDensity dependent effects may be delayed
by development time and by storage of nutrients.
Density-dependent effects can act with little delay when adults produce eggs quickly from resources stored over short periods.
Once displaced from an equilibrium at K, behavior of any population will depend on the nature of time delay in its response.
(c) 2001 W.H. Freeman and Company
Metapopulations are discrete subpopulations.
Some definitions: areas of habitat with necessary resources
and conditions for population persistence are called habitat patches, or simply patches
individuals living in a habitat patch constitute a subpopulation
a set of subpopulations interconnected by occasional movement between them is called a metapopulation
(c) 2001 W.H. Freeman and Company
Figure 15.15
(c) 2001 W.H. Freeman and Company
Metapopulation models help managers.
As natural populations become increasingly fragmented by human activities, ecologists have turned increasingly to the metapopulation concept.
Two kinds of processes contribute to dynamics of metapopulations: growth and regulation of subpopulations within
patches colonization to form new subpopulations and
extinction of existing subpopulations
(c) 2001 W.H. Freeman and Company
Connectivity determines metapopulation dynamics.
When individuals move frequently between subpopulations, local fluctuations are damped out.
At intermediate levels of movement: the metapopulation behaves as a shifting mosaic
of occupied and unoccupied patches
At low levels of movement: the subpopulations behave independently as small subpopulations go extinct, they cannot be
reestablished, and the entire population eventually goes extinct
(c) 2001 W.H. Freeman and Company
The Basic Model of Metapopulation Dynamics
The basic model of metapopulation dynamics predicts the equilibrium proportion of occupied patches, ŝ:
ŝ = 1 - e/cwhere e = probability of a subpopulation going extinct
c = rate constant for colonization
The model predicts a stable equilibrium because when p (proportion of patches occupied) is below the equilibrium point, colonization exceeds extinction, and vice versa.
(c) 2001 W.H. Freeman and Company
Behavior of the Metapopulation Model
The relative rates of extinction and colonization (e/c) are of critical importance. when e = 0, ŝ = 1 and all patches are occupied when e = c, ŝ = 0, and the metapopulation
heads toward extinction when 0 < e < c, the result is a shifting mosaic
of occupied and unoccupied patches, with the value of s somewhere between 0 and 1
(c) 2001 W.H. Freeman and Company
Is the metapopulation model realistic?
Several unrealistic assumptions are made: all patches are equal rates of colonization and extinction for all
patches are the same
In natural settings: patches vary in size, habitat quality, and
degree of isolation larger subpopulations have lower probabilities
of extinction
(c) 2001 W.H. Freeman and Company
(c) 2001 W.H. Freeman and Company
The Rescue Effect
Immigration from a large, productive subpopulation can keep a declining subpopulation from going extinct: this is known as the rescue effect救援效应 the rescue effect is incorporated into
metapopulation models by making the rate of extinction (e) decline as the fraction of occupied patches increases
the rescue effect can produce positive density dependence, in which survival of subpopulations increases with more numerous subpopulations
(c) 2001 W.H. Freeman and Company
Chance events may cause small populations to go extinct.
Deterministic models assume large populations and no variation in the average values of birth and death rates.
Randomness may affect populations in the real world, however: populations may be subjected to catastrophes灾变 other factors may exert施加 continual influences on
rates of population growth and carrying capacity stochastic (random sampling) processes can also
result in variation, even in a constant environment
(c) 2001 W.H. Freeman and Company
Understanding Stochasticity
Consider a coin-tossing experiment: on average, a coin tossed 10 times will
turn up 5 heads and 5 tails, but other possibilities exist:a run with all heads occurs 1 in 1,024 trialsif we equate a “tail” as a death in a population
where each individual has a 0.5 chance of dying, there is a 1 in 1,024 chance of the population going extinct
for a population of 5 individuals, the probability of going extinct is 1 in 32
(c) 2001 W.H. Freeman and Company
Stochasticity can affect births.
Consider a population in which only births occur, such that N(t) = N(0)ebt.
On average we expect the population to grow by a factor of 1.65 (e0.5) in one time interval.
For a small population of 5 individuals: the average size after one time interval would
be 5 x 1.65 = 8.24, but this could vary from as few as 5 to as many as 20, just by chance
(c) 2001 W.H. Freeman and Company
Stochastic Extinction of Small Populations
Theoretical models exist for predicting the probability of extinction of populations because of stochastic events.
For a simple model in which birth and death rates are equal, the probability of extinction increases with: smaller population size larger b (and d) time
(c) 2001 W.H. Freeman and Company
Stochastic Extinction with Density Dependence
Most stochastic models do not include density-dependent changes in birth and death rates. Is this reasonable? density-dependence of birth and death
rates would greatly improve the probability that a population would persist
however, density-independent stochastic models may be realistic for several reasons...
(c) 2001 W.H. Freeman and Company
Figure 15.19
(c) 2001 W.H. Freeman and Company
Density-independent stochastic models are relevant.The more conservative density-independent
stochastic models are relevant to present-day fragmented populations for several reasons: most subpopulations are now severely isolated changing environments are likely to reduce fecundity when populations are low, the individuals still compete
for resources with larger populations of other species small populations may exhibit positive density-
dependence because of inbreeding effects and problems in locating mates
(c) 2001 W.H. Freeman and Company
Size and Extinction of Natural Populations
Evidence for the relationship between population size and the likelihood of extinction comes from studies of avifauna 鸟类 on the California Channel Islands: smaller islands lost a greater proportion of
species than larger islands over a 51-year period
proportions of populations disappearing over this interval were also related to population size
(c) 2001 W.H. Freeman and Company
Figure 15.20
(c) 2001 W.H. Freeman and Company
Summary 1
Populations of most species fluctuate over time, although the degree of fluctuation varies considerably by species. Some species exhibit regular cyclic fluctuations.
Both discrete and continuous population models show how species populations may oscillate震荡 .
(c) 2001 W.H. Freeman and Company
Summary 2
Population oscillations predicted by models are caused by time delays in the responses of individuals to density. Such delays are also responsible for oscillations in natural populations.
Metapopulations are divided into discrete subpopulations, whose dynamics depend in part on migration of individuals between patches.
The dynamics of small populations depend to a large degree on stochastic events.
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