Population and Community Ecology:
Revision Notes
Compiled as a third-year student at the University of Edinburgh, based on the information given in lectures.
General points are shown in normal font; specific examples are given in italics.
Exponentially growing populations
- example: musk ox on
Nunivak Island
- per capita growth is constant
- straight line on a logarithmic graph
- usually applies to introduced species and pathogens
Discrete time model
- R = N(t+1)/N(t) where R is per capita growth rate, N is
population, t is time
- R = f + s where f is fecundity and s is survivorship
- N(t) = RtN(0) ... if R >
1, population increases, if R < 1, population declines
- log(N(t)) = log(R).t + log(N(0)) ... log(N(t)) plotted against t
is straight line with slope log(R)
Continuous time model
(appropriate for organisms such as bacteria)
- dN(t)/d(t) = rN(t), which has the solution N(t) = N(0)ert
- R = er ... population increases if r > 0, R > 1
Variability in population growth rate
- environmental stochasticity
(example: California quail population depends on good rainfall)
- demographic stochasticity (example:
dusky seaside sparrow, extinct because last 7 were all male)
Population dynamics and competition
Regulation of population growth
- Populations need regulation by density-dependent factors
- Sexually-transmitted diseases cannot regulate populations -
they aren't density-dependent
- 'K' is the 'killing power' of a stage in the life cycle (also
includes immigration/emigration)
- K = log(number before/number after) ... K=0 if none die; K=infinity if all die
Time model
- hypothetical graph can be plotted, relating N(t) on x-axis to
N(t+1) on y-axis
- carrying capacity (K) is the point on x-axis where 45° line,
N(t) = N(t+1), is crossed
- 'cobwebbing' along the graph models (often fluctuating)
population growth
- continuous time model:
dN/dt = rN(1 -
N/K) where K is carrying capacity
Time delays
- time delays in the action of density-dependence are
destabilising
- dN(t)/dt = N(t).r(1 - N(t-t)/K) where t is time
delay
- example: plants
producing long-lasting toxins in response to predation
- example: blowflies -
time delay is the time taken for the larva to develop
Maximum sustainable yield (MSY)
- Problems with MSY - assumes all individuals the same and
harvesting curve constant
- Can be regulated by fixed quota management (risky), or by
regulating effort (better)
Allee effect
- Inverse density dependence (depensation) at low population
densities
- Example: failure of
fish stocks (North Sea herring, Pacific sardine, etc) to recover from
overfishing
Intraspecific competition
- Example: rabbits at
Stirling University - males compete for females, females compete for
burrows, all compete for food
- scramble (exploitation) competition is destabilising
(overcompensating)
- contest (interference) competition - individuals interacting
directly - is stabilising
- competition affects fertility (example: song sparrows) and/or mortality (example: trout, soybeans)
Interspecific competition
- Lotka-Volterra equations:
dN1/dt =
N1r1(1 - N1/K1 - aN2/K1)
dN2/dt = N2r2(1
- N2/K2 - bN1/K2)
- coexistence is not possible if competition coefficients, a or b, are large
- competitive exclusion (Gause's
principle) - stable populations of two species cannot continuously occupy
the same niche
- asymmetric competition - some competitors take a
disproportionately large share of resources
- character displacement - two competing species will diverge
- fundamental vs. realised niche - example: bedstraw Galium hercynium (prefers acidic soil) and Galium pumilum (prefers
calcareous soil); each excludes the other from its preferred soil type
- Example: barnacles Chthalamus stellatus (higher
tidal zone) and Balanus balanoides
(lower zone) - Balanus is superior competitor
but less tolerant of desiccation
- "mutual antagonism" - example: flour beetles, Tribolium confusum and Tribolium castaneum - larvae and adults eat eggs and pupae,
preferring those of the opposite species
- Example: house wrens
vandalise nests of Bewick's wrens
Predators and prey
Predator-prey dynamics
- Lotka-Volterra model...
prey: dN/dt = rN - aPN where a is prey capture
rate; predators: dP/dt = faPN - qP
where f is how prey numbers relate to
predator numbers, q is predator death rate
- Prey regulated by predator, but with a time delay, same for
predator - unstable dynamics
Predator functional response
- Functional response graphs: predation rate (y-axis) against
prey density (x-axis)
- Type 1: linear slope (with gradient of a), which levels off
sharply
- Type 2: curve that slowly levels off
- Type 3: sigmoid curve
Mutualism
- Difficult to construct a pure ecological model of mutualism,
and hard to generalise
- In contrast to parasites, mutualists have simple life
histories, stability and flexibility
- Sexuality is suppressed in endosymbionts
- Mutualism can extend the ecological range of both species
- Prisoner's dilemma (game theory) - betrayal is rewarding in the
short-term, but in the long-term co-operation is better (if game is played
repeatedly with same players)
Metapopulation dynamics
- population: a group of individuals all capable of interacting
with one another
- metapopulation: a set of populations connected by dispersal
Source-sink dynamics
- 'sink' populations in poor habitats are sustained by
immigration from 'source' populations
- sink populations may be larger than source populations
- example: plant Cakile edentula on dunes -
beach is source, inland is sink, highest density is in between
Levin's-type metapopulation dynamics
- Dynamic process of local colonisation and extinction
("blinking Christmas tree lights")
- Model assumes that all habitat is similar in quality
- Sessile organisms, and parasites in a host, can be thought of
as metapopulations
- Model predicts empty patches - example: snails in Hertfordshire ponds (Boycott 1930)
- Conservation implications - not all patches have to be
exterminated to cause extinction - species is in
danger if colonisation rate falls below extinction rate
- inferior competitor may coexist with superior one if it has
higher colonisation/lower patch extinction rates (example: Daphnia in rock pools) - patch destruction favours
inferior competitors
Model of metapopulation dynamics
- Colonisation rate (a hump-shaped curve?) and patch extinction
rate (a linear slope?) can be plotted against fraction of occupied patches
(p)
- Point where these curves intersect is p*, the equilibrium
proportion of occupied patches
- p* = h - e/c where h is fraction of patches habitable, e is
extinction rate, c is colonisation rate
- if h < e/c, population will go extinct... e/c is fraction of
patches that must be preserved for population to persist; it is also the
number of empty patches
Crop diseases
- Crop pathogens can be classified as: stand reducers,
photosynthetic rate reducers, leaf senescence accelerators, light
stealers, assimilate sappers, tissue consumers, turgor reducers
- Disease triangle: interaction between pathogen, host and
environment
- A disease progress curve (DPC) plots the amount of disease
present over time
The monomolecular model of disease progress
- Rate of increase is proportional to amount of host tissue that
is disease free
- Rate equation: dx/dt = r(a-x) where x
is level of disease, t is time, r is rate parameter (units t-1),
a is asymptotic level of disease
- Disease progress curve:
x = a - be-rt where b is
constant of integration (b = a - x0)
- As t increases, x tends towards a (the upper asymptote)
- log(a - x) = log(b) - rt ... parameters
can be estimated by plotting log(a - x) against t
- Early stages of epidemic described quite well by linear model
(x = rx0t)
The logistic model of disease progress
- Rate of increase is proportional to amount of disease and
proportion of host tissue that is disease free
- Rate equation: dx/dt = rx(1 - x/a)
- Disease progress curve (sigmoid): x = a/(1 + be-rt)
where b = (a - x0)/x0
- log(a/x - 1) = log(b) - rt ...
parameters can be estimated by plotting log(a/x - 1) against t
- Early stages of epidemic described quite well by exponential
model (x = x0ert)
Disease management
- Concerned with early stages of epidemic - we don't want disease
to approach upper limit!
- Reducing initial inoculum (x0) merely delays the
epidemic; reducing rate (r) is better
The power law model of disease progress
- Amount of disease is inversely proportional to some power of
the distance from the source
- y = as-b where y is amount of disease, s is distance
from source, a and b are parameters
- For estimating parameters:
log(y) = log(a) - b log(s)
- Parameters do not have useful biological interpretations
- a depends on distance units used, b is dimensionless
The exponential model of disease progress
- Amount of disease decreases exponentially with increasing
distance from source
- y = ae-bs
- For estimating parameters:
log(y) = log(a) - bs
- a is amount of disease when s=0 (source strength); b has units
of length-1
- Choice of model (power law or exponential) is usually based on
goodness-of-fit to data
Spatial patterns of disease
- Random pattern of 'count' data often described by Poisson
distribution
- Aggregated (patchy) patterns often described by negative
binomial distribution
- If disease pattern is random, progress can be described by dN/dt = rN(1 - N/K) where K
is carrying total number of hosts, N is number of infected hosts (Waggoner
& Rich 1981)
- If disease is patchy, dN/dt = rN(1 - N/K)(1 + 1/k) where k is
'aggregation parameter' of negative binomial distribution (patchiness
increases as k decreases towards 0)
- Increasing patchiness (lower k) reduces the rate of disease
progress
- Increasing patchiness in a pathogen epidemic increases yield
loss by reducing ability of healthy plants to contribute to compensatory
growth
Weed populations
Crop response to weed infestation
- Damage curve: graph of level of yield reduction brought about
by increasing weed density
- Crop response to weed infestation is often well described by a
rectangular hyperbola
- L = vx / (1 + (v/u)x) where L is
yield loss, x is weed density, u and v are parameters
- Estimating parameters:
inverting equation gives 1/L = (1/v)(1/x) + 1/u
- Straight line relationship between 1/L and 1/x with slope 1/v
and intercept 1/u
- As x increases, L tends towards u, so u represents an upper
limit to percentage yield loss
- At small values of x, L =~ vx, so v
is rate of percentage yield loss per weed density at low density (the
initial slope of the relationship between yield loss and weed density)
- Crop losses can be estimated by critical (single) point models (simple
damage curves), multiple point models, or area under disease progress
curve (AUDPC) models
Spatial patterns of weed infestation
- Negative binomial distribution often used to describe
variability in weed population density
- Yield losses are decreased with increasing weed patchiness,
because patchiness increases intra-specific competition among weeds and
decreases competition between crops and weeds
- Weeds thus differ from pathogens (where patchiness increases
yield losses)
Communities
- Community: an association of populations that interact with one
another
- Individualistic view of communities (Gleason) - composition of
a community can be predicted from the characteristics of the species in it
- minimal interaction between species
- Organismic view (Clements) - community is like a superorganism
(as in Gaia hypothesis)
- 'Closed' communities have distinct boundaries (separated at
'ecotones')
- 'Open' communities show continuous variation along an
environmental gradient
- Closed communities are more consistent with organismic view,
open communities are more consistent with individualistic view
- Change in communities may be 'allogenic' (caused by external
forces) or 'autogenic'
Describing communities
- Measures for describing communities... species richness (S),
dominance (population/biomass of species in the community), diversity
(combines species richness and dominance)
- Rarefaction - the number of species you find depends upon the
sampling effort
- Describing physical structure... growth form, vertical
stratification (e.g. according to light/temperature/chemical gradients
etc), seasonality (e.g. perennial vs. annual plants)
Measures of alpha-diversity (diversity within communities)
- Simpson's index: D = 1
/ S(pi2)
where pi is proportion of individuals belonging to species i
- Shannon-Weaver index:
H' = -S(pi)
log(pi)
- Simpson's index gives more weight to rare species than
Shannon-Weaver index
- Equitability (evenness):
E = H'/Hmax where Hmax = log(S), and S = number of species
Measures of beta-diversity (diversity between communities)
- Jaccard's coefficient: Cj = a / (a+b+c)
where a is number of species in both samples, b is number of species in
first sample, c is number of species in second sample
- Euclidean distance: Djk
= Ö S((Xij - Xik)2) where Xij
is number of individuals of species i in sample
j, Xik is number of individuals of
species i in sample k
- Euclidean distance is very sensitive to species number; this is
corrected for by taking average Euclidean
distance: djk
= Ö (Djk2/n) where n is total number of
species involved
Food webs
- S = species richness
- L = number of trophic links
- Linkage density, d = L/S, indicates specialist (low density)
vs. generalist
- Connectance, C = 2L / S(S-1), is the proportion of possible
links that are realised
- Models show, counterintuitively, that complex webs (high
connectance) are unstable
- Chain length = number of trophic levels
- % omnivory = % of species that feed from more than one trophic
level
- Degree of omnivory = number of closed omnivorous loops / L
- Food webs can be simplified by grouping trophic levels or
'functional feeding groups'
- Guild - a group of species that exploit the same resources in
the same way
- Well-documented
examples of food webs: organisms living inside pitcher plants and tree
holes.
- Nepenthes pitchers are most diverse in Borneo, and
food webs inside them are most complex there.
Species-area relationship
- log-log plot of species against area should be a straight
line: log(S) = log(c) + Z log(A)
- Species richness on an island depends upon balance between
immigration and extinction - this differs between large and small
islands - experiments on mangrove islands
show this
- Greater species richness in larger areas may reflect greater
habitat diversity. Example: spider diversity
relates to vegetation tip height diversity
- Latitudinal cline - more species in tropics (even when area is
corrected for) - Rapoport's Rule – may be
because tropical species inhabit narrower niches (but is this cause or
effect?)
Predation in communities
- Predation - consumption of one organism by another, with prey
alive when predator attacks
- Generalist predators may increase species diversity by
preventing certain species becoming too dominant (exploiter-mediated
coexistence). Example: excluding rabbits from an area results in a
species-poor community dominated by tall grasses
- A selective predator may increase diversity by taking dominant
species (example: starfish eating
mussels) or reduce diversity by taking inferior species (example: periwinkles eating green
algae)
- Frequency-dependent predation (switching) ensures that no
species is wiped out completely
- Highly specialised predators (such as parasites) can never
totally exterminate their prey
Trophic cascades
- Top-down control ("the world is green") - predators
control community structure
- Example: a study found productivity in lakes to be due
to presence or absence of big fish...
few phytoplankton --> many
zooplankton --> few small predators --> big fish
many phytoplankton --> few
zooplankton --> many small predators
(no big fish)
- Bottom-up control ("the world is brown") - producers
control community structure
- Differences in food chain and nutrient base may determine type
of control
Landscapes
- A landscape is a heterogeneous land area made up of 'patches'
- Ecotope - a relatively homogenous patch (usually tens of metres
on a human scale)
- Land facet - a group of related ecotopes
- Land system - a larger area (such a forest or a city)
- Patch characteristics: quality of habitat/resources, type of
edge (gradual or discrete), contrast between patches, connectivity, scale
Disturbances
- Types of disturbance: press, pulse, ramp
- Characterising a disturbance: spatial extent, temporal extent,
magnitude, synergism
- After disturbance, predator-prey ratio gradually rises
- Disturbance-mediated co-existence - disturbances can help
maintain species richness. Example: mussels and sea palms - mussels would
outcompete sea palms if left undisturbed, but storms clear patches on rock that
sea palms can colonise - non-equilibrium community.
- Disturbances may force animals to shelter in 'refugia';
predators can take advantage of this. Example: caddis flies in streams prey on animals that
gather in low-flow patches during floods.
- Physical disturbance may be created by organisms (ecosystem
engineers)
- Autogenic ecosystem engineers are passive - example: trees blocking wind
- Allogenic ecosystem engineers actively disturb environment - example: beavers building dams
- A community 'adapts' to regular disturbances (the organisms
present are those capable of surviving the disturbances); only
disturbances that do not occur regularly are catastrophic. Example: mild fires kill pine trees less than 20 years
old, so pine will not be present in communities that are burned more than once
every 20 years.
- An intermediate level of disturbance may produce the highest
diversity. Example: heather vs. grassland - very frequent burning
increases abundance of grass, very infrequent burning also causes grass to
dominate because fires are very intense and heather recovers poorly.
- Types of fire - surface fires, crown fires, ground fires
- Byram's fire line intensity - measured in watts of heat output
per metre of fire front
- Fire-resistant plants: ephemerals, obligate seeders and
resprouters
Plant communities
- Different plants have different 'phenology' (patterns of
seasonal development). Example: grass is more palatable to herbivores in
summer but heather is more palatable in winter.
- Reduction in cattle numbers has led to spread of undesirable Nardus grass
- Grass patches on heath land can be created by adding lime
- Sheep congregate in grass patches - their dung causes net
import of nutrients, altering soil
- If grass patches are small and scattered, sheep spend more time
on heather instead
Plant succession
- Succession in vegetation may be autogenic or allogenic
- Clements' processes of succession: denudation, immigration,
ecesis (establishment), competition and interaction, reaction (plants
change the environment), stabilisation
- Pathway of succession is a 'sere' (e.g. lithosere on rock) - an
ordered sequence of 'seral stages'
- Models of succession: facilitation, inhibition, tolerance
- Cyclical succession:
Calluna (heather) --> Cladonia (lichen) --> bare soil --> Arctostaphylos (bearberry) --> Calluna
More notes and essays
© Andrew Gray, 2004