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.

*example: musk ox on Nunivak Island*- per capita growth is constant
- straight line on a logarithmic graph
- usually applies to introduced species and pathogens

- 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) = R
^{t}N(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)

(appropriate for organisms such as bacteria)

- dN(t)/d(t) = rN(t), which has the solution N(t) = N(0)e
^{rt} - R = e
^{r}... population increases if r > 0, R > 1

- environmental stochasticity
*(example: California quail population depends on good rainfall)* - demographic stochasticity
*(example: dusky seaside sparrow, extinct because last 7 were all male)*

- 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

- 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 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*

- 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)

- Inverse density dependence (depensation) at low population densities
*Example: failure of fish stocks (North Sea herring, Pacific sardine, etc) to recover from overfishing*

*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)*

- Lotka-Volterra equations:

dN_{1}/dt = N_{1}r_{1}(1 - N_{1}/K_{1}- aN_{2}/K_{1})

dN_{2}/dt = N_{2}r_{2}(1 - N_{2}/K_{2}- bN_{1}/K_{2}) - 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 - e
*xample: 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*

- 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

- 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

- 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)

- population: a group of individuals all capable of interacting with one another
- metapopulation: a set of populations connected by dispersal

- '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*

- 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

- 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 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

- 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 - x_{0}) - 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 = rx
_{0}t)

- 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 - x_{0})/x_{0} - 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 = x
_{0}e^{rt})

- Concerned with early stages of epidemic - we don't want disease to approach upper limit!
- Reducing initial inoculum (x
_{0}) merely delays the epidemic; reducing rate (r) is better

- 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

- 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

- 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

- 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

- 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)

- 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'

- 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)

- Simpson's index: D = 1
/ S(p
_{i}^{2}) where p_{i}is proportion of individuals belonging to species i - Shannon-Weaver index:
H' = -S(p
_{i}) log(p_{i}) - Simpson's index gives more weight to rare species than Shannon-Weaver index
- Equitability (evenness):
E = H'/H
_{max}where H_{max}= log(S), and S = number of species

- Jaccard's coefficient: C
_{j}= 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: D
_{jk}= Ö S((X_{ij}- X_{ik})^{2}) where X_{ij}is number of individuals of species i in sample j, X_{ik}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: d
_{jk}= Ö (D_{jk}^{2}/n) where n is total number of species involved

- 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.*

- 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 - 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

- 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

- 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

- 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

- 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

- 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*