Measuring relative vs. absolute density, density dependance, and distribution and abundance
Population
A group of individuals of the same species occupying a particular area at the same time
They are natural biological units: inidividuals are portentially interfertile and share the same resources (interact)
These are the basic unit of evolution: natural selection operates on organisms, but the population evolves
Occupying a particular area
Boundaries of populations are sometimes clear, sometimes vague (sufficient size that reproduction and survival maintains the population for many generations)
May exist in heterogeneous landscapes, but only suitable habitats are occupied within the particle area
This is dynamic (disperal immigration and emmigration among local populations)
Population boundaries in practice
Often set arbitrarily: an elk in Elk Island National Park
Population Properties Structure
Static, snapshot description of the population
How many? spatial distribution? Ages? Sizes? Sex ratio? Survival patterns?
Population Properties Dynamics
Changes through time (rates)
Birth rate, death rate, immigration rate, emmigration rate...?
Population "size"
Abundance (how many individuals? how much biomass?)
Density- numbers (biomass) per unit area or volume (absolute (crude) density: density without regard to habitable area or variation in habitat quality. Absolute density: population density in appropriate habitat only)
Problems with population density
What is an individual? (clonal organisms, seedling vs. adult, larvae vs. adult)
Biomass density, or cover for plants
Measuring density
Relative estimate (indices presumed to be related to the abundance of target organisms: used for comparison)
Absolute estimates (direct counts, sampling)
Trends in density
# of individuals/area declines with increasing body size
Many ecological processes are desity dependent
Density dependence
An effect whose magnitude is increased (positively or negatively) with population density (denser = more effect)
Examples are predation, competition, disease, schools, allee effects
Density independence
An effect whose magnitude is unaffected by population density (denser/less dense=no matter)
Random distribution
Reference pattern (what you would expect if the species where completely indifferent), position of individuals is independent of other individuals
Relatively rare: homogeneous environment, random dispersal, no social structure, or at least neurtal interactions
Uniform
Inidividuals are MORE EVENLY spaced than expected by chance
Relatively common: intra-specific competition, territoriality in a relatively uniform environment
Clumped
neighbors are CLOSER than expected by chance
Common: patchy habitat/resources, reproduction and dispersal, social structure
Distribution pattern can:
Reveal underlying spatial patterns in the environment, reflect past and/or future interactions, influence the ecological density of the population, influence accuracy/precision of population estimates
Distribution pattern can be due to:
Intrinsic characteristics of the species
Extrinsic factors
Population distribution has many potential causes:
Geography/climate
Predation
Competition
Disease
Social structure
Etc
It is dependant on the niche (where conditions suit a species' niche, the species should thrive
Metapopulations
A population made up of sub-populations
Sub-populations joined by the movement of individuals
Any subpopulation can go entinct; but, on average, sources produce more emigrants than they recieve immigrants, and sinks do the opposite
Small sub-populations = greater risk of extinction
Density-dependent and density independent effects also contribute
Species range and tolerance
Geographic range (broad or restricted)
Habitat tolerance (broad or narrow)
Local population (large or small)
The fewer characteristics of RARITY, and the more of ABUNDANCE, that an organism has, the better its chances of survival in the face of environmental change
Dispersal
Can increase or decrease local density, can be density independent (passive: wind, gravity, etc) or density dependent (competition, habitat quality or size)
Sources
Consistently produce more emigrants than immigrants while maintaining their existing population
Sinks
Consistently recieve more then they produce
A patch of insuficient size or quality may become a temporary source while going extinct
Population structure and variation
Variation among individuals within populations can (potentially strongly) influence dynamics such as birth rates, death rates, immigration, emigration, etc
Age frequency distributions
Dominant age classes may be visible, likely reflects non-random recruitment
environment (climate? fire?)
intra-specific/inter-age-class inhibition?
(class make ingerences about the species history)
Even-aged stands
Referrs to forrest that most times the trees are the smae age, instead of patchy mixed bag of ages like in the past
Natural fire cycles
Human activity
Cohort - age frequency distributions
A cohort of larger fish preys upon smaller fish, until they "grow out of it"
Age pyramids
Snapshots of age (and sex) structure
3 "ecological" age classes
Juvenile phase dominated by growth
Reproductive phase
Post-reproductive phase
Age distribution
Reflects a population's history = clues for the ecologist
survival
reproduction
potential for future growth
May be complex in a highly variable environment
(allows us to predict "forward" what may happen)
Sex ratio = the result of natural selection
1:1 sex ratio is an evolutionarily stable strategy
more females than males
males would have more reproductive chances-> fitness
the same advantage (=selection pressure) declines near 1:1
same logic works if more males than females
--> frequency dependent selection
May be exceptions (reed frog which begins as female)
Humans can effect this as well, with herbicides
Simple life tables
_{}A useful tool for summarizing survivorship
Data can be used to create a survivorship curve, which will reveal different life histories
x= age
n_{x}= # surviving to age "x" (cohort size)
l_{x}=proportion suriving to age "x" (age-specific survivorship
xl_{x}m_{x}= (summation / R_{0}) equals T (generation time)
Type 1 survival
Juvenile survival is high and most mortality occurs amoung older individuals
Type 2 survival
Individuals die at equal rates regardless of age
Type 3 survival
Individuals die at high rates as juveniles an then at much lower rates later in life.
Population growth (basics)
BIDE
B- births
I - immigration
D - deaths
E - emigration
For comparisions amoung populations, rates of change can be more useful (signified by small case letters)
Rate
An amount of change (in something) over time
Discrete rate
Average rate of change during delta time
Instantaneous rate
Rate of change over a very short time (t-->0)
Crude rate
Total change in numbers over time (delta N/delta t)
Specific rate
Rate scaled per organism (delta N/N_{0 }delta t)
Reproductive rate (natility)
Specific reproductive rate = # of offspring per individual per unit time
Reproductive rate and age
Reproductive rate often varies with age, every age group will have its own R_{0}_{}
Age specific reproductive rate (m_{x})
# of offspring per female of age "X" per unit of time
Gross Reproductive rate (GRR)
# of offspring produced during a female's life IF she lives to age omega (sum of m_{x})
Age-specific survivorship (l_{x})
_{}Need to know what % of population survives or dies at each age "X"
l_{x} = % of cohrot alive at start of age "X"
l_{x} = n_{x}/n_{0}
Geometric rate of increase
# of daughters born in generation t+1/# of daughters born in gerenation t = N_{t+1}/N_{t} = lambda
lambda > 1, pop'n growing
lambda = 1, pop'n stable
lambda < 1, pop'n shrinking
Net reproductive rate (R_{0})
If R_{0} > 0 pop'n growing
R_{0} = 0 pop'n remains constant
R_{0} < 0 pop'n is declining
sum of l_{x}m_{x}
little r is per capita rate of increase (otherwise same concept)
Generation time (T)
The average age at which a female gives birth
Typically the larger you are, the longer it takes to become reproductively active
_{}N_{x}=N_{0}R_{0}^{x}
The rate a population wuld increase if R_{0} remains constanct and >1 and there are no limits on population growth
Geometric growth
Discrete, non-overlapping generations
N_{t}=N_{0}lambda^{t}
N_{t}= # of individuals at time t
N_{0}=# of inidividuals at start
Lambda = geometric rate of increase
t = # of time intervals or generations
Or if you only care about the next generation:
N_{t+1}=N_{t}lambda
Exponential growth
Continuous population growth can be modelled exponentially
dN/dt = r_{max}N
dN/dt = change in the # of individuals per unit time
r_{max}= intrinsic rate of increase
->max possible under ideal conditions
Size of population at any time can be calculated as
N_{t}=N_{0}e^{rmaxt}
N_{t}=# of individuals at time t
N_{0}=intial # of individuals
e = base of natural logarithms
r_{max}_{ }=intrinsic rate of increase
t = # of time intervals
Exponential growth under stable conditions
r -> r_{max}
But.... r_{max} is balanced by extrinsic factors
As population density increases:
per capita resources decline
Growth decreases
age at maturity increases, fecundity decreases
Higher densities attract predators, so mortality increases
Social strife within populations and disease increase
Environmental resistance increased (birth rate decrease, or death rate increases, or both)
Upper equilibrium level
carrying capacity (k)
Populations below K
below inflection point, growth is accelerating
above inflection point, growth > 0 but decelerating
Populations above K decrease
Populations at K remain approx. constant
K is a property of the environment; the max. sustainable population size
Logistic population growth
dN/dt=r_{max}N((K-N)/K)
r_{max}=intrinsic rate of increase
K=carrying capacity
When N nears K, the right side of the equation nears zero, (change in pop'n size approaches 0)
When N is low, the right side of the equation is near 1 (change in pop'n size is exponential)
Size of pop'n at any time can be calculated as
N_{t}= K/(1+(K/N_{0}-1)e^{-rmaxt})
N_{t} = # of inidividuals at time t
N_{0} = intial # of individuals
e = base of natural logarithms
r_{max}=intrinsic rate of increase
t = # of time intervals
K = carrying capacity
Density (in)dependence
Density independence - effects independent of N, e.g. severe weather
Density dependence - effects depent on N, e.g. "environmental resistance" (two examples; song sparrows in BC, at high density, more floater males, lower fecundity, lower juvenile survival, and plants, at high density decreased growth rate, decreased survival, decreased seed production)
Why different cycles?
Identifying and understanding the processes that affect plant and animal structure is a major challenge in ecology
r is affected by both extrinsic (abiotic) and intrinsic (biotic) factors
Negative feedback between r and N - ie., density dependence - is necessary for population regulation, but can vary in relative importance
Expirpation
Extinction from a specific global region
Background extinction
Species lifespan = 1-10 million years
Causes are highly variable; local disturbance, Pseudo-extinction, or co-extinstion
Mass extinction
Sudden change in intensity, such as a volcano or meteroites
Anthropogenic extinction
Extinction caused by humans, caused by climate change, or fragmentation by roads, exploiting at a large rate
Extinction risk
Larger populations are likely to persist for longer
Age and spatial structure of the population also affects extinction risk
Population resillience - long "return time" = low resillience, short "return time' = high resillience
Body size, longevity, and population size interact to affect extinction risk (Large organisms should have the advantage in small populations, and small organisms in large populations)
Conservation
The preservation of ecological systems in a natural or near-natural condition
(requires knowledge to decide waht is and isn't harmful)
Resoration ecology
The branch of ecology concerned with restoring ecological sytems to their natural condition
(requires it to decide what is and isn't vital to restore)