
Population density
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: intraspecific 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 subpopulations
 Subpopulations 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 subpopulations = greater risk of extinction
 Densitydependent 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 nonrandom recruitment
 environment (climate? fire?)
 intraspecific/interageclass inhibition?
 (class make ingerences about the species history)

Evenaged 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
 Postreproductive 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" (agespecific survivorship
 m_{x}= (summation) Gross reproductive rate (agespecific repro)
 lxmx=(summation) net reproductive rate
 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})

Agespecific 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, nonoverlapping 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((KN)/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

Kstrategists
 slower development, delayed reproduction, longer lifespan, larger size, competitive
 growth regulated by intrinsic factors
 Many exhibit logistic growth and populations are stable near the carrying capacity (k)

rstrategists
 Faster development, faster reproduction, shorter lifespan, smaller size, not competitive
 Growth regulated by external factors
 Many exhibit irruptive population dynamics in response to temporary environmental change

Irruptive dynamics
 Due to seasonal variation in K
 N_{peak} depends on r_{max} and length of season > weather dependent
 Density factors can vary in actual importance

Cyclic dynamics (observations)
 1. A species may not be cyclic everywhere
 2. Not all related species in a region are cyclic
 3. The cyclic species in a region may or may not be in phase
 4. Density ratios (max vs. min) can be really high (in the hundreds)
 5. Period of cycle more regular than amplitude
 6. During early increase phase: high reproductive rates and high dispersal. During high but declining phase: low reproduction and dispersal
 7. Aggressiveness varies throughout cycle
 8. Cycle not symmetrical: rapid explosion, rapid crash, several low density year

Cyclic dynamics: Proximate mechanisms
 Populations gain "momentum"... high birth rates at low densities
 Populations "overcompensate"... low survival and birth rates at high dens.
 Population response is time delayed

Cyclic dynamics: untimate hypothesis
 Abiotic (weather, sunspots)
 Biotic  intrinsic factors (stress, territoriality, dispersal)
 Biotic  extrinsic factors (food, predation, disease)

Cyclic dynamics: summary
 It's complicated
 Population regulation is complex
 Even components (e.g.K) can be complex
 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 = 110 million years
 Causes are highly variable; local disturbance, Pseudoextinction, or coextinstion

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 nearnatural 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)

