BIO 208

Measuring relative vs. absolute density, density dependance, and distribution and abundance

• 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

• 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)

Often set arbitrarily: an elk in Elk Island National Park

• Static, snapshot description of the population
• How many? spatial distribution? Ages? Sizes? Sex ratio? Survival patterns?

• Changes through time (rates)
• Birth rate, death rate, immigration rate, emmigration rate...?

• 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)

• What is an individual? (clonal organisms, seedling vs. adult, larvae vs. adult)
• Biomass density, or cover for plants

• Relative estimate (indices presumed to be related to the abundance of target organisms: used for comparison)
• Absolute estimates (direct counts, sampling)

• # of individuals/area declines with increasing body size
• Many ecological processes are desity dependent

• An effect whose magnitude is increased (positively or negatively) with population density (denser = more effect)
• Examples are predation, competition, disease, schools, allee effects

An effect whose magnitude is unaffected by population density (denser/less dense=no matter)

• 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

• Inidividuals are MORE EVENLY spaced than expected by chance
• Relatively common: intra-specific competition, territoriality in a relatively uniform environment

• neighbors are CLOSER than expected by chance
• Common: patchy habitat/resources, reproduction and dispersal, social structure

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

• Intrinsic characteristics of the species
• Extrinsic factors

• Geography/climate
• Predation
• Competition
• Disease
• Social structure
• Etc
• It is dependant on the niche (where conditions suit a species' niche, the species should thrive

• 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

• 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

Can increase or decrease local density, can be density independent (passive: wind, gravity, etc) or density dependent (competition, habitat quality or size)

Consistently produce more emigrants than immigrants while maintaining their existing population

Consistently recieve more then they produce

A patch of insuficient size or quality may become a temporary source while going extinct

Variation among individuals within populations can (potentially strongly) influence dynamics such as birth rates, death rates, immigration, emigration, etc

• 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)

• 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

A cohort of larger fish preys upon smaller fish, until they "grow out of it"

Snapshots of age (and sex) structure

• Juvenile phase dominated by growth
• Reproductive phase
• Post-reproductive phase

• 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)

• 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

• 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
• m_x= (summation) Gross reproductive rate (age-specific repro)
• lxmx=(summation) net reproductive rate
• xl_xm_x= (summation / R₀) equals T (generation time)

Juvenile survival is high and most mortality occurs amoung older individuals

Individuals die at equal rates regardless of age

Individuals die at high rates as juveniles an then at much lower rates later in life.

• 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)

An amount of change (in something) over time

Average rate of change during delta time

Rate of change over a very short time (t-->0)

Total change in numbers over time (delta N/delta t)

Rate scaled per organism (delta N/N₀ delta t)

Specific reproductive rate = # of offspring per individual per unit time

• Reproductive rate often varies with age, every age group will have its own R₀
• Age specific reproductive rate (m_x)
• # of offspring per female of age "X" per unit of time

# of offspring produced during a female's life IF she lives to age omega (sum of m_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/n₀

• # 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

• If R₀ > 0 pop'n growing
• R₀ = 0 pop'n remains constant
• R₀ < 0 pop'n is declining

• sum of l_xm_x
• little r is per capita rate of increase (otherwise same concept)

• The average age at which a female gives birth
• Typically the larger you are, the longer it takes to become reproductively active

The rate a population wuld increase if R₀ remains constanct and >1 and there are no limits on population growth

• Discrete, non-overlapping generations
• N_t=N₀lambda^t
• N_t= # of individuals at time t
• N₀=# 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_tlambda

• Continuous population growth can be modelled exponentially
• dN/dt = r_maxN
• 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=N₀e^r_maxt
• N_t=# of individuals at time t
• N₀=intial # of individuals
• e = base of natural logarithms
• r_max =intrinsic rate of increase
• t = # of time intervals

• 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)

carrying capacity (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

• dN/dt=r_maxN((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/N₀-1)e^-r_maxt)
• N_t = # of inidividuals at time t
• N₀ = intial # of individuals
• e = base of natural logarithms
• r_max=intrinsic rate of increase
• t = # of time intervals
• K = carrying capacity

• 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)

Identifying and understanding the processes that affect plant and animal structure is a major challenge in ecology

• 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)

• 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

• 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

• 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

• Populations gain "momentum"... high birth rates at low densities
• Populations "overcompensate"... low survival and birth rates at high dens.
• Population response is time delayed

• Abiotic (weather, sunspots)
• Biotic - intrinsic factors (stress, territoriality, dispersal)
• Biotic - extrinsic factors (food, predation, disease)

• 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

Extinction from a specific global region

• Species lifespan = 1-10 million years
• Causes are highly variable; local disturbance, Pseudo-extinction, or co-extinstion

Sudden change in intensity, such as a volcano or meteroites

Extinction caused by humans, caused by climate change, or fragmentation by roads, exploiting at a large rate

• 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)

• The preservation of ecological systems in a natural or near-natural condition
• (requires knowledge to decide waht is and isn't harmful)

• 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)