A group of individuals of one species in an area

size of area varies; depends on type of animal (eg. size of animal)

population density

causes of local density variation

Competition: intra/inter specific

Resource Availability: more resource abundance = more density

Predation: limits density (based on # of preds)

Environmental Conditions: drought (finch example)

factors used to predict density; body size

Metabolic Rate

Life history patterns

predator-prey interactions

population densities

Allometry: change in morphological, physiological, ecological parameters of organisms in relation to body size; non-linear in Nature

Animal Size and Population Density

x-axis: body mass kg

y-axis: animal density (per km²) 

Overall: average population density decreases with increasing body size

Aquatic INverts: live at higher pop densities than other animals of comparable sizes

Terrestrial: Mammals tend to live at higher pop densities than birds

Correlation is not causation: Mechanisms for patterns in data are not apparent

Predictive relationships: y=mx+b or y=xb^m 

*body size is used to predict potential density*

How to estimate population size

population density

Sub-sample a population, measure the density at a smaller scale and extrapolate

Animals:

Plants: % cover

*Must sample enough of an area to get a good idea*

How to estimate population size

Population size

Count ALL individuals; impractical in most situations

Mark-recapture Method: used for pops which you cannot directly census; ex. whales, fish, birds

Lincoln-Peterson Index

Assumptions

Mark a portion of the population on one occasion, comeback later and resample the population to see how many marked individuals are recovered.

-Marked/unmarked ratio is the same as in the population

-all individuals have same porbability of being captured

-Mark does not compromise survival

-Mark is not lost btw samplings

-pop is closed or does not have significant growth btw samplings

Lincoln-Peterson Index

Equation

N = M(n+1) / (m+1)

N: # of individuals in pop

M= # of marked and released animals

n= total # of individuals in the second sample

m= # of recollected marked individuals

Population Distribution

Geographic

(Macro-scale)

macro-scale refers primarily to "Natural" distributions

Primarily constrained by local envrionment

-morphological, behavioral and physiological adaptations in response to selection pressures from specific envrionments

Geographic Distribution Example

Tiger Beetle in North America

Facts: Live at higher latitudes and higher elevations; boreal and montane forests, prefer cooler climates in local areas

Beetles had a more southern distribution the last glaciation; beetles moved north with receeding glaciers

Relatively isolated local populations exist in southern latitudes in highe mountain areas

2 seperate populations of C. longilabris in maine/wisconsin and colorado/arizona all have equal temperature preference at 34°C.

*They adapted equally, but differ geographically.  Increased latitude can be replaced by increased elevation*

Warren et al. 2001

Geo dristribution of 46 non-migratory butterflies in Britian

Two acting forces: 

-climate warming: (1.0-1.5°C); butterflies at limit of their northern distribution-warmer temps would potentially expand area available

-lost of habitat; 70% loss

changes in distribution and adundance over a 30-year period

Warren et al. 2001

Results

Sedentary Specialists: 89% declined in distribution; cannot disperse long distance

Mobile Specialists: could disperse

Mobile Generalists: 50% increased distribution

All species: 3/4 of all species declined in distribution over 30 years.

**Habitat is critical too**

Distribution of Non-native invasive sepecies

Zebra Mussel (Dreissena polymorpha) example

Facts:

they obtain extreme pop densities

ecosystem impact; changes nutrient cycle

bio-fouling: clogs pipes, sinks docks etc

Original Distribution: black/caspian seas

local predators co-evolved with other species; been in US since 80s

Non-native invasive species

mussel example

Ecological Release: indroduction to new environment lacking co-evolved predators, diseases etc.

Possible that non-natve invasive species can overwhelmingly dominate organism numbers; replacement of natives

Local Population Distribution

Small Scale local

Micro-scale

Area is relatively unifrom in envrionmental conditions; no large envrionmental gradients (moisture/sunglight)

Neutral interactions between individuals (non-aggressive)

Resources abundant throughout the area

ex. abundant nesting sites for birds

Small Scale Distribution

Regular

Individuals are uniformly spaced throughout the area; rare in nature

Highly aggressive interactions between individuals

Resources limited throught the area

ex. Blackfly larvae in streams

Small Scale Distribution

Clumped

individuals have a higher probability of being in localities inhabited by other individuals

individuals attracted to one another

resources are concentrated areas

limited dispersal ability from a parent

ex. dispersal of seeds or spores 

yes, most show clumped distribution

animal distribution can vary seasonally

Population example

Periodical Cicadas

-Geographic Distribution: overall, limited to eastern temperate forests

-Large scale of individual broods: concentrated in specific areas; random and clumped distributions can be isolated by geographic barriers

-Large scale distr. in an area: emergence and chorusing centers are patchy in local landscape

-Small scale: highest emergence densities clumped, preference for edges of woodlots

Forister et al. 2010

butterflies/climate change/habitat

Predict butterfly richness delcines at low elevation sites due to habitat alteration

predict upslope shift in ranges due to warming and range expansion

2 species examined: ruderal and non-ruderal

ruderal: weedt species that use weedy plants in distributed places

Forister et al. 2010

Results

Species richness declined in both groups at the low elevation sites

-Ruderal species declined at high elevation sites, but non-ruderal species remained constatnt or increased

-Abundance of species has generally increased at high elevations; half of the apline specialist declined

General upslope shit in elevation range of butterflies

Forister et al. 2010

Reasons for Results

Interacting negative effects of climate change and habitat loss lead to changes in butterfly abundance and dirstribution

loss of ruderal species from low elevations indicates that traditional focus on sedentary specialist species needs to be re-examined

Population Growth

2 senarios

1) unlimited resources, space, etc, populations will grow unchecked indefintely (not realistic)

2) Environmental conditions limit population growth rates

*pops with abundant or unlimited resources exhibit geometric or expontential growth*

Biotic (competition/predation) and Abiotic (temp, pH) factors affect population growth rates and limit the number of organisms in the environment

Population growth

2 approaches to examine growth

Mathematical and Empirical

Both are valid and complimentary

-Empirical evidence supports the mathematical predictions

-mathematical predictions give insight to characteristics of populations

Example of a geometric growth curve

x-axis: time

y-axis: population size (# of individuals)

Geometric Growth - Estimation of population size

N_t= number of individuals at time t

N₀= number of individuals at initial time

λ= geometric rate of increase or the average number of offspring left by an individual during a given time interval

t= number of time intervals

Geometric Growth - Estimation of Population GROWTH RATE

N/T = change in population size with change in time

Geometric: cannot be maintained indefinitely by a population; exhaust resources/overcrowding, most organisms have overlapping generations

Exponential: describes pops with overlapping generations under conditions of abundant resources; natural pops exhibit exponential for short periods; resources eventually become limited

The per capita rate of increase -- r

r_max vs. r

r= realized or actual per capita rate of increase

r= difference between birth rate and death rate; r=b-d

death rate= the proportional chance each individual has of during per unite of time

r_max: intrinsic rate of increase; maximum per capita rate of increase under ideal or unlimited conditions

N/t= change in number with change in time

r_max= maximum per capita rate of increase

N=number of individuals

Trends:

-As N increases, rate of pop growth increases (exponentially); the slope gets steeper

-r_max is constant

Exponential Growth 

Population Size

Use this equation to estimate population size @ time t

like geometric, expoential cannont continues indefinitely; resources become limited; food,light,space,breeding sites

a Population will appreac the carrying capacity of the environment

Carrying Capacity: max pop size an environment can support (K); limitation is incorporated into logistic growth models

examples of exponential growth: collard doves, whooping cranes

ΔN/Δt = r_{maxN(1-(K/N))}

Logistic Growth Equation

N/t= rate of change (slope)

rmax= max growth rate (exponential growth)

(1-K/N)= slows growth as population size approaches carrying capacity (K)

realized rate of growth per unit time= potential rate of growth x pop size x unutilized opportunity for pop growth

dN/dt slows as pop size (N) approaches K

(1-N/K) becomes SMALLER as N approaches K

dN/dt is the greatest when N=K/2, or when N is half of carrying capacity

when N is SMALL, r = rmax

when N is LARGE, r = 0

When N is small b > d

When N is large b = d

Relationship between N and r

in the logisitic model, r, the realized per capita rate of increase, decreases as N increases

1) The max rate of increase, rmax, occurs at a ver low pop size

2) If N<K, r is positive and the pop grows

3) If N=K, r=0 and pop growth stops

4) if N>K, r is negative and the populations declines

example: Daphnia

Environmental factors limit pop growth by affecting birth and death rates

Proportion of population dying or per capita birth rate depends on population density

Biotic Factors: predation, disease, food limitation

Proportion of population dying or percapit birth rate does NOT depend on pop density

Abiotic Factors: flooding, drought, extreme weather conditions

Assumption of Linear Relationship between N and r

Gilpin and Ayala study (1973)

traditionall assuemd a linear relationship 

Proposed the use of θ

θ= scaling factor that defines the shape of the relationship btween growth rate and population size

Negative values = concave shape

Positive values = convex shape

-Initial spring bloom of diatoms (Large realized r); abundant dissolved nutrients (N&P), low zooplankton

-Decline of the spring bloom (N>K)

grazers become abundant in respone to rapid growth of diatoms (density-DEPENDENT)

deplete dissolved nutrients (P), in upper water (density DEPENDENT)

temp and light intensity increases (Density INdependent)

-Bloom of blue-green algae in late summer

High light and warm water temp (density INdependent)

deplete nitrogen leads to dominance of N-fixers (density DEPENDENT)

Body size vs. r_max

r is related to body size

r_max decreases with body size

r_max decreases from viruses to large land mammals by more than 100,000x

Both birth and death rates are age dependent; sexual maturity, mortalilty reates often increase with age

Life Tables: tabular depiction of survival or mortality of a population according to age (ie age-specific survival)

used for:

population age structure: proportion of individuals of different ages within a population

age specific fecundity: birth rates according to age

Measures survival by keeping record on individuals in a population that were born at/around the same

Cohort: groups of individuals in a pop

life table: a cohort's birth and death are followed through time

Can calculate population growth rate and age structure

Difficult to do: intensive work, mobile or long-lived animals present big logistical issues

Record the age at death of individuals in a populationl a snapshot of a population over a very short time interval

Measures age of death

individuals which die were born at different times

techniques: tags on animals, rings on trees

Static Life Table example

usually standardized at 1000

ex. dall sheep survivorship

A - B = C

C - D = E

E - F = G

A graph depicting population life and eath patterns as a function of age

Model Curves:

-based on repeated observation of organisms age specific patters

-provide theorectical basis for looking at actual curves

-useful for predictions or comparison

-species variation-not all organisms "follow" curves

-Environmental factos influence response

Type I - High survival of juveniles, older individuals have highest mortality rates (Ex. dall sheep, humans)

Type II - Consistent rates of survival; linear relationship between age and survival (ex. song birds)

Type III - High juvenile mortalilty; exponential decay (ex. sea turtles, many fishes)

Type I - juvenile survival is high and most mortality occurs among other individuals

Type II - linear; individuals die at equal rates, regardless of change

Type III - die at a high rate as juveniles and then much lower rates later in life

Type I curve example (Floscularia) a rotifer

low juve death rate

Type II Curve Example Sparrow and Robin

like many bird species; these two show approx constant rates of mortality

Type III curve example in Cleome plants

high juve death rate

Suggests historical changes in reproductive success; look for strong or weak cohorts (eg. drought or abundance)

Indicates pop growth rates; number of young in relation to number of adults of reporductive age (ex. replacing themselves plus more)

Population Age Distribution Example

Galapagos Cactus Finch 1983 

*Highly Variable Climate*

Age years 1-5 had even distribution of individuals among age classes

Age 6 Finches are absent because the birds didn't nest during a previous drought

Population Age Distribution example

Cactus Finch 1987

Age 2 and 3 finches are non existant, due to droughts in 1984-85

Age 4 finches show a very strong year class

Droughts in 84-85 reduced the numbers of older birds

Pop growth rates balance between birth and death rates

Static and cohort life table data gives you age-specific death rates; birth rates are needed

Note pops with overlapping or non-overlapping generations

Life Tables and Population Dynamics

Terms defined

x: age

n_x: # surviving to day 

L_x: Proportion surviving to day x

m_x: average number of young produced per female during time interval

R₀: net reproductive rate; average L_xm_x

R₀ > 1 - growing

R₀ < 1 - shrinking

Animals and plants reproduce in pulses

In NON-overlapping generation situations, R₀ = λ; the geometric rate of pop increase

*In pops with non-overlapping generations exhibiting geometric growth, λ is analogous to r in exponential or logistic pops (overlapping)

adaptations present in specific species (evol)

abundance and biomass of populations

Competition will lead to decreased allocation of resources or energy to reproduction

Competition

Animals

No requirements for organsims to perceive their competitors; ex. 2 species, 1 plant, different times

Most organisms anmials perceive will not be competitors, even if they share same resource; ex. Oxygen use

Competition

Plants

Plant Competition differs from mobile animal competition; ex. spacing of individuals plants

Effects or magnitude of competitive interactions are density-dependent; ex. more individuals, small area, greater competition

interactions of members within a species

Shows logistic growth:

-# of pop ultimately limited by competition, keeps population around carrying capacity

Intraspecific Competition

Self-Thinning in Plants

*population biomass increases overtime, but is composed of fewer individuals*

3/2 self-thin rule: average weight of individual plants increases as the density decreases. 

1/2

Self-thinning Model for Plant Populations

-Predicts that plants will self-thin as the total biomass of the population increases

x-axis: log # of indiv.

y-axis: log of biomass

*All pops converge on a state of low density and high total biomass. Slope is 1/2

ex. Alfalfa (plant), Planthopper (animal)

*the role of an organism in its community

Competitive Exclusion Principle

overlapping niches

Niche cannot be completely determined

Niche model is static, nature is dynamic

1) limit niche dimensions; 1-2

2) limit discussions -- what an organism feeds on; related to trophic ecology

ex. Galapos finches- beak size;seed hardness

Metapopulation

Conditions

1) habitat occurs in discrete locations (patches)

2)all patches have probability of local extinction

3)patches must not be too isolated to prevent colonization

4) independent population dynamics

C = rate of colonization

E = rate of extinction

C = rate of colonization

dependent upon availability of patches

m = constant; rate of dispersal

E increases linearly with P

C has a unimodal relationship with P

When P=C, no change (ΔP/Δt=0) for metapop

patch size: greater size=greater pop, thus lower probability of extinction; allele effect

Interpatch distance

Patch heterogeneity: increase resource availability

ex. Bush Cricket

Rescue effect: immigrants increase the pop size, lowering extinction

Mainland - Island Metapops

Source - Sink Dynamics: patches are categorized

sinks have r < 0

sources have r > 0

Lotka-Volterra Model

Mathematical expression of competing species
draws from the logistic population growth model
Population size at time t is controlled by population size at N.
Controlled by intraspecific competition

Lotka-Volterra Competition

2 species together

limited amnt of Resource (X)

Species 1 use X, envrionment will hold K₁ individuals

X also used by species 2

different amnt of X used by species 2

species 1 reaches capacity; species 2 extinct

N1 = K1; N2 = 0

species 2 reaches capacity; species 1 extinct

N2 = K2; N1 = 0

Unstable Equilibrium: can coexist, but variation can cause decline in one species; depends on initial densities

species 1 ZNGI (Zero Net Growth Isocline)

K2 < (K1/α)

N1 limited by K1

Either species can win

sp1: K2/β < K1

sp2: K1/α < K2

Stable Equilibrium

sp1: K2/β > K1

sp2: K1/α > K2

Abundances of both species is greater than 0

limited more by their own species opposed to competitor

switched food items and habitat

inceasing levels of competition can also lead shift

Niche Shift Sunfishes example

Hypothesis/experiment

Competitive Exclusion Hypothesis: how can 3 species with same niche inhabit same area?

Pumpkinseed: small; eats snails

Bluegill: medium

Green Sunfish: largest of 3 species

1 species in 1 pond: intraspecific competition only

Manipulated interspecific competition by using same # of each species in same pond

Niche Shift Sunfishes Example

 Results

Pumpkinseed: fed on snail on bentho

Bluegill: shifted diet

Green Sunfish: Best competitor; continued same diet

Increased competition (interspecific) caused two species to shift food source

Mechanistic: predicts outcome of competitve interactions based upon supply and depletion of recources in the envrionment

Outcome depends on: ratio of resrouce supply and ratio of resources being used

Use exploitative competition situtation