__Population and Community Ecology__

*The scientific study of interactions that determine the distribution and abundance of organisms.*

**Coevolution**: when two species evolve in response to the other.*“reciprocal evolution”*- Examples:
- A pathogen and its host- the host must develop immunity or it will die off, the pathogen must respond to these changes to continue thriving in/on the host.
- Predator/prey relationships- specialists, selective food choices

- Examples:

**Experimental design:**

- Observational studies detect
*correlations*and relationships in the environment, correlations are a linear association between two quantitative variables - Experimental studies detect causation due to the manipulation of variables by the experimenter to test a hypothesis and run statistical analysis on.
__Replicates:__observations or experimental units allow us to test whether the patterns we see are general and repeatable. What ‘counts’ as a replicate depends on the scale of inference we are trying to achieve.- For example: one male and one female each run 30ft 20 times and times recorded.
- If the scale is dependent on the individual him/herself then each has 20 replicates.
- If the scale is dependent on gender then there is only one male and one female and therefor there is only one replicate.
- If there were three males and three females then there would three replicates for each gender

- In experiments, the control is the group to which you compare your treatment group(s); without it, you have nothing to compare to. A good control should be EXACTLY like the experimental group in all ways, EXCEPT the factor being tested.
- Types of variables:
__continuous__(numerical and can be used in arithmetic, decimal places) vs.__categorical or discrete__(specific group, type, or item, characteristic, etc. that is finite/nonnumerical) __Predictor variable__the factor that is being tested/manipulated, placed on the X-axis.__response variable__– the factor that is measured, placed on the Y-axis.- IF the data are not normally distributed then the data can be transformed using a square-root function
__General hypothesis:__a testable statement that is inferred due to deductive/inductive reasoning__prediction or specific hypothesis:__IF…..THEN…… statement that states the general hypothesis in the “IF” clause and the experiment/manipulation in the “THEN” clause.__Null hypothesis__in inferential statistical tests: States that there is no difference between groups, that the results are coincidental/random.__Descriptive stats:__describes tendencies in the data set such as center (mean/median/mode), spread (variance, standard deviation, IQR, standard error). Describes the samples.__inferential stats__: Allow you to make predictions about larger groups, predict future population sizes. (Correlation/regression/confidence intervals etc.)__Strengths__of observational vs. experimental studies- Both can be time consuming/costly/fail
- Observational studies are a good place to start when beginning to study a population
- Experiments are useful in testing specific hypothesis where factors can be manipulated

__Orthogonal design__= all possible combinations of two or more factors are tested for in an experiment.__independent vs. paired t-test__- A paired T-Test is used when there is correlation/association between the variables being tested, or the same individual is used to compare to itself before/after the manipulation
- An independent T-test is used when the data points collected cannot be associated/linked with another data point.

__one-tailed vs. two-tailed tests__- One tailed-the hypothesis gives a direction of difference
- Two-tailed there is not direction of difference

__assumptions of parametric statistics__- Independent/replicated samples
- If not met then it is a fault with the experimental design

- Normally distributed- ie. Frequency histogram
- If not normal then do the square root/log of the data or use a nonparametric test

- The groups should have equal variance
- Intrinsic to the populations

- Independent/replicated samples

- For example: one male and one female each run 30ft 20 times and times recorded.
__Inductive Reasoning:__going from one or several specific examples to infer a general truth__Deductive Reasoning__: the process of going from a general truth to a specific prediction

**Evolution:**

- Mechanisms of microevolution:
- Genetic drift:
__random__changes in gene frequencies within a population over time. More likely to occur in smaller populations because changes are more dramatic if certain individuals are eliminated. - Gene Flow: Intermixing of two different populations, individuals move from one population to another and breed.
- Mutations: random changes to DNA that cause phenotypic variations that are passed onto offspring
__Selection:__those with the most well adapted traits for their environment will survive and pass on their genes.

- Genetic drift:
__Local adaptation__: when after several generations in a population an advantageous trait acts to increase fitness and respond to stress so that the individuals within that populations with the trait can tolerate that stressor more.- Allopatric speciation: two populations are separated by a physical barrier.
- Traits as
__adaptations__, and__constraints__on adaptations- Such as genetic constraints, history of species, energetic trade offs, etc.)

__Phenotypic plasticity:__one gene is responsible for two phenotypes due to varying environments of different populations.__Acclimation:__a compensation for stress, is not a genetic change, occurs within individuals and is reversible.__Transgenerational plasticity = maternal effects:____Phylogenetic conservatism__: The tendency of species to retain ancestral traits.__Phenology__: the timing of seasonal events such as budding in tree species, plant germinations, and reproductive cycles. Cues that species use are temperature, amount of sunlight/day length.

**Sampling populations:**

__Census:__A count of every individual in a population__Area Based Sampling:__use of randomly placed**quadrats**of a certain size to estimate the number of individuals in a population__distance-based sampling:__An estimate of population size based upon the distance between two individuals of a population.- Nearest Neighbor Sampling: distance of two individuals within a population from a random point to determine distribution.
- Individuals along a straight line are sampled

__random vs. haphazard sampling:__- Random sampling employs a random number generator to choose locations for quadrat placement
- Haphazard sampling is biased in that the investigator influences the location to sample with the quadrat

__uniform vs. stratified random sampling:__- Uniform sampling employs the use of transects, sampling is done at regularly set intervals.
- Stratified Random sampling is when a habitat is divided based upon perceived differences, the samples within each zone are randomly chosen.

__Mark recapture method:__use a trap to catch specimen, tag them, and then release them, then repeat. Monitor how many are recaptured vs. new specimen to estimate population size.- Total # marked / Population size = # marked in second group /total in second group
- Assumptions of the model:
- Probability of recapturing a marked mouse does not change
- Assume marking does not increase mortality in specimen- otherwise will never recapture a mouse and it will seem as if there is an infinite population size
- Mixed organisms, not territorial species- or will always catch the same ones, small population size
- All individuals are equally likely to be caught- naïve and elderly mice, or is there division of labor?

- Population
__dispersion__patterns: how organisms are arranged on the landscape__clumped or aggregated-__small groups are spread across the landscape, herding animals.__Random-__organisms have no pattern is dispersion, based on resources.__uniform/regular__usually seen with territorial species.

__fundamental niche:__the area where the abiotic factors of an environment would allow for a species to thrive__realized niche:__the actual location of the species dues to abiotic/ biotic factors such as interspecies interactions.__R-selected life history-__many offspring, rapid reproduction, instantaneous growth-bunnies- K selected life history- long living, few offspring, high parental care, long gestation-tigers
__Bergman’s Rule:__animals become bigger at higher altitudes and as they move away from the equator__Allen’s Rule:__vertebrate endotherm that live in cold environments have shorter appendages to decrease the escape of heat.- The artic fox has short ears while the desert fox has long ears
- Volume to surface area and the need for heat conservation: as surface area increases there is a larger surface for heat exchange.

*Describing Communities*

__Assemblage:__a group of different species living in the same habitat, sharing/competing for resources, and interacting with abiotic/biotic factors.__Richness:__The number of different species in a habitat__Evenness__: The relative abundance of each species in a habitat__Rank-abundance curve__: the relative abundance of each species in your sample (pi for all species i), and ranking them from most abundant to least abundant. Then you simply graph that as a line graph, with rank on the x-axis and abundance on the y.__Rarefaction__– to compare two sites with different sampling effort. Basically, rarefaction uses either a resampling methods (bootstrapping, or resampling with replacement, or jack-knifing, resampling without replacement). to predict how many species we WOULD have found at site A if we’d only sampled 40 individuals rather than 80 – it ‘rarifies’ the bigger data set, so that the two can be compared to each other.__Alpha diversity:__diversity within a site/habitat, due to the role of dispersal and chance events.__Beta diversity:__diversity between sites, the shift in composition__Gamma diversity:__the diversity of an entire region,- The historic processes (e.g. geography, continental drift, adaptive radiation) and broad climatic factors (e.g. regional patterns of rainfall, temperature) are the main drivers of biodiversity
- At local spatial scales (e.g. comparing one site to another, within a region), species’ particular physiological tolerances and their interactions with other species (competition, predation, etc.), act to determine how many species (and which ones) are present at any given site.

*Population Growth Models*

- When left unchecked population growth is
**geometric**(staircase shape, births occur only in spirts) or**exponential**(J shaped curve, continuous births and deaths, constant rate of growth)- Resources are a population check ***limit growth***

- Terms that are used:
- N – population size, # of individuals
- N
_{t}– Number of individuals at time “t” - N
_{0 }– initial population size, population size as t=0 - “n” – sample size

- Factors that change “N”
- N
_{t+1 }= N_{t}+ Births – deaths (in a closed population) - Immigration (added)
- Emigration (migrated away-subtract)
- N
_{t+1 }= N_{t }+ b (birth rate, per capita rate)X N_{t }– d(death rate per capita) N_{t}- N
_{t+1 }= N_{t }+ (b-d) X N_{t}

- N
- N
_{t+1 }– N_{t }change in population size =∆N - (b-d) = r ***
**instantaneous per capita rate of increase******- Which is the r selected life history

- ∆N/∆t = rN

- N
- dN/dt = rN ***
**only equation that describes a change in a population size*****- if r= 0 then no population growth
- r>0 is population growth
- r<0 is population decline

- if r= 0 then no population growth
**Assumptions of the model (dN/dt = rN)**- closed population
- b and d are constant
- r is constant
- all individuals contribute equally to population growth rate “r”
- but what about populations that differ in relative number of individuals who can contribute (ie. Stage of life/ability to reproduce/sex ratios)
- but what about resource limits/competition?

**Integrate model for the differential equation- can predict population sizes based on time**- N
_{t}=N_{0}e^{rt} - Can figure out a population size at any time “t”
- Also describes compounded interest

- N
**Discrete Model- geometric**(staircase shape)- N
_{t}+1 = N_{t}(ƛ)- ƛ=1 is a constant/stable population size, ƛ<1 = decreasing populations size, ƛ>1 = increasing population size

- general form: N
_{t}=ƛ^{t}N_{0 } - predict population size at any time (t)
- discrete intervals of growth, populations where births occur at regular intervals, non-overlapping generations
- ƛ is population growth rate
- ratio of population sizes
- dimensionless, but associated with a particular time step.

- Ranges from 0 to infinity

- N
**Differential Model- Exponential:**(J shaped)- N
_{t}=N_{0}e^{rt} - growth occurs continuously, births are year-round, use calculus and differential models., overlapping generations.
- “r” is the instantaneous per capita rate of increase
- # individuals/per individual; instantaneous
- Negative to positive infinity range
- Stability is when “r”=0

- N
**To convert between discrete and differential equations:**- ƛ
^{t}N_{0 }= N_{0}e^{rt}

- ƛ
**Take natural log of data and plot it on the graph, the slop of the line is “r”**__logistic__**growth:**(s-shaped)- When there are limited resources and competition the birth rate and/or death rate change.
- Less births
- More death (not enough food, space, increased illness)

- To model this: d N/dt= r N (1-(N/K))
- S-shaped curve
- If the birth rate increases so that “r” increases then the population will reach K faster.
**Assumptions of logistic growth curve:**- Closed population
- All individuals contribute equally to the population size/r
- All individuals use resources and contribute equally to carrying capacity (K)
- Instantaneous affect

- When there are limited resources and competition the birth rate and/or death rate change.
- When the birth and death rates intercept there is a density dependent in the population growth. Occurs when per capita population growth rate changes with population density
**Negative density dependence**is when r is decreasing because birth rate is decreasing. Increase of death rate/decrease in birth rate as population density changes. Due to intraspecific competition. Form of regulation.- When b=d then r=0, graph plateaus

- K is the carrying capacity, the population size that the environment can sustain stably, is the intercept of death and birth rates. To keep population stable at K.
- Increase resources will increase K
- The Y-value where the s-shaped graph plateaus

**Delayed density dependence:**population growth rate is affected by population size at some point in the past-time lag in density dependence. (deterministic model-logistic)- d N/dt= r N (1-(N
_{(lag)}/K)) - if no or small r X lag then model appears to have no lag
- if there is a medium r X lag model has damped oscillations until it evens out at K.
- if there is a large r X lag model limit cycle around K, large oscillations about K.
- Very large r X lag creates chaos
- dynamics are intrinsic to the population itself à shape of curve is internal property of the population. (abiotic and biotic factors affect the population).

- d N/dt= r N (1-(N
*Deterministic models:*(geometric, exponential, logistic, delayed dd) no randomization, the output directly depends on the input. Determined preexisting constants and known values.**Stochasticity-**randomness. Extrinsic factors that influence population size such:__Environment:__change in climate, conditions are more or less favorable for any given year for each species. Affects all populations regardless of their size.__Demographic:__randomness that results from applying a rate (ie. “b”, “d”, “r”) to real whole numbers. Most impact on small populations.- Similar to genetic drift

- There are an Infinite number of outcomes (iterations), similar pattern for a single input.
- Randomness can hurt population growth (make is smaller at any time when compared to deterministic model).
__Geometric mean__: √(a * b *c *….)- Bad years hurt population growth more than good years help it.
- Is always less than the deterministic mean.

- Population growth trajectory for
__density independent growth__is an exponential growth curve. dN/dt=rN - Population growth trajectory for
__negative density dependent growth__. Logistic, S-shaped curve. dN/dt=rN(1-N/K) - Relationship of Per capita population growth and N:
- X-axis is N
- Y-axis is r
- Exponential relationship is horizontal line
- Logistic relationship is a decreasing line. (negative density dependence)

- Logistic models show population regulation.
__Positive density dependence:__when small populations show lower per capita growth rates than bigger populations do. This is not a straight line-right skewed graph, the smaller population has an increasing per capita growth until it reaches a larger size when the negative density dependence takes over.- 1/N dN/dt vs. N

**Allee Effect**– due to positive density dependence.- Mechanisms:
- Problems finding a mate at low densities.
- Group formation-foraging success, detection, avoidance, saturation of predators.

- Mechanisms:

**Smaller populations at a greater risk for extinction than larger ones.**

- Environmental changes can decrease population growth rates
- Habitat loss, hunting, invasive species

- Due to Allee Effect (smaller dN/dt)
- More sensitive to randomness
- Environmental stochasticity-good years and bad years
- Demographic stochasticity- randomness that occurs when rates are applied to whole numbers. Ie. Average number of children an individual has, do not expect same outcome in each case.

- Genetic reasons-inbreeding, inbreeding depression (reduction of fitness due to deleterious recessive traits that are passed to these offspring that have low fitness-lower birthrates and higher death rates occur), loss of genetic diversity.
- Genetic rescue- introduce new individuals to increase genetic diversity.

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AWESOME notes! you ROCK! 🙂 -Dr. H

Thank-You!!! I used this as my study guide for the midterm exam.