# Midterm Review

Population and Community Ecology

“Butterfly” by Genuine Creators (CC0 1.0)

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

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
• 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.
• 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.
• 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 dispersionpatterns: 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.

“Arctic Fox Glowing” by Eric Kilby (CC BY-SA 2.0)

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
• Nt – Number of individuals at time “t”
• N0 – initial population size, population size as t=0
• “n” – sample size
• Factors that change “N”
• Nt+1 = Nt + Births – deaths (in a closed population)
• Emigration (migrated away-subtract)
• Nt+1 = Nt + b (birth rate, per capita rate)X N– d(death rate per capita) Nt
• Nt+1 = Nt + (b-d) X Nt
• Nt+1 – Nt change in population size =∆N
• (b-d) = r ***instantaneous per capita rate of increase****
• Which is the r selected life history
• ∆N/∆t = rN
• 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
• 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
• Nt=N0ert
• Can figure out a population size at any time “t”
• Also describes compounded interest
• Discrete Model- geometric (staircase shape)
• Nt+1 = Nt(ƛ)
• ƛ=1 is a constant/stable population size, ƛ<1 = decreasing populations size, ƛ>1 = increasing population size
• general form: NttN0
• 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
• Differential Model- Exponential: (J shaped)
• Nt=N0ert
• 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
• To convert between discrete and differential equations:
• ƛtN0 = N0ert
• 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 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).
• 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.

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.