Question Bank Questions

Question 1

What is microevolution? What is macroevolution?

Answer 1

Microevolution: changes in allele frequencies within a population over generations (i.e. below the species level); influenced by selection, genetic drift, and/or mutation

Macroevolution: broad patterns of evolution above the species level; results from microevolution over longer timescales – i.e. speciation

Question 2

What is fitness?

Answer 2

Relative fitness: the contribution an individual makes to the gene pool of the next generation, compared to other individuals

Absolute fitness: the contribution an individual makes to the gene pool of the next generation, without consideration for the contribution of other individuals

Question 3

In a few sentences, briefly describe the conceptual basis for phylogenetic reconstruction.

Answer 3

Phylogeny reflects the evolutionary history of a species or group of species, and is intended to show patterns of descent and common ancestry within the chosen group

Grouping organisms with shared derived characters (synapomorphies) into, forming a tree-like diagram; the logic is that taxa that are closely related will share more characters than those that are not

Relies on the things being compared being homologous – i.e. they are evolutionarily the same

Clustering of taxa/specimens traditionally relied on the principle of parsimony, but recent analyses also use maximum likelihood and Bayesian methods

Question 4

Evolutionary biologists are often interested in whether two traits tend to evolve together (e.g., metabolic rate and body size). This often involves asking if there is a correlation between traits across species. Why are phylogenetic relationships important in this context? Conceptually, what are “independent contrasts”?

Answer 4

Phylogenetic relationships are important because, by virtue of all life being related, they are also statistically non-independent; the more closely related two species are, the more similar they are likely to be

Independent contrasts is a statistical method (proposed by Felsenstein) designed to incorporate phylogenetic information into an analysis; works by transforming original tip data from a cladogram into values that are statistically independent from one another and identically distributed, typically using a Brownian motion model of evolution

Question 5

What is the biological species concept? Briefly discuss why it is difficult for speciation to occur in sympatry but easier in allopatry.

Answer 5

Biological species concept: the concept that organisms that can successfully reproduce with one another and are reproductively isolated from other populations belong to the same species; this is problematic for taxa that do not reproduce sexually, as well as the fact that hybridization is kinda rampant, or in palaeontology, where we have no idea if organisms could successfully reproduce

For speciation to occur, barriers to reproduction must evolve (whether prezygotic or postzygotic); it is easier for these barriers to evolve in populations that are allopatric rather than sympatric, as there will be little to no gene flow between allopatric populations

Note there are many other recognized species concepts
(e.g. Phylogenetic species concept: a species is an evolutionarily divergent lineage that has maintained hereditary integrity through time and space)

Question 6

Compare how plants, animals, and fungi acquire C, water, and nutrients.

Answer 6

Plants (autotrophs) acquire carbon through photosynthesis, by converting carbon dioxide + water to carbohydrates and oxygen (6CO2 + 6H2O + photons → 6C6H12O6 + 6O2); water from their environment (contained within soil), and nutrients from their environment (contained within soil)

Animals (heterotrophs) acquire carbon and nutrients through consuming plant matter or other animals; they acquire water from their environment and food; breakdown of carbon and nutrients occurs within the body

Fungi (heterotrophs) acquire carbon, water, and nutrients through consumption; they lack an efficient system for long-distance transport of water and nutrients (some fungi will form rhizomorphs, which look superficially like roots); breakdown of complex molecules occurs externally through excretion of digestive enzymes, with constituent parts being absorbed through hyphae after

Question 7

Why does altruistic behaviour seem, on the surface, a problem for the theory of evolution by natural selection? How can altruism evolve?

Answer 7

Altruistic behaviour superficially appears to risk affecting the fitness of an individual by providing the potential to decrease fitness of the altruistic individual or increase the fitness of another individual, and thus allowing that individual to contribute more genes to the next generation

Altruism can occur due to kin selection (see above), reciprocation (individual aids another, with the expectation that the “favour” will be returned; e.g. warning calls), or individual advantage (cooperative actions that result in benefits to the individual; e.g. schooling)

Altruism is maintained when cheaters are selected against; occurs more frequently in taxa with long lifespans, long growth periods, high parental care, high mutual dependence, and/or low dispersion

Inclusive fitness: the total effect an individual has on proliferating its genes by producing both its own offspring and providing aid that enables close relatives to produce offspring; the concept (by Hamilton) that an animal can increase its genetic representation in the next generation by helping closely related individuals, which share a large proportion of the individual’s genetic material; altruism occurs when relatedness * benefit > cost

Question 8

What is parent-offspring conflict? Give an example of a behaviour thought to be involved in parent-offspring conflict and discuss what factors might affect selection on this trait.

Answer 8

Definition: Trivers 1974; the discrepancy between optimal parental investment from the perspective of the parent vs. the perspective of the offspring

Since parents are equally related to each of their offspring, it benefits them to invest in all offspring equally; offspring are at most half related to their siblings (and fully related to themselves), so they will monopolize parental investment if possible, even at a detriment to siblings

In certain bird species (such as raptors), parents will try to raise all eggs in nest (typically 2), but often a single offspring becomes dominant, eats more food, and often kills its sibling(s)

Parent-offspring conflict typically evolves in cases where a single parent invests, there is a low coefficient of relatedness between siblings, there are small brood/clutch/litter sizes, and/or there is intra-brood competition

Question 9

Females tend to mate more often with certain types of males more than others. Briefly discuss how the concepts of sensory bias, good genes, and sexual conflict relate to this observation.

Answer 9

Sensory bias: females have a pre-existing bias for a certain trait that is unrelated to mating, and this is exploited by males to increase mating opportunities; can be maladaptive for females but adaptive for males; typical example is in guppies, where females prefer to mate with males that have more orange body colouration

Good genes: when a trait in males accurately reflects health/”good genes”, then this trait will be preferred by females; e.g. brighter male cardinals feed their offspring more frequently than duller males, and are chosen more readily by females

Sexual conflict: females and males have conflicting optimal fitness strategies; for females it’s beneficial to reproduce with only super high-quality males, since eggs are costly AF; for males its more beneficial to just bone everything, because sperm are energetically inexpensive to make and whatnot; e.g. duck penises and vaginas

Question 10

What processes might result in an even spatial distribution of individuals within a population?

Answer 10

Intraspecific competition: territory defence, control of nesting sites, chemical warfare between plants; may maximize resource acquisition for each individual

Resource limitation

Question 11

Should parasites evolve to become more or less virulent over time? Briefly discuss some of the key issues.

Answer 11

The key is to strike a balance: a virulent parasite creates a lot of offspring (i.e. high fitness), but if the parasite is too virulent, it runs the risk of killing off its host before it can spread to enough other hosts

There is an evolutionary trade-off here: want to maximize both virulence (reproductive output) and transmission probability

Transmissibility is affected by host population, so optimal level of virulence is in turn affected by demographics of host population; high virulence is found more often in parasites that occur in hosts with high population densities or turnover rates

Coinfection: if multiple strains infect a host, then each strain wants to be the most virulent but also doesn’t want to kill the host… adds another complication to the equation

Question 12

Describe some of the primary costs and benefits of outcrossing relative to selfing.

Answer 12

Selfing Benefits: no need to find a mate (can always reproduce), which is good for taxa that are sparsely distributed and minimally mobile; highly fit genotypes are easily preserved

Selfing Costs: less genetic diversity (increased homozygosity), leading to less resilience to perturbations; inbreeding depression

Outcrossing Benefits: increased genetic diversity

Outcrossing Costs: energetically expensive; may not conserve highly fit genotypes

Question 13

What is a genetic correlation? Give an example of how a genetic correlation might affect evolution.

Answer 13

The correlation between the genetic influences on two traits, or the degree of pleiotropy between the traits

0 implies genetic effects on one trait are independent of the other, while 1 implies that all genetic influences on the two traits are identical

Genetic correlation can occur when two neighbouring genes tend to be inherited together, a single gene having multiple biological effects, gene causes trait X and trait X causes trait Y, or biases (assortative mating, etc.)

Positive disequilibrium: associated genes are both advantageous; promotes rapid fixation of both genes

Negative disequilibrium (antagonistic pleiotropy): one associated gene is advantageous and the other is deleterious; makes it difficult for both the advantageous gene to reach fixation, and for the deleterious gene to be purged, leading to suboptimal fitness

Question 14

What are “selfish genetic elements”? Discuss the selective forces governing their evolution.

Answer 14

Parts of the genome that enhance their own transmission relative to other parts of the genome, but are neutral or harmful to the individual

Three main types of biased transmission: (1) overreplication (e.g. transposable elements); (2) interference with transmission of other genes; (3) biased representation in cells that will become gametes

Natural selection typically favours the rest of the genome over SGEs, but this can be counteracted by e.g. small population sizes

(More notes on this in your study doc)

Question 15

Briefly discuss several reasons why genetic variation may exist in natural populations.

Answer 15

Genetic drift (decrease genetic variation): change in the frequency of alleles in a population due to random sampling; i.e. a population bottleneck (which presumably causes some genes to be randomly “pulled” from the overall population) may lead to an overrepresentation of one gene over the other

Gene flow (increase genetic variation): migration of organisms between populations will allow for intermixing of genotypes, and thus will prevent genes with high frequencies in one population from spreading to fixation

Mutation (increase genetic variation): random mutations in genes will create new alleles, which may then be passed through the population

Selection (decrease or increase genetic variation): beneficial genes will tend to spread to fixation; this may be counteracted through genetic correlation, etc.

Recombination (increase genetic variation): in sexually reproducing organisms, recombination of genetic material during meiosis can lead to novel combinations of genes

Question 16

Can deleterious mutations ever spread to fixation? What factors affect the chance of this happening?

Answer 16

Yes.

Drift/inbreeding depression: if a small population contains individuals with a deleterious mutation, then inbreeding can cause the deleterious mutation to become fixed

Genetic correlation: if a deleterious mutation with small effect and a beneficial mutation with large effect are linked (i.e. highly correlated), then the net effect is positive, and the pair can spread to fixation even though there is a deleterious mutation involved

Taxa with low effective population size (Ne), while they may have a healthy absolute population size, essentially experience inbreeding depression

Question 17

Even very closely related species typically differ by hundreds or thousands of base-pairs across their genomes. Discuss how various evolutionary forces are likely to contribute to these base-pair differences.

Answer 17

Selection may have acted differently on the same gene in each species, causing permanent differences in the base-pairs
- There should be differences in loci that affect reproductive isolation between closely related species

Neutral evolution: synonymous substitutions (ones that don’t change the identity of the codon or gene product)
- Different mutation rates

Question 18

Conceptually, what is effective population size, Ne? What types of factors affect Ne?

Answer 18

Number of individuals within a population that are actually capable of breeding

Incorporates sex ratio of breeding individuals and uses the formula: Ne = 4NfNm / Nf + Nm

If not all individuals breed OR there is not a 1:1 sex ratio, then the effective population size is less than the total population size

Impacts: family size, age at maturation, genetic relatedness, gene flow, population fluctuations, sexual selection, intrasexual competition

Question 19

The classic model of logistic population growth is characterised by two parameters: the intrinsic rate of growth, r, and the carrying capacity, K. Draw a graph of logistic population growth (abundance vs. time, beginning at a very low initial abundance) and explain how parameters r and K affect the shape of this graph. What types of life history traits affect r and K?

Answer 19

Parameter r will affect the shape of the graph by altering the amount of time it takes for the population to reach K (the “steepness” of the curve)
- Organisms with slower life history (long time to sexual maturity, low growth rate, e.g.) will have a lower r; organisms with large brood sizes will have higher r

Parameter K will affect the shape of the graph by changing where the upper asymptote falls on the y-axis
- Range size (competition) and availability of resources can affect K, as can longevity

Question 20

Define reproductive value. What determines the reproductive value of an individual in an age-structured population?

Answer 20

Definition: Vx, or the number of offspring an individual is expected to produce over its remaining lifespan, adjusting for the growth rate of the population

Reproductive value is affected by age (it tends to be low at birth, peak at age of first reproduction, then decline), survivorship (Sx), fecundity (bx), population growth

Question 21

Briefly describe the theory of island biogeography.

Answer 21

First developed by MacArthur & E.O. Wilson

Species richness of an island (whether that is an actual island within water or an “island” of suitable habitat, such as between urban areas) is affected by two major things:

• Size of the island: bigger island, lower probability of extinction; smaller island, higher probability of extinction
• Distance of the island from the mainland: closer island, higher probability of colonization; further island, lower probability of colonization

A small/distant island will have very few species, whereas a large/nearby island will have many species; small/nearby and large/distant islands will be somewhere in between

Question 22

What is the “enemy release” hypothesis as it relates to biological invasions? How might this hypothesis be tested?

Answer 22

ERH: spread of invasive species is facilitated by them being “released from their enemies” (i.e. no longer interacting with competitors or predators); lack of co-evolved natural enemies meaning there are no longer the same restrictions to the population growth of invasives

Testing the hypothesis requires answering specific questions about if natives and non-natives experience things differently

• Are natives predated more than non-natives?
• Are non-invasive exotics predated more than invasive exotics?
• Are non-native species with broader new geographic ranges predated more than non-native species with restricted new geographic ranges?
• Do non-native species that have been present in their new range longer get predated more?

Question 23

Explain one mechanism by which productivity might increase with diversity.

Answer 23

Complementarity: niche partitioning between coexisting species will allow the community to use resources more completely

Facilitation: modification of the environment by one species creates favourable conditions for other species; e.g. nutrient enrichment by nitrogen-fixers for plants

Sampling Effect: in an area that is more diverse, there is simply a greater chance of a species with high productivity being included; greater chance of selecting a species that:

• Is adapted well to that site’s conditions
• Has greater inherent productivity
• Is highly complementary to another species in that area
• Has a large facultative effect on other species in the area

Question 24

What is the neutral theory of ecology?

Answer 24

Neutral theory assumes that all individuals are ecologically identical and predicts that species have perfectly overlapping niches

Highly diverse communities of equivalent species arise because chance extinctions are balanced out by speciation; all species have equivalent niches but stochastic patterns like death, immigration from a regional pool of species, and speciation lead to species-rich communities

Key assumptions:

• Individuals are identical (species may have differences, but these don’t matter because all individuals have the same fitness)
• Other assumptions re: how species are added to and lost from communities

Neutral theory only applies to groups of similarly-functioning species (e.g. trees in a forest are like corals in a reef), which are of similar size and serve at the same trophic level

This is intended to serve in opposition to niche partitioning, where everything has a separate niche, and are ecologically different

Mostly intended to serve as a null hypothesis, since nothing really fits this (or perfect niche partitioning)

Question 25

Briefly discuss at least two hypotheses for why the tropics may be more diverse than temperate zones.

Answer 25

Hypothesis 1.
The time theory proposes that the species richness of communities increases with time due to ecological (immigration) and evolutionary (speciation) processes. Multiple glaciations in northern latitudes reduced the time available for diversification, while tropical regions remained relatively undisturbed, leading to the LDG.

Hypothesis 2.
The theory of spatial heterogeneity suggests that the LDG results from the greater heterogeneity and/or complexity of physical and biotic factors (e.g., foliage height diversity) in the tropics. This is essentially an argument that the number of available habitats controls the number of species in a community.

Hypothesis 3.
The competition hypothesis proposes that natural selection in the temperate zone is governed more by abiotic than by biotic factors, and as a result, competition is stronger in the tropics, niches are narrower, and more species can be supported.

Hypothesis 4.
The predation hypothesis is an alternative to the competition hypothesis, suggesting that competition is actually lower in the tropics due to a reduction in population sizes caused by higher predation in tropical environments. Lower competition reduces the likelihood of competitive exclusion and increases species richness.

Hypothesis 5.
The theory of climatic stability predicts that the stable climate in tropical regions leads to greater specialization, narrower niches, and higher species richness.

Hypothesis 6.
The productivity hypothesis suggests that the greater productivity of tropical regions increases species richness, perhaps by allowing narrower niches, tighter species packing, and greater niche overlap.

Question 26

Briefly discuss the ideas of local vs. regional control in understanding species diversity

Answer 26

Local controls: niche properties; e.g. vegetation complexity, productivity, habitat area, competition, predation, disturbance

Regional control: biogeographical properties; dispersal ability, barriers, speciation/extinction rates, history of area, climatic factors

These both work in concert, but one can affect an area more than the other
- E.g. if dispersal is high, then local factors may not be as important; if it is low, then local factors will dominate

Question 27

Discuss at least two mechanisms that would allow species that consume the same resources to co-exist

Answer 27

Temporal partitioning: variations in diel pattern

Spatial partitioning: foraging locations differ
- E.g. Anolis lizards; all the ones in the Caribbean eat insects, but spatially segregate and have different ecomorphology based on this

Availability of resource: if it’s super common, they can share
- This is supposed to be a temporary state? (I’m assuming this is if none of the other controls mentioned here exist)

Population controls: if one or both species have a population kept in check by external factors (predators, or competitors for a different resource), then the species in question may not compete as strongly

Question 28

Contrast the fundamental and the realised niche. Which one of these will be affected by a competitor and in what way would a competitor change this niche?

Answer 28

Fundamental niche: maximum theoretical niche; all of the abiotic conditions an organism can tolerate, and all the resources it can use

Realised niche: the truly visible niche; the ACTUAL resources an organism consumes, and the ACTUAL abiotic factors it is found in
- This is the one that will be affected by competitors; it would restrict the niche

Question 29

How might the removal of a predator from a system result in a less diverse prey community?

Answer 29

By being released from predation pressures, prey will explode in numbers and potentially begin outcompeting other prey species; this will in turn lessen diversity

This will favour one or a few relatively competitive species

Question 30

What is a trophic cascade? Distinguish between top-down and bottom-up control of the density or biomass of a species.

Answer 30

Trophic cascade: removal/depletion/change in composition of a trophic level within a community, causing negative effects to the community as a whole

Top-down control: initial disturbance happens to predators (i.e. at the top of the food web)

• Pattern of increase/decrease of population happens sequentially: so decreased predator > increased prey > decreased secondary producer > increased primary producer
• e.g. population of wolves reduced > increased population of deer/elk > decreased plants (b/c of consumption by deer/elk)

Bottom-up control: initial disturbance happens to producers (i.e. at the bottom of the food web)
- Decrease of producers will decrease the population(s) of every level higher in the trophic web

Question 31

Predators negatively affect prey populations directly by consuming them, but the mere presence of a predator may also cause prey to change their behaviour and morphology. Describe one or two ways that these indirect effects of predators on their prey could have a large negative influence on the productivity of a prey population.

Answer 31

Stress will cause behavioural changes, so they may not invest as much in reproduction/gathering resources

May also affect morphology: some tadpoles and fish may alter their body/tail shapes throughout ontogeny if there’s increased predation pressure

Maturation may occur more quickly (i.e. at a smaller size) in response to predation, which can result in reduced competitive ability or reproductive output

Question 32

What is eutrophication in lakes and seas? Briefly discuss possible causes and consequences.

Answer 32

Eutrophication: an overproduction of primary producers like algae or cyanobacteria in response to an extremely high concentration of nutrients (especially phosphorus and nitrogen)
- Lakes/rivers usually phosphorus, oceans usually nitrogen

Possible causes: AGRICULTURE (run-off from fertilizers and animal waste), industry (fossil fuel burning  increased atmospheric phosphorus  increased phosphorus in rainfall), sediment infill can bring these nutrients in, land clearing increases surface erosion and decomposition including these nutrients, fixed nitrogen in the atmosphere

Possible consequences: increase in algae/cyano leads to decreased oxygen availability, causing MASS DEATH; rate of photosynthesis increases, using up more inorganic carbon, and causing an increase in pH; toxic algae can cause die-offs of terrestrial animals that drink the water

Question 33

Describe two substantially different explanations for how relatively slow-growing organisms like plants can dominate terrestrial ecosystems in the face of herbivore communities full of organisms with much higher maximum population growth rates.

Answer 33

Defence mechanisms: reducing grazing pressure using chemical (e.g. volatile organic compounds) or mechanical (e.g. spines) defences; these defences not only deter herbivores, but can distribute herbivore pressure differently amongst species (i.e. herbivores may specialise on particular plants whose defences they can overcome)

Top-down trophic effects: despite high population growth rates, predators consume a lot of the herbivores, reducing the impact of this high population growth rate on the plant species the herbivores eat

Herbivory is not always fatal to the plant itself, so the plant can continue growing and reproducing despite predation; in some taxa that are well-adapted to grazing, herbivory may actually stimulate growth

Temporal limitations: plants may only be edible during certain periods, allowing them to re-grow in the “off” periods; if all plant species in an area develop edible parts at the same time this can also overwhelm herbivores

Question 34

What is a metacommunity? Describe some of the processes that distinguish it from a local community.

Answer 34

Metacommunity: a set of ecological communities that are connected through dispersal of at least one of their common species

Local communities are driven by the interactions of species within the community, whereas metacommunities are driven by interactions between communities by dispersal

Examples: series of islands; forest patches with disturbed terrain in between; series of lakes, table mountains

Question 35

What are patch dynamics?

Answer 35

Interaction between local communities within a metacommunity

How community composition varies between patches

How patches differ in population sizes, extinction risks, etc.
- Larger, better-connected patches will be more stable and will be at a lesser risk for species extirpations

Question 36

What would happen to a metapopulation in which you blocked the movement of individuals between patches? Why?

Answer 36

It would no longer be a metapopulation

Sink patches (patches that rely on input from other patches to avoid extirpation) would collapse

Population reductions within a patch can no longer be compensated through colonization – higher risk of extinction

Theoretically, this could also lead to allopatric speciation
- To a lesser extent, this should lead to greater within-patch homogeneity and between-patch heterogeneity

Question 37

What is the rescue effect and how might the size and distance between patches affect its role in a metapopulation?

Answer 37

Rescue effect: “rescue” of a patch-at-risk due to colonization/migration from a larger, more stable patch

Effect of size: larger patches are more likely to be “sources” and smaller patches are more likely to be “sinks” that require rescuing

Effect of distance: when patches are closer together (and better connected in general), it will be easier for these “rescues” to take place

Question 38

Contrast the process of adaptation with the process of acclimation and give an example of each.

Answer 38

Adaptation: population level; evolutionary; phenotypic changes underlain by heritable genetic changes

Acclimation: at individual level; not heritable in the same way adaptive traits are (beyond the fact that phenotypic plasticity can be heritable)

Question 39

Aquatic communities often have more trophic levels than terrestrial communities. Discuss physiological and energetic reasons that might help explain this difference.

Answer 39

Physiological: more ectotherms in aquatic ecosystems, meaning more efficient transfer of nutrients up the web of foods; because primary producers are small in size, this allows for more “steps” in body size toward the top of the food chain (i.e. more levels in the web)

Energetic: faster turnover of primary producers (because they’re mostly single-celled); less biomass being decomposed; most of the energy in terrestrial systems is tied up in large plant bodies

Question 40

Plants are often more physiologically challenging foods for animals than are other animals. Describe some of the challenges of eating plants.

Answer 40

Breaking down cellulose is hard; most organisms do not have the enzymes necessary to effectively break down cellulose
- Symbiotic relationships with microbes can help with this

Silica can be found in the bodies/leaves of plants and that is most certainly not digestible

Volatile organic compounds can be toxic, or at least seriously unpalatable

Also, when consuming other animals, you’re consuming essentially what you are and therefore will probably be able to use most of the compounds you’re consuming directly, without intermediate steps

Question 41

What are the predictions of the intermediate disturbance hypothesis?

Answer 41

Species diversity is maximized when the frequency of disturbance is in a nice lil’ Goldilocks zone

• When disturbances are too frequent, species with high colonization ability (i.e. r-selected species) will outcompete/exclude K-selected species
• When disturbances are not frequent enough, slow-growing species with relatively high competitive ability will outcompete/exclude r-selected species

Species that thrive at both early and late successional stages can coexist when disturbance is intermediate

Question 42

Discuss why there may be a trade-off between colonisation ability and competitive ability in plants. What would this trade-off predict about the traits of species across time during the process of succession?

Answer 42

Optimal strategy colonisation (r-selection): grow fast, reproduce early, and produce many offspring that can then disperse to colonise new habitats; this will likely resuly in offspring of relatively poor quality
- Early succession species are expected to express these traits

Optimal strategy for competition (K-selection): grow slowly, reproduce later, and produce a few really high-quality offspring
- Late succession species are expected to express these traits

Question 43

Explain the meaning of “p < 0.05” associated with the result of a [frequentist] statistical test.

Answer 43

There’s less than a 5% chance of type-1 error (false posistive, or rejecting a true null hypothesis)

P-value: probability of obtaining your observed distribution of values under the null hypothesis

Note that this is NOT a direct test of your alternative hypothesis/hypotheses, so rejecting the null hypothesis ≠ accepting the alternative hypothesis

0.05 is typically the threshold used for significance in scientific disciplines, but this is an arbitrary decision and is more a matter of convention on what is deemed acceptable type-1 error rates

Question 44

Explain the difference between type-1 and type-2 errors.

Answer 44

Type I: Incorrect rejection of a null hypothesis (false positive)

Type II: Failure to reject an incorrect null hypothesis (false negative)

The story of the boy who cried wolf is type 1 and type 2 errors being committed, in that order

• Null hypothesis: there is no wolf
• First, villagers think there IS a wolf when there isn’t
• Then, they think there isn’t a wolf when there is

Question 45

Define statistical power. Specify several ways that you might go about increasing it if a power analysis for a planned experiment indicated that your initial plans would not provide sufficient power.

Answer 45

Statistical power: probability of correctly rejecting the null hypothesis when an alternative hypothesis is true

Higher statistical power typically corresponds to lower type II error rates

Improving statistical power:

• Increase sample size: increases probability of detecting significant differences
• Increase acceptable Type I error rate
• Increase effect size: this can be done by removing outliers, or use standardised test statistics

Question 46

Distinguish between statistical and biological significance.

Answer 46

Statistical significance: simply, your ability of reject the null hypothesis; an effect can be statistically significant without being biologically significant

Biological significance: is the effect biologically meaningful? Is there an effect on fitness? Reproduction?; an effect can be biologically significant without being statistically significant (e.g. if you can’t measure that trait in a meaningful way, or if you don’t have the right variables, or if you don’t have a good sample)

Question 47

Explain the difference between comparison-wise and experiment-wise type-1 error rates.

Answer 47

Comparison-wise: probability of type I error rate for each comparison
- False positive rate for any one test

Experiment-wise: probability of making at least one type I error within an experiment; cumulative type I error
- False positive rate across all tests used within an experiment

Say you have three sets of data you want to test for differences: S1, S2, and S3

• You could run these with three separate two-way tests, so:
• Ho: S1 = S2; S2 = S3; AND S1 = S3
• If we’ve set α = 0.05 for each of the above tests, you’re TRUE (experiment-wise type I error rate is as follows): 1 – (1 – α)3 = 1 – (1 – 0.05)3 = 0.142525

You can run a Bonferroni correction, which “involves dividing the desired cumulative α by the number of comparisons that will be made, thereby deriving an α for use in each of those comparisons (ex. For a cumulative α of 0.05 in an experiment with 5 tests, each comparison should operate with an α equal to 0.01.” (thanks Tom)

Or, you could do a single multiple sample test like an ANOVA or MANOVA

Question 48

Explain why the F-value statistic from an analysis of variance is positively correlated with the degree of difference among the groups being compared.

Answer 48

First, what is the F-value statistic? Ratio of between group variance/within group variance

Because between/among group difference is the numerator in the ratio, we’d expect that the F-statistic would be positively correlated with this numerator

Question 49

Under what circumstances would it be most informative to state or plot the value of a biological parameter such as animal size as:

a) Mean ± standard deviation
b) Mean ± standard error
c) Mean ± 95% confidence interval
d) Median, quartiles, range

If sample size were reported along with a) above, explain how you could calculate b) and c) from a) for that population.

Answer 49

Mean ± standard deviation: variation in the observed variable within a population; most useful when describing the spread of your data

Mean ± standard error: measure of how precise our mean is; takes into account the sample size and is S.E. = S.D. / √n useful when we’re trying to test the differences between samples/populations

Mean ± 95% confidence interval: this is the range around the mean for we’re 95% sure contains the true mean; calculated by multiplying the standard error by a z-value (so 95% confidence interval = mean +/- S.E.*1.96); we’d want to use the CI when we want to know the range of values that are likely to be representative of the population

Median, quartiles, range:

• Q1 = median of the first half of data
• Q2 = median of the whole dataset
• Q3 = median of the second half of data
• Interquartile Range = Q3 – Q1; full range = max - min
• Useful when your data follow a non-normal distribution, and thus the mean and standard deviation (+ derivatives) are unreliable ; allows you to detect skew and outliers