Spring 2001
Practice Problem Answers--Unit 1
Ecological Tools (back to menu)
1. Ecological models precisely describe what we think is the way a system works. In order to construct it, we must define the assumptions under which we are working, so it makes assumptions explicit. It also forces us to precisely define the mechanisms we think underlie the predictions. No model will be absolutely correct, or in other words, every model is wrong in some aspects. Those aspects of the model that we find are wrong allow us to focus our limited energy, time, and money on places that we see we don't understand very well.
2. Experimental data are more powerful than descriptive data in that the researcher has manipulated the variable(s) of interest and controlled other variables. This allows the researcher to make causal inferences from the data. Experimental data should be collected whenever it is possible to set up a controlled experiment because of the added power of causal inference. However, there are many instances in which experiments cannot be constructed, either because of the time frame or the scale at which the mechanisms of interest operate. For example, evolutionary questions are not amenable to experimentation for most organisms because of the time frame involved. Similarly, global, continental, or regional scale phenomena cannot be investigated experimentally. In addition, there may be cases where experimental manipulation of an endangered species is too hazardous to the population so that descriptive data are the only safe kinds of data to collect.
3. Doing experiments in an artificial environment (aquarium, petri dish, greenhouse pot, cage, zoo, etc.) allows an experimentor to control many variables that are not of interest while (often) precisely varying those that are of interest. This control maximizes the chances of finding significant effects of the variable(s) of interest. However, conducting experiments in an artificial environment cannot give any clues about the importance of the variable or mechanism of interest in the real world. You might find a very strong effect of your mechanism in the artificial environment and extrapolate that the mechanism is important in the field, but be completely wrong. In the alternative approach of doing experiments in the field, the experimentor gives up control over many extraneous variables and gives up a measure of precision in applying experimental treatments, but gains insight into the importance of the variable or mechanism in the real world. One can mitigate the lack of control by having lots of replicates to increase the power to see an effect despite the uncontrolled variation. Because of the issue of importance in the real world, most current ecological work published in leading journals is done in the field. However, whenever possible, the strengths of the two approaches should be combined by doing complementary experiments in both venues.
4. A hypothesis is a proposed explanation ( or mechanism) for a particular phenomenon. A prediction is the outcome based on that proposed mechanism expected in a given situation.
5. Pattern: slugs eat some weeds but not others
a. Hypothesis: slugs choose to eat some weeds because they taste better (behavioral, instantaneous mechanism; not evolutionary). Other answers are certainly possible: the weeds they eat are in a moister microhabitat than the ones they don't eat, etc. The test of the hypothesis would change accordingly.b. To test this hypothesis: allow slugs to choose between a plant slugs have been eating in the wild (treatment) and a plant they have not been eating in the wild (control or vice versa) and see which one they eat more of. IF slugs prefer the taste of the treatment plant, THEN they should eat significantly more of it. If the slugs ate both plants equally or ate significantly more of the control, that would falsify the hypothesis.
Evolution (back to menu)
1. Evolution by natural selection requires 1) variation, 2) heritability, and 3) differential survival or reproduction. Variation is necessary because natural selection must have differentces to select among. Without differences there could be no differential survival/reproduction. Heritability (genetic control) is necessary because surviving parents must be able to faithfully transmit those selected characteristics to their offspring. Differential survival or reproduction is necessary to increase the proportion of individuals in the next generation that carry the selected characteristics.
2. A genetic component can be suggested qualitatively by comparing growth, survival, etc. in a common environment. If there is still significant variation, then it is likely that there is a genetic component. But because we can never be sure that one individual's environment is exactly like another's, it is a better test to compare the amount of variation among clonal copies of a genotype with the amount of variation when both genotype and environment vary. If there is significantly less variation among the clonal copies in varying environments than among non-clones, then the difference is the genetic component. A more quantitative way to assess the genetic component is to look at the slope of a regression line when offspring character values are compared with parental character values. The slope measures the relative amount of genetic control over that character.
3. Assumptions underlying natural selection by bird predation as a mechanism for the change in abundance of the black vs white speckled forms of peppered moth:
1) Birds see black moths better on lichen-covered trees and speckled moths better on soot-covered trees,
2) bird predation is the major cause of mortality in these moths,
3) color is a genetically-controlled trait in these moths,
4) there is no significant migration of moths from areas where other color forms predominate, and 5) black and speckled forms reproduce at similar rates...
There are probably more.
4. Fish and dolphin body form represents convergence because fish and mammals come from lineages that did not look similar. The dolphin body form adapted to swimming after the return to the aquatic environment. Therefore, it was the environment that caused the similarity. Fish and sharks are from very close lineages and all common ancestors share that body form. No change in body form was required to make these groups similar. The environment may reinforce the design, but it did not cause a significant change in either lineage.
5. Actual performance may not be at the theoretical optimum for many possible reasons.
1) Natural selection can only select from among the genotypes available. Perhaps the optimal genotype has not arisen or cannot arise within the group.2) Environmental changes may be faster than natural selection can keep up with. We assume that the environment has been stable when we predict theoretical optima.
3) Gene flow from other populations subject to differing selective pressures may move a population away from its theoretical optimum.
4) Tradeoffs between optimal performance in one area and optimal performance in another area can keep a population from a theoretical optimum. Typical tradeoffs are present fecundity (offspring production) vs. future fecundity, fecundity vs. survival, growth vs. reproduction, etc.
Species' Distributions (back to menu)
1. Species distributions can be limited by many things but these can be grouped into the following categories: 1) inability to disperse into suitable habitat outside the range, 2) physical or chemical factors outside the range, or 3) interactions (or lack thereof) with other species outside the range.
2. To test to see whether a species' distribution is limited by dispersal ability, one would do a transplant experiment. A transplant experiment must have a control in which the effect of transplantation is tested within the current range. One must also be careful not to allow successful transplant test individuals to colonize the new habitat in the event that the species might become an invasive pest.
3. Range limits
a. It is possible that the distributions of either or both sea anemones are still expanding but that dispersal is slow enough that the range limits expand slowly. You could test this by transplanting individuals of species A to an area north of its present range and species B to an area south of its present range and see if they can survive and reproduce. If they can, then dispersal was limiting their distributions. If they can't survive or reproduce, some other factor is limiting their distributions. Because you are introducing a non-native species, you should find some way to contain the individuals so that they can be removed from the area once the experiment is complete. This includes removal of any offspring produced.b. It is possible that anemone A cannot tolerate the cold temperatures farther north and that anemone B cannot tolerate the warm temperatures farther south. To test this, the best experiment would be to manipulate temperature within the present ranges of each species. You would have to decide whether the altered temperatures should represent averages or extremes from outside the habitats. Then artificially lower the temperature for some individuals of species A and artificially raise the temperature for some individuals of species B. In both experiments, compare the temperature manipulation group with a control group in which temperature was not altered. If either species cannot survive and reproduce in the artificial conditions or if there is a significant difference between survival or reproduction when compared to the controls, then temperature may well limit the species to its present range.
c. If some resource limited the populations, you could manipulate the resource of interest and see if that changed the outcome as compared to unmanipulated controls. For example, if you hypothesized that space to settle on a hard surface was the resource that limited the populations, you could clear some areas on hard surface, allow larvae access to those cleared surfaces as well as uncleared control surfaces, and compare the success of the larvae between the treatment and control sites. If space were a limiting factor, then the success of larvae on cleared surfaces should be much higher than the success of larvae on the control surfaces.
4. A species' niche is defined in two rather different ways. One definition describes the range of conditions and resources (temperature, moisture, light levels, food resources, etc.) that are required for the species to occupy a site. Because there are potentially many such factors, we can think of this range as an "n-dimensional hypervolume" within which the species has the capacity to maintain a population. The other definition focuses on the species' ecological role in the community, i.e., its positive and negative interactions with other species and its potential importance to the maintenance or destruction of the community.
5. The fundamental niche is essentially the "n-dimensional hypervolume" defined by all the physical and chemical factors in the environment. The realized niche is the part of the fundamental niche the species is actually able to occupy after interactions with other species (competition, predation, mutualisms) are taken into account.
Climate (back to menu)
1. The climate is warmer at the equator than at the poles because solar radiation strikes the equator perpendicularly and is spread over very little surface area. At the poles, solar radiation strickes the earth obliquely and is spread over a very large surface area. (In addition, because of the oblique angle, the radiation striking the poles has traveled through much more atmosphere and has lost a significant amount of heat on the way.)
2. If the earth rotated the opposite way, the surface winds travelling toward the equator would still travel more slowly than the land surface and fall behind, but since the rotation was in the opposite direction the winds would be from the west (westerlies). Similarly, surface winds travelling away from the equator would still travel faster than the land and get ahead of the land surface. Since the rotation was in the opposite direction, the winds would be from the east (easterlies). Therefore, from 30oN to 30oS (and from 60o to the poles), the winds would be westerly, while from 30o to 60o (both north and south) the winds would be easterly.
3. Rainy seasons occur because the 23.5o tilt of the earth on its axis causes the most intense solar radiation, and therefore the rains produced by the rising air, to move latitudinally during the year. The northernmost position of this intense radiation band is 23.5oN, essentially the same latitude as Calcutta. Therefore, during Calcutta's summer, it is very rainy. As the intense radiation band and rains move south again, Calcutta has a relatively dry winter (so, one rainy and one dry season each year). The intense radiation band and its rain moves past the equator once in the spring on its way north and again in the fall on its way south (to 23.5oS). Therefore, Entebbe has two rainy seasons and two dry seasons a year.
4. Deserts occur on the lee sides (the sides away from the prevailing winds) of mountain ranges. The Andes mountain range extends north-south along the western side of South America. At 25oS, the prevailing winds are from the east, so deserts form on the western side of the mountains as in northern Chile. At 35oS, the prevailing winds are from the west, so deserts form on the eastern side of the mountains as in Argentina.
5. Climate diagrams
a. The climate diagram shows abundant rainfall with two peaks a year in spring and fall. This suggests a latitude of 0o, the equator.b. Tropical rainforest would be the most likely biome.
6. The key features of the western Washington climate are moderate, wet winters and moderate, dry summers. The moderation in temperature is caused by our proximity to the Pacific Ocean, since water changes temperature with the seasons much less drastically than the land (high specific heat). The westerly winds bring ocean air over western Washington, air that is warmer in the winter and cooler in the summer than the land surface, and that moderates our temperatures. That ocean air also is responsible for the precipitation pattern: wet in the winter and dry in the summer. In the winter, as the warmer air comes in over the cooler land, the air cools, can't hold its moisture, and rains. In the summer, as the cooler air comes in over the warmer land, the air warms and can hold more water, and doesn't rain. As the air moves inland still further, and rises over the Cascades, the it cools again and it does drop its moisture on the mountain slopes. However, that effect is not what gives most of western Washington (except the west side of the Olympics) its winter rains.
7. The problem I see with the student's proposed research is the timing. Soil moisture is highly variable, both seasonally and from day to day. It is likely that the moss species the student is interested in is not limited by soil moisture in the winter when there is abundant rainfall. If soil moisture is limiting the moss species at all, it is much more likely to be a limiting factor during the summer drought period, or at a time when the soil is drying leading into the summer drought. I would not fund the student unless s/he altered the timing of the sampling.
8. Space is a resource for organisms that are limited by how closely they can pack their bodies. For organisms like plants, however, other resouces are more likely to limit growth before individuals are packed "shoulder to shoulder."
Lab 1: Sampling designs (back to menu)
1. Quadrat sampling: Because you have only 3 m of distance vertically, but unlimited distance horizontally, you should delimit a rectangular area 3m by some distance that incorporates a homogeneous density of the anemones, let's say 50 m. Within that area you have room for 600 of your 25 cm radius (= 50 cm diameter) circular quadrats (6 x 100). You can determine which 10 of these you are going to sample by using your random number table by reading the first single digit and then the next two digits to tell you in which of the 6 vertical rows and in which of the 100 horizontal columns your quadrat will be placed. It is probably easiest to simply discard single digit numbers that are 0 or exceed 6.
2. Mark-recapture sampling: 18 snails were marked and released. In the second sample, 5 marked snails were among the 22 snails captured.
Population estimate: 18x22/5 = 79 snails
3. Depletion sampling: To estimate the population size from these data, you first need to calculate the previous cumulative catch for each sites, then run a regression for each site and calculate X when Y=0 (or graph them and read the X intercepts from the graph). My calculations are shown below:
field y
field x
orchard y
orchard x
25
0
18
0
22
25
18
18
21
47
15
36
18
68
16
51
15
86
12
67
10
101
11
79
8
109
9
90
5
114
8
99
3
117
8
107
1
118
7
115
Running regressions on these (x,y) pairs resulted in
Field: Y = 27.96 - 0.193X Solving for X when Y=0: X = 145
Orchard: Y = 19.26 - 0.107X Solving for X when Y=0: X = 180
4. Sampling schemes for each of the following:
a. Starfish in a rocky bay several hundred meters wide - A quadrat sampling method would work well since starfish don't move very quickly. Define the area over which you want sample (whatever area you want to be able to say something about, as long as the starfish population is reasonably homogeneously distributed over the area you've chosen). Make the quadrats small enough to count the animals easily, but large enough that your quadrats typically have at least a couple of animals in each (you don't want lots of quadrats with 0 individuals in them).b. Fruit flies around your compost pile - The only choice you really have is depletion sampling since the flies are highly mobile and you can't really mark them. You have to assume that there isn't much immigration from other areas during the sampling to replace the flies you've captured.
c. Pitcher plants in a bog - Quadrat sampling would also work well here. Again, you need to check that the plants are reasonably homogeneously distributed over the area you've chosen to sample. Make the quadrats big enough to include several pitcher plants, but small enough to count easily.
d. Deer mice in an area of forest - Mark-recapture sampling is the preferred method here, but it has more assumptions than the other methods. You must assume that the marked individuals integrate themselves randomly into the population, that the marked individuals are no harder or easier to catch than the others, and that there is no birth, death, immigration, or emigration between the samples.
e. Orcas in Puget Sound - This one is a bit tricky. You can't do quadrats, you can't do depletion sampling, and traditional mark-recapture is not exactly practical. What people do is sort of a version of mark-recapture; people sight and recognize orcas as individuals, then relocate them. One real problem here is that the orcas violate a basic assumption. Orcas stay in family pods--sighted and recognized individuals don't integrate themselves randomly into the population. So, in fact, none of the methods we've talked about work well at all. Because they have home ranges and stay in pods, most population estimates for orcas are done through counts after exhaustive searching.
5. More sampling designs
a. You could estimate the population of mosquitoes at your campsite by the river in June by depletion sampling, (obviously, mark-recapture and quadrat sampling wouldn't work). You must be able to catch enough individuals in your sampling to deplete the population significantly. If mosquitoes quickly come in from other campsites to replace those you've caught, you will estimate an infinite population (just as you always suspected).b. You could estimate the population of mice by mark-recapture. Mice do not move over large distances so the field may well constitute a population. After marking and releasing the first sample, you are assuming that the marked individuals mix randomly into the population, that marked individuals are no more or less likely to be caught than other individuals in the second sample, that there is no birth, death, immigration, or emigration between samples.
c. You could estimate the percent of your "lawn" that is actually moss using a quadrat sampling method. A square quadrat of perhaps 25 cm x 25 cm would be relatively easy for estimating the percent of each quadrat that is moss. The number of quadrats you do would depend on your time and energy and the accuracy you want from your estimate. You should choose your quadrat positions randomly, i.e., using a random number table. The assumption you are making with this method is that the moss is distributed homogeneously over the area you sample.
6. Your marmot population estimate would be 15 individuals. The calculations follow:
6/N = 2/5, or N = 6 x 5/2 , and N = 15
7. Using your equation (Y = 48 - .0711X), you can estimate the population size by solving for the X intercept (the value of X when Y = 0). In this example,
0 = 48 - .0711X
X = 48/.0711
X = 675 individuals
Statistics (back to menu)
1. Because you would be comparing the means of the two treatments (dry vs. wet), the null or statistical hypothesis would be that the two means were equal.
2. If P = 0.01, it means that there is a 1% probability that the null hypothesis (that there really isn't a difference/relationship/effect) is true. If you've rejected the null hypothesis because P < 0.05, then you have a 1% chance of having made a mistake (a type I error).
3. The most general way to increase the power of a test is to increase the sample size.
4. Which statistical test?
a. Fisher's test: 3 means of a continuous variable (tidal height)b. X2 goodness of fit test (count data and only a single variable)
c. Regression with soil nitrogen on the X-axis and columbine biomass on the Y-axis (relationship between two continuous variables)
d. Paired t-test (since overall moisture among trees might differ more than moisture from one side to another of an individual tree)
e. Two-way ANOVA (two variables: light/temperature; group means of a continuous variable)
f. ANCOVA (two groups of X-Y related variables)
g. t-test (two means)
h. X2 test of independence
i. Correlation. There is no expectation of a direct causal link between these two variables.
6. Interpreting statistical tests
a. The two-way ANOVA results indicate that the mean abundance of species is lower in the summer than in the winter, and that the overall mean abundance of species 1 is not different from the overall mean abundance of species two. However, both of these results should be viewed skeptically since the interaction is significant. The interaction indicates that the two species respond differently to season: species one decreases in winter whereas species two increases in winter. Although the overall abundance is lower in summer than in winter, only species 2 actually increases. Species 1 decreases from summer to winter. Notice how you would interpret this incorrectly if you had not included the interaction in the analysis.b. The ANCOVA results indicate that the overall number of moss stems increases with light, and that stem density of species 1 is not different from stem density of species 2. However, the two species respond quite differently to light: species 1 has a much stronger positive response to light than species 2.
c. Fisher's test indicates that growth is significantly better in low salinity than in medium or high salinity, and that growth is not different between medium and high salinity.
d. Because the data are apparently paired and show a consistent pattern within pairs but a lot of scatter between pairs, the best test is probably the paired t-test which shows that there is generally more moss cover than lichen cover on logs.
Demography (back to menu)
1. Survivorship curves
Type I survivorship curves: humans and other large mammals, esp. those with parental care.
Type II curves: birds, seeds in soil, some invertebrates (Hydra)
Type III curves: plants, marine invertebrates, amphibians, fish, parasites, most insects
2. A stable age distribution means that the proportions of the individuals in each age class remains constant but the total population size could increase or decrease. A stationary age distribution means that the numbers of individuals will occupying each age class remains constant over time.
3. Cohort-based life tables follow a group of individuals from birth through death, keeping track of how many were living and the numbers of offspring they produced at each age or stage. A static life table looks at the number of individuals in each age class at a given time and records their probability of survival and numbers of offspring from age x to age x+1. Both make the assumptions that the lx and bx are constants and that the population size is at equilibrium.
4. Unita ground squirrel survivorship curves with the y-axis plotted on a log10 scale:
The curves are roughly linear, suggesting Type II survivorship. Reducing the density enhanced survivorship of all ages, but didn't change the shape of the survivorship curves.
5. Snail data
a. Calculations and interpretation of rl(x): 1.00, 0.80, 0.08, 0.00
R0 = …l(x)b(x) = 2.5(0.8)+3.0(0.08) = 2.24 offspring/ individual-generation
G = …l(x)b(x)x/…l(x)b(x) = 2.48/2.24 = 1.107 years
estimated r = ln(R0)/G = ln(2.24)/1.107 = 0.729 offspring/individual-year
This r suggests that the population is growing.b. V(x) for each age class
V0 = 2.24 expected offspring/ind, V1= 2.5 + (.1)3.0 = 2.8 expected offspring/ind, V2= 3.0 expected offspring/ind., V3= 0.0 expected offspring/ind.
6. Collinsia verna data
a. Calculations and interpretation of rl(x): 1.0, .261, .200, .113, .030, (.000)
R0 = .03(10.754) = .323 offspring/individual-generation
G = 13-14 (or 13.5) months
estimated r = -0.084 individuals/individual-month
This r suggests that the population is declining.b. V(x) calculations
stage
V(x)
expected offspringseed
0.323 seedling
1.236 overwinter
1.613 flowering
2.860 fruiting
10.754
Life History Theory (back to menu)
1. Species that are good invaders are usually small so that they go undetected, produce many offspring, produce offspring that are highly competitive, many reproduce asexually, reproduce early in their lifespan, live a long time, move rapidly over space, tolerate a wide range of climatic regimes, have few or no predators to reduce their populations. No species has all of these characteristics, however, because tradeoffs are inherent. Small species tend to have relatively short lifespans; energy constraints limit the competitiveness of offspring produced in large numbers; because climatic tolerances usually involve the expenditure of energy, wide tolerances usually imply lower reproductive rate; rapid movement also uses more energy and decreases energy available for reproduction.
2. Species that become invasive in a new habitat were probably controlled in their original habitat by predators, parasites, competitors, etc. When intentionally or unintentionally released into a new habitat, these species are released from the constraints that had been imposed.
3. Life history tradeoffs
a. Comparisons among related species indicate a tradeoff between number and size of offspring because there is a finite amount of energy that organisms have to spend on reproduction. Given that reproductive energy, it can be divided into many small offspring or into fewer larger offspring.b. Conditions that favor many small offspring are 1) relatively abundant resources (offspring won't have to compete), and 2) high offspring mortality rates that are not size dependent (weather conditions, predation--if larger offspring are just as likely to get eaten as smaller offspring). Conditions that favor fewer large offspring are 1) limited resources due to competition (larger individuals usually compete more successfully), and 2) low offspring mortality rates from factors that are not size dependent.
c. Organisms that spend a large portion of their energy in reproduction have less stored energy for survival. There is usually a reproduction-survival tradeoff. As the probability for adult survival increases, the energy devoted to reproduction decreases so that the individual can reproduce again the next year.
d. Semelparity usually evolves where there is a low chance of survival to reproduce again. In habitats that are extremely severe in the non-reproductive season (e.g., deserts), or where reproduction takes an enormous amount of energy (e.g., salmon--they put all their energy into one large reproductive event and then die). Iteroparity evolves when there is a high chance that the adults will survive to reproduce again--in relatively benign habitats.
4. Life history theory suggests that senescence, aging and becoming non-functional, arises because of a lack of selection pressure after most or all of reproduction is finished. When the residual reproductive value falls to zero, then there is no possible selection pressure left. Without selection, there is no way to increase fitness over time for that age group.
Population Growth (back to menu)
1. Exponential growth:
2. Exponential growth calculations
a. A population that doubles in 6.9 years under exponential growth would have an r of approximately 0.1. (Nt/N0 = 2; ln 2 = rt; .6931/6.9 = r)b. With an r of 0.08, the world population would double in 8.66 years. (.6931/0.08 = t)
c. Given the two populations estimates (N0= 21, Nt=125) and the time elapsed (t = 40 yrs), the estimate of r is 0.0446 (r = ln(Nt/N0)/t).
3. Doing the estimate of r statistically involves running a regression on the log of the population estimates over time. The slope gives you r. Since the regression shown below gives a slope of 0.0444, the two methods (statistical and analytical) give amazingly consistent estimates of r. There does seem to be an intriguing pattern to these data in that the population increases one year, stays the same for a year and then increases again. One might investigate whether these birds are biennial breeders or what other factors might be causing this interesting pattern. (The moral of the story here is to look at your data not only to answer your question(s), but to see any new questions that they pose.)
4. Logistic growth:
4. Rate of population growth (assuming logistic growth over time)
5. Predation, weather catastrophes, or other density-independent factors might keep a population low relative to its carrying capacity.