代做EART11200 Statistics for Natural Scientists Assessment调试R程序

Statistics for Natural Scientists Assessment

Academic Year 2024/25, Semester 1

Instructions: This is the assessment for EART11200 Natural Scientists’ Toolkit: Statistics for Natural Scientists. The assessment includes the following files:

SFNS Assessment S1 2024.pdf: This document presents the questions that you will need to answer in this assessment.

SFNS Assessment S1 2024 answer sheet.docx: This is the document on which you will answer the assessment questions. You will need to consult “SFNS Assessment S1 2024.pdf” for a full explanation of the questions to be answered.

After you have answered the questions on “SFNS Assessment S1 2024 answer sheet.docx,” please save the document as a PDF. Name the file with your student number followed by “_stats_assessment.pdf” (for example, 123456789_stats_assessment.pdf) and submit the PDF via Blackboard by 9 January 2025 at 9:00 am.

The assessment is divided into three sections, each with several parts. In section 1, you will choose statistical tests to use, but you will not need to conduct the analyses. In section 2, you will interpret analyses where R output has been provided for you. In question 2.2.3 you will also provide a figure to illustrate your conclusion. All the information you need to answer the questions in section 2 can be found in the R output or in the questions themselves. In section 3, you will analyse datasets that have been provided for you, either in the text of the question (as in question 3.1) or in separate CSV files (questions 3.2 to 3.4).

You should attempt to answer all parts of all questions. The marks for each question are clearly indicated. You may use the unit handbook, your notes or completed practicals, starter code for practicals, code you have written during the semester, and the answer keys to completed practicals while completing this assessment. You may also use online resources or external handbooks/textbooks (but I hope you will not need to!). However, you must not collaborate with others while completing this assessment. Collaboration on this assessment is detectable, so please do not do it! If you have questions about the assessment, you can post them to the discussion board so I can answer publicly. This ensures that everyone has the same information about the assessment. You can find the discussion board here:

https://online.manchester.ac.uk/ultra/courses/_81724_1/cl/outline

If you have not done so already, I recommend that you subscribe to the discussion board so you get a message anytime I post a new answer.

If you have a DASS plan that specifies an extension on coursework assessments, then you can apply that extension to this assessment. In practice, I recommend that you do not use your extension even if you are entitled to one. The assessment is designed so that everyone can complete it before the deadline. If you apply an extension to the standard deadline, then this assessment will drag into the exam period, and it may not be in your interest to allow that to happen. Please note that the discussion board will close at the standard submission deadline. This is important because it ensures that no new information about the assessment becomes available after some students have been required to submit. So, if you have a DASS extension and intend to use it, please make sure that you have asked any questions you need to ask before the standard submission deadline.

Section 1 (4 marks each)

For each question in section 1, answer i) what is the predictor and is it numerical or categorical (if there is more than one predictor, answer this for all the predictors); ii) what is the response and is it numerical or categorical, and iii) what test would you use to

answer the question?

1.1 Benthic macrophytes are plants that grow on the bottoms of water bodies like lakes, ponds, and streams. Your research team has observed one sampling site in each of 100 different rivers in the UK. (So, in all, you observed 100 sites.) Each sampling site   had a mean annual depth of 20 cm. Your team measured the mean annual turbidity in NTUs and the mean annual flow rate in ms-1  at each site, and recorded whether there were macrophytes growing at each site. You did not count the macrophytes, you just recorded whether they were present or absent. You want to understand how the probability that macrophytes grow at a particular site depends on the mean annual turbidity and mean annual flow rate at that site. What test would you use to  answer this question?

1.2 You are conducting a study to assess whether it is possible to learn statistics by osmosis. You enrol 100 students as participants. You assign 50 students randomly to a treatment group, and you assign the other 50 to a control group. You supply each participant with a handbook on statistical methods. You instruct each student to study as they ordinarily would. However, you instruct students in the treatment group to place their handbook under their pillow when they goto bedon the night before their exam. You instruct students in the control group to leave their handbook on their desk when they goto bed. You obtain the marks for the participants from the unit coordinator. The marks are anonymisedin such away that you cannot match them to particular students, but you can match them to either the treatment or control group. Your goal is to test the hypothesis that students in the treatment group earned higher marks. What test would you use to answer this question?

1.3 Following on your study about learning by osmosis, you are also interested in whether student’s breakfast choices affect their exam performance. You recruit 120  students who are enrolled in the second year Animal Behaviour unit to participate in a study. You randomly assign each student to eat one of three breakfasts on the day of the exam: oatmeal, cornflakes, or nori and rice. You conjecture that familiarity with the breakfast may also be important, so you ask each student whether the breakfast they have been assigned is something they commonly eat. Their options when answering this question are simply “yes” or “no.” There are at least 10 students in both the “yes” and “no” groups for each breakfast type. After the exam, you obtain the anonymised marks for each of the six groups (ie, oatmeal-yes, oatmeal-no, cornflakes-yes, etc) from the unit coordinator. You want to know whether breakfast choice affects exam performance, whether having a familiar breakfast affects exam performance, and whether the effect of familiarity is different for the different breakfast types. What test would you use to answer this question?

1.4 You work for a company that sells three flavours of breakfast cereal: Coco Sugar Bombs, Atomic Strawberry Loops, and Marshmallow Puffies. Using data collected when customers scan their loyalty cards at grocery store checkouts, your company has assembled a list of customers who bought exactly one of these cereals and bought exactly one of the following brands of candy on the same day: Rouse’s Peanut Butter Balls, Life Preservers Hard Candy, or Twisters Cranberry Liquorice. Your company wants to design a targeted marketing campaign, and to do this they want to know whether the candy that people buy predicts which cereal they will choose. What test would you use to answer this question?

1.5 It is widely believed that the biodiversity of ecosystems is higher closer to the equator, but this has rarely been studied for aquatic microorganisms. Your ship-based research team has sampled seawater from the surface of the Atlantic Ocean along a north-south transect starting at (60.00。, -45.60。) (approximately 20 km southwest of Nanortalik, Greenland) and ending at (1.50。, -45.60。) (approximately  20 km northeast of Belém, Brazil). You collected one sample every 10 km along the transect, for a total of 650 samples. You used shotgun sequencing to estimate the microbial community composition of each sample, and you computed the Shannon diversity index for each community. The Shannon diversities in your samples ranged from 2.1 to 5.9. You want to know if the Shannon diversity of aquatic microbiota increases as you approach the equator. What test would you use to answer this question?

Section 2

Each question in this section is followed by a block of R code and output. The output provided is sufficient to answer the questions. You may not need to use all the output.

Question 2.1 (16 marks)

You are studying winter wheat yields in experimental plots using three different brands of fertiliser: brands A, B, and C. You want to understand the performance of each fertiliser in each of two conditions. In the “constant” condition, winter wheat was grown in the experimental plot for five consecutive years before your study. In the “fallowed” condition, winter wheat was grown in the experimental plot for four consecutive years, but a cover crop of red clover was grown in the plot in the year before your study. You plant winter wheat in a total of 72 experimental plots, 36 of which were constant and 36 of which were fallowed. Each plot has an area of 1 hectare. You assign 12 constant and 12 fallowed plots to be treated with each fertiliser brand according to the manufacturers’ instructions. Six plots are destroyed by flooding in the spring, so you end up with 66 plots in total. At the end of the growing season, you record the harvest from each plot in metric tons. Thus, your data includes the fertiliser, the condition, and the yield for each plot. Your colleague has conducted the analyses shown below. Use these analyses to answer the following questions:

2.1.1    Controlling for the plot condition, is there evidence that the fertiliser brand affects the crop yield? If so, which brand(s) provide higher yields than which others? Report your results clearly and concisely.

2.1.2    Controlling for the fertiliser brand, is their evidence that the plot condition affects the crop yield? If so, in what way? Report your result clearly and concisely.

2.1.3     Is there evidence that the performance of the fertiliser brands depends on the condition of the field being fertilised? Report your result clearly and concisely.

2.1.4    Fertiliser brand A is running an advertising campaign to take market share from brand C. The company that produces brand A claims that constantly cropped fields fertilised with their brand yield as much winter wheat as recently fallowed fields fertilised with brand C. Does your study provide evidence to support or refute this claim? If so, what is that evidence?

model.y1=aov(yeild~condition+fertiliser+condition*fertiliser,data) summary(y1) Df Sum Sq Mean Sq F value Pr(>F) condition 1 59.39 59.39 65.267 3.6e-11 *** fertiliser 2 9.86 4.93 5.417 0.00688 ** condition:fertiliser 2 1.62 0.81 0.888 0.41680 Residuals 60 54.60 0.91 Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 TukeyHSD(y1) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = yeild ~ condition * fertiliser, data = data) $condition diff lwr upr p adj fallowed-constant 1.897237 1.427483 2.366991 0 $fertiliser diff lwr upr p adj B-A -0.9112102 -1.6031428 -0.219277638 0.0067901 C-A -0.7009556 -1.4003533 -0.001557787 0.0493741 C-B 0.2102547 -0.4734082 0.893917534 0.7413272 $`condition:fertiliser` diff lwr upr p adj fallowed:A-constant:A 1.50219676 0.275210739 2.72918278 0.0080068 constant:B-constant:A -1.11891362 -2.291117787 0.05329055 0.0695691 fallowed:B-constant:A 0.81928222 -0.378133528 2.01669796 0.3466859 constant:C-constant:A -1.09702419 -2.324010207 0.12996183 0.1053138 fallowed:C-constant:A 1.18146225 0.009258084 2.35366642 0.0471388 constant:B-fallowed:A -2.62111038 -3.823505003 -1.41871575 0.0000004 fallowed:B-fallowed:A -0.68291454 -1.909900560 0.54407148 0.5769400 constant:C-fallowed:A -2.59922095 -3.855081176 -1.34336072 0.0000013 fallowed:C-fallowed:A -0.32073451 -1.523129132 0.88166012 0.9690044 fallowed:B-constant:B 1.93819583 0.765991665 3.11040000 0.0001211 constant:C-constant:B 0.02188943 -1.180505198 1.22428406 0.9999999 fallowed:C-constant:B 2.30037587 1.153937576 3.44681416 0.0000026 constant:C-fallowed:B -1.91630641 -3.143292425 -0.68932039 0.0003138 fallowed:C-fallowed:B 0.36218004 -0.810024134 1.53438421 0.9425841 fallowed:C-constant:C 2.27848644 1.076091814 3.48088107 0.0000089 model.y2=aov(yeild~condition+fertiliser,data) summary(model.y2) Df Sum Sq Mean Sq F value Pr(>F) condition 1 59.39 59.39 65.503 2.73e-11 *** fertiliser 2 9.86 4.93 5.436 0.00668 ** Residuals 62 56.22 0.91 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 TukeyHSD(model.y2) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = yeild ~ condition + fertiliser, data = data) $condition diff lwr upr p adj fallowed-constant 1.897237 1.428643 2.365832 0 $fertiliser diff lwr upr p adj B-A -0.9112102 -1.6013293 -0.221091149 0.0065961 C-A -0.7009556 -1.3985202 -0.003390864 0.0486406 C-B 0.2102547 -0.4716164 0.892125697 0.7404923 model.y3=aov(yeild~fertiliser+condition,data) summary(model.y3) Df Sum Sq Mean Sq F value Pr(>F) fertiliser 2 9.17 4.58 5.056 0.00924 ** condition 1 60.08 60.08 66.263 2.26e-11 *** Residuals 62 56.22 0.91 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 TukeyHSD(model.y3) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = yeild ~ fertiliser + condition, data = data) $fertiliser diff lwr upr p adj B-A -0.9072822 -1.5974012 -0.2171631 0.0068613 C-A -0.5695452 -1.2671099 0.1280195 0.1306677 C-B 0.3377370 -0.3441341 1.0196080 0.4639370 $condition diff lwr upr p adj fallowed-constant 1.904262 1.435667 2.372856 0 model.y4=aov(yeild~fertiliser,data) summary(model.y4) Df Sum Sq Mean Sq F value Pr(>F) fertiliser 2 9.17 4.585 2.484 0.0916 . Residuals 63 116.30 1.846 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 TukeyHSD(model.y4) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = yeild ~ fertiliser, data = data) $fertiliser diff lwr upr p adj B-A -0.9072822 -1.8916015 0.07703718 0.0768128 C-A -0.5695452 -1.5644843 0.42539390 0.3605350 C-B 0.3377370 -0.6348182 1.31029218 0.6837249 model.y5=aov(yeild~condition,data) summary(model.y5) Df Sum Sq Mean Sq F value Pr(>F) condition 1 59.39 59.39 57.53 1.74e-10 *** Residuals 64 66.07 1.03 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 TukeyHSD(model.y5) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = yeild ~ condition, data = data) $condition diff lwr upr p adj fallowed-constant 1.897237 1.397525 2.396949 0

Question 2.2 (12 marks)

You are studying blood lead levels in children in a small US city. The city has two elementary schools: Dana School in the relatively affluent part of the city and Park Street School in the less affluent part of the city. There is no bussing programme in the city, so children go to school in the areas where they live. The city has done a voluntary screening for blood lead levels among students at each school and you have obtained the anonymised data (Dana, 36 students; Park Street; 35 students). For each child, you have two pieces of information: the school they attend (either Dana or Park Street) and their blood lead level (in µg/dL). Your colleague has performed the analyses below. Use these analyses to do the following:

2.2.1    Test the hypothesis that children at Park Street School have higher blood lead

levels than children at Dana School. Report your results clearly and concisely.

2.2.2    Provide a figure to illustrate your results.

head(lead.data) school blood.lead.level 1 Dana 2.60 2 Dana 2.04 3 Park Street 6.66 4 Park Street 8.60 5 Park Street 4.91 6 Park Street 5.75 bll.dana=lead.data$blood.lead.level[which(lead.data$school=="Dana")] bll.park=lead.data$blood.lead.level[which(lead.data$school=="Park Street")] t.test(bll.park,bll.dana) Welch Two Sample t-test data: bll.park and bll.dana t = 2.21, df = 53.955, p-value = 0.03137 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.1314382 2.7017047 sample estimates: mean of x mean of y 5.346571 3.930000 t.test(bll.park,bll.dana,alternative="less") Welch Two Sample t-test data: bll.park and bll.dana t = 2.21, df = 53.955, p-value = 0.9843 alternative hypothesis: true difference in means is less than 0 95 percent confidence interval: -Inf 2.489326 sample estimates: mean of x mean of y 5.346571 3.930000 t.test(bll.park,bll.dana,alternative="greater") Welch Two Sample t-test data: bll.park and bll.dana t = 2.21, df = 53.955, p-value = 0.01568 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 0.3438165 Inf sample estimates: mean of x mean of y 5.346571 3.930000 #compute standard errors sd(bll.dana)/sqrt(length(bll.dana)) [1] 0.3161369 sd(bll.park)/sqrt(length(bll.park)) [1] 0.5576077

Section 3

In this section, data is provided in each question or datasets are provided separately. Analyse the datasets to answer each question.

Question 3.1 (4 marks)

It is commonly believed that the police are more likely to issue tickets to drivers in red cars than to drivers in cars of other colours. Often, this is attributed tobias on the part of the police. You want to test an alternative explanation: perhaps drivers in cars of some colours are more likely to commit traffic violations. To test this idea, you obtain a Doppler radar unit and setup a monitoring experiment in a school zone on a small two-lane road in South Manchester. You monitor traffic on the road for 4 hours. For each car that passes, you record the colour (red, white, black, or blue – other colours are rare or ambiguous so you do not record them) and whether the car was exceeding the 20 mph speed limit (yes or no).

You also record the registration number on each car’s number plate. If you observe the same car more than once, you only count the first observation. This ensures that your study  does not suffer from pseudoreplication. Counting only the first observation for each car, you observe a total 285 cars. Of these, 48 were red, 143 were white, 60 were black, and 34 were  blue. In all, 91 cars were exceeding the speed limit. Of these, 24 were red, 37 were white, 20 were black, and 10 were blue.

3.1.1    Does your study provide evidence that car colour is non-randomly associated

with speeding at the study site? Report your result clearly and concisely.

3.1.2    You show your results to a friend and they notice that the speeding rate is

lowest among white cars. They sum up the red, blue, and black cars that were obeying the speed limit (88 cars) and those that were exceeding the speed limit (54 cars). They conduct a test comparing the numbers of white cars that were obeying or exceeding the speed limit to the numbers of all other cars combined that were obeying or exceeding the speed limit, and they obtain ap-value of 0.0381. They argue that this is evidence that the drivers of white cars are less likely than the drivers of other cars to exceed the limit. Is their conclusion valid? Why or why not?

Question 3.2 (20 marks)

There are nearly 300 moons orbiting planets or dwarf planets in the Solar System. The file “moon_size.csv” contains the following data on those moons:

name: the name of the moon

parent: the name of the planet or dwarf planet around which the moon orbits log.radius: the log of the mean radius (in km) of the moon

log.parent.radius: the log of the radius (in km) of the planet or dwarf planet around which the moon orbits

You want to know whether the moons around larger planets tend to be larger than the moons around smaller planets. You recognise that the planets and dwarf planets in the Solar System differ in many ways other than their radii (eg, density, distance from the sun), and that some of these differences may affect the sizes of the moons they collect.

3.2.1    Conduct an analysis to answer your question of interest. Report your

results clearly and concisely. (Note: logged radii are unitless.)

3.2.2    Provide a figure to illustrate your result.

3.2.3    Is there evidence from your data that moon sizes differ among planets for

reasons other than the size of the planet? If so, what proportion of the variability in moon size that is not explained by the size of the planet is explained by some other (unknown) attributes of the planet?

Question 3.3 (8 marks)

Leucopsar fictitious is a starling species native to Indonesia. It is critically endangered in the wild, but is maintained in captivity by aviculturalists.

Like many birds, juvenile L. fictitious learn their behaviours from their parents. The set of behaviours birds need in captivity is different from the set they need to survive in the wild.

If adult birds stop using some behaviours when they are brought into captivity, then juveniles may not learn those behaviours. If these behaviours are not available to birds that are released from captivity into the wild, then this may limit the success of reintroductions from captive populations as a conservation tool. If behaviours are passed from parents to offspring, then each generation in captivity provides a new risk for the loss of behaviours, and birds that have been maintained in captivity for more generations may be less valuable to conservation. (See Tanimoto et al (2017) for a similar concern in the Hawai’ian crow, Corvus hawaiiensis.)

The pedigrees of captive L. fictitious individuals have been carefully tracked since the birds were brought into captivity, so for any individual we can count the number of generations since its most recent wild ancestor. Your team is doing a study to understand whether the number of generations that birds have been in captivity affects their success when they are reintroduced to the wild. You have obtained 70 breeding pairs of L. fictitious and released them into the wild at different sites in their native range. Pairs are matched for generations in captivity – that is, in each pair, the male and female were maintained in captivity for the same number of generations. You monitor each pair after release, and record whether both birds in the pair are still alive one year after the release date. (If one bird in a pair dies then  the other usually disperses, and you cannot track birds that have dispersed. So, in general, you do not know if both birds have died, you only know whether at least one has died.) If both birds are still alive, you record whether the pair has successfully reproduced (ie, whether they are raising at least one juvenile). Juvenile L. fictitious remain in their parents’ nest for a year, so if the parents reproduced successfully since release, you will certainly observe the juvenile on the monitoring date.

Your data is stored in the file “L_fictitious.csv.” The columns in the dataset are:

ID: a unique identifier for each breeding pair

generations: the number of generations that the birds in the pair were in captivity survived: an indicator with value 1 if both members of the pair were alive and 0 if either member of the pair had died one year after the release date

bred: an indicator with value 1 if the pair was raising at least one juvenile one year after the release date and 0 if they were not Use this data to answer the following questions:

3.3.1    Does the probability that a breeding pair survived after release into the wild

depend on the number of generations they were in captivity? If so, how? Report your results clearly and concisely.

3.3.2    A conservation organisation you work with has obtained a pair of birds that

have been in captivity for 5 generations. They plan to release these birds into the wild, and they have asked you to predict the probability that the birds will survive for at least one year after reintroduction. What is your prediction?

3.3.3    If a breeding pair survived for at least one year, does the probability that the

pair bred successfully in the wild depend on the number of generations for which the birds had been in captivity? If so, how? Report your result clearly and concisely.

Question 3.4 (20 marks)

Several widely used flame retardants are known to persist in the environment and to bioaccumulate in animals. One class of flame retardants, polybrominated diphenyl ethers (PBDEs), has been shown to reduce eggshell thickness in at least some bird species (Guigeuno and Fernie 2017) . Similar reductions in eggshell thickness caused by the bioaccumulation of DDT led to the near-extinction of some raptor species before DDT was banned by most countries in the 1970s. For this reason, understanding the effects of PBDEs on eggshell thickness may be important for conservation.

Your research team is studying the effect of bioaccumulated PBDEs on eggshell thickness in two populations of house sparrows (Passer domesticus). You have sampled 50 nests in each of two house sparrow populations: an urban population in Brooklyn, NY, USA and a rural population in Castleton, VT, USA. You have taken a blood sample from the female in each nest and assessed the PBDE concentration in the female’s blood. You have randomly selected one egg from each nest and measured the thickness of the shell using terahertz reflectance spectroscopy (Khaliduzzaman et al. 2020) . The file “eggshells.csv” contains the data your team collected. The columns in the data set are:

ID: a unique identifier for each nest

population: the population of each nest (either “NY” or “VT”)

PBDE: the concentration of PBDE in the blood of the female in each nest (in ng/g) thickness: the thickness of each shell (in μm)

There is at least some reason to believe that eggshell thickness in the Brooklyn and Castleton populations may differ independent of any effects of PDBEs. The urban (Brooklyn) site is likely to have higher concentrations of industrial chemicals and the rural (Castleton) site is likely to have higher concentrations of agricultural chemicals, and either or both of these may affect eggshell thickness. Therefore, your team wants to study the relationship between PBDEs and eggshell thickness while controlling for population.

Use the data in “eggshell.csv” to answer the following questions:

3.4.1    Controlling for population, is there a relationship between the concentration of

PBDEs in a female house sparrow’s blood and the thickness of the shells of the eggs she lays? If so, what that relationship? Report your results clearly and concisely.

3.4.2    Is there a difference in eggshell thickness in the two study populations that

cannot be attributed to the concentration of PBDEs in the mothers’ blood? Report your results clearly and concisely.

3.4.3    Does the effect of PDBE concentration in the mothers’ blood affect eggshell

thickness differently in the two populations? Report your results clearly and concisely.

3.4.4    Provide a figure to illustrate your results.

3.4.5    You sample a female house sparrow and find she has a PBDE concentration of

4.6 ng/g in her blood. How thick would you expect her eggshells to be if she comes from the Brooklyn population? How thick would you expect her eggshells to be if she comes from the Castleton population?

Notes

All of the data we used in practicals this semester was real, but most of the data in this assessment is made up. The exception is the moon data in question 3.2, which is real.

References

Guigeuno MF, Fernie KJ, 2017. Birds and flame retardants: A review of the toxic effects on birds of historical and novel flame retardants. Environmental Research 154:398-424. doi:

10.1016/j.envres.2016.12.033.

Khaliduzzaman A, Konagaya K, Suzuki T, Kashimori A, Kondo N, et al., 2020. A

nondestructive eggshell thickness measurement technique using terahertz waves. Scientific Reports 10:1052. doi: 10.1038/s41598-020-57774-5.

Tanimoto AM, Hart PJ, Pack AA, Switzer R, Banko PC, et al., 2017. Changes in vocal repertoire of the hawaiian crow, corvus hawaiiensis, from past wild to current captive   populations. Animal Behaviour 123:427-432. doi: 10.1016/j.anbehav.2016.11.017.