Isotopes to Quantify Food Webs

Question 1

What kind of information did early stable isotope studies provide?

Answer 1

descriptive and qualitative

ex. from the graph we always see of uplands v. plankton v. salt marsh plants, we can see that C4 plants and plankton support more production in the salt marsh than the uplands C3 plants, but we can’t say by how much

ex. the martens shifting their diet to salmon - we can make broad claims about seasonal diet variations but no quantitative measurements

Question 2

Why do the organisms that make up the marten diet vary in their isotopes? Ex. why is the salmon so different from the deer mice, voles, squirrels and berries?

Answer 2

trophic position? dietary source of salmon and p.p. in marine ecosystems different than terrestrial?

Question 3

Interpret the graph with the marten and its diet

Answer 3

the first graph depicts the martens dietary sources in the fall and summer

summer - when the marten diet consists mostly of terrestrial sources (deer mice, vole, squirrels, berries) - this is shown because the marten’s isotopic signatures are closer to the terrestrial diet sources’

fall - when salmon are spawning, there is more variation in signatures between dietary sources and the marten’s more closely matches salmon’s (marine) - so the martens are probably ingesting more marine dietary sources than terrestrial

Question 4

what are 3 useful food web metrics?

Answer 4

1. sources of production
2. trophic positions (dNanimal v. dNdiet)
3. changes in entire food web structure (before and after a disturbance such as salmon spawning)

Question 5

How is looking at the sources of production useful for quantifying food webs?

Answer 5

because stable isotopes vary among primary producers, there is variation between dietary sources (ex. marine v. terrestrial C) and measuring the difference between them can tell us how much the organism derived from dietary sources

Question 6

How can we quantify the sources of production for a food web? why?

Answer 6

fractionation between primary producers and secondary consumers is responsible for creating the variability between sources of production and different trophic levels

ex. it explains why C3 and C4 plants are different, or why N-fixers v. nitrate users are different, or phytoplankton in ocean gyres v. coastal zones are different

it creates the diversity in signatures

Question 7

How do we quantify the sources of production in a food web?

Answer 7

by calculating the % carbon (or nitrogen or energy) that an organism derived from each production source

Question 8

T or F: the isotopic signatures of consumers reflect a MIXTURE of the isotopic signatures of their dietary sources

Answer 8

true

Question 9

What are mixing models?

Answer 9

models used to determine proportions of carbon (or N) an organism derived from different sources of production

ie., how we quantify sources of production

Question 10

What are the 4 families of mixing models?

Answer 10

geometric
linear
IsoSource
Bayesian

Question 11

Describe the geometric mixing model

Answer 11

uses Euclidean distance measurements on isotopic bi-plots (ex. martens and their diet sources) to measure the distance between consumers and their dietary sources

Question 12

what are the pros and cons of the geometric mixing model?

Answer 12

PROS:
easy
measures euclidean distances (basically puts numbers on an isotopic biplot) = intuitive results
could be good for comparing seasonal diets

CONS:
susceptible to bias - you can put whatever you want on your plot, even if the animal isn’t eating it, you can calculate an ED which can lead to:
- over-estimating the contribution of abundant prey
- underestimating the proportion of rare prey

limited application
- all you can really say is that there is a difference between the sources

only provide point estimate

Question 13

What is the Euclidean distance formula?

Answer 13

ED2 = (Xa - Xb)2 + (Ya - Yb)2

where X and Y are coordinates on the isotopic bi-plot

Question 14

describe linear mixing models

Answer 14

uses simple equations (algebra) to calculate the proportion of the isotope the animal is getting from source A and B including fractionation of the sources in its diet

2 sources + 1 isotope

dXanimal = Pa * dXa + Pb * dXb

where Pa + Pb = 1 (because it’s a proportion/% = 100%)
and P = fraction of the source

Question 15

what are the pros and cons of the linear mixing model?

Answer 15

PROS:
more robust than geometric - gives more detailed information

CONS:
most food webs have more than 2 dietary sources and we don’t have enough isotopes to work with to be able to find a unique solution

only provide point estimate

Question 16

In a salt marsh food web,

d13C for a C4 plant = -10 ppt
d13C for a C3 plant = -30 ppt
d13C for the crab = -15 ppt

calculate the contributions of each source to the crab (PC3 and PC4), assuming big delta (trophic) = 0 ppt cause there is no fractionation between the animals and their diets

Answer 16

use the linear mixing model formula

dXcrab = PC4 * dCC4 + PC3 * dCC3

and Pa + Pb = 1

Question 17

If the previous question about calculating the contributions for each dietary source for the crab in the salt marshes was looking at N isotope instead of C, what would we have to consider in the equation?

Answer 17

looking at N, the trophic fractionation (fractionation between the crab and its diet) would not equal 0, like it does for C, instead it would be 3.5 ppt

Question 18

If you had 3 dietary sources in the linear mixing models, how many isotopes would you need?

Answer 18

2 because it only works if you have 1 less isotope than the number of dietary sources

it is impossible to determine the contribution of 3 things to an animal if you only have 1 thing to consider - you can’t substitute to solve (infinite solutions) iPa + Pb + Pc = 1

Question 19

Describe IsoSource mixing models

Answer 19

can handle multiple dietary sources in a food web without needing to consider more than 2 isotopes but it creates a range for which each dietary source may be contributing to the animal

it uses principles of mass balance to consider all possible combinations that created the animal’s isotopes

Question 20

Pros and cons of IsoSource

Answer 20

PROS:
free and available online
doesn’t have restrictions for number of isotopes v. number of dietary sources

CONS:
only computes a range for the % contribution of each dietary source

Question 21

Describe Bayesian mixing models and how they overcome the challenges of the other models

Answer 21

uses prior information to narrow down possible solutions and accounts for sources of error, then considers all possible combinations that led to the animal’s isotopic value, and provides a probability of distributions of solutions (not just a range, but how likely and how confident) that you can calculate confidence intervals for

the other models provide only point estimates or ranges, which you cannot do statistical analyses on cause you can’t calculate means, SE or SD (variability)

Question 22

What are examples of prior information which can inform a Bayesian model?

Answer 22

gut content analysis
natural history
isotopic turnover
fractionation
food quality

Question 23

Pros and cons of Bayesian models

Answer 23

PROS:
- free packages on R
- provides probability distributions for your range of contribution %
- can do statistical analyses on these data
- uses prior information about the organism to determine which solutions are most likely and calculate CIs to determine how confident

CONS:
- not always necessary / too fancy for some questions

Question 24

What are some other potential biases in quantifying sources of production for a food web?

Answer 24

accurate measures of trophic fractionation (especially when looking at N where it contributes ~3.5 ppt every trophic level)

isotopic overlap between different food sources

turnover differences between consumer and diet (especially in herbivores) - ex. fish eat zooplankton, zooplankton have way shorter lifespans and are responding to changes in the environment much faster than fish so a samples of a fish will not represent the zooplankton it ate that day = the more different the organisms are, the more variation there is

accounting for variation in time and space

Question 25

Define trophic position

Answer 25

the distance between an animal and the base of the food web - ie., how many trophic steps are between the animal and the base? (how many 3.5 ppt fractionation steps)

Question 26

What 3 things do you need to know to calculate trophic position? Which isotope is always considered?

Answer 26

only considering Nitrogen isotope

1. the isotopic signature of the BASE of the food web (trophic position of the base = 0) - ie., what are the primary producers doing?
2. the isotopic signature of the animal (usually it’s 3.5 ppt, unless lit suggests otherwise)
3. trophic fractionation (big delta)

Question 27

What is the trophic position equation for an animal feeding on one diet source?

Answer 27

TP = TPbase + [(d15Nanimal - d15Nbase) / big delta trophic]

in words: the trophic position of an animal is = to the trophic position of the base + the isotopic difference between the animal and the base, divided by the trophic fractionation

TP = the number of steps that have occurred

almost always, the TPbase = 0 because working from primary producers

Question 28

If the base of the food web is a single source, and you’re calculating the lemur TP where

dNlemur = 7 ppt
dNlegume = 0 ppt
TPbase = TPlegume = 0ppt
big delta trophic = 3.5 ppt

What is the TP of the lemur? What does the TP suggest?

Answer 28

TP = TPbase + [(d15Nanimal - d15Nbase) / big delta trophic]

TP = 0 + [(7 - 0) / 3.5]
TP = 7/3.5 = 2

if the lemur was only a herbivore, then the trophic level should be closer to 1, but obviously it is consuming something else - which is true, lemurs are omnivores

Question 29

How can we adapt the TP equation to examine an organism that is consuming more than 1 diet source? for example, a salt marsh crab consumes both a C3 and C4 plant?

Answer 29

TP = TPbase + [(d15Nanimal - d15Nbase) / Dtrophic]

we need to calculate what the d15N for the base of the food web is when there are 2 diet sources

d15Nbase = Psource1 * d15Nsource1 + Psource2 * d15Nsource2

where Psource1 + Psource2 = 1

you can also use Psources from the d13C calculations if you’ve already done them from the linear model

Question 30

A salt marsh crab consumes both a C3 and C4 plant. Use the following to calculate the TPcrab:

PC4 = 0.75
d15NC4 = 5 ppt
PC3 = 0.25
d15NC3 = 0 ppt
d15Ncrab = 8 ppt

assume Dtrophic = 3.5 ppt and TPbase = 0

And what information can we glean from these data?

Answer 30

from this data, we can guess that the C3 plant is an N-fixer (d15NC3 = 0 ppt) and C4 plant is a nitate user (d15NC4 = 5 ppt)

and the crab gets 75% of its N from the C4 plant and 25% of its N from the C3 plant and fractionates at 3.5 ppt

TPcrab = 0 + [(8 - d15base) / 3.5)] –> need to solve for d15Nbase first

d15Nbase = PC4 * d15NC4 + PC3 * d15NC3, where PC4 + PC3 = 1

d15Nbase = 0.755 + 0.250.25 = 3.75 –> sub this back into the TP equation

TPcrab = 0 + [(8 - 3.75) / 3.5] = 1.21 –> the crab is not quite at TP = 1, we have assumed with the Psource1 + Psource 2 = 1 equation that we have accounted for all the dietary sources, so:
- it’s possible that the 3.5 ppt fractionation is off, but more likely that:
– the crab is a herbivore so it’s starved for protein which inflates the d15N

Question 31

Why might a herbivore like the salt marsh crab have an inflated TP?

Answer 31

a herbivore’s diet is not high in protein, so a lack of protein can cause the TP to be inflated