Food chain length

BIO605

Define food chain length

Trophic position

Trophic position (TP) is the vertical position in a food web

  • Basal species have a value of one (e.g., plants)
  • Primary consumers have a value of two (e.g., hevivores)

Trophic position

Trophic position (TP) is the vertical position in a food web

  • Predators have continuous values (1 < TP)
  • How would you define them?

Fractional trophic position

\[ TP_i = 1 + \sum_{i}^{S}{F_{j}TP_{j}} \] Consumer

  • \(TP_{i}\) Trophic position of species \(i\)

Prey

  • \(F_{j}\) Fraction of species j in the diet
  • \(TP_{j}\) Trophic position of species j

Pauly and Palomales 2005, Bulletin of Marine Science

Fractional trophic position

\[ TP_i = 1 + \sum_{i}^{S}{F_{j}TP_{j}} \]

Food chain length

Food chian length is the TP of the apex predator

Why food chain length is important

Food chain length is a summary measure of a food web

Why is it important?

Why food chain length is important

Food chain length influences

  • Energy flows\(^1\)
  • Top down control\(^2\)
  • Primary production\(^2\)
  • Atomospheric carbon exchange\(^2\)
  • Contaminant concentrations in top predators\(^3\)

\(^1\)Wang et al. 2018 Ecology Letters \(^2\)Pace et al. 1998 TREE \(^3\)Kidd et al. 1998 CFJAS

Measuring food chain length

Methods

There are many methods, but stable isotopes (nitrogen) is the most common approach

Method 1

Connectance web

  • Binary interactions (0 or 1)
  • Ignores energy flow

Method 2

Energy web

  • Quantitative interactions
  • Extremely time consuming

Method 3

Stable isotopes

  • Composite measure of food chain length
  • (Relatively) easy to measure
  • Food web structure itself is unknown

Food chain length with stable isotopes

Collect stable isotope data (nitrogen) for the baseline and top predator

Baseline can be producer or primary consumer

Equation

Food chain length (top predator’s TP) is calculated as:

\[ FCL = \frac{\delta ^{15}N_{predator} - \delta ^{15}N_{base}}{\Delta_N} + TP_{base} \]

\(\Delta_N\) is TEF for nitrogen, and \(TP_{base}\) is the trophic position of the base species (1.0 or 2.0)

The advantage

Recall: stable isotopes are the mixed signature of prey resources

It can account for complicated food web structure without knowing the specifics

Tottabetsu river

Tottabetsu River, Japan

Ground beetles

Ground beetle - generalist predator

Brachinus stenoderus

R exercise: data

Download sample_data.csv and read it into R

dat <- read.csv("data/sample_data.csv")
head(dat)
##         site     date     species   d13C  d15N
## 1 tottabetsu 6/9/2014 grasshopper -28.03 -0.04
## 2 tottabetsu 6/9/2014 grasshopper -27.86  2.53
## 3 tottabetsu 6/9/2014 grasshopper -28.18  0.99
## 4 tottabetsu 6/9/2014 grasshopper -28.24  0.81
## 5 tottabetsu 8/9/2014 grasshopper -26.94  0.23
## 6 tottabetsu 8/9/2014 grasshopper -27.92  1.65

R exercise: data formatting

Check species column

unique(dat$species)
## [1] "grasshopper"  "L_noguchii"   "B_stenoderus"

grasshopper is the base species

R exercise: mean N

Calculate mean \(\delta ^{15}N\) for each taxon

library(tidyverse)

datN = dat %>%
  group_by(species) %>% # grouping by 'species'
  summarize(meanN = mean(d15N)) # calculate means for each group

datN
## # A tibble: 3 x 2
##   species      meanN
##   <chr>        <dbl>
## 1 B_stenoderus 5.88 
## 2 grasshopper  0.933
## 3 L_noguchii   5.06

R exercise: trophic position

\[ TP_{predator} = \frac{\delta ^{15}N_{predator} - \delta ^{15}N_{base}}{\Delta_N} + TP_{base} \]

Calculate trophic positions of L. noguchii and B.stenoderus

*\(\Delta_{N} = 3.4\) and \(TP_{base} = 2\) for this example

Ngh <- datN$meanN[which(datN$species == "grasshopper")]
Nln <- datN$meanN[which(datN$species == "L_noguchii")]
Nbs <- datN$meanN[which(datN$species == "B_stenoderus")]

fcl <- function(Nbase, Ntop, deltaN, TPbase) {
  y <- (Ntop - Nbase)/deltaN + TPbase
  return(y)
}

TPln <- fcl(Nbase = Ngh, Ntop = Nln, deltaN = 3.4, TPbase = 2)
TPbs <- fcl(Nbase = Ngh, Ntop = Nbs, deltaN = 3.4, TPbase = 2)

R exercise: trophic position

Check values

L. noguchii: TP = 3.21
B. stenoderus: TP = 3.46

TPln
## [1] 3.213063
TPbs
## [1] 3.456478

Long lasting debate

Food chain length varies in nature

What determines food chain length?

H1: basal resource

Basal resource availability

The productivity hypothesis predicts that food chain length should increase with increasing resource availability - why?

Rationale

Energy would be lost through predation

Post (2002) summarized energetic efficiency in predator-prey interactions

  • Average: 10%
  • Range: 5 - 50%

Post 2002, TREE 6: 269-277

Diminishing energy

Energy available to the top predator will be limited by basal resource availability or energetic efficiency

Empirical evidence

Highly controlled microbial system

As nutrient supply increased, population abundance of predatory ciliate increased

  • Basal bacterium Serratia marcescens
  • Bacterivorous ciliate Colpidium striatum
  • Predatory ciliate Didinium nasutum

Kaunzinger and Morin 1998, Nature

Counter evidence

Natural lakes

No response of food chain length to nutrient levels

  • Top predators vary by lakes
  • Greater diversity

Post et al. 2000, Nature

Theory impaired?

Contradicting results in experimental and natural systems

Why does the difference emerge?

Food web structure

Intraguild predation

Predation on the species that shares a prey item(s)

Intraguild predation

Intraguild predation can drive intraguild prey extinction

Resource availability

  • Low: predator and/or consumer cannot invade into the system
  • Medium: predator and consumer coexist
  • High: predator extirpate consumer

Post & Takimoto. 2007, Oikos

Theoretical evidence

Ward et al. 2017, Nature Communications

H2: disturbance

The dynamic stability hypothesis

The dynamic stability hypothesis predicts that food chain length will decrease with increasing disturbance frequency/intensity - why?

Pimm and Lawton 1977, Nature

Rationale

Long food chains take time to recover - frequent/intense disturbance will inhibit recovery

Pimm and Lawton 1977, Nature

Empirical evidence

Often tested in rivers

US river ecosystem

  • River flows stongly influences ecological communities
  • Flow variation was quantified with long-term discharge records

Sabo et al. 2010, Science

Counter evidence

Often tested in rivers

Australian river ecosystem

  • River flows stongly influences ecological communities
  • Flow regimes were categorized into three levels

Warfe et al. 2013, Plos One

Theory impaired?

Contradicting results in different regions

Why does the difference emerge?

Intraguild predation

Again, theory suggests intraguild predation may mediate the effect of disturbance

Disturbance

  • Low: coexistence of IG-prey and IG-predator depends on the strength of IG predation
  • Medium: IG-prey and IG-predator coexist
  • High: no species can invade into the system

Takimoto et al. 2012, Ecological Research

H3: ecosystem size

The ecosystem size hypothesis

The ecosystem size hypothesis predicts long food chains in large ecosystems (area or volume) - why?

Rationale

Multiple possibilities

  • More space, more refugia
  • Habitat heterogeneity
  • More species
  • and more…

i.e., mechanisms are unclear

Metapopulation-based theory

Consumers live on the patches of prey species - this builds up nested metapopulations

\[ \begin{align} \frac{dp_1}{dt} &= mp_1(h-p_1) - ep_1 &&\text{basal only}\\ \frac{dp_2}{dt} &= mp_2(p_1-p_2) - 2ep_2 &&\text{basal & consumer}\\ \frac{dp_3}{dt} &= mp_3(p_2-p_3) - 3ep_3 &&\text{all}\\ \end{align} \]

\(h (0 \le h \le 1)\) is the fraction of habitat patches livable to the basal species

Modified from Holt 2002, Ecological Research

Metapopulation-based theory

Metapopulation-based theory suggets the effect of ecosystem size is less sensitive to local food web structure (strength of intraguild predation)

Takimoto et al. 2012, Ecological Research

Empirical evidence

Ample empirical evidence - lakes, ponds, and islands

Post et al. 2000, Nature