Kandlikar lab slides

Belowground regulation of
aboveground dynamics

Gaurav Kandlikar
Louisiana State University
web: https://gklab.org/
slides: https://talks.gklab.org/umn-26
contact: gkandlikar@lsu.edu

Sal (Shorea) dominated forests in northern India, Photo by Dhritiman Mukherjee

Intercropping of soybean and wheat; image from U. Iowa

“Christmas tree scientists work to manage grinchy fungal foes”; image from Washington State Univ

As an ecologist, my research is motivated by two overarching goals:

Explain patterns of diversity in nature
Predict responses to perturbations

Approach

Today’s talk

Advancing ecological theory and experiments to quantify microbial effects on plant coexistence
Microbial effects on plant communities in variable environments: Ongoing work and new directions
Reflections on broadening representation and equity

Today’s talk

Advancing ecological theory and experiments to quantify microbial effects on plant coexistence

Mathematical underpinning of plant–soil feedback

See also Bever, Westover, and Antonovics (1997) and Kandlikar (2024)

Plant dynamics

\[\frac{dN_1}{dt} = w_1N_1 ~~~~ \text{and} ~~~ \frac{dN_2}{dt} = w_2N_2\]

\[w_i = m_{iA}f_A + m_{iB}(1-f_A)\]

where \(f_i\) is the relative frequency of microbial community \(i\) in the soil (e.g. \(f_A = \frac{N_A}{N_A+N_B}\))

Interpretation: Plants have exponential population growth at a rate determined by the composition of the soil community.

Microbe dynamics

\[\frac{dN_A}{dt} = N_A\frac{N_1}{N_1 + N_2}~~~\text{and}~~~\frac{dN_B}{dt} = \nu N_B\frac{N_2}{N_1 + N_2}\]

Interpretation: Soil communities grow at a rate determined by the frequency of each plant (and the relative strength of each plant’s conditioning effect, \(\nu\)).

R code to simulate model dynamics

Code

psf_model <- function(time, init, params) {
  with (as.list(c(time, init, params)), {
    # description of parameters (see Bever et al. 1997)
    # N1 and N2: abundance of the plant species 1 and 2
    # p1: frequency of plant species 1; p2 = 1-pA
    # m1A, m1B, m2A, m2B: conspecific and heterospecific effects of microbial community A or B on the growth of plant 1 or 2
    # pA: frequency of the soil microbial community A
    # v: influence of plant species 2 on the microbial community relative to that of plant 1
    
    # Differential equations
    dN1 <- (m1A*pA + m1B*(1-pA))*N1
    dN2 <- (m2A*pA + m2B*(1-pA))*N2
    dp1 <- p1*(1-p1)*((m1A-m2A)*pA + (m1B-m2B)*(1-pA))
    dpA <- pA*(1-pA)*(p1-v*(1-p1))
    
    
    # Return dN1 and dN2
    return(list(c(dN1, dN2, dp1, dpA)))
  })
}

\[ \overbrace{(m_{1B} + m_{2A})}^{\text{interspecific effects}}- \overbrace{(m_{1A} + m_{2B})}^{\text{intraspecific effects}} > 0 \]

\[ \underbrace{\frac{1}{2}\big[\overbrace{(m_{1B} + m_{2A})}^{\text{interspecific effects}}- \overbrace{(m_{1A} + m_{2B})}^{\text{intraspecific effects}}\big]}_{\text{Stablization}} > 0 \]

Lasting influence of the Bever model

Code

# Dataset downloaded from Figshare: 
# curl::curl_download("https://figshare.com/ndownloader/files/14874749", destfile = "../crawford-supplement.xlsx")

read_excel("../data/crawford-supplement.xlsx", sheet = "Data") |> 
  mutate(stab = -0.5*rrIs) |> # show in terms of stabilization instead of I_s
  filter(stab > -3) |> # Remove the pair with Stab approx. 6 -- according to McCarthy Neuman (original author), this is likely due to bad seed survival
  ggplot(aes(x = stab)) + 
  geom_histogram(color = "black") +
  geom_histogram(fill = "#56A0D3") +
  geom_rug(color = "grey25") + 
  geom_vline(xintercept = 0) + 
  annotate("text", x = Inf, y = Inf, label = "N = 1037 pairwise comparisons\n
           57% experience positive stabilization",
           vjust=1, hjust = 1, size = 6) +
  xlab("Stabilization") + ylab("Count")

Data from Crawford et al. (2019)