Hypothesis testing of the drivers of long-term ecological change in Michigan

Quinn Asena, Jack Williams and Tony Ives

UW-Madison

2024-08-19

Outline

Two lakes:

  1. Huffman Lake in Northern Michigan
  2. Story Lake in Northern Indiana (near Southern Michigan border)

Two parts:

  1. Introduction to the modelling framework
  2. Results from applying the method

The Lakes


Huffman Lake (North)

  1. Pinus dominated
  2. Dynamics in Tsuga and Fagus


Covariates:

  1. Charcoal as local driver
  2. Northern regional temperature reconstruction
  3. \(\delta^{18}O\) regional winter precipitation indicator

Story Lake (South)

  1. Quercus dominated
  2. Dynamics in Fagus, Ulmus and Hardwood


Covariates:

  1. Charcoal as local driver
  2. Southern regional temperature reconstruction
  3. Lake level as regional indicator of moisture

Huffman lake target taxa (North)

Story Lake (South)

Shared focal taxa and drivers

Taxa:

  • Fagus: Shared more mesic taxa

Local drivers:

  • Charcoal: Shared covariate (local indicator of fire)

Regional drivers:

  • Regional temperature reconstruction (different reconstructions for North and South)
  • Different proxies for moisture

Multiple possible hypotheses

  • Are local (charcoal) or regional (lake level, temperature, \(\delta 18O\)) variables more important drivers community change?
  • Are species interactions more important than local and regional drivers?
  • Is there a common result between Northern and Southern Michigan?


Hypothesis / Drivers Rank Coefficients
Interactions + local + regional ? ?
local + regional ? ?
Interactions + local ? ?
Local ? ?

Modelling framework for hypothesis testing


State-space modelling to estimate coefficients of:

  • Driver-taxa relationships
  • Taxa-taxa interactions


Multiple possible explanations of community change:

  • Set up multiple working hypotheses
  • Model each hypothesis and rank them by best fit

Ranking model results: Huffman Lake (North)


Hypothesis / Drivers Rank Coefficients
Interactions + local + regional 1 Tsuga-Fagus
\(\delta^{18}O\)-Fagus
local + regional 2 \(\delta^{18}O\)-Fagus
Interactions + local 3 Char-Tsuga
Local 4 Char-Tsuga

Ranking model results: Story Lake (South)


Hypothesis / Drivers Rank Coefficients
Interactions + local + regional 1 Quercus-Fagus
Charcoal, lake level
Interactions + local 2 Quercus-Fagus
Charcoal
local + regional 3 lake Level-Ulmus
Charcoal-Ulmus
Local 3 Charcoal

Is there a common result?


Yes! Highest ranked model: Regional + local + interactions.


Huffman Lake (North)

  • Regional drivers are key
    • Winter precipitation important to Fagus
  • Interaction between Tsuga-Fagus

Story Lake (South)

  • Fagus-Quercus interactions are key
    • Lowest raked models have no interactions
  • Regional drivers are also important

Discussion and questions

Huffman Lake (North)

                       Coef.         se           t            P
sp.Tsuga.Fagus -0.4875405418 0.12334002 -3.95281707 7.723648e-05
char_acc.Fagus  0.0941820547 0.08255616  1.14082402 2.539432e-01
Nmean.Fagus     0.4086973180 0.18406717  2.22037046 2.639363e-02
d18OVPDB.Fagus -1.3266630849 0.24087584 -5.50766354 3.636276e-08
char_acc.Tsuga  0.0770176820 0.07481308  1.02946809 3.032598e-01
Nmean.Tsuga     0.1323216302 0.21648601  0.61122485 5.410507e-01
d18OVPDB.Tsuga -0.6905925176 1.06391677 -0.64910389 5.162712e-01
char_acc.Pinus -0.0008726922 0.01632358 -0.05346206 9.573638e-01
Nmean.Pinus    -0.0886466636 0.12558435 -0.70587351 4.802668e-01
d18OVPDB.Pinus  0.0362156450 0.32382831  0.11183594 9.109535e-01

Story Lake (South)

                                    Coef.         se          t            P
sp.Quercus.Fagus grandifolia  0.052920105 0.01711304  3.0923843 1.985556e-03
sp.Fagus grandifolia.Quercus -0.150256789 0.02649823 -5.6704469 1.424255e-08
lake_level.hardwood           0.007096171 0.05115471  0.1387198 8.896716e-01
char_acc.hardwood            -0.174607352 0.03167155 -5.5130671 3.526338e-08
lake_level.Fagus grandifolia -0.007778810        NaN        NaN          NaN
char_acc.Fagus grandifolia   -0.189118872 0.05048197 -3.7462655 1.794866e-04
lake_level.Ulmus              0.415126717 0.06589033  6.3002678 2.971318e-10
char_acc.Ulmus               -0.208034501 0.04775793 -4.3560204 1.324484e-05
lake_level.Quercus            0.055568728 0.06694003  0.8301270 4.064670e-01
char_acc.Quercus             -0.202274011 0.02517910 -8.0334102 9.480006e-16

A few caveats

  • Palaeo-data uncertainty
    • Chronolological uncertainty
    • Proxy uncertainty (e.g., differential pollen production, observer error…)
    • Error per data source
  • Data may be information poor (i.e., not enough information to recover coefficients)
    • Huffman overwhelming Pinus counts!
  • Only two lakes (for now)