title: Modelling range expansion in heterogeneous environments
Creators: name: Scott, David
Publisher: name: University of Liverpool Repository
Year: 2024

description: As climates warm, species have been observed to shift their range either in latitude or elevation to maintain
their thermal conditions (climate tracking). Those that fail to track their climate envelope risk being exposed
to temperatures beyond their thermal limits with associated reduction in fitness and eventual extinction once
they are left behind by their climate envelope. Therefore, it is important to gain a better understanding of the
processes which govern climate induced species range shifts and how spatio-temporal fluctuations impact it.
Furthermore, current networks of potential habitat beyond species current range margin may not be sufficient
to accommodate such range shifts. For conservationists to apply limited resources in facilitating range shifts,
they need computationally efficient metrics to rank potential landscape configurations (on how quickly a species
can move through them) to make the most informed decisions as to where habitat is most needed either through
protection, restoration or creation.
Of the species that track their climate margin in response to climate change, little is known of what determines
how successful they will be. We define success as how close the population range margin is to the climatic range
margin (thermal limit in space) for species that can track their climate (maximum invasion speed &gt; climate
speed). We simulate theoretical species (using a single species integro-difference equation on a 2D discrete
lattice landscape) in the northern hemisphere on a spatial gradient (representing latitudinal cooling) for a range
of climate warming rates. This creates a climate gradient which moves northwards over time. For a warming
climate (with zero spatio-temporal fluctuations), a negative climate tracking position (CTP) emerges where the
population range margin lags behind the climate margin at a fixed distance. We ask what determines how close
a population can ‘keep up’ to its climatic range margin (its CTP). We find the CTP is determined by the ratio
between the species’ maximum invasion speed and the climate speed, with the CTP becoming more negative as
the ratio gets closer to 1. We also find that the negative CTP can be approximated as the location (relative to
the climate margin) where the local invasion speed (based on local temperature) is equal to the climate speed,
which we define as the equal velocity position (EVP).
We further ask how the CTP is impacted by spatio-temporal fluctuations in temperature. We simulate two
theoretical species with the same maximum invasion speed but one (‘the disperser’) has a higher dispersal fraction
and the other (‘the reproducer’) has a higher growth rate. We find opposing effects from spatial and temporal
fluctuations. Generally, temporal fluctuations had a negative effect on the CTP and spatial fluctuations had a
positive effect. When both were combined, we find an interaction where the CTP is further north than if the
relationship was additive. Furthermore, how species responded to spatial fluctuation varied depending on their
biological parameter values. The species with a greater maximum growth rate (the reproducer) responded more
positively to all degrees of spatial fluctuations than the species with a larger dispersal fraction (the disperser).
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For the landscape summary metric, current techniques are either too computationally demanding or not based
on biological analogies. We propose mean first passage time (mFPT) of a random walker as an alternative
metric of the time taken for a species starting at a source site to traverse through a network and reach a target
site, as it is both computationally efficient and is based on an analogy of movement. To assess its accuracy,
we simulate a stochastic patch occupancy metapopulation model to represent ‘real time’. We then compare its
accuracy against ‘Conductance’ which is based on an analogy of an electrical circuit. We find mFPT was able
to approximate landscape invasion time; however, Conductance had a greater accuracy when fitted to general
additive models (GAM). In certain circumstances (when there was a larger number of source and target sites)
mFPT was more accurate than Conductance. The most accurate GAM was when both metrics were combined.
Including an interaction term with known variables (number of patches, number of source and target sites, mean
dispersal distance) also increased accuracy.
Our results show the importance of considering the effects of spatio-temporal fluctuations when modelling
climate induced range shifts. Furthermore, they highlight the importance of conserving potential climate refugia
when managing range shifts. We show how landscape summary metrics can be used to design landscapes that
are robust to future range shifts.