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Journal ArticleDOI

Persistence and stability of interacting species in response to climate warming: the role of trophic structure

26 Apr 2020-Theoretical Ecology (Springer Netherlands)-Vol. 13, Iss: 3, pp 333-348
TL;DR: In this paper, the authors investigated the effect of climate warming on the trophic complexity and community structure of a tri-trophic food web and found that at low temperatures, warming can destabilize the species dynamics in the food chain, a diamond food web, and an omnivorous interaction.
Abstract: Over the past century, the Earth has experienced roughly 0.4–0.8 ∘C rise in the average temperature and which is projected to increase between 1.4 and 5.8 ∘C by the year 2100. The increase in the Earth’s temperature directly influences physiological traits of individual species in ecosystems. However, the effect of these changes in community dynamics, so far, remains relatively unknown. Here, we show that the consequences of warming (i.e., increase in the global mean temperature) on the interacting species persistence or extinction are correlated with their trophic complexity and community structure. In particular, we investigate different nonlinear bioenergetic tri-trophic food web modules, commonly observed in nature, in the order of increasing trophic complexity: a food chain, a diamond food web, and an omnivorous interaction. We find that at low temperatures, warming can destabilize the species dynamics in the food chain as well as the diamond food web, but it has no such effect on the trophic structure that involves omnivory. In the diamond food web, our results indicate that warming does not support top-down control induced co-existence of intermediate species. However, in all the trophic structures, warming can destabilize species up to a threshold temperature. Beyond the threshold temperature, warming stabilizes species dynamics at the cost of the extinction of higher trophic species. We demonstrate the robustness of our results when a few system parameters are varied together with the temperature. Overall, our study suggests that variations in the trophic complexity of simple food web modules can influence the effects of climate warming on species dynamics.

Summary (3 min read)

Introduction

  • Increasing heat waves, severe thunderstorms, rising sea levels, coral bleaching, and loss of ecosystems are a few indicators of current unprecedented global warming (IPCC 2018).
  • As the declining performance-temperature relationship has been rarely incorporated into ecological models studied in the recent past, understanding the consequences of warming on trophic interactions forms a major knowledge gap.
  • Ecological communities are composed of complex trophic interactions (McCann et al 1998, Davis et al 1998), and models restricted only to lower levels of trophic interactions can put light on limited ecological consequences.
  • Moreover, through sensitivity analysis, the authors demonstrate that their observations are valid in a rather large region in parameter space.

Models

  • Here, the authors analyze tri-trophic food web modules (see Fig. 1) with temperature-dependent traits.
  • These models include a resource, either one or two intermediate consumers, and a top predator.

Tri-trophic food chain

  • Here, temperature is incorporated into the metabolic rates of species by using the Boltzmann-Arrhenius relationship for reaction kinetics (Van der Have and De Jong 1996, Gillooly et al 2001, Savage et al 2004, Brown et al 2004).
  • Empirical studies account for both the monotonically increasing/unimodal temperature dependence of resource growth rate.
  • Figure 2 shows the temperature dependence of the resource growth rate, foraging traits (attack rate and handling time), and metabolism for C1.

Diamond food web

  • To understand how increasing the complexity influences ecosystem dynamics, the authors move from the food chain to investigate the diamond food web module (see Fig. 1(b)).
  • The diamond food web is a four species food web module composed of energy pathways from a resource to two competitive consumers (apparent competition) vulnerable to predation by a top predator (Leibold 1996, McCann et al 1998, Levin 1970).
  • Both C1 and C2 exhibit Type-II functional response over resource per-capita growth rate and are linked with R through preference parameters α and β, respectively.
  • Ec1 , ep1 have same explanation as for previous models.

Omnivorous interaction

  • To elucidate the outcome of complex trophic interactions in response to warming, the authors increase the complexity further from the diamond food web to an omnivorous interaction (Fig. 1(c)).
  • Omnivory is a feeding classification in which a species (an omnivore) consumes resources from more than one trophic level.
  • The parameter η governs the top predator’s preference for consumption of the two species, R and C1.
  • Starting at η = 0, the system behaves the same as the tritrophic food chain (Eqn. (1)) with no omnivorous link.
  • The temperature dependence of the physiological traits is similar to that of the food chain and parameter values are described in the Table 1.

Methods

  • The authors examine temperature dependence of species responses leading to their growth/consumption relative to the traits accounting for their metabolism or predation induced mortality, while moving from one trophic structure to another.
  • K is the inverse enrichment ratio, which determines the resource density perceived by the species consuming the basal resource.
  • Therefore, species ingestion capabilities relative to their predation induced mortality is defined as Ω/hx Γ/hp , where Γ determines the preference of the top predator towards the consumer x.
  • Initially, the authors study the system(s) sensitivity towards stability and persistence in the temperature–resource carrying capacity space, from one module to the other.
  • Each of the deterministic systems is solved numerically either using MATLAB (R2015b) or the continuation package XPPAUT (Ermentrout 2002).

Results

  • Following the analytical expressions described in the methods section, qualitative behaviours of species relative physiological traits are depicted along the thermal gradient in Fig.
  • The increase or decrease in species abundance and extinction risk in the trophic structures due to changing temperatures are associated with the species relative traits.
  • At very low temperatures, the food chain exhibits oscillatory dynamics via a Hopf bifurcation (HB), making the system unstable (see Fig. 4), while all the species co-exist.
  • At the same time, maximum consumption of C1 increases at a faster rate than its metabolism as well as predation induced mortality (see Figs. 3(c)3(d)).
  • As the temperature crosses the intermediate range, the inverse enrichment ratio declines (see Fig. 3(b)), creating more availability of the resource for C1.

Dynamics of the diamond food web

  • The authors also assume that the top predator has consumption preference (i.e. δ = 0.6) towards C1.
  • Thus the authors observe that an interaction mediated by the top predator over the competitive consumers benefits the consumer C1 leading to the extinction of C2.
  • In other words, ingestion abilities of C2 improves and overpowers the ingestion capability of C1.
  • Further warming generates bi-stability exhibiting both, steady state (oscillation free) and oscillations.
  • The survival of the competing species depends upon their preference for the basal resource; species having a weaker preference towards R is expected to face extinction under the influence of temperature.

Dynamics of the omnivorous interaction

  • Evolving from the linear flow of energy in the food chain module, here the authors consider the direct acquisition of the resource by the top predator (Eqn. (5)).
  • The authors start their analysis by considering a weak influence of omnivory, where P has less effectiveness towards R and manifests preferential consumption of C1.
  • For η = 0.06, initial oscillations earlier observed in the food chain die out, making the omnivorous system more stable at low temperatures (see Figs. 6(a)-6(c)).
  • These factors reduce the flux of energy from R to C1, leading to consumer extinction at early temperatures and thus declining species co-existence.
  • Further, C1 re-invades the interaction network, but for a small temperature span (up to ≈ 30.3◦C).

Sensitivity analysis

  • Up to now, the results presented are for fixed carrying capacity K, preference parameters α and β (for the food web), and omnivory strength η (for the omnivorous interaction), while the temperature is varied.
  • To test the robustness of the dynamical outcomes observed in each of the tri-trophic modules, the authors perform sensitivity analysis in two-dimensional planes for a few experimentally accessible model parameters, through stability and persistence boundaries.
  • The stability boundary corresponds to the HB curve (beyond which system exhibits oscillatory dynamics in species density), and the persistence boundary corresponds to the TB curve (beyond which species co-existing equilibrium fails to exist) (see Fig. 8).
  • In the diamond food web, the influence of resource carrying capacity towards the system’s stability depends upon the selective interaction of the competing consumers towards the basal resource (see Figs. 8(b)–8(g)).
  • The initial oscillations further suppress in the omnivorous interaction, and species persistence drops at intermediate temperatures (see Fig. 8(h)).

Discussion

  • In ecological interactions, the temperature–performance relationship serves as one of the essential factors to understand the impact of warming on biodiversity maintenance (Johnson and Amarasekare 2014).
  • The first finding, indicating the extinction of species at high temperatures, emphasizes on the consequences of warming on community as well as individual species dynamics.
  • Binzer et al (2012) incorporated monotonically increasing temperature dependence of species biological traits interacting in a food chain, and showed the extinction of the top predator, later followed by the loss of an intermediate consumer.
  • Thus, work addressing periodic variability and stochastic variations in climatic warming in food webs may determine a wide range of effects of warming on trophic interactions.
  • T.K. acknowledges Ramesh Arumugam for his help on computation.

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Persistence and stability of interacting species in response to climate
warming: The role of trophic structure
*
Taranjot Kaur
1
and Partha Sharathi Dutta
1
1
Department of Mathematics
Indian Institute of Technology Ropar
Rupnagar, Punjab 140 001 India
Corresponding author: parthasharathi@iitrpr.ac.in
*
This article contains supplementary materials.
1
.CC-BY-NC 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted March 2, 2020. ; https://doi.org/10.1101/2020.02.28.970012doi: bioRxiv preprint

Abstract
Over the past century, the Earth has experienced roughly 0.4–0.8
C rise in the average
temperature and which is projected to increase between 1.4–5.8
C by the year 2100. The in-
crease in the Earth’s temperature directly influences physiological traits of individual species
in ecosystems. However, the effect of these changes in community dynamics, so far, remains
relatively unknown. Here we show that the consequences of warming (i.e., increase in the
global mean temperature) on the interacting species persistence or extinction are correlated
with their trophic complexity and community structure. In particular, we investigate differ-
ent nonlinear bioenergetic tri-trophic food web modules, commonly observed in nature, in
the order of increasing trophic complexity; a food chain, a diamond food web and an om-
nivorous interaction. We find that at low temperatures, warming can destabilize the species
dynamics in the food chain as well as the diamond food web, but it has no such effect on the
trophic structure that involves omnivory. In the diamond food web, our results indicate that
warming does not support top-down control induced co-existence of intermediate species.
However, in all the trophic structures warming can destabilize species up to a threshold
temperature. Beyond the threshold temperature, warming stabilizes species dynamics at
the cost of the extinction of higher trophic species. We demonstrate the robustness of our
results when a few system parameters are varied together with the temperature. Overall,
our study suggests that variations in the trophic complexity of simple food web modules can
influence the effects of climate warming on species dynamics.
Keywords: global warming, food web modules, omnivory, competition, species co-existence,
biodiversity loss
2
.CC-BY-NC 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted March 2, 2020. ; https://doi.org/10.1101/2020.02.28.970012doi: bioRxiv preprint

Introduction
Increasing heat waves, severe thunderstorms, rising sea levels, coral bleaching, and loss of
ecosystems are a few indicators of current unprecedented global warming (IPCC 2018). Tem-
perature is a major abiotic factor that causes variation in species interactions and abundances
(Parmesan and Yohe 2003, Deutsch et al 2008). It is well established that climate warming
can lower species abundance, which in turn may affect their persistence (Parmesan and Yohe
2003). In fact, the increasing temperature creates negative impacts on populations, pushing
our ecosystems closer to the face of mass extinction and a considerable loss of biodiversity
(Drake and Lodge 2004, Urban 2015, Ceballos et al 2017). However, the understanding of
the consequences of warming on ecological communities and individual species is still in its
infancy, as warming simultaneously affects different levels of biological organizations ranging
from changes in species physiological traits to their interaction networks (Fussmann et al
2014, Uszko et al 2017, Englund et al 2011).
Several experimental and theoretical studies have reported diverse impacts of warming on
ecosystem stability and persistence (Vasseur and McCann 2005, O’Connor et al 2011, Binzer
et al 2012, Uszko et al 2017, Rudolf and Roman 2018). For instance, Vasseur and McCann
(2005), while framing a bioenergetic consumer-resource model, predicted that warming does
not cause species extinctions, whereas, with a decrease in the inverse enrichment ratio, it
increases the tendency to show oscillations in species abundance. In a herbivore and plant
model, O’Connor et al (2011) showed that warming could result in increased stability but
decreased persistence of the species. Ohlberger et al (2011) used a size-structured fish pop-
ulation model and predicted that warming might increase intraspecific competition among
consumers, and induce regime shifts that destabilize population dynamics. The variation
in the impacts of warming on ecosystems observed in recent studies emerges from the in-
teractions among biological and physical processes as well as species associations with one
another.
Species response to different biotic and abiotic factors is complex, and often induce
3
.CC-BY-NC 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted March 2, 2020. ; https://doi.org/10.1101/2020.02.28.970012doi: bioRxiv preprint

changes in the foraging (e.g., attack rate, handling time) and life-history (e.g., growth rate,
reproduction, survivorship) traits. Recent evidences show that the strength of biotic factors
on population dynamics is influenced by the strength of abiotic factors between them and
vice-versa (Holling 1973, Walther et al 2002, Traill et al 2010, O’Connor et al 2011, Atkin-
son and Urwin 2012, Post 2013, Fussmann et al 2014). On that account, several empirical
studies reveal monotonically increasing relationship between species performance/biological
traits with increasing temperature (Van der Have and De Jong 1996, Gillooly et al 2001,
Savage et al 2004). The monotonically increasing formulations of growth rate and metabolic
rates have been widely used by ecologists (Vasseur and McCann 2005, O’Connor et al 2011,
Binzer et al 2012, Fussmann et al 2014, Gilbert et al 2014, Amarasekare 2015), and forms the
foundation of the Metabolic Theory of Ecology (MTE) (Brown et al 2004). Yet, there are ev-
idences that the thermal habituation of attack rates and handling times of most ectotherms
represents unimodal functions of temperature (Englund et al 2011, Dell et al 2011, Ama-
rasekare 2015); the attack rate varies in a bell-shaped manner while the handling time varies
in a U-shaped fashion (Zamani et al 2006, Dell et al 2011, Englund et al 2011, Clusella-Trullas
et al 2011, Amarasekare 2015). As the declining performance-temperature relationship has
been rarely incorporated into ecological models studied in the recent past, understanding
the consequences of warming on trophic interactions forms a major knowledge gap. Thus,
it is important and timely to emphasize the interplay between species realistic biotic factors
with the abiotic factors.
Majority of the recent theoretical studies on the impacts of changing temperatures on
species interactions and performance have considered models of pairwise consumer-resource
interactions, to maintain the mathematical tractability (Vasseur and McCann 2005, O’Connor
et al 2011, Fussmann et al 2014, Gilbert et al 2014, Uszko et al 2017). However, ecological
communities are composed of complex trophic interactions (McCann et al 1998, Davis et al
1998), and models restricted only to lower levels of trophic interactions can put light on
limited ecological consequences. As various mechanisms that regulate co-existence or abun-
4
.CC-BY-NC 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted March 2, 2020. ; https://doi.org/10.1101/2020.02.28.970012doi: bioRxiv preprint

dance of species, e.g. top-down hypothesis or green-world hypothesis (Levin 1970, Fretwell
1987, Hairston Jr and Hairston Sr 1993) cannot be considered while investigating lower-order
trophic interactions. Furthermore, trophic structures of ecosystems play a significant role
in propagating the immediate as well as concurrent effects of warming on species dynamics
(Tylianakis et al 2008, Cardinale et al 2012, Urban et al 2017). For instance, warming can
affect direct as well as indirect negative feedbacks within a species, which may suppress or
fuel the oscillatory dynamics of the system (Johnson and Amarasekare 2014). Further, a rise
in the temperature may disrupt the performance of an invading species (in a competitive
interaction), which may moderately reduce the adverse effects of warming on other com-
petitors (Rudolf and Roman 2018). Thus, exploring the influence of warming in population
models involving complex trophic interactions can provide a broader scope to understand
ecosystem behaviors (Pimm et al 1991, Murdoch et al 2003, Touboul et al 2018).
To predict the ecological responses to climate change, Davis et al (1998) and Tylianakis
(2009) experimentally demonstrated the importance of understanding the interaction be-
tween temperature dependent consumer-resource systems in altering food web dynamics.
Also, Edwards and Richardson (2004) studied how warming affects marine pelagic commu-
nities leading to a lack of congruence between the trophic levels. Later, Binzer et al (2012)
investigated a food chain model that incorporates body mass and temperature dependencies
of species traits, and projected extinction of higher trophic species. Nonetheless, we still have
a limited understanding of how complex trophic interactions can alter the consequences of
warming on species persistence and stability.
To fill this knowledge gap, here we use frameworks that integrate temperature depen-
dence of species biological traits into trophic dynamics and study the influence of different
community structures/food web modules in altering warming effects on species persistence
and stability. By stability, here we mean the tendency of species to exhibit oscillation free
behavior (i.e. system exhibits stable equilibrium forming an interior point attractor) (Mc-
Cann and Hastings 1997). The food web modules have been studied in the order of their
5
.CC-BY-NC 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted March 2, 2020. ; https://doi.org/10.1101/2020.02.28.970012doi: bioRxiv preprint

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"Persistence and stability of intera..." refers background in this paper

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"Persistence and stability of intera..." refers background or methods in this paper

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Q1. What are the contributions in "Persistence and stability of interacting species in response to climate warming: the role of trophic structure" ?

8◦C rise in the average temperature and which is projected to increase between 1. 4–5. 8◦C by the year 2100. Here the authors show that the consequences of warming ( i. e., increase in the global mean temperature ) on the interacting species persistence or extinction are correlated with their trophic complexity and community structure. In particular, the authors investigate different nonlinear bioenergetic tri-trophic food web modules, commonly observed in nature, in the order of increasing trophic complexity ; a food chain, a diamond food web and an omnivorous interaction. The authors demonstrate the robustness of their results when a few system parameters are varied together with the temperature. The authors find that at low temperatures, warming can destabilize the species dynamics in the food chain as well as the diamond food web, but it has no such effect on the trophic structure that involves omnivory. Overall, their study suggests that variations in the trophic complexity of simple food web modules can influence the effects of climate warming on species dynamics.