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\begin{document}

\title{Body size and trophic position determine the outcomes of species
invasions along temperature and productivity gradients}



\author[1]{Samuel Dijoux}%
\author[2]{Noémie Pichon}%
\author[3]{Arnaud Sentis}%
\author[4]{David Boukal}%
\affil[1]{University of South Bohemia in Ceske Budejovice Faculty of Science}%
\affil[2]{University of Oulu Faculty of Science}%
\affil[3]{INRAE}%
\affil[4]{University of South Bohemia in Ceske Budejovice}%


\vspace{-1em}



  
  \date{May 28, 2024}


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\selectlanguage{english}
\begin{abstract}
Species invasions are predicted to increase in frequency with global
change, but quantitative predictions of how environmental filters and
species traits influence the success and consequences of invasions for
local communities are lacking. Here we investigate how invaders alter
the structure, diversity and stability regime of simple communities
across gradients of habitat productivity, temperature, and community
size structure. We examine all three-species trophic modules (apparent
and exploitative competition, trophic chain and intraguild predation)
with empirically derived temperature and body mass scaling of vital
rates. We show that the success of an invasion and its effects on
community stability and diversity are predictably determined by the
effects of environmental factors on each species and the relative
strengths of trophic interactions between resident and invading species.
We predict that successful invaders include smaller competitors and
comparatively small predators, suggesting that species invasions may
facilitate the downsizing of food webs under global change.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Human-induced global change is transforming local communities and
ecosystems through five main drivers: climate change, pollution,
overharvesting, land and sea use change, and invasive species (Isbell et
al. 2017; IPBES 2019). Invasive species threaten biodiversity (Sala et
al. 2000) and persistence of local communities worldwide (Gurevitch \&
Padilla 2004; Bellard et al. 2016). Shifting species ranges to higher
elevations and latitudes in response to climate change (Parmesan \& Yohe
2003; Sunday et al. 2012), combined with increased tourism, pet trade
and commodity transport (Chan et al. 2019; McCarthy et al. 2019; Essl et
al. 2020), are expected to accelerate species invasions globally over
the next century (Seebens et al. 2021; Sentis et al. 2021). Species
invasions can exacerbate or mitigate the pressures that ongoing
environmental change exerts on local communities by altering
biodiversity and community resilience to abiotic stressors (Walther et
al. 2002; Wardle et al. 2011; Hong et al. 2022).

Warming and nutrient enrichment are two pervasive aspects of global
change that structure local communities in aquatic (Fussmann et al.
2014; Boukal et al. 2019) and terrestrial systems (Meyer et al. 2012;
Clark et al. 2017). They modulate food web dynamics (Binzer et al. 2012;
Sentis et al. 2017) and can facilitate or prevent species invasions.
However, a general consensus on how invaders influence community
structure and persistence along temperature and habitat productivity
gradients is currently lacking. In particular, the mechanisms underlying
community-level responses to species invasions in future environments
affected by global change remain incompletely understood (Sentis et al.
2021).

Exploring the nexus between invasibility, diversity and stability of
communities (Rooney \& McCann 2012; Catford et al. 2019) can help us
better understand the impacts of global change on local ecosystems
(Francis et al. 2014). The effects of species invasions on the
diversity-stability relationship have been studied in different types of
animal, animal-plant and plant interaction networks (Rooney \& McCann
2012; Brose et al. 2017; Tomiolo \& Ward 2018). However, previous
studies considered relatively species-rich communities with many direct
and indirect effects; focusing on food web modules could allow for more
mechanistic, causal insights.

One promising avenue towards a better understanding of these mechanisms
is to disentangle the role of environmental filters and species traits
in biological invasions (Chesson 2000; Kraft et al. 2015). Environmental
filters constrain the invader per se but also structure the local
community, which is a biotic filter that restricts the invader's
realised niche (Kraft et al. 2015). The roles of both filters are
therefore closely linked (Thompson et al. 2018a, b). This link is often
neglected in studies that estimate future shifts in species
distributions caused by climate based on the expected performance of
invading species in new habitats (Bellard et al. 2013; Buckley \& Csergo
2017; Seebens et al. 2021), but ignore the accompanying impacts of
environmental change on resident communities.

The invader's realised niche is constrained by its trophic position and
the topology of the local food web. Available niches may be occupied by
resident species that interact with the invader directly through
consumptive interactions or indirectly through competition (Due\selectlanguage{ngerman}ñas et
al. 2018). Classic work on species coexistence has proposed general
rules for community assembly (Chesson 2000; Shea 2002). The `R* rule'
for exploitative competition states that the species with the lowest
resource requirements is competitively superior (Tilman 1985). An
analogous `P* rule' for apparent competition states that the prey that
can withstand the highest predation pressure will prevail (Holt et al.
1994). Both rules can also inform when species invade and how they
affect resident communities in the context of global change.

Among species traits, individual body mass can be used to predict
invasibility because it affects individual fitness, species interactions
and energy flows (McCann \& Rooney 2009; Brose et al. 2017; Dijoux \&
Boukal 2021). For example, larger species tend to prey on smaller
species, especially in aquatic habitats (Ou et al. 2017) and
warming-induced metabolic meltdown is more likely for larger consumers
than smaller ones (Rall et al. 2010, 2012). Food webs may therefore be
simpler in warmer habitats, with fewer species at higher trophic
positions (Brose et al. 2012). This could create niches for future
invaders, which could subsequently attenuate or alter food web responses
to global change through cascading effects (Reynolds \& Aldridge 2021).
However, little is known about how the body mass and trophic position of
the invader affect community responses to invasions under climate
change, and simple predictions are difficult to make. For example,
previous models have shown that high consumer-resource mass ratios
associated with large consumer species can either confer a higher
extinction risk for top predators under warming or buffer the effects of
eutrophication by dampening population fluctuations (Binzer et al. 2016;
Sentis et al. 2017).

Here, we investigate in detail how consumer-resource systems respond to
species invasions along temperature and habitat productivity gradients.
To this end, we develop biomass-based models (Yodzis \& Innes 1992) with
mass- and temperature-dependent biological rates parameterised using
empirically estimated relationships (Binzer et al. 2012; Fussmann et al.
2014). We simulate all possible invasions in a consumer-resource system
that can lead to the four baseline three-species food web modules
(apparent and exploitative competition, food chain, and intraguild
predation). Our aim is to decouple the influence of the invaders and
abiotic drivers. We explore (i) how temperature, nutrient levels and
body mass ratios between the resident and invading species influence
invasion success and (ii) how invasion-induced changes in species
composition, diversity and stability of local communities vary across
different food web topologies and environmental gradients.

Our main expectations are: (1) all else being equal, community responses
to invasions (Box 1) follow known mechanistic processes from community
ecology (Box 2); (2) based on the R* and P* rules and the higher
susceptibility of larger species to metabolic meltdown at warmer
temperatures, smaller invaders are more successful at warmer
temperatures, especially in less productive environments, while larger
invaders are more successful in more productive environments, especially
at lower temperatures; and (3) invasions that result in larger and
smaller consumer-resource size ratios will tend to stabilise and
destabilise the community dynamics.

\textbf{Methods}

Community structure and dynamics

We consider a resident consumer-resource system and examine five
scenarios that differ in the trophic position of the invader, including
another basal resource, another consumer, a top predator, an intraguild
predator feeding on both resident species, or an intraguild prey feeding
on the (shared) resident resource while being consumed by the resident
consumer (Fig. 1a-e). This corresponds to apparent competition
(hereafter AC), exploitative competition (EC), tri-trophic chain (TC)
and intraguild predation (IGP) (Tables S1--S3).

We simulate the dynamics of each module for each combination of
temperature between 0°C and 40°C (step size 0.1°C) and nutrient levels
(\emph{I\textsubscript{K}} ) available to the basal resource species the
between 0.1 g.m\textsuperscript{-2} and 20 g.m\textsuperscript{-2} (step
size 0.1 g.m\textsuperscript{-2}), yielding 80,200 combinations of
temperature and nutrient levels as in Binzer et al. (2012) and Sentis et
al. (2017). We also vary the body masses of species in each module,
constraining consumers to be at least as large as their resources, which
is true for most predator-prey pairs (McCauley et al. 2018). For
simplicity, we set the body mass of the basal resource species to 1 mg
and express the other masses in relative values (Fig. 1a-e).

We denote the body mass ratio between competing
resources\emph{R\textsubscript{INV}:R\textsubscript{RES}} (AC module)
and the consumer:resource ratio \emph{C:R} (TC and IGP modules) as
\selectlanguage{greek}\emph{α} , \selectlanguage{english}the mass ratio between competing
consumers\emph{C\textsubscript{INV}:C\textsubscript{RES}} (EC and IGP
modules) or between predators and intermediate consumers \emph{P:C} (TC
and IGP modules) as \selectlanguage{greek}\emph{β} , \selectlanguage{english}and the mass ratio between resident
resource and consumer \emph{C\textsubscript{RES}:R\textsubscript{RES}}
(AC and EC modules) and between the top predator and resident basal
resource (\emph{P:R} ; TC and IGP modules) as \selectlanguage{greek}\emph{γ} \selectlanguage{english}= \selectlanguage{greek}\emph{αβ.}
\selectlanguage{english}Furthermore, we quantify the asymmetry in size ratios between adjacent
trophic levels with a ratio parameter \selectlanguage{greek}\emph{δ} \selectlanguage{english}= \selectlanguage{greek}\emph{β} /\selectlanguage{english}\selectlanguage{greek}\emph{α}
\selectlanguage{english}(Table S4). We consider module-specific sets of mass ratios to reflect
the different trophic positions of the invader: 4 or 15
consumer-resource body mass ratios for the resident system, and 16 or 25
combinations of species mass ratios (i.e., at least all pairwise
combinations of \selectlanguage{greek}\emph{α} \selectlanguage{english}and\selectlanguage{greek}\emph{β} \selectlanguage{english}= 1, 2, 5 and 10, Text S1) in each
module (Tables S5--S7). All numerical simulations were run in the
packages `deSolve' and `rootSolve' in the R software (Soetaert \& Herman
2009; Soetaert et al. 2010).

Analyses of community structure and stability before and after invasion

We distinguish six mechanisms of invasion-induced change in the
community based on the observed changes in local composition and
diversity (hereafter \emph{invasion outcomes} , Box 1). The
invasion-induced change in diversity\(\Delta D=N_{\text{INV}}-\ N_{\text{RES}}\) is calculated as
the difference between the number of species in the invaded and resident
community \emph{N\textsubscript{INV}} and
\emph{N\textsubscript{RES}}present after 5000 years (end of simulation)
under the same environmental conditions and species masses.

To assess how invaders affect the stability of the resident system, we
first calculate the Jacobian matrix at the equilibrium with the species
present after 5000 years (Eqs 10--13, Table S8) and use its dominant
eigenvalue to determine the stability of the resulting community. We
distinguish three stability regimes for the invaded community
(hereafter\emph{S\textsubscript{INV}} ) and the resident system
(hereafter\emph{S\textsubscript{RES}} ): stable equilibrium (\emph{E} ),
population oscillations (\emph{O} ), and a collapsed system with no
remaining species (\emph{N} ) (Binzer et al. 2012; Sentis et al. 2017),
to which we arbitrarily assign values \emph{v} (\emph{E} ) = 2, \emph{v}
(\emph{O} ) = 1 and \emph{v} (\emph{N} ) = 0. We then compare the
stability regimes between the resident system and the invaded community
under the same environmental conditions and species mass ratios. Nine
outcomes (hereafter \emph{regime states}
,\emph{S\textsubscript{RES}-S\textsubscript{INV}} ) define all possible
changes in stability caused by species invasion. Similar
to\(\ \Delta D\), we calculate the invasion-induced change in
stability as\(\Delta S=v\left(S_{\text{INV}}\right)\ -\ v\left(S_{\text{RES}}\right)\). Positive, zero and negative values of
\(\Delta S\) correspond to stabilizing (\emph{O-E} , \emph{N-O}
and \emph{N-E} ), neutral (\emph{O-O} , \emph{E-E} and \emph{N-N} ) and
destabilising (\emph{O-N} ,\emph{E-O} , \emph{E-N} ) effects of the
invader on the local consumer-resource system, respectively.

To assess how the body mass of the invader affects the community
responses across food web modules and abiotic conditions, we calculate
the percentage of each invasion outcome (Box 1) and regime state for a
given set of body mass ratios across all 80,200 combinations of
temperature (0--40\selectlanguage{ngerman}ºC) and nutrient levels (0.1--20
g.m\textsuperscript{-2}) for each combination of body masses in each
food web module (Tables S4--S7), and average these percentages across
all combinations of body masses considered for each module.

\textbf{Results}

Community response to invasion: the role of environmental conditions and
food web topology

Temperature, nutrient levels and size structure of the resident
community influence its composition, stability (Text S2 and Fig. S1) and
response to invasion. We first focus on responses for fixed body mass
ratios \selectlanguage{greek}\emph{α} \selectlanguage{english}= \selectlanguage{greek}\emph{β} \selectlanguage{english}= 10 describing invasions by a 10-fold larger
resource species in the AC module (Fig. 1a), a 10-fold smaller consumer
species in the EC module (Fig. 1b), a large top predator in the TC
module (Fig. 1c), and a medium-sized intraguild prey (Fig. 1d) or a
large intraguild predator (Fig. 1e) in the IGP module.

The impact of an invader on the resident community varies with
temperature, nutrient levels and the invader's trophic position (Fig.
1f-p). The community resists invasion in the following cases: (1) the
invading consumer or predator suffers from metabolic meltdown at
combinations of relatively high temperatures and low nutrient levels
(Fig. 1g-1j, blue area top left), (2) the invading resource (AC module)
or consumer (IGP module) is competitively inferior to resident resource
or intraguild predator, respectively, at a wide range of intermediate
temperatures and nutrient levels (Fig. 1f and 1i, blue area away from
top left and bottom right) and (3) the consumer-resource system
collapses due to the paradox of enrichment at combinations of relatively
low temperatures and high nutrient levels (Fig. 1f-1j, blue area bottom
right).

Successful invasion and occupancy of a vacant niche occur at
combinations of relatively high temperatures and low nutrient levels
that are above the extinction limit (caused by metabolic meltdown) of
the local consumer or predator, but also below the extinction limit of
the invader for invading larger resource species (AC module), smaller
consumers (EC module) and intraguild prey (IGP module; Fig. 1f, 1g and
1i, yellow areas). Invading intraguild predator occupies a vacant niche
when the intraguild prey goes extinct due to the paradox of enrichment
at sufficiently low temperatures and high nutrient levels (Fig. 1j,
yellow area).

Furthermore, a larger resource outcompetes and substitutes the resident
resource in the AC module under environmental conditions just below the
extinction limit of the resident consumer (Fig. 1f, green area), because
a larger resource provides more energy to the consumer due to lower
consumer: resource body mass ratio. An invading smaller consumer (EC
module) and intraguild predator (IGP module) substitute the
competitively inferior resident consumer over a much wider range of
intermediate temperatures and nutrient levels; in the latter case, the
environmental conditions must be sufficiently below the extinction
threshold of the invading predator (Fig. 1g and 1j, green area).

Only invading top predator (TC module) can integrate into the community
across a broad range of environmental conditions (Fig. 1h, light brown
area). Intraguild prey integrates into the community when environmental
conditions are just below the metabolic meltdown threshold of the
resident intraguild predator, making the latter a poor competitor for
the shared prey (Fig. 1i, light brown area). Intraguild predator
integrates into the community when conditions are just below its own
extinction threshold (Fig. 1j, light brown area; note that the
extinction threshold is higher than in Fig. 1i due to the additional
intraguild prey).

Vulnerability to invasion occurs for a smaller consumer in the EC module
at low temperatures and sufficiently high nutrient levels (Fig. 1g,
black area), where the resulting lower consumer-resource mass ratio
triggers population oscillations. Finally, at sufficiently low
temperatures and high nutrient levels, an invading top predator (TC
module) rescues the resident resource by dampening population
oscillations during its temporary presence in the system, so that only
the top predator and resident consumer die out (Fig. 1h, ochre area).

These module-specific outcomes of invasions are reflected in different
effects on community stability. Invading basal resource (AC module),
intraguild prey and intraguild predator (IGP module) does not alter
system stability except the invading intraguild predator, which can
stabilise the dynamics over a narrow range of combinations of nutrient
levels and (low to moderately high) temperatures (Fig. 1l, 1o and 1p).
Successful invasion at low temperatures and high nutrient levels in the
EC module always destabilises the community towards cycles or complete
collapse due to the paradox of enrichment (Fig. 1m). Finally,
successfully invading top predator may or may not change system
stability depending on temperature and nutrient levels (TC module, Fig.
1n).

Community response to invasion: the role of species body mass ratios

We examine the role of body mass ratios in community response to
invasion from two perspectives: competition in the AC, EC and
IGP\textsubscript{C} module and predation in the TC and
IGP\textsubscript{P} module. To this end, we investigate the role of
body mass ratios \selectlanguage{greek}\emph{α} \selectlanguage{english}and \selectlanguage{greek}\emph{β} \selectlanguage{english}between competitors and the role
of size structure asymmetry between multiple trophic levels given
by\selectlanguage{greek}\emph{δ} . \selectlanguage{english}For brevity, we summarise here only the general patterns of
invasion outcomes (Fig. 2) and effects on community regime state (Fig.
3); Text S3 and Table S9 provide further details.

Resistance to invasion and species substitution dominate the results for
the three modules with invading competitors (Fig. 2a-c, S2ab and S3a-c),
with predominantly neutral effects on the community regime (\selectlanguage{greek}Δ\selectlanguage{english}\emph{S} =
0; Fig. S2cd, dotted lines in Figs. 3a-c and S3f-j). Invasion-induced
increase in stability is less frequent but occurs in all modules except
EC (Figs. 2b and S3g). Integration of the invader and rescue of the
resident species are rare and limited to TC and IGP modules (Figs. 2a-c
and S2ab). Invasion-induced vulnerability occurs only for smaller
(\selectlanguage{greek}\emph{β} \selectlanguage{english}\textless{} 1) or, very rarely, much larger (\selectlanguage{greek}\emph{β}
\selectlanguage{english}\(\gg\)1) invading consumers in the EC module (Fig. 2b) and
promotes system instability (Figs. 2b and S3g).

The predominant outcomes in the AC, EC and IGP\textsubscript{C} modules,
i.e. resistance to invasion or substitution of the resident competitor,
correspond to predictions based on the P* and R* rules (Box 2) and
depend strongly on the resident: invader body size ratio (Fig. 2a-c,
Text S4). In the AC module, a smaller competitor can sustain a higher
equilibrium predator biomass and exclude a larger competitor (P* rule,
Figs. 2a, S4a-l and S5a-l). In the EC module, a smaller consumer has
lower resource requirements at equilibrium and therefore excludes a
larger competitor (R* rule, Figs. 2b, S4s-x and S5s-x). Invading smaller
resource in the AC module can stabilise the dynamics and prevent
collapse (\selectlanguage{greek}Δ\selectlanguage{english}\emph{S \textgreater{}} 0 for \selectlanguage{greek}\emph{α} \selectlanguage{english}\textless{} 1; Figs.
3a and S3f), while invasion of a smaller consumer in the EC module can
destabilise the dynamics, leading to population cycles or collapse
(\selectlanguage{greek}Δ\selectlanguage{english}\emph{S \textless{}} 0 for \selectlanguage{greek}\emph{β} \selectlanguage{english}\textless{} 1; Figs. 3b and S3g).
In the IGP module, a smaller intraguild prey is competitively superior
to the intraguild predator (Fig. S6g-l) but cannot withstand its
predation pressure (Figs. 2c and S6m-o). Intraguild prey therefore
collapses immediately after its introduction (Fig. S6m-o) or is
displaced by an invading intraguild predator (Fig. S6a-f) as soon as the
biomass of the latter becomes too high, with a stabilising effect
similar to that in the AC module (for \selectlanguage{greek}\emph{β} \selectlanguage{english}\textgreater{} 1; Fig.
3c).

Community responses to an invading top predator in the TC and IGP
modules vary predictably with the size-structure asymmetry between
trophic levels characterised by \selectlanguage{greek}\emph{δ} \selectlanguage{english}(Figs. 2de and 3de). Successful
invasion of the top predator in the TC module requires the presence of
an intermediate consumer, which is more common with large \selectlanguage{greek}\emph{α} \selectlanguage{english}(Fig.
S1) and thus smaller \selectlanguage{greek}\emph{δ} \selectlanguage{english}values. That is, an invading top predator
is more likely to integrate or to rescue a resident species than to fail
if it is more similar in size to the resident consumer (for
\selectlanguage{greek}\emph{δ}\selectlanguage{english}\textless{} 1, Fig. 2d). In this way, the top predator triggers
oscillations more frequently, but prevents community collapse through
the rescue effect (Fig. 3d). Changes in community composition and
stability decrease when the resident consumer and the resource become
more similar in size (\selectlanguage{greek}\emph{δ} \selectlanguage{english}\textgreater{} 1 in Figs. 2d and 3d). In
this case, the invasion of a comparatively large top predator usually
fails and the resident system collapses due to the paradox of enrichment
driven by the resident consumer-resource interaction (cf. Fig. S1b). On
the other hand, the intraguild predator in the IGP module feeds on two
prey populations, which explains the independence of community
resistance from \selectlanguage{greek}\emph{δ} \selectlanguage{english}(Fig. 2e). Given the influence of the
intraguild prey-resource mass ratio on the dynamics of the resident
system (Fig. S3), species substitution occurs more frequently the more
similar the size of the intraguild predator and intraguild prey
(\selectlanguage{greek}\emph{δ} \selectlanguage{english}\textless{} 1), while niche occupancy occurs more often the
more similar the size of the intraguild prey and shared resource
(\selectlanguage{greek}\emph{δ} \selectlanguage{english}\textgreater{} 1, Fig. 2e). Invading intraguild predator
stabilises the resident community and prevents its collapse more often
as it gets more dissimilar in size to the intraguild prey
(\selectlanguage{greek}\emph{δ}\selectlanguage{english}\textgreater{} 1; Fig. 3e).

Invasion outcomes and the diversity-stability relationship

The effects of invasion on community stability and diversity observed in
our simulations depend on the outcome of the invasion. Invasion-induced
destabilisation occurs primarily under vulnerability, where it almost
always leads to community collapse (regime states \emph{E-N}
and\emph{O-N} ; Figs. 4 and S8, Tables S9--S11). More than half of the
invasions leading to integration and some leading to substitutions also
trigger a loss of stability, with invasion-induced cycles replacing
equilibrium (\emph{E-O} ). We do not observe invasion-induced
destabilisation under resistance, occupancy and rescue mechanisms. An
invasion-triggered increase in stability, which would prevent a complete
collapse of the resident community and is characteristic of the rescue
(\emph{N-E} ), occurs less frequently under occupancy (\emph{N-E}
and\emph{N-O} ) and integration (\emph{N-O} ). An invasion-triggered
increase in stability associated with a shift from oscillations to
stable equilibria (\emph{O-E} ) is rare and occurs only under
substitution and vulnerability (Fig. S1a).

As a result, we find that invasion-induced changes in diversity and
stability are interrelated, but one cannot be predicted from the other
alone (Fig. 4b). Diversity loss (\selectlanguage{greek}Δ\selectlanguage{english}\emph{D \textless{}} 0) is almost
always associated with invasion-induced loss of stability (\selectlanguage{greek}Δ\selectlanguage{english}\emph{S
\textless{}} 0). No net change in diversity (\selectlanguage{greek}Δ\selectlanguage{english}\emph{D =} 0) is mostly
associated with no change in stability as expected, but loss of
stability (invasion-induced cycles in EC) or increased stability (dampen
cycles induced by invasion through species substitution in
IGP\textsubscript{P}) also occur as a result of invasion. Interestingly,
invasions leading to increased diversity (\selectlanguage{greek}Δ\selectlanguage{english}\emph{D \textgreater{}} 0)
have the most evenly distributed effects on stability. About one third
of the simulations each lead to reduced, increased or unchanged
stability across species mass ratios, food web topologies and
environmental conditions (Fig. 4b).

\textbf{Discussion}

Our study summarises how simple communities respond to the combination
of three major drivers of global change: warming, eutrophication and
species invasions (IPBES 2019). While these drivers have received
considerable attention separately (Bellard et al. 2013; Binzer et al.
2016; Gallien \& Carboni 2017), their combined impacts on local
communities remain poorly understood despite some recent advances
(Latombe et al. 2021; Sentis et al. 2021). We focused on two ubiquitous
interactions through which invaders affect resident
communities---predation and competition (Gallardo et al. 2016; Due\selectlanguage{ngerman}ñas et
al. 2018)---to understand how invasion outcomes relate to changes in
community composition, diversity and stability (Tilman 1999). We showed
that the outcomes depend predictably on the interplay between
environmental conditions and differences in body mass and trophic
position between the invader and its local competitor or predator/prey
(Table S12). This allowed us to (i) identify combinations of
environmental conditions, invader traits and community size structure
that characterise communities prone to successful invasions, and (ii)
describe the community-level consequences of such invasions.

What drives successful invasions and when do they occur?

Environmental and biotic filters underpin invasion success in local
communities (Mitchell et al. 2006; Blackburn et al. 2011; Gray et al.
2015). Species living in warm, nutrient-poor environments such as
tropical and subtropical seas (Sunday 2020; Trisos et al. 2020) may be
at risk of metabolic meltdown (Pörtner \& Farrell 2008), while species
living in relatively cold, nutrient-rich environments such as shallow
lakes at higher latitudes (Janssen et al. 2014; Glibert 2017) are
vulnerable to unstable dynamics and community collapse (Oksanen et al.
1981). Previous models have shown that (1) ``intermediate''
environmental conditions that balance the opposing effects of warming
and eutrophication can prevent biodiversity loss and maintain food web
structure and that (2) larger consumer-resource body mass ratios
mitigate the destabilising effect of eutrophication but tend to increase
the vulnerability of top predators to warming (Binzer et al. 2016;
Sentis et al. 2017). Our results extend these findings in the context of
species invasions. That is, large species cannot invade warm,
nutrient-limited habitats because of the risk of metabolic meltdown
(Pörtner \& Farrell 2008), while nutrient enrichment in colder habitats
limits invasions by smaller species due to the paradox of enrichment and
community collapse (Oksanen \emph{et al.} 1981).

Size structure of the local community plays an additional filtering role
in invasions (Gray et al. 2015). We observed that invasion success was
mainly determined by size differences between resident and invading
competitors, while asymmetries in size structure between adjacent
trophic levels determined the fate of invading predators. This can be
explained by the limiting similarity hypothesis, which states that the
coexistence of species sharing the same (trophic) niche requires similar
traits (MacArthur \& Levins 1967), while this requirement does not hold
for invaders in different trophic positions. Apart from competition for
resources, we did not consider self-limiting mechanisms that would lead
to stronger intraspecific than interspecific competition in our models
and favour species coexistence (Holt et al. 1994). In our case, the
application of the R* and P* rules (Box 2; Tilman 1985; Holt et al.
1994) can explain why only smaller competitors could successfully
invade. We also considered a homogeneous environment, which tends to
amplify the impact of invasive species on resident communities through
high levels of interspecific competition, leading to limited coexistence
due to frequent species replacement or strong resistance to the invader
(Melbourne et al. 2007). This is in contrast to heterogeneous
environments, where competing species with different traits can coexist
through niche partitioning (Ricklefs 1977).

Our results also extend previous theory by showing that successful
invasions in the IGP module depend on asymmetric competition between the
intraguild predator and prey (Wootton 2017). Intraguild predators have a
double advantage over pure competitors (as in the EC module) or
specialist predators (as in the TC module): they depend less on a
particular food source and can suppress intraguild prey through high
predation pressure, even if the latter is a better competitor for the
shared resource (Wootton 2017). These results are corroborated by
experiments on intraguild predation between poeciliid fishes along a
productivity gradient (Schröder et al. 2009), where the
larger\emph{Poecilia reticulata} most often successfully invaded the
system and drove the smaller \emph{Heterandria formosa} to extinction.
Here we found that intraguild prey and predator can only coexist when
environmental conditions are close to the metabolic meltdown threshold
of the latter species, i.e. when high temperatures are combined with
nutrient limitation.

Comparing results between modules, we found that intraguild prey
(regardless of body size, IGP module), larger consumer (EC module) and
larger resource (AC module) species were the least likely to
successfully invade. This contrasts with the frequent successful
invasions of intraguild predators (IGP module). Overall, we predict that
successful invasions should involve comparatively smaller species, i.e.
smaller competitors at lower trophic levels and predators that are not
much larger than their prey. Invaders with other traits may need
specific environmental conditions to be successful: for example, larger
competitors at lower trophic levels and intraguild prey may only invade
relatively warm and nutrient-poor environments that are not suitable for
their predators.

When and how do invasions change the diversity and stability of resident
communities?

Overall, our results were consistent with the classic
diversity-stability hypothesis which states that more diverse ecosystems
are more resilient to disturbance (Elton 1927; Tilman \& Downing 1994;
Rooney \& McCann 2012). However, we also observed results that deviated
from this relationship: invaders could either stabilise communities by
increasing local diversity, or they could disrupt initial community
stability (e.g. by integrating an invading predator that destabilises
the local community) and cause species extinctions. Invaders affected
the diversity and stability of resident communities even when their
presence was only temporary. These contrasting findings highlight the
ambivalent role of invasions as both contributors to and threats to
local biodiversity (e.g., Henriksson et al. 2016; Tomiolo \& Ward 2018).

The effect of invasion on the diversity-stability relationship depended
on the outcome of the invasion in our models. Successful invasions led
to variable, outcome-dependent changes in system stability. Our results
suggest that one-to-one species substitutions in simple communities
rarely alter system stability, while invasions that lead to increased
diversity can both destabilise (outcome type: integration) and stabilise
(occupancy and, to a lesser, extent integration) community dynamics. We
have found that these potential changes in stability occur primarily in
relatively cold, nutrient-rich environments in communities that are
vulnerable to population fluctuations caused by eutrophication. These
communities are sensitive to changes in vital rates, which determine the
population dynamics and interactions of their constituent species
(Binzer et al. 2012; Fussmann et al. 2014). For example, a long-term
study of the plankton community in Lake Washington found that community
stability was lowest during a period of increased nutrient loading
following a successful invasion by a subsequently dominant
cyanobacterium (Francis et al. 2014).

Surprisingly, our study revealed that failed invasions can still affect
the diversity and stability of local communities in cold, nutrient-rich
habitats prone to the paradox of enrichment. Diversity could decrease
due to increased population cycles after failed invasions of smaller
consumers (EC module). Diversity could also increase due to rescue by
invading top predators (TC module) if their temporary presence dampened
consumer-resource cycles and rescued the basal resource, but not the
consumer, from the collapse caused by enrichment. Such feedbacks from
transient top predators on resident species might also arise from
cascading effects of an invading top predator on lower trophic levels in
more complex food webs (Woodward \& Hildrew 2002; Gallardo et al. 2016;
Reynolds \& Aldridge 2021). However, adequate evidence of the rescue
effect would require long-term data, ideally from experiments with
controlled introductions and subsequent removal of the invading species
(Bell et al. 2003).

\textbf{Conclusion and perspectives}

Warming and eutrophication are expected to alter the dynamics and
simplify the structure of larger food webs (Brose et al. 2012),
facilitating species invasions and increasing their impact on invaded
systems (Sentis et al. 2021). We have shown how body size and trophic
position determine the fate of species invasions and that species
invasions can mitigate or amplify the negative effects of environmental
stressors on local communities. Our predictions showed that smaller
species are particularly likely to invade communities in warmer,
nutrient-limited environments, while communities facing cold
temperatures and nutrient enrichment are vulnerable to invasions by
larger predators. Invaders can also fill vacant niches when resident
species disappear. For example, the predicted poleward shift of smaller
zooplankton species may benefit warming Arctic habitats (Evans et al.
2020). Invading predators may also buffer local communities against
eutrophic effects at lower temperatures (as in Hughes et al. (2013)).
Therefore, invasive species may not always need to be eradicated or
controlled (Simberloff 2009; Glen et al. 2013), especially if the
associated costs are too high. On the other hand, our findings support
active management and eradication of invaders with negative impacts on
local communities, including those that destabilise local communities
such as small consumers in cold, nutrient-rich habitats (Robertson et
al. 2020). Overall, we predict that species invasions may contribute to
the downsizing of food webs (Young et al. 2016), as successful invaders
will include smaller competitors and comparatively small predators.

\textbf{Acknowledgements:} This research was supported by the Grant
Agency of the Czech Republic (Grant no. 21-29169S). NAP was supported by
the University of Oulu and the Academy of Finland Profi4 Grant 318930
Arctic Interactions (ArcI). AS was supported by the ANR project EcoTeBo
(ANR-19-CE02-0001-01) from the French National Research Agency (ANR).
Computational resources were supplied by the project ``e-Infrastruktura
CZ'' (e-INFRA CZ ID:90140) supported by the Ministry of Education, Youth
and Sports of the Czech Republic. The authors have no conflict of
interest to declare.

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\textbf{Legends}

\textbf{Fig. 1. Community responses to species invasion along
environmental gradients for each food web module.} (a-e) Trophic
position of the invader (blue circle) relative to the resident species
(green circles) under apparent competition (AC, panels a, f and l),
exploitative competition (EC, panels b, g and m), trophic chain (TC,
panels c, h and n), and intraguild predation (IGP) with invading
consumer (IGP\textsubscript{C}, panels d, i and o) and with invading
predator (IGP\textsubscript{P}, panels e, j and p). Invasion outcomes
(panels f-j) as in Box 1 summarize community changes with gain in
diversity (\selectlanguage{greek}Δ\selectlanguage{english}D \textgreater{} 0), no net change (\selectlanguage{greek}Δ\selectlanguage{english}D = 0) or loss in
diversity (\selectlanguage{greek}Δ\selectlanguage{english}D \textless{} 0) after invasion. Regime
states\emph{S\textsubscript{RES}.S\textsubscript{INV}} (panels l-p)
summarize all possible combinations of the system qualitative state
prior to (\emph{S\textsubscript{RES}} ) and after
(\emph{S\textsubscript{INV}} ) invasion leading to a gain of stability
(stabilizing, \selectlanguage{greek}Δ\selectlanguage{english}S \textgreater{} 0), no net change (neutral, \selectlanguage{greek}Δ\selectlanguage{english}S = 0) or
loss of stability (destabilizing, \selectlanguage{greek}Δ\selectlanguage{english}S \textless{} 0) after invasion.
Regime state abbreviations: N = no species present, O = population
oscillations with at least two species present, E = 1 to 3 species in
stable equilibrium. Species body mass ratios fixed at \selectlanguage{greek}\emph{α} \selectlanguage{english}=
\selectlanguage{greek}\emph{β} \selectlanguage{english}= 10.

\textbf{Fig. 2. Module-specific effects of species body mass ratios on
the averaged proportions of invasion outcomes that drive local diversity
change} . Body mass ratio given for (a-c) invader and its resident
competitor (d, e) and adjacent trophic levels. Food web modules: (a) AC
= apparent competition, (b) EC = exploitative competition, (c) IGP =
intraguild predation with invading intraguild prey (\selectlanguage{greek}\emph{β} \selectlanguage{english}[?] \selectlanguage{english}1) and
invading intraguild predator (\selectlanguage{greek}\emph{β [?]}\selectlanguage{english} \selectlanguage{english}1), (d) TC = trophic chain and
(e) IGP\textsubscript{P} = intraguild predation with invading intraguild
predator. Species: \emph{R} = basal resource, \emph{C} =
consumer,\emph{P} = predator. Symbols denote gain of diversity
(squares), no net change (circles) or diversity loss (triangles)
following invasions. Colours as in Fig. 1f-j.

\textbf{Fig. 3. Module-specific effects of species body mass ratios on
the averaged proportions of regime states following invasion.} Body mass
ratio between (a-c) invader and its resident competitor, and (d, e)
between adjacent trophic levels. Food web modules and species as in Fig.
1. Regime state abbreviations: N = no species present, O = population
oscillations with at least two species present, E = 1 to 3 species in
stable equilibrium. Lines = neutral (dotted lines) and non-neutral
(solid lines): influence of invader on local stability regime; symbols =
gain of stability (squares), neutral change (circle) and loss of
stability (triangles) following invasions. Colours identical to Fig.
1l-p.

\selectlanguage{greek}\textbf{Fig. 4. Differences in stability change (Δ\emph{S})between (a)
invasion outcomes and (b) biodiversity change (Δ\emph{D})}\selectlanguage{english}
\textbf{following successful species invasions.} Values = cumulative
proportions of regime states shown in Fig. S1. Biodiversity change in
(b) illustrates the cumulative proportions observed across invasion
outcomes in (a) broken by their effect on diversity, i.e. \selectlanguage{greek}Δ\selectlanguage{english}\emph{D}
\textgreater{} 0 for integration, occupancy and rescue, \selectlanguage{greek}Δ\selectlanguage{english}\emph{D} = 0
for substitution and \selectlanguage{greek}Δ\selectlanguage{english}\emph{D} \textless{} 0 for vulnerability. Change
in stability: \selectlanguage{greek}Δ\selectlanguage{english}\emph{S} \textless{} 0, loss of stability; \selectlanguage{greek}Δ\selectlanguage{english}\emph{S} = 0,
no change; \selectlanguage{greek}Δ\selectlanguage{english}\emph{S} \textgreater{} 0, increase in stability. Note that
resistance to invasion (with \selectlanguage{greek}Δ\selectlanguage{english}\emph{S}= 0 and \selectlanguage{greek}Δ\selectlanguage{english}\emph{D} = 0) is excluded
in both panels.

\textbf{Box}\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
\textbf{Box 1: Invasion outcomes driving local diversity change.}
\textbf{Integration:} Invader integrates and coexists with resident
species (Moyle \& Light 1996), leading to increased diversity.
\textbf{Occupancy:} Invader occupies a niche vacated by a species lost
from the resident community prior to the invasion event (Herbold \&
Moyle 1986), leading to increased diversity. \textbf{Rescue:} Invader
fails to persist in the system but facilitates the persistence of a
resident species that would otherwise go extinct (Brown \& Kodric-Brown
1977), leading to increased diversity. \textbf{Substitution:} Invader
replaces its resident competitor (B\selectlanguage{ngerman}øhn et al. 2008), leaving the
diversity unchanged. \textbf{Resistance:} Invader disappears without
affecting the resident community. This includes both environmental and
biotic resistance to invasion (Moyle \& Light 1996) and leaves the
diversity unchanged. \textbf{Vulnerability:} Invading species
permanently or temporarily destabilizes the resident system and triggers
diversity loss through extinctions (Downing et al. 2012; Macdougall et
al. 2013).\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{ngerman}\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
\textbf{Box 2: Principles of species coexistence and exclusion in
trophic modules} \textbf{P* rule (apparent competition):} The basal (or
prey) species capable of sustaining the highest predation pressure
dominates the competition and can indirectly exclude its competitor due
to higher predation mortality (Holt et al. 1994). \textbf{R* rule
(exploitative competition):} Consumer species with the lowest resource
requirements is competitively superior (Tilman 1985). This can lead to
the exclusion of the inferior competitor or its presence at a lower
biomass density. \textbf{Extinction cascade (trophic chain):} A
specialist predator cannot persist without its prey. Any species loss
within a chain leads to a cascading collapse of all species at higher
trophic levels in that chain. \textbf{Omnivory (intraguild predation):}
Coexistence in the IGP module relies on two principles, i.e., intraguild
prey must be competitively superior to the intraguild predator (R* rule)
and must be resilient to predation-induced mortality to avoid its own
exclusion (Holt \& Polis 1997; Wootton 2017).\tabularnewline
\bottomrule
\end{longtable}

\textbf{Figures}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Fig. 1}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Fig. 2}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Fig. 3}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Fig. 4}

\selectlanguage{english}
\FloatBarrier
\end{document}

