Stochastic Resonance in Climate Reddening Increases the Risk of Cyclic Ecosystem Extinction via Phase-tipping

2025-05-02 0 0 2.21MB 29 页 10玖币

侵权投诉

Stochastic Resonance in Climate Reddening Increases

the Risk of Cyclic Ecosystem Extinction via

Phase-tipping

Hassan Alkhayuon∗

, Jessa Marley†

Sebastian Wieczorek∗, Rebecca C. Tyson†

March 10, 2023

Abstract

Human activity is leading to changes in the mean and variability of climatic param-

eters in most locations around the world. The changing mean has received considerable

attention from scientists and climate policy makers. However, recent work indicates

that the changing variability, that is, the amplitude and the temporal autocorrelation of

deviations from the mean, may have greater and more imminent impact on ecosystems.

In this paper, we demonstrate that changes in climate variability alone could drive

cyclic predator-prey ecosystems to extinction via so-called phase-tipping (P-tipping), a

new type of instability that occurs only from certain phases of the predator-prey cycle.

We construct a mathematical model of a variable climate and couple it to two self-

oscillating paradigmatic predator-prey models. Most importantly, we combine realistic

parameter values for the Canada lynx and snowshoe hare with actual climate data

from the boreal forest. In this way, we demonstrate that critically important species in

the boreal forest have increased likelihood of P-tipping to extinction under predicted

changes in climate variability, and are most vulnerable during stages of the cycle when

the predator population is near its maximum. Furthermore, our analysis reveals that

stochastic resonance is the underlying mechanism for the increased likelihood of P-

tipping to extinction.

1 Introduction

The climate experienced in any local area is rarely consistent from one year to the next.

A series of dry years, will eventually be followed by wet ones, cold winters will eventually

be followed by warm ones. The rate of switching between these climate regimes can be

plotted to determine the expected number of years when conditions will remain either in

alow productivity state, or a high productivity state. Excessively long series of years under

one type of climate, such as that experienced during the extended drought of the Great

Depression in North America, can occur but are unusual under typical variability.

Much attention has been given to the fact that anthropogenic climate change (hence-

forth, climate change) is resulting in a gradual warming of global mean temperatures. Cli-

mate change, however, is also altering the climatic variability, that is, climate variations on

∗University College Cork, School of Mathematical Sciences, Western Road, Cork, T12 XF62, Ireland

†CMPS Department (Mathematics), University of British Columbia Okanagan, Kelowna, BC, Canada

arXiv:2210.02797v2 [q-bio.PE] 9 Mar 2023

the scale of years (also called environmental stochasticity). Existing work has shown that

alterations in climatic variability can have much greater and more immediate impacts on

ecosystems than changes in mean climatic conditions (Hastings et al., 2021; Petchey et al.,

1997; Yang et al., 2019).

Short-term variations in climate metrics (e.g. precipitation, temperature) can be quan-

tiﬁed by their standard deviation, a measure of the amplitude of deviations from the mean,

and their temporal autocorrelation, a measure of the typical frequencies present. One of

the major alterations possible under climate change is a shift in the typical frequencies of

climate variability. More speciﬁcally, if the variability in local climates is analysed to de-

termine the dominant frequencies present, climate change in many geographic locations is

expected to lead to a downshift of these frequencies, or an increase in the temporal auto-

correlation of the climatic variability. In other words, climatic variability has a particular

“colour” (a non-uniform frequency spectrum) in any given location on the globe, and these

frequency spectra are changing shape, on average tending to more “reddened” - or more

autocorrelated - climatic variability (Di Cecco and Gouhier, 2018; T. Lenton et al., 2017; C.

Boulton and T. M. Lenton, 2015). The amplitude component of climatic variability is also

expected to increase with global warming, leading to greater extremes in climate conditions.

Since extreme climate conditions tend to be detrimental or, at the very least, challenging

for ecosystems, these extremes correspond to a further decrease in productivity during low

productivity years. While local conditions can certainly follow diﬀerent patterns of change,

most geographic regions are expected to experience an increase in both the autocorrelation

and the amplitude of climatic variability (Di Cecco and Gouhier, 2018). The combined ef-

fect of these two changes in variability is that poor conditions will last longer, and be more

detrimental, than would be typical under normal variability. This scenario is the focus of

this paper.

The eﬀect of changes in climatic variability on population dynamics has become a matter

of deep concern for ecologists (Vasseur and Yodzis, 2004; Vasseur, 2007b; Vasseur, 2007a;

Petchey et al., 1997; Yang et al., 2019; Hastings et al., 2021). It has been well-established that

environmental stochasticity has a strong eﬀect on population dynamics, and so it is critical

that we understand the eﬀect of changes to this stochasticity. Whether these changes will be

beneﬁcial or detrimental to a given ecosystem is a complex issue (Yang et al., 2019; Petchey

et al., 1997), often with no clear answer (Barraquand and Yoccoz, 2013).

Recent work has demonstrated that increased reddening of climatic variability signif-

icantly increases extinction risk in populations whose dynamics include two stable states

that are stationary, one with high population numbers and one with very low population

numbers (van der Bolt et al., 2018). Here we consider the much less-studied case of a cyclic

system of interacting populations with two stable states: A self-oscillating (or cyclic) coexis-

tence state and a stationary extinction state. Below we describe the importance of oscillatory

states in real ecosystems, and the challenges these states present under climate reddening.

High amplitude multi-annual oscillations around cyclic coexistence states are ubiquitous

in consumer-resource systems, including predator-prey populations (Boutin et al., 1995; Han-

ski and Korpimaki, 1995; B. Kendall et al., 1999). Cyclic predator-prey systems are common

in the Northern Hemisphere (B.E. Kendall et al., 1998), and it is generally accepted that

their oscillations are inherent in the interaction dynamics of the system, i.e., they are not

simply the result of some external environmental forcing (Turchin, 2003). That is, while

external environmental factors certainly inﬂuence predator-prey cycles, these cycles would

continue in the absence of such forcing.

Many climate systems also exhibit either periodic oscillations or typical frequencies

(Bathiany et al., 2018), which can have strong eﬀects on demographic rates (births, deaths,

predation, etc) (Paniw et al., 2021; De Jager et al., 2020; Bastille-Rousseau et al., 2018;

Northﬁeld and Ives, 2013; Svensson et al., 2006). The full ecological-climate system is thus

an oscillator with an external forcing that has characteristic oscillatory components. One

such component is the variability in climate metrics. A classic example is the variability in

the typical frequency and intensity of the El Ni˜no Southern Oscillation (ENSO), which is

associated with the frequency and intensity of wet, cold winters on the eastern coast of the

Paciﬁc (Latif and Keenlyside, 2009). Meaningful changes in the amplitude and/or frequency

of climate metrics are being observed around the globe and are accelerating as climate change

proceeds (T. Lenton et al., 2017; Hodgkins, 2014). These changes could have a strong ef-

fect on environments in which cyclic predator-prey systems currently exist (Bathiany et al.,

2018).

One important example is the snowshoe hare and Canada lynx predator prey system

in boreal North America: This system exhibits high amplitude multi-annual cycles that

aﬀect the entire boreal food web, and is also subject to particularly rapid climate change

(Hodgkins, 2014). The snowshoe hare is a keystone species in the boreal forest, and so its

survival is of critical importance to the entire food web, and to the ecosystem services it

provides to human populations. At the moment, however, it is unknown how the hare-lynx

system will respond to changes in the irregular oscillatory forcing of climatic variability.

It is well-known that externally-driven nonlinear oscillators can exhibit extremely com-

plex behaviour (Martens et al., 2013; Coullet and Emilsson, 1992), and so it is possible that

changes in the colour and frequency of climate variability could put the persistence and

stability of oscillating populations at risk. Here we refer to the stable oscillatory state as

the base state, and to the extinction state as the alternative stable state. We are interested

in the possibility of critical transitions from the base state to extinction due to changes in

the colour and amplitude of climatic variability. Recent analysis of two classic predator-

prey models (Alkhayuon, R.C. Tyson, et al., 2021) shows that oscillatory predator-prey

trajectories are vulnerable to collapse under sudden shifts between high productivity and

low productivity climatic conditions, even if the oscillatory behaviour is stable under both

climates. This new mechanism of collapse, which occurs only during certain phases of the

cycle, is called phase-tipping or P-tipping. This tipping mechanism is in contrast to the more

classical bifurcation-induced tipping or B-tipping that occurs when the base state disappears

in a dangerous bifurcation (e.g. a fold bifurcation), and extinction becomes the only stable

state.

Figure 1 illustrates the basic mechanism of P-tipping, and the accompanying escape

events and rescue events. The purple track represents the limit cycle (the expected steady-

state behaviour under constant climate). It is a ribbon bent in a circle, which we are viewing

from a slightly elevated angle, so that we can see the upper and lower halves of the circular

track, but the sides appear skinny. The green roller-coaster car represents the predator-prey

system, which is oscillating as it follows the limit cycle around the circular track. Climatic

variability results in a stochastic left-and-right movement of the entire track (limit cycle), as

per the black arrows.[Note that changes in climatic variability alter the shape as well as the

position of the limit cycle, and both play a role in determining those phases of the limit cycle

that are vulnerable to P-tipping. In Figure 1, however, we focus only on position changes,

for the purposes of illustration]. If the climatic variability is small, and occurs while the car

is on side (phase) A or C, then, no matter which way the track moves, the car will remain

on the track. That is, the predator-prey system will remain in the basin of attraction of the

limit cycle. If the track shifts rightward while the car is at phase D, the car also remains in

contact with the track. If, on the other hand, the track shifts rightward while the car is at

phase B, the car will escape, i.e., disassociate from the track and fall outside the limit cycle

basin of attraction. So the car is only at risk of falling oﬀ the track if climate variability

occurs in a particular direction and during particular phases of the limit cycle. The system

Figure 1: Illustration of phase-tipping or P-tipping. The purple elliptical track represents the

limit cycle, and the green roller-coaster car represents the predator-prey system. Climate

variability results in movement of the entire limit cycle, as per the black arrows. The car

remains in contact with the track if the limit cycle shifts either right or left while the car is

on side A or C of the track, or if the shift is left/right and the car is in position B/D. If the

limit cycle shifts left/right while the car is in position D/B, the car will fall oﬀ the track.

So the car is only at risk of falling oﬀ the track if climate variability occurs in a particular

direction and during particular phases of the rotation. Hence, the name phase-tipping. In

this example the points A,B,C, and D represent four diﬀerent phases of the cycle.

may not have tipped, however, as it is possible, for at least a short interval, for climatic

variability to shift the system far enough left to rescue the car and put it back in contact

with the track. If the escape event is not followed by a rescue event, however, then the car

will never again be able to return to the track, and the system will have tipped to extinction.

In comparison with the more extensively studied B-tipping, where the base state disap-

pears, extinction via P-tipping can occur in parameter ranges where the traditional under-

standing based on classical bifurcations would predict no vulnerability. Thus, our work is

demonstration in principle of a ubiquitous but far less obvious mechanism for extinction that

occurs even though the base state persists. This mechanism arises from intricate interactions

between the timescale of self-oscillatory predator-prey systems and the timescale of changes

in the local climatic variability.

Having identiﬁed this new tipping mechanism, we are led to ask: Will changes in con-

temporary climate variability interact with the oscillations of real predator-prey systems to

trigger P-tipping to extinction? If so, what is the nature of this interaction and the ensuing

likelihood of P-tipping?

We explore these questions using two paradigmatic predator-prey models with climatic

forcing and an Allee eﬀect in the prey equation so that we can determine if extinction is

deterministically possible. The predator-prey dynamic is parametrised using the critically

important Canada lynx and snowshoe hare system (Krebs et al., 2001; Peers et al., 2020;

Krebs, 2011). Climate variability is represented as changes in the productivity rate of the

prey, and is parametrised using climate data from the boreal forest in North America.

We show that P-tipping can indeed occur for realistic parameter values and changes in

climate variability. Furthermore, we show that tipping likelihood depends nonmonotonically

on the colour of climatic variability, leading to the phenomenon of stochastic resonance

(Gammaitoni et al., 1998; Berglund and Nader, 2022). Our results suggest that the combined

eﬀect of anticipated alterations in the climatic variability and stochastic resonance will result

in an increased likelihood of P-tipping to extinction in the Canada lynx and snowshoe hare

ecosystem in particular, and potentially other cyclic ecosystems in general.

2 Models

Our study requires that we model two systems: The predator-prey system, and the climate

system.

For the predator-prey system we use two paradigmatic predator-prey models presented

in Alkhayuon, R.C. Tyson, et al. (2021) and described in detail in Section 2.1. To ensure

relevance to real predator-prey systems, which is a key aspect of our work, we use realistic

parameters of the extensively studied Canada lynx and snowshoe hare interaction. The

snowshoe hare is a keystone species in the boreal forest, meaning that its survival is critical

to sustaining the boreal forest ecosystem, and the Canada lynx is the hare’s most important

specialist predator. Both species are famous for exhibiting high amplitude multi-annual

oscillations (Krebs, 2011; Turchin, 2001; Krebs et al., 2001).

For our climate model, we need a framework that allows us to control the variability in the

climate time series, and couple it to the predator-prey system. Each variability component,

that is, the amplitude and autocorrelation, responds to global warming in diﬀerent ways. We

therefore model each component with a separate random process; see Section 2.2 for details.

Coupling to the predator-prey system is achieved through the prey productivity rate, which

we consider to be a function of randomly changing climatic conditions. We use data from

four locations in the boreal and deciduous-boreal forest of North America to determine the

appropriate value of the autocorrelation parameter in our climate model; see Section 2.3.

2.1 Predator-prey models

We use the Rosenzweig-MacArthur and May (or Leslie-Gower-May) predator-prey models,

both including an Allee eﬀect, as formulated in Alkhayuon, R.C. Tyson, et al. (2021). We

refer to these models the Rosenzweig-MacArthur-Allee (RMA) and May-Allee (MayA) mod-

els. The variables Nand Prepresent prey (snowshoe hare) and predator (Canada lynx)

respectively. We write the RMA model as

N=r(t)N1−c

r(t)NN−µ

ν+N−αNP

β+N,(1a)

P=χαNP

β+N−δP, (1b)

and the MayA model as

N=r(t)N1−c

r(t)NN−µ

ν+N−αNP

β+N,(2a)

P=sP 1−qP

N+.(2b)

The time-varying productivity rate [In the absence of the Allee eﬀect, r(t) is the prey

intrinsic growth rate, i.e., the prey growth rate at low prey density. With the Allee eﬀect

included in (1a) however, r(t) is no longer the intrinsic growth rate. Nonetheless, this name

continues to be used in the scientiﬁc literature, and there is no established name for the new

role of r(t) in models with an Allee eﬀect. As a compromise, we have chosen here to call

r(t) the prey productivity rate], r(t), is directly proportional to the intrinsic growth rate and

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

StochasticResonanceinClimateReddeningIncreasestheRiskofCyclicEcosystemExtinctionviaPhase-tippingHassanAlkhayuon*,JessaMarley,SebastianWieczorek,RebeccaC.TysonMarch10,2023AbstractHumanactivityisleadingtochangesinthemeanandvariabilityofclimaticparam-etersinmostlocationsaroundtheworld.Thechangingmea...

展开>> 收起<<

Stochastic Resonance in Climate Reddening Increases the Risk of Cyclic Ecosystem Extinction via Phase-tipping.pdf

共29页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Stochastic Resonance in Climate Reddening Increases the Risk of Cyclic Ecosystem Extinction via Phase-tipping

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: