Local intraspecific aggregation in phytoplankton model communities spatial scales of occurrence and implications for coexistence

2025-05-02 0 0 7.89MB 51 页 10玖币

侵权投诉

Local intraspeciﬁc aggregation in phytoplankton model

communities: spatial scales of occurrence and

implications for coexistence

Coralie Picoche1,∗, William R. Young2, Frédéric Barraquand1,∗

1Institute of Mathematics of Bordeaux, University of Bordeaux and CNRS, Talence, France

2Scripps Institution of Oceanography, La Jolla, California, USA

Abstract

The coexistence of multiple phytoplankton species despite their reliance on similar resources

is often explained with mean-ﬁeld models assuming mixed populations. In reality, observa-

tions of phytoplankton indicate spatial aggregation at all scales, including at the scale of a

few individuals. Local spatial aggregation can hinder competitive exclusion since individu-

als then interact mostly with other individuals of their own species, rather than competitors

from diﬀerent species. To evaluate how microscale spatial aggregation might explain phyto-

plankton diversity maintenance, an individual-based, multispecies representation of cells in a

hydrodynamic environment is required. We formulate a three-dimensional and multispecies

individual-based model of phytoplankton population dynamics at the Kolmogorov scale. The

model is studied through both simulations and the derivation of spatial moment equations,

in connection with point process theory. The spatial moment equations show a good match

between theory and simulations. We parameterized the model based on phytoplankters’ eco-

logical and physical characteristics, for both large and small phytoplankton. Deﬁning a zone

of potential interactions as the overlap between nutrient depletion volumes, we show that

local species composition—within the range of possible interactions—depends on the size

class of phytoplankton. In small phytoplankton, individuals remain in mostly monospeciﬁc

clusters. Spatial structure therefore favours intra- over inter-speciﬁc interactions for small

phytoplankton, contributing to coexistence. Large phytoplankton cell neighbourhoods ap-

pear more mixed. Although some small-scale self-organizing spatial structure remains and

could inﬂuence coexistence mechanisms, other factors may need to be explored to explain

diversity maintenance in large phytoplankton.

Keywords: aggregation; coexistence; individual-based model; phytoplankton; spatial

moment equations; spatial point process

∗correspondence to: frederic.barraquand@u-bordeaux.fr &cpicoche@gmail.com

Published in Journal of Mathematical Biology with DOI:10.1007/s00285-024-02067-y

arXiv:2210.11364v2 [q-bio.PE] 22 Apr 2024

Introduction

Phytoplankton communities are among the most important photosynthetic groups on Earth,

being at the bottom of the marine food chain, and responsible for approximately half the

global primary production (Field et al.,1998). Their contribution to ecosystem functions

is only matched by their contribution to biodiversity. Indeed, phytoplankton communities

are characterized by a surprisingly high number of species. For example, a single sample

as small as a few mL can contain up to seventy species (REPHY,2017;Widdicombe &

Harbour,2021). This observation is usually called the “paradox of the plankton” (a term

coined by Hutchinson,1961), which refers to the conﬂict between the observed diversity of

species competing for similar resources in a seemingly homogeneous environment, and models

predicting that only a few species will persist by outcompeting the others (MacArthur &

Levins,1964;Huisman & Weissing,1999;Schippers et al.,2001). Phytoplankton models for

coexistence are now almost as diverse as their model organisms (Record et al.,2014), but they

often describe only a handful of species, which does not correspond to the diversity observed in

the ﬁeld. When modeling rich communities (> 10 species), classical answers to the plankton

paradox involving temporal ﬂuctuations (e.g., Li & Chesson,2016;Chesson,2018) are not

suﬃcient to maintain a realistic diversity. For instance, we found that a phytoplankton

community dynamics model with environmental ﬂuctuations and storage eﬀect still requires

extra niche diﬀerentiation for coexistence, which manifests in stronger intraspeciﬁc than

interspeciﬁc interactions (Picoche & Barraquand,2019). However, it is not clear that we

should resort to hidden niches to explain phytoplankton coexistence, as most models also

make hidden simplifying assumptions that could be relaxed. One that we relax here is mean-

ﬁeld dynamics at the microscale. Indeed, ﬁeld observations have revealed phytoplankton

patchiness for decades, with early records in the past centuries (Bainbridge,1957;Stocker,

2012), from the macro- to the micro-scale (Leonard et al.,2001;Doubell et al.,2006;Font-

Muñoz et al.,2017).

Phytoplankton patchiness can at least be partly explained by the hydrodynamics of their

environment: the size of these organisms is mostly below the size of the smallest eddy (i.e.,

the Kolmogorov scale). In a typical aquatic environment such as the ocean, phytoplankton

individuals are embedded in viscous micro-structures (Peters & Marrasé,2000) while phy-

toplankton populations are displaced by a turbulent ﬂow at slighly larger scales (Martin,

2003;Prairie et al.,2012). Phytoplankton organisms therefore live in an environment where

ﬂuid viscosity dominates at the scale of an individual but turbulent dispersion dominates on

length scales characteristic of a small population of those individuals (Estrada et al.,1987;

Prairie et al.,2012).

This leads us to consider demography in the context of this environmental variation cre-

ated by hydrodynamic processes. Individual-based models provide a convenient depiction of

population dynamics and movement at the microscale (Hellweger & Bucci,2009). In this

framework, population growth is a result of individual births and deaths. Aggregation of

individuals can emerge from local reproduction coupled with limited dispersal, which can

happen in a ﬂuid where turbulence and diﬀusion are not strong enough to disperse kin ag-

gregates (Young et al.,2001). The resulting local aggregation can then aﬀect the community

dynamics at larger spatial scales, even when all competitors are equivalent (i.e., with equal

interaction strengths irrespective of species identity). Indeed, the combination of local dis-

persal after reproduction and local interactions leads to stronger intraspeciﬁc interactions

than interspeciﬁc interactions at the population level (Detto & Muller-Landau,2016). This

mechanism stabilizes the community, as a high intra-to-interspeciﬁc interaction strength ratio

makes a species control its abundance more than it controls the abundance of other species,

which is associated with coexistence in theoretical models (Levine & HilleRisLambers,2009;

Barabás et al.,2017) and often observed in the ﬁeld at the population level (Adler et al.,

2018;Picoche & Barraquand,2020). Therefore, the microscale spatial distribution of indi-

viduals likely aﬀects the interaction structure within a community, and may sustain diversity

(Haegeman & Rapaport,2008).

Existing models of phytoplankton populations near the Kolmogorov scale — between 1

mm and 1 cm in an oceanic environment (Barton et al.,2014) — focus on a single species and

the clustering of its individuals (Young et al.,2001;Birch & Young,2006;Bouderbala et al.,

2018;Breier et al.,2018). These models share similarities to dynamic point process models

(Law et al.,2003;Bolker & Pacala,1999;Plank & Law,2015) developed initially with larger

organisms in mind. When phytoplankton individual-based models consider multiple types of

organisms, they focus for now on how organisms with opposite characteristics (e.g., increase

versus decrease in density with turbulence in Borgnino et al.,2019;Arrieta et al.,2020)

segregate spatially, or on coexistence of species that have contrasting trait values (e.g., size

in Benczik et al.,2006). Such models are useful as an explanation of how species with marked

diﬀerences might coexist. The diﬃculty of the coexistence problem, however, is that we also

have to explain how closely related species or genera (e.g., within diatoms), many of whom

have similar size, buoyancy, chemical composition, etc., manage to coexist within a single

trophic level. This requires modelling similar species in a spatially realistic environment and

objectively quantifying whether they aggregate or segregate in space.

To do so, we build a multispecies version of the Brownian Bug Model (BBM) of Young

et al. (2001), an individual-based model which includes an advection process mimicking a

turbulent ﬂuid ﬂow, passive diﬀusion of organisms, as well as stochastic birth and death pro-

cesses. The initial version of this model (Young et al.,2001) coupled limited dispersal and

local reproduction with ocean-like microscale hydrodynamics, and showed spatial clusters of

individuals of the same species. The original BBM was limited to a single species and was

illustrated with two-dimensional simulations. The model was not strongly quantitative (Pic-

oche et al.,2022) in the sense that parameters were not informed by current knowledge on

phytoplankton biology (numbers of cells per liter, diﬀusion characteristics, etc.). As phyto-

plankton organisms live in a three-dimensional environment, informing the model with more

realistic parameters requires us to shift to three dimensions. We also extend the model to

multiple species, and consider two size classes for our phytoplankton communities, which are

either made of nanophytoplankton (3 µm diameter, ≈106cells L−1) or microphytoplankton

(50 µm, ≈104cells L−1). We populate each community with 3 to 10 diﬀerent species.

The Brownian Bug Model (in its original single-species form as in the multispecies ver-

sion considered here) is related to spatial branching processes. Without advection, it com-

bines a continuous-time, discrete-state model for population growth and a continuous-time,

continuous-space Brownian motion for particle diﬀusion (Birch & Young,2006). It is fur-

ther complexiﬁed by a turbulent ﬂow in Young et al. (2001); Picoche et al. (2022) as well

as here. In spite of this complexity, it remains possible to derive the dynamics of pair den-

sity functions, which quantify the degree of intra- and interspeciﬁc clustering of organisms,

via correlations between positions of organisms (see next section). Thus we can understand

emergent spatial structures in analytic detail and compare these predictions to the results

from three-dimensional simulations. Furthermore, because we do not consider direct inter-

actions between organisms, the multispecies spatial point process that represents the stable

state of the BBM is a random superposition of spatial point processes for each species (Illian

et al.,2008). This enables us to derive, in addition to pair correlation functions, analytical

formulas for the species composition in the neighbourhood of an individual, which are more

readily ecologically interpreted than pair density or correlation functions.

Model and spatial statistics

Brownian Bug Model

The Brownian Bug Model (BBM) describes the dynamics of individuals in a turbulent and

viscous environment, including demographic processes. The model is continuous in space

and time. Here we extend the mostly two-dimensional, monospeciﬁc version in Young et al.

(2001), to three dimensions and Sspecies.

Each individual is characterized by its species identity iand its position xT= (x, y, z).

The population dynamics are modelled by a linear birth-death process with birth rate λi

and death rate µi. Each individual independently follows a Brownian motion with diﬀusivity

Di, and is advected by a common stochastic and chaotic ﬂow modelling turbulence. The

model applies in the Batchelor regime, which means that the separation s(t)between two

individuals kand lgrows exponentially with time with stretching parameter γ, i.e., s(t) =

ln (|xk−xl|(t)) ∝3γt (Kraichnan,1974;Young et al.,2001).

Within a given community (the set of all individuals of the Sspecies), all species share the

same parameters: λi,µiand Divalues can change between communities, as we later consider

small and large phytoplankton, but are set to common values within a community. On the

contrary, γdescribes the environment and is not community-speciﬁc, i.e., all individuals

are displaced by the same turbulent stirring. For numerical simulations, time needs to be

discretized (this is required for diﬀusion and advection modelling). The approximated model

advances through time in small steps of duration τ. During each interval, events unroll as

follows:

1. Demography: each individual can either reproduce with probability pi=λiτ(forming

a new individual of the same species iat the same position xas the parent), die with

probability qi=µiτ, or remain unchanged with probability 1−pi−qi.

2. Diﬀusion: each individual moves to a new position x(t′) = x(t) + δx(t), with t < t′<

t+τ. The random displacement δx(t)is drawn from a Gaussian distribution N(0,∆2

with Di= ∆2

i/2τthe diﬀusivity. This diﬀusive step separates the initially coincident

pairs produced by reproduction in step 1 above.

3. Turbulence: each individual is displaced by a turbulent ﬂow, modelled with the Pier-

rehumbert map (Pierrehumbert,1994), adapted to three dimensions following Ngan &

Vanneste (2011). Thus given the position at time t′the updated position at time t+τ

x(t+τ) = x(t′) + Uτ

3cos (ky(t′) + ϕ(t))

y(t+τ) = y(t′) + Uτ

3cos (kz(t′) + θ(t))

z(t+τ) = z(t′) + U τ

3cos (kx(t+τ) + ψ(t)) .

(1)

Above, Uis the velocity of the ﬂow, k= 2π/Lsis the wavenumber for the ﬂow at the length

scale Ls(see below) and ϕ(t),θ(t),ψ(t)are random phases drawn from a uniform distribution

between 0and 2π; these phases remain constant during the interval between tand t+τ.

The shift from continuous to discrete-time turbulence modelling is described in Section S1 in

the Supplementary Information. The velocity Uis related to γ. As the separation between

two points grows exponentially with parameter 3γdue to turbulence, the exponent γcan be

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：

Localintraspecificaggregationinphytoplanktonmodelcommunities:spatialscalesofoccurrenceandimplicationsforcoexistenceCoraliePicoche1,∗,WilliamR.Young2,FrédéricBarraquand1,∗1InstituteofMathematicsofBordeaux,UniversityofBordeauxandCNRS,Talence,France2ScrippsInstitutionofOceanography,LaJolla,California,U...

展开>> 收起<<

Local intraspecific aggregation in phytoplankton model communities spatial scales of occurrence and implications for coexistence.pdf

共51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！

Local intraspecific aggregation in phytoplankton model communities spatial scales of occurrence and implications for coexistence

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: