The metabolic origins of big size in aquatic mammals William Roberto Luiz S. Pereira1and Fabiano L. Ribeiro2 Dated October 6 2022

2025-05-06 0 0 2.36MB 16 页 10玖币

侵权投诉

The metabolic origins of big size in aquatic mammals

William Roberto Luiz S. Pereira1and Fabiano L. Ribeiro2*

(Dated: October 6, 2022)

The group of large aquatic mammals has representatives being the largest living beings on earth,

surpassing the weight and size of dinosaurs. In this paper, we present some empirical evidence

and a mathematical model to argue that fat accumulation in marine mammals triggers a series

of metabolic events that result in these animals’ increased size. Our study starts by analysing 43

ontogenetic trajectories of species of diﬀerent types and sizes. For instance, the analyses include

organisms with asymptotic mass from 27g (Taiwan ﬁeld mouse) to 2.107g (grey whale). The available

data allows us to determine all available species’ ontogenetic parameters (catabolism and anabolism

constant, scaling exponent and asymptotic mass). The analyses of those data show a minimisation

of catabolism and scaling exponent in marine mammals compared to other species analysed. We

present a possible explanation for this, arguing that the large proportion of adipose tissue in these

animals can cause this minimisation. That is because adipocytes have diﬀerent scaling properties

in comparison to non-adipose (typical) cells, expressed in reduced energetic demand and lower

metabolism. The conclusion is that when we have an animal with a relatively large amount of

adipose tissue, as is the case of aquatic mammals, the cellular metabolic rate decreases compared to

other animals with the same mass but with proportionally smaller fat tissue. A ﬁnal consequence

of this cause-eﬀect process is the increase of the asymptotic mass of these mammals.

1Independent Researcher.

2Departmento de Fisica (DFI), Universidade Federal

de Lavras (UFLA), Lavras MG, Brazil;

*fribeiro@uﬂa.br

william.roberto.luiz@gmail.com

Key-words: allometric scaling, fractals, length-

weight relationship, ontogenetic growth, fat storage,

metabolism, gigantism.

I. INTRODUCTION

The blue whale (Balaenoptera musculus) is the largest

and heaviest living being, having up to 180 tons [1], [2].

It is 30 times bigger than the heaviest land animal, the

African elephant (Loxodonta africana), weighing around

6 tons [3][4], and twice the size of the largest terrestrial

animals that ever lived, the argentinosaurus (Argenti-

nosaurus huinculensis) [5], a species of Sauropoda di-

nosaur. This enormous diﬀerence in size between whales

and terrestrial animals has to do, in part, with the re-

duced gravity eﬀect in the aquatic environment [6]. How-

ever, what other factors, complementary to gravity, are

acting on the appearance and persistence of such large

marine animals?

Some common explanations for the appearance of large

animals – the so-called gigantism eﬀect [7] – is that es-

sential resources need to be abundant and eﬀectively re-

cycled and reused in a highly developed ecological infras-

tructure; this is a rare biological condition [2]. Moreover,

large animals have an advantage against predators [8]

and also improve the capacity to forage food [7]. Nev-

ertheless, there are also other non-trivial explanations

for the phenomenon, such as genetic adaptations in the

transition from land to water lifestyle [9], intense envi-

ronmental pressure (the Contingency Rule ([10]), and the

evolutionary memory to favour biomass accumulation1.

To sum up, the gigantism eﬀect is, in fact, a multifaceted

phenomenon in which each factor cited above, among

others, contributes to some degree (see [7]).

One trademark of marine mammals is their capacity

to stock fat, especially in pinnipeds (seals), sirenia (man-

atees) and cetaceans (whales). The thickness of the fat

layer (blubber) in cetaceans reaches 20 cm (for example,

in Eschrichlius robustus) and makes up from 15 to 55%

of the body mass [12–15]. In addition to energy stor-

age, the blubber acquired many physiological and physi-

cal functions, such as thermal insulation, aid in ﬂotation

and locomotion, and increasing swimming eﬃciency by

smoothing the body contour [13].

Empirical evidence suggests that the way to store

fat evolved from single-celled organisms (bacteria and

yeasts) to specialized multi-cellular beings. While single-

celled organisms developed regions accumulating lipid

in droplets, the multi-cellular organisms developed their

own adipose organ (in ﬁsh, amphibians, and reptiles)

with the subsequent organization of subcutaneous adi-

pose tissue (in mammals) [16]. It shows that the

adipocytes, cells that store fat and compose the adi-

pose tissue, had their very evolutionary history, which

occurred along with the evolution of large taxonomic

groups.

Here we connect these fat properties with the

metabolism and the ontogenetic scaling properties, spe-

cially using as a starting point the theories developed by

1The biggest aquatic animals, which include the Pinnipedia (seals)

and Cetaceans (whales), have a common ancestor with the com-

mon hippo (Hippopotamus amphibius) [11], one of the heaviest

land animals (up to 3 tons). It suggests that marine mammals

have a genetic framework and an evolutionary memory to favour

biomass accumulation.

arXiv:2210.02183v1 [q-bio.PE] 4 Oct 2022

West et al. [17–20] and expanded by other researchers

[21–26]. Those theories try to explain the empirical evi-

dence that the metabolic rate Rof an organism obeys an

allometric scaling law with its mass min the form [27]

R=R0mβ.(1)

This relation is known by Kleiber’s law, where R0is the

allometric constant and βthe scaling exponent. Empir-

ical evidence suggests that β < 1, which implies that

larger animals are more eﬃcient energetically – demand-

ing less energy per cell [18]. Kleiber’s Law is valid in

inter-species context (i.e. using adult mass of diﬀerent

species) and in intra-species context during ontogenetic

process (using time evolution of mass of a single species)

[23, 28].

West et al. [17] explain such scaling properties as a

transport optimisation process. Natural selection oper-

ates in the eﬃciency of resource distribution, generating

an optimum network distribution where the calibre of the

vessels is hierarchically decreased until capillaries at the

lowest level of branching that are invariant. This opti-

mum network distribution reduces energy expenditure on

transportation, leading to an optimal value of β= 3/4 in

vascular multi-cellular Metazoa [25]. The original West

et al. model is derived with details in [29].

All hypotheses and models to explain transport op-

timization were intensively debated and improved [30]

since the the publication of West et al. work in the later

90s [17]. However, there is no theoretical background yet

to explain why some organisms deviate to lower values of

βfrom the expected values predicted by the West et al.

theory. For instance, there are mathematical foundations

to explain the superior-limit β→1 from microscopic in-

teractions between non-specialized cells [26], but to our

best knowledge lower βvalues have not been treated from

the metabolic/scaling point-of-view.

There are substantial empirical metabolic scaling ﬁnd-

ings in virtually all taxonomic groups and in various ex-

perimental conditions/designs. In relation to theoretical

studies, Glazier [30] describes four research lines to ex-

plain biological scaling: (I) surface-area hypothesis, (II)

network of resource distribution hypothesis, (III) system

composition hypothesis, and (IV) resource demand hy-

pothesis. This classiﬁcation helps us to organize the hy-

pothesis, theories and experimental designs, even though

these theories are not exclusionary, mainly III and IV,

where our work is based.

In the present work, we try to shed some light on this

discussion by combining theoretical (analytical) and ex-

perimental data, showing and explaining the small values

of the metabolic scaling exponent that we observed in

marine mammals (details in section (III)). More speciﬁ-

cally, we use a careful methodology to ﬁt curve-to-data

from ontogenetic trajectories to show that aquatic mam-

mals present a scaling exponent βsigniﬁcantly smaller

than 3/4 – the value predicts by West et al. theory. We

justiﬁed this trend and also the increased size in these an-

imals by the large composition of their adipocytes. More

speciﬁcally, we oﬀer some empirical ﬁndings and a the-

oretical approach to argue that fat accumulation in

aquatic mammals triggers a series of events that culmi-

nates in the increase in the size of these animals.

The paper is organized as follows. In Section (II), we

present the ontogenetic growth model – and its param-

eters – on which our analyses will be based. In sec-

tion (III), we present our analyses for 43 species, in which

we get the ontogenetic parameters for each species. In

section (IV), we discuss the role played by the fat tissue

in marine mammals and present a mathematical model

to demonstrate how the scaling properties of adipose cells

yield a minimization of the energetic demand in such an-

imals. In section (V) we present some biological founda-

tion to the arguments proposed. The paper ﬁnish with

ﬁnal considerations in section (VI).

II. ONTOGENETIC GROWTH MODEL

The ontogenetic models, from Bertalanﬀy and

Richards’s primordial works [31, 32] to the most ad-

vanced and contemporary studies [18, 21, 33], have

been successful in describing individual organism growth.

Speciﬁcally in the seminal work of West et al. [18], the

authors derive the logistic shape of the temporal organ-

ism growth considering that the total energy metabolised

can be used either to create new cells – the anabolism –

or to maintain existing cells – the catabolism.

The idea can be expressed in the mathematical form

R=Ec

dt +NRc,(2)

where Ris the metabolic rate (measured in Watts, i.e.

Joules per second). The ﬁrst term on the right of this

equation, EcdN/dt, is the energy per time dt spend to

create dN new cells, with Ecbeing the energy necessary

to create one new cell, also called activation energy [20]2.

The second term on the right of Eq. (2), NRc, is the en-

ergy per time dt to maintaining the existing Ncells, and

Rcis the cellular metabolic rate, i.e. the energy necessary

to maintain one cell.

The metabolic rate also obeys the allometric law

Eq. (1), and then if mcis the mass of a single cell and

m=Nmcis the mass of the organism, then Eq. (2) leads

dt =Amβ−Bm . (3)

Here, we introduce

A≡R0mc

Ec,(4)

2The activation energy Ecis a meaningful but also controversial

variable. There is a paucity of empirical observations and any

well-established experimental design to measure it.

namely the anabolism constant (measured in

grama1−β/time), which deﬁnes the rate at which

the mass is incorporated into the organism. Note that

A∝1/Ec, which means that this parameter is a measure

of the energy necessary to create a new cell. We also

introduce

B≡Rc

,(5)

namely the catabolism constant (measured in unit of fre-

quency 1/time), which deﬁnes the rate at which the or-

ganism uses the energy for vital demands. Eq. (5) ex-

presses that the catabolism can also be understood as

the relation between cellular metabolic rate and activa-

tion energy.

Eliminating Ecin Eqs. (5) and (4) yields

Rc∝B

A,(6)

that means cellular metabolic rate can be inferred by

the anabolism-catabolism relation. The anabolism con-

stant Ais invariant among species of the same taxonomy

group, since it depends only on scaling invariant param-

eters3. This fact, together with Eq. (6), suggest that

inside the same taxonomy group the cellular metabolic

rate can be understood solely by the catabolism constant,

i.e. Rc∝B.

Equation (3), in turn, has as solution

m(t) = A

B+m1−β

0−A

BeB(β−1)t1

1−β

,(7)

where m0is the initial mass of the organism. This so-

lution diverges for tsuﬃciently large when β > 1 and

B > 0, or when β < 1 and B < 0. However, for β < 1

(sublinear regime) and B > 0, which is in agreement with

biological systems[18], this solution converges to

m(t1) ≡M=A

B1

1−β

.(8)

Here we deﬁne Mas the mature (asymptotic) mass of the

organism. For the special case that β < 1 and B≈0+,

and according to the Eq. (7), the mass growth initially

as power law (given by m(t)∼t1

1−β) and then saturates

to M[26]. More details about the solution of this model

are presented in Appendix A.

III. EMPIRICAL ANALYSES

The empirical base used in this work consists 43 on-

togenetic trajectories collect from the literature, includ-

ing organisms with asymptotic mass ranging from 27g

3However, Amust to diﬀer between distinct taxonomic groups,

since it depends directly on the allometric constant R0, which

varies between taxonomic groups.

Figure 1: Graph showing how the four ontogenetic param-

eters (A,B,βand M) are interconnected one each other.

The straight line, given by Eq. (8), ﬁts the data very well,

regardless of the species. It means that any change in one

of these parameters reverberates automatically in the other

parameters, always maintaining the constraints imposed by

Eq. (8).

(Taiwan ﬁeld mouse) to 2 ·107g (grey whale). The data

and the methodology, described in Supplemental Mate-

rials (B) and (E), allow us to determine the ontogenetic

(macroscopic) parameters (A,B,βand M) for all in-

cluded species.

The ﬁrst ﬁnding that we can obtain after estimating

the four ontogenetic parameters are the strong correla-

tions between their numeric values, as suggested by the

results presented in Fig. (1). One can see that all anal-

ysed species, independently of their type or size, rigor-

ously obey Eq. (8). From this result we can infer that any

change in one of these parameters – for instance caused

by adaptation – automatically reverberates in the other

parameters, always maintaining the constraints imposed

by Eq. (8).

However, when sub-groups of ontogenetic parameters

are analysed, some particularities can be observed, espe-

cially concerning marine mammals. For instance, there

is an evident diﬀerentiation between the marine mam-

mals and the other analysed species in respect to the

anabolism-catabolism relation. One can see in Fig (2)

that there is a strong linear dependence between Aand

B(and the slope is related to Rc, cf. Eq. (6)), which

implies that animals with higher anabolism also tend

to have higher catabolism. However, marine mammals

break this rule, maintaining their catabolism (B) much

lower than it should be (according to this linear rule).

Figure 2: The catabolism constant Bas a function of the

anabolism constant A(in a log-log plot). The data suggest

a strong linear relationship between these constants, and the

slope is related to the cellular metabolic rate (Rc), conform

Eq. (6). However the marine mammals (blue points) break

this rule, presenting a much lower catabolism (B) than should

be (according to this rule). The rainbow trout was the animal

with the lowest anabolism and catabolism constants among

the analysed species, while the male Taiwanese wood rat is the

species with the highest numerical value for these metabolic

constants.

This result, together with Eqs. (5) and (6), suggests that

these mammals have lower cellular metabolic rates.

The catabolism reduction in marine mammals is also

accompanied by a lower scaling exponent βamong these

animals. The scaling exponent of the considered terres-

trial mammals lies in the interval 0.70 < β < 0.99. How-

ever, the scaling exponent for the analysed marine mam-

mals is β≈0.5, that is much lower than the other species.

Fig (3) shows that these large mammals diﬀer from the

other species in terms of both βand B. Marine mam-

mals are the biggest animals among the analysed species

and, at the same time, the ones with lowest scaling ex-

ponent (β) and catabolism constant (B). Consequently,

this large mammals’ metabolism is relatively slow com-

pared to the other analysed species. It is valid to call

the attention that the minimisation of these parameters

in marine mammals is constrained by the relation (8),

which apparently governs the connection between the on-

togenetic parameters (A,B,Mand β).

Extreme cases

To ﬁnalise this section, we would like to discuss two

species of our database that exhibit extreme values of

the anabolism and catabolism constants, i.e. the rain-

bow trout and the Taiwan ﬁeld mouse. The intention

is to show that the organism’s energetic demand – its

Figure 3: Linear-log graph of the scaling exponent βand the

catabolism constant B. The marine mammals (blue points)

diﬀerentiate from the other species: they are the biggest an-

imals between the analysed species and, at the same time,

the ones with lower βand Bvalues. It suggests that these

large mammals’ metabolism is relatively slower compared to

the other analysed species.

metabolism – reﬂects directly in the values of A,Band

β.

The rainbow trout (Oncorrhynchus mykiss), which

lives in the Pongokepuk River, a low-temperature re-

gion in Alaska [34], is the animal with the lowest an-

abolism and catabolism constants among the analysed

species (see Fig. (2)). It is valid to say that ectothermic

animals, like this one, have metabolism directly inﬂu-

enced by temperature [35]. That means that the slower

metabolism of this ﬁsh (small Band A, simultaneously)

is associated with the lower temperatures in its environ-

ment. Moreover, this species exhibits a smaller scaling

exponent than the other non-marine mammal’s species

(β≈0.69).

In contrast, the male Taiwan ﬁeld mouse (Apodemus

semotus) is the species with the highest value of the an-

abolism and catabolism constants (see Fig. (2)), which

is evidence of high metabolism. In fact, this species

reaches sexual maturity very quickly (in 25 days after

being born) [36], expressing a high growth rate (related

to anabolism), demanding a high metabolism. Moreover,

this animal exhibits a larger value of the scaling exponent

(β= 0.99), which is also compatible with this rodent’s

high metabolic demand.

These extreme cases reveal to be consistent with the

assumption that the energetic demand of an organism

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：

ThemetabolicoriginsofbigsizeinaquaticmammalsWilliamRobertoLuizS.Pereira1andFabianoL.Ribeiro2*(Dated:October6,2022)Thegroupoflargeaquaticmammalshasrepresentativesbeingthelargestlivingbeingsonearth,surpassingtheweightandsizeofdinosaurs.Inthispaper,wepresentsomeempiricalevidenceandamathematicalmodelto...

展开>> 收起<<

The metabolic origins of big size in aquatic mammals William Roberto Luiz S. Pereira1and Fabiano L. Ribeiro2 Dated October 6 2022.pdf

共16页,预览4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！

The metabolic origins of big size in aquatic mammals William Roberto Luiz S. Pereira1and Fabiano L. Ribeiro2 Dated October 6 2022

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: