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Impure Systems and Ecological Models (II): Components and Thermodynamics

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Abstract

This paper refers to a subjective approach to Ecosystems, referred to as Impure Systems to capture a set of fundamental properties. There are four main phenomenological components: directionality, intensity, connection energy and volume. A fundamental question in this approach to Impure Systems is the intensity or forces of a relation. Concepts as the system volume, and propose a system thermodynamic theory based in the Law of Zipf and the temperature of information are introduced. It hints at the possibility of adapting the fractal theory by introducing the fractal dimension of the system.

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Notes

  1. Methane production can be described as a dissipative process of entropy when a highly organized organic structure is decomposed to basic simple compounds.

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Funding

This work has been funded by the Conselleria de Educación, Investigación, Cultura y Deporte of the Community of Valencia, Spain, within the programme of support for research under project (GV/2018/061).

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Alicante, Alicante, Spain

    Josué-Antonio Nescolarde-Selva, José-Luis Usó-Doménech & Miguel Lloret-Climent

Authors
  1. Josué-Antonio Nescolarde-Selva
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  2. José-Luis Usó-Doménech
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Correspondence to Josué-Antonio Nescolarde-Selva.

Appendix

Appendix

1.1 The Mariola Model

a. State variables

Y

Description (unit)

BL

Woody biomass (g)

BV

Green biomass (g)

MOTS

Total organic soil material (%)

NRO

Organic material of animal origin on the ground (g)

RBL

Litter of woody biomass on the ground (g)

RBV

Litter of green biomass on the ground (g)

b. Flow variables

X

Description (unit)

ARRS

Rate of loss of the organic soil material through dragging and washing (%)

CRBL

Rate of production by growth of the woody biomass (g)

CRBV

Rate of production by growth of the green biomass (g)

DBLAR

Rate of destruction of the woody biomass through the action of arthropods (g)

DBLPL

Rate of destruction of the woody biomass through the action of phytoplagues (g)

DBVFS

Rate of destruction of the green biomass through the action of mammals (g)

DBVI

Rate of destruction of the green biomass through the action of insects (g)

DBVPL

Rate of destruction of the green biomass through the action of phytoplasgues (g)

DCBL

Rate of catastrophic destruction of the woody biomass (g)

DCBV

Rate of catastrophic destruction of the green biomass (g)

DF

Rate of defoliation (g)

DMOTS

Rate of decomposition of the total organic soil material (%)

DRBL

Rate of decomposition of the litter of the woody biomass on the soil (g)

DRBV

Rate of decomposition of the litter of the green biomass on the soil (g)

DRO

Rate of decomposition of the detritus of an animal narure (g)

MOFD

Rate of finely divided organic material (%)

PMOTS

Rate of production of organic soil material (humus) (%)

PRO2

Rate of production of organic detritus of animal origin (g)

VMN

Rate of destruction of the woody biomass (g)

c. Exogenous variables [semes of first level]

e

Description (unit)

H

Environmental humidity (%)

IFAP

Maximum intensity of precipitation (max.l/h)

PLU

Precipitation (l)

POBHV

Population of mammals (Oryctolagus cuniculus) (number of individuals)

T

Environmental temperature (°C)

VEVI

Wind speed (km/h max)

d. Auxiliary variables and parameters

a

Description (unit)

BT

Total biomass (g)

CRO2

Parameter of residual production of the rodents (g)

PORDT

The herbivore diet (%)

1.1.1 State Equations

$$\begin{aligned} \frac{dBV}{dt} & = CRBV - DF - DCBV - DBVFS - DBVI - DBVPL \\ \frac{dBL}{dt} & = CRBL - VMN - DCBL - DBLAR - DBLPL \\ \frac{dRBV}{dt} & = DF + DCBV - DRBV \\ \frac{dRBL}{dt} & = VMN + DCBL - DRBL \\ \frac{dNRO}{dt} & = PRO2 - DRO \\ \frac{dMOTS}{dt} & = PMOTS + MOFD - DMOTS - ARRS \\ \end{aligned}$$

Flow and auxiliary equations for MARIOLA (Cistus albidus) [SEMEMES]

CRBV = BT(0.0011T + 0.0028 H − 0.0271) + 0.012 PLU − 0.1436

CRBL = 0.6773 BT − 0.0079 BT H + 0.0004 BT PLU − 3.1864

BT = BV + BL

DF = 1.2382BV 2 − 0.0025BV − 0.0063BV T − 0.0081 BV H + 17.47630/PLU) − 0.9696

DBVFS = 0.000428BV 2 + 0.087560BVPOBHV − 0.184747

DCBV = 0.0020 BV IFAP + 0.0007 BV VEVI + 0.0007 exp(0.1 IFAP) + 0.0020

DBVPL =− 0.00064BV 2 + 0.0066BV T − 0.3142cos H − 1.0665

VMN = 0.0187 BL + 0.0001 BL PLU − 0.5732

DCBL = 0.7023 cos BL + 0.0005 BLIFAP + 0.0003 BL VEVI − 0.4707

DBLPL = 0.0022BL T + 259.9959exp(− 0.1 BL) − 1.4981cosBL − 3.59

CR02 = 1900

PORDT = 2.8949log(DBVFS) − 5.0052

PR02 = POBHV CR02 × (PORDT/100)

DRBV = 0.0007 T 2 − 0.0041T RBV + 0.0021 H RBV + 0.00002exp(0.1 H) − 0.3774

DRBL = − 0 .0030 T 2 + 0.0005 TH + 0.121 exp(0.1T) + 0.0170cos H − 0.3125

DRO = 0.0538NRO T − 0.0016 T 2 + 1.1457cosNRO − 0.8088

PMOTS = (0.0045T 2 − 0.0013 TH − 0.1623 T DBL + 0.3111T DBV + 0.5191 cos T + 1.1102DRO + 1.0542)/100

MOFD = (− 0.0287 T 2 + 0.0058 TH + 1.0304exp(0.1T)− 0.0002exp(0.1 H)− 2.3152)/100

DMOTS = [MOTS(− 0.0509 MOTS + 0.0133 T + 0.0012 H + 0.0014 PLU) + 0.0018 T 2 − 0.0509)/100

ARRS = (− 0.0065 T 2 + 0.0024

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Nescolarde-Selva, JA., Usó-Doménech, JL. & Lloret-Climent, M. Impure Systems and Ecological Models (II): Components and Thermodynamics. Found Sci 24, 427–455 (2019). https://doi.org/10.1007/s10699-018-9575-x

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