Gifting for ecosystem services: Economic and ecological analysis of soil
biodiversity services in agricultural lands
Ernst-August Nuppenau
T.S Amjath Babu
May 2010
Names and Institutional Affiliation of Authors:
Ernst-August Nuppenau, Professor (First Author)
T. S. Amjath Babu, Postdoctoral fellow (Co author)
Institute for Agricultural Policy and Market Research
Justus Liebig University
Senckenbergstrasse 3
D-35390 Giessen, Germany
Email: [email protected]
Key words: Gift economy, reciprocity, soil biodiversity, valuation
Sunmitted to: 12th Annual BIOECON Conference "From the Wealth of Nations to the Wealth of
Nature: Rethinking Economic Growth"
Gifting for ecosystem services: Economic and ecological analysis of soil
biodiversity services in agricultural lands
1. Introduction
Soil organisms are essential service providers for all ecosystems by providing a variety of functions
such as recycling of nutrients, controlling physical structure of soil, enhancing nutrient absorption by
plants, protecting plants from diseases and augmenting plant health (Altieri, 1999). In ecological
terms, soil organisms have value in the sense that they contribute to the condition or to the ‘fitness’ of
an ecological system where the ultimate objective is the ‘survival’ (Farber et al., 2002). Nevertheless,
ecological services provided by the soil biota have value in an economic sense, only when they are
scarce (Underwood, 1998). The value is reflected by the price, which is the willingness to pay for a
marginal increase in their scarce services (Heals, 2000). The appreciation of functions soil biota when
a price can be attached to their services leads to unappreciation of a major share of their contributions
to the ecosystem survival. In this scenario a discussion on alternatives to monistic valuation of
ecosystem services based on willingness to pay instrument is essential (Norton and Nooman, 2007).
In a capitalistic framework, it is implicitly assumed that goods are having value only when they are
exchanged through a market. In this paper, we discuss gifting and reciprocity as an alternate mode of
exchange. The motivations of gift exchange are different from market transactions and hence it is an
under estimated alternative. But persistence of non-market transactions even in current times is hard
evidence that it is a viable alternative (Offer, 1997). The core of market mechanism lies in the
assignment of property rights. The fact that one can not attach property rights to nature, in our case, to
soil organisms and can not confer the right to demand compensation, makes the alternate exchange
mechanisms much more appropriate. It is not possible to abstract the nature and human exchanges to a
level of commoditization and service extraction and hence these exchanges do not have the
characteristics of market transactions. Considering nature and human interaction in the form of a gift
exchange could reflect human behavioral aspects such as recognition of rights, voluntary provision,
non-pecuniary evaluation, and relative importance of value in natural and human spheres. This
possibility will eventually allow us to gain a different insight into an exchange between humans and
nature.
In the field of anthropology, gifting as an exchange mechanism is long been recognized. In the case of
hunting and gathering economy, gifting acted as an exchange mechanism in the absence of money.
The theory of gifting worked out by anthropologists (Sahlin, 2002) documents the role of such
exchange mechanisms based on reciprocity. The modern times witnessed ‘great transformation’ from
such socially embedded reciprocity to impersonal price mediated market exchange (Offer, 1997).
From the latter, a new transformation to environmentally embedded reciprocity is currently required.
The aim of this paper is to contribute towards gifting and reciprocity as mechanism to coordinating
exchange between humans and nature in general and farmers and soil biota in particular. Reciprocal
exchanges preferred when the goods and services are unique, multi dimensional in quality or
expensive while market is a better medium when the goods are inexpensive and standardized (Offer,
1997). It can be easily appreciated that the soil biodiversity services fall in the former category. The
paper is organized in three sections viz. 1) establishment of the problem statement, 2) introduction into
the provision and optimization of farmers and soil biodiversity services, and 3) elucidation of co-ordination mechanisms that lead to mutual resource allocation as well as allows exposition of corresponding values. Formulation of the exchange system is through a mathematical approach that uses linear
and non-linear programming as well as a formal approach on expectations in terms of probabilities for
reciprocal action. As a systematic result, this modeling on gift exchange can be considered an
alternative to market pricing.
2) Problem statement
Taking the philosophical debates on human nature relationship for granted, it is argued that there is a
need of reciprocity and mutual benefits can be obtained. It is estimated that soil microbes in the topsoil
process over 100 tons of organic matter per hectare per year (Chiurazzi, 2008). Indeed, the soil
microbes will not think that their services (having costs) are translated to goods and demand labour or
goods from humans. Nevertheless, humans can visualize a non-exploitative relationship with nature
and healthy soils can provide better services. This is equivalent to a change from slavery to free
labour. Delineating the economics of the mutual appreciation (human utility and nature fitness) and
deriving the labour and wage exchange rates is daunting task. One way to address this problem is to
simulate behaviour of the soil biota as if to achieve an objective function, for instance survival of
species (Farber et al., 2002 and Eichner and Pethig, 2006). In this respect, an action (gift) from
humans is needed to relax the constraints on soil biota’s objective and to allow a better ‘performance’.
Such actions cost humans as they have to sacrifice something of value for nature. However, such a
sacrifice may bring them a net-return of greater value, increased eco-system service. To frame such an
exchange system, a response function has to embed in soil Biota’s objective function. This response
function has to be in the form of an incentive scheme as no humans work with out incentives. It is to
be noted that the incentive scheme embedded in the objective function is devoid of money.
Let us now discuss on what could replace the role money in the proposed exchange system. To have
some idea, we have to go back in time and observe in periods where there were no states, money and
contracts. Gifting as an exchange mechanism evolved in such tribal economies which allowed them to
profit from tool exchange and material bartering (Sahlin, 1972). The gifting and reciprocity allowed
them in mutual valuation of exchanged goods. It is evident, that the tribal exchange was done by
independent parties and that it contained a prestation (the obligation to return a gift if one receive a
gift). This human to human gifting in tribal economy is extended towards human to nature gifting and
the probabilities take the role of money. How the probabilities inform participants in the exchange on
expected gifts will be subsequently shown. Gifts are obtainable by the mutually providing gifts
(reciprocation).
3) Model outline
3.1 The concept
In the case of soil biota, gifting and counter gifting is relative to the state of nature. In natural
ecosystems where scarcity might not be the problem, gifting with humans may be irrelevant. But in
agro-ecosystems, the exchange with humans can relax the constraints over rendering of microbial
services. Again it depends on frameworks what is a gift. For example, in case of a soil microbial
biodiversity of agricultural lands, laboring for agricultural practices favouring microbial growth are
gifts of humans. The question is what should be the size of labor rendered to nature. In a classical
sense the answer would be a nature production function (Wossink et al., 2001). Implicitly, it can be
assumed that nature is optimizing its behavior to achieve an objective function, for instance survival of
species (Farber et al., 2002) and hence a maximizing mechanism is ‘built’ in nature. A number of
studies assume greater efficiency in assimilating energy as objective of species and argue that it is
implicit in natural selection (Finnoff and Tschirhart, 2003 quotes studies of Lotka (1925), Herendeen
(1991) and various studies of Hannon). This is also in line with species-energy theory (Wright, 1983).
In the current study, we postulate that nature (here soil biota) minimizes its energetic losses given
organic and in-organic constraints and such a postulation of objective function can be used to receive
an optimizing performance (following Eichner and Pethig, 2006). It allows the set-up a behavioral
equation that emulates a response function to gifts. The distinctive feature is that the medium of
exchange is not money but the probable “willingness” of nature to provide a gift (see later sections for
the description). The chosen approach does not say what nature ‘should do’, rather follows an ‘as-ifapproach’ which will allow us to retrieve coefficients of expected gifting. This will fit nature into a
‘gift economy’ with humans.
The modeling concept in this respect is those of a food producing farmer who has the choice to rely on
soil microbial biodiversity services or buy these services as equivalents. By the term ‘soil microbial
biodiversity’, we mean the functional diversity. Services from soil biota that, the farmer seems to
receive for free, are of values but are actually calculated at opportunity costs. If he facilitates the
proper conditions for the soil micro organisms to develop, the capacity of the soil to deliver services
increases. For this increase the farmer devotes labor. His gifting behavior will be retaliated by
probable gift receipts as services from nature through a microbial species vector. Assigned
probabilities on efforts, in a two directional choice, will direct on how much resources farmers have to
devote for nature. Expected services play a major role and expectations become interrelated.
3.2 Role of probabilities
Probabilities have a crucial role in modeling interconnectivity, reciprocity, learning and dynamics and
hence driving the system to a steady state. Steady states can be interpreted as system equilibriums in
which, under certain conditions, optimal gifting evolves. There is no physical balancing foreseen at the
moment like in markets. Balancing means that a mismatch between expected and actual exchange will
have future impacts through forces rearrangement and adjustment. As it could be foreseen, there may
not be any immediate reactions like of the supply and demand concepts which will enforce the gift
equilibrium. In this respect probabilities play a different role than price. They are not to be considered
the same as prices. For instance, if a mismatch has occurred, the system wealth may decline. From the
decline humans learn and nature adapts. Declines can be offset by actions demanding reciprocity with
a certain probability. The system can stabilize again. Learning is considered a positive self-enforcing
process where match or mismatch of actual and expected gifts leading to learning on probabilities of
reciprocity.
Since we work with probabilities, a short explanation is needed how probabilities are to be interpreted
in our given context of learning on probabilities. Usually, the interpretation is that probabilities are
exogenous to the individual. A departure from ordinary statistics in our context is that they shall not be
purely driven by chance; rather they are portrayed as been subjective. In a pure stochastic case, the
probability depends on the underlying probability density function. We slightly change the meaning
and consider probabilities as subjective assessment of chance. The assessment of behavior using
probabilities serves to find directions for devoting resources, i.e. which gift to nature offers higher
promise (likelihood, confidence or chances) to get eco-system services. The size of probabilities, again
has to be seen as subjective assessment of chances and it changes based on the trust in nature’s
delivery of service. A gradual process shall underpin the process of trust formation depicted as
learning. For our purpose we choose a simple way of adaptive learning in which the previous experiences allow a recalculation of chances to get a gift. Such learning can be even named rational if a
trend is, for instance, foreseen (Pashigian, 1970). In order to do so we have to identify expectations,
chances and realizations of chances for a mutual gifting or gift-exchange in a sense of a systematic
change (tendencies). The match or mismatch of both, expectations and realization, is another core
aspect. For this we derive a dependency of the learning functions on matching of expectation and realization. As been necessarily done in dynamic models for the depiction of an adjustment (mismatch
between supply and demand as well as incentives to correct), our model contains an explicit dynamic
formulation of the adjustment. Furthermore we have to include a residual stochastic element in the
exchange. So a mismatch can happen due to a residual stochastic (no-recognition, no-mutual esteem,
no gifting, and no co-operation) term. The skill is in finding a ‘willingness’ of nature to reciprocate to
the ‘willingness’ of humans to concede exploitation. This aspect matters when it comes to an
investigation of empirical cases and practical application. Learning is empirical. For the moment we
want to establish the underlying theory of exchange.
3.4 learning of probabilities
The consecutive part of this outlay is based on the distinction between expectations and its realization.
Gifting is voluntary, but not random. It is characterized by expectations, corrections and constraints.
For example, eco-system services ‘required’ by humans can be ‘under-provided’ by nature and then
farmers face shortages. The farmer behavior is optimized based on expectation of delivery of soil ecosystem service. If the expectation is not realized, a discrepancy occurs. An initial discrepancy will
have an impact on the willingness of farmers to deliver labor in exchange with soil microbial diversity
services. Discrepancies and directions of change impact on probabilities of response. Only, finally, in
a steady state, a reasonable match of expectation and delivery is presumed. In the model, it means a
feedback loop has to be anticipated. Learning could go along the premise that the chance ‘π’ of receiving a gift as soil biodiversity service ‘z’ for a farmer depends on his last expected probability
(chance). Adjustment is the difference between anticipated and realized eco-system services. So
modifications of expectation take place on chances and adapted match of physical “delivery” in (1)
(Pashigan, 1970).

e
f ,t
  f ,t 1   11[ f ,t 1   f ,t 1]   12 [ z f ,t 1  z f ,t 1]   13 [l f ,t 1  l f ,t 1]
e
e
a
e
a
e
a
(1)
where:
πe
= probability; subscript: f: farmer, t: period, t-1: pervious period ; superscript: e: expected, a:
actual
z
= soil eco-system service; subscript: t-1: pervious period; superscript: e: expected, a: actual
l
= labour devoted; subscript: t-1: pervious period; superscript: e: expected to be to delivered, a:
actual
The subjective assessment of chances ‘π’ will be used as indication of chances of receiving the gift
(ecosystem service) in the objective function of farmers.
4) Rational of farmers for gifting
4.1 Programming overview
For modeling the behavior of a farmer who offers a gift to soil biota and receives eco-system
services as a gift, a linear programming (LP) approach is used. Instead of income
maximization used in usual farm programming models, the current model works with effort
minimization (Ellis, 2003) as the objective. Note, since a dual outcome of labor (effort)
minimization is a benefit function, income maximization is dual to labor (effort) cost
minimization under certain conditions. For our purpose the essential modification is the
inclusion of a gift as a constraint. Here the gifts are labour provision for management
practices that enhances better soil biodiversity services. For the reason to reduce complexity
we further assume that farm gate prices reflect scarcity and perfect markets for food exists
(De Janvry et al., 1991). Whence a primal problem of a linear programming approach can be:
 [ p f
 c] ' x f
n
n
A x
s.t.
f
n
f
 rf
where:
x
n
f
rf
= choice of crops
= constraints
It results in a solution for farm activities xf, which is complemented with a dual problem of
Lr f 
n
s.t.
n
A '  nf
f
(2)
f

pf
c
where additionally:
λn
= shadow price for restrictions
As shown, the method used to infer rationality of gifting and demonstrating how a gift
response function is obtained, is linear programming (LP). LP is used to depict choices.
Additionally LP can be expanded to quadratic programming (QP) by the statistical concept of
maximum entropy (Following Paris and Howitt, 2000). In this approach a limited data set of
constraints, objectives, and a representative farm technology are the only requirements to infer coefficients of a quadratic objective function of farmers. This specification can be used to
derive supply and factor evaluation function (inverse of factor demand functions). These
behavioral functions are linear by mathematical reasoning. Gifting to nature is added on the
side of constraints. This perspective requires some amendments on the side of programming.
First we have to decide on what a gift for nature is and what a gift of nature is, from the
perspective of farming.
 [ p f
 c] ' x f
n
n
s.t.
A x
f
n ,l
A x
f
n
f
n ,n
A x
f
(3)
 rf
n
f
n
f
 lf lf
t
n ,o
n ,n
 sn  a of
z
h ,a
f
where additionally:
z: soil biodiversity service
l: labor as special constraint from r
s: basic service as reference
In this new set up, gifts for nature are deducted from the initial resource availability and gifts
of nature are added to resource availability and quality. From the point of view of farmers,
gifts of nature relax their technological constraints or augment trade-off opportunities. Again
it is not a ‘free’ gift, because labor must be devoted. In our modeling problem, when the
farmer offers labor for nature elements, the vector of change in species composition will be
‘gifted’, by nature.
There can be a number of soil eco-system services gifted through species. For example,
nutrient recycling, nitrogen fixation, augmentation of plant health etc are services of concern.
From the programming perspective, the gift of nature can be considered as the relaxation of
constraints expressed in the last equation of system (3). It has to be appreciated that gifting for
soil biodiversity services requires changes in normal activities oriented towards food
production. For that reason a new variable δxf = xf,t - xf,t-1 is introduced. It reflects an
optimization of change in farm activities over time. Nevertheless, gifts, received and offered,
are not a part of decision making, themselves, so far. However, they impact on decisions and
activities. Activities may not change if costs are prohibitive. It means that a farmer can decide
to be a conventional farmer or become a farmer who engages in gifting. To model these
aspects, the dynamic adjustments in gifting will be directly modeled. Here by we weaken the
position that gifts are exogenous.
Though gifts in its very nature are exogenous and gifting is dependent on the probability of
receiving a gift, it is also inevitable that farmers deliberate about the costs of change for gifts.
An increasing probability of gifts in the form of biodiversity services can be associated with
increasing costs of gifting through changes accomplished in farm activities. In the programming, this is addressed by an extension of activities viz. ‘change’ denoted by ∂, which
request resources and allow adjustment. Moreover, we confine the analysis to the adjustment
costs reflected in labor deliveries and to the probability of receipt of gifts. To depict dynamics
of exchange, a two step strategy is adopted. . 1. Optimization without the dynamic aspect and
receive optimal levels, for instance, at an average level of nature service availability.
Alternatively, the case of no gifting can be taken. Important point is that one receives a
benchmark. For the adjustment cost analysis, a constraint is identified as xfn,t-1 for a second
optimization. 2. Optimization runs now with an expected gift delivery. Gifts are received with
a probability. The tableau (4) gives an overview on the needed changes of variables which are
then used for the Maximum-Entropy-analysis. This will be explained soon and it gives us the
needed response function.
c
 [1 f ][ p f  c nf ] ' x 
f
s.t.
n
A f xcf 
n ,l
c
A x
f
f

f
[p f
 cf
c
] 'x
n
n
A x
n
f
f
 cf '
c ,c
l ,c
n ,l
f
n ,n
A x
f
n
f
n
xf
n
f
 A x
f
f
A x
x
n
f
 rf
(4)
 lf lf
n
t
f
n ,c
 A x
f


n
f

n
xf 
s
n ,n
n
n
xf
n ,o
 a of
z
h ,a
f
t 1
The optimization of tableau (4) will allow us to specify gifting, its dynamics, and response
contingent on probabilities of receiving the gift. This is important for reciprocity or even a depiction of the dynamics, itself. Cost of changes is denoted by ‘cд’. The core aspect of the
inclusion of a gift from nature and gifting to nature is the relaxation of the constraints in ecosystem services (3rd constraint). Farmers will offer labor to get gifts and one should foresee
labor costs which translate into opportunity costs via constraints. Farmers’ reference level of
gifts to nature, ecological services (through a change in species vector) received as gift and
appraisal of probabilities of their receipt can be used to depict their reaction function. This
function is built in the optimization of farmers. As a further step in it’s delineation, one can
link the change in activities of the ‘nature- gifting-farming’ to the expected change in the
“gifted species vector” δsfh,a . The expectations are formed through learning. To give already
an idea, we can use the third constraint in tableau (4) to see the link. Now by taking the
derivative of the species delivery constraint and neglecting the second derivative, the
relationship depicted (5) allows an expansion or contraction of activities according to
A x
n ,n
n
f
f
n ,n
 sn  aof
z
h ,a
(5)
f
It means that the farmer can optimize adjustment costs based on a likely change in the gifting
of ecological services. It also means that farmers have to have experiences on functional
relationships in nature. We depict this translation as a dynamic constraint. (Nevertheless,
farmers do not do dynamic optimization in the model but optimize for periods as they face
adjustment cost.)
4.2 Flexible response functions and Maximum Entropy (ME)
To achieve the calibration of behavioral functions a Maximum Entropy (ME) approach can be
employed. The aim of ME here is to translate a linear objective function into a quadratic
function for analytical optimization. This function is consecutively subject to the definition of
corresponding matrices. The quadratic approximation can reflect technology, behavior and
can perform optimization, given the constraints. The constraints are implicitly reckoned by
shadow prices λ. The linear objective function of farmers is,
O
f
[
p
 c ] x  0.5
Q
/
1

Q x
/
2
 0.5 x
/
Q x
(6)
3
where:
λ
= shadow price for restrictions
x
= activity and b=Ax.
This objective function enables a generic formulation of response functions. In an ordinary
case of determining choices of food production, the objective function serves as basis for the
incentive response function, such as the gross margins. For a representation of farm behavior
towards incentives, we can obtain the derivatives to x and λ and determine the constraints for
the ME analysis. The derivatives are:
  f b f  A x
O f
O f  x f  A   
/
Q
f
c 
1
p

Q
2
f
Q
2
x
(7a)
f
 Q x
(7b)
3
Note, underlined variables in the representation (7a and 7b) are variables obtained by the
linear programming approach, where ‘x’ is the activity and ‘λ’ is the shadow price. The first
optimization towards λ (7a) can be interpreted as a “demand” function for “b”, where Ax < b
is the technological constraint. In that case the shadow price is linearly dependent on b and x.
By using the second equation (7b) and elimination of x, b becomes dependent on price p (or
the probability as we will see soon in our case).
Let us explain the maximum entropy approach on determining coefficients through an
example; The Cholezky factorization of the matrix Q gives,
(8)
Q L DL
1
1
/
/
1
1
Whereby D is a diagonal matrix and L is a lower and L’ is an upper triangular matrix. Then,
basically maximum entropy (Golan et al. 1996) works with a concept and a specification of
probabilities ‘p’ that are used to find the most likely distribution function for the coefficients
of L and D. The set of probable coefficients depends on the range of the coefficient (known a
priory), specified by the matrix Z (support matrix). The number of observation can be even
singular.
L jj   Z ( j , j , s ) P ( j , j , s )
/
/
L
1
s
D
i, j

s
Z
D
/
L
(
j , j ,s )P ( j , j ,s )
1
with j, j/ = 1, …, J
(9a)
with s = 1, …, S
(9b)
1
D
1
The Z coefficients are exogenously presumed according to plausibility. Relevant probabilities
‘p’ are maximized. For a mathematical solution of maximizing , a specification of the entropy function is necessary (10). This entropy function has to maximized given the constraints
H
 
j , j´, s
s.t. A x
A
/

P
L
(
j
,
/
j , s )  log( P
1
L
(
j
,
j , s ))   P
/
 ( Z L ,1 PL ,1) / ( Z D ,1 PD ,1) ( Z L ,1 PL ,1)
z c p
D
1
j ,s

(
j
,
j , s )  log( P
1
D
(
j
 ( Z L , 2 PL , 2 ) / ( Z D , 2 P D , 2 ) ( Z L , 2 PL , 2 )
  ( Z L , 2 PL , 2) ( Z D , 2 PD , 2) ( Z L , 2 PL , 2) /

,
/
j , s ))
1
x
 ( Z L , 3 PL , 3) / ( Z D , 3 PD , 3) ( Z L , 3 PL , 3)
x
(10)
and (10) gives the needed information on the coefficients. The presented approach shall be
applied to a gift exchange system with nature on basis of constraints in production ‘b’. So we
get the coefficients as in (6). A more elaborated outline will explain the envisaged
applications of the methodology described.
5) Application
As already suggested, the broader aspect of decision making under dynamic assessments of likelihood for reciprocal gifting is to get flexible response functions. With the help of linear
programming and Maximum Entropy one can translate decision making in gifting into a
quadratic objective function. Coefficients can be determined and this enables us to derive general behavioral equations. In the next step is the inclusion of constraints posed by nature in the
generated objective function. The objective encompasses (1) activities for farm production,
(2) devoting of resources (labor as gift) for nature elements, and (3) receipt of gifts as species.
The generated objective function is (11)
O   [ p  c ] ' x   x   l   z   x  o.5 x '  x  o.5 l '  l  o.5 z '  z
 o.5x '  x  x '  l  x '  z  l '  z  x '  l  x '  x  x '  z
f
f
n
n
f
f
f
n
f
n
n
f
f
14
 [r f , l f , s n
t
n ,n
n
f ,11
11
n ,o
f
f ,12
n ,o
n
f
f
h ,a
f
f
13
h ,a
n ,o
f
f
12
n
n
f
f
14
21
h ,a
n
f
f
31
11
n
n ,o
f
f
n ,o
n
f
f
32
22
n
n
f
f
n ,o
h ,a
f
f
33
h ,a
f
h ,a
23
f
n
n ,o
n
h ,a
, x nf ,t 1 ]' [41 x f  42 z f  43 l f  44 x f ]
(11)
where: lf = labor
xf = crops
zf = eco-system
service
From this objective function we can derive behavioral functions. By taking first derivatives to
l, x, z and δx, a system of response emerges. Mutual gifting is part of this linear response.
 O f  x f  [ p  c f ]  f   11  11 x f  11 l f  12 z f  32 x f ' 41 r f  0
n
n
n
n ,o
n
h ,a
f
 O f  l f   12  22 l f  11 x f  21 z f  31x f  43 r f  0
n ,o
n ,o
n
(12)
n
h ,a
 O f  x f   14  14 x f  31 l f  32 x f  23 z f  44 r f  0
n
n
n ,o
n
h ,a
From the derived system (12), we can eliminate the x and then equations (12) can be reduced
to (12a) and (12b). Probabilities are exogenous to the farm but endogenous to the system.
Gifts to nature ‘l’ are dependent on the expected gifts ‘z’, received gifts ‘r’ and probability
‘π’, and the change in species vector ‘∂x’. Farmers’ behavioral response (12a) is identified.
l
n ,o
f ,t


*
 12
*
11

e
f ,t
 12 z f ,t  12
*
h ,e
*
z
h ,e
f ,t
 12 sn  12 r ft
*
n ,n
*
(12a)
Since equations are associated to a time period, the difference between two periods can be
analyzed. Then a relationship emerges which is a reduced form linking change to optimality.
 l
*
n ,o
21
f
 22  f ,t  23z f  24 r f  25 sn  25 z n  25 l f  0
*
e
*
h ,a
*
h ,a
*
n ,n
*
n ,n
*
n ,o
(12b)
The response function (12b) contains three variables (π, z, r) which are endogenous to the
system. They are not time invariant variables because we use expected availability of a gift
from nature. But notice that we maintain the distinction between “a” for actual and “e” for expected. Now we can add the learning procedures written in the mode of a difference equation.

e
f ,t
 [1  11] f ,t  12z f ,t
e
h ,e
(13)
The result is a dynamic behavioral system on the side of farming which includes gifting as a
reaction to learning how nature behaves. From the point of view of farmers, additionally, a
shadow price can be assigned to gifting. Nevertheless, the willingness to relax the constraints
depends on optimization. Structurally one can receive similar results if one uses profit
maximization or effort minimization. The above approach can be eventually supplemented
with decisions how to close the model. 1. One could simply take the food need as exogenous
and then model primarily the substitution between human labor and eco-system services
aiming at food. 2. It is then possible to supplement the farm supply side approach by a
demand side approach for food. We can consider food prices endogenous in the supply
modeling. This would give us an association between food prices and food availability
through nature. Food provision becomes dependent on eco-system services. 3. Also, a
simplistic approach on a carrying capacity can translate food availability to numbers of
humans, i.e. the effect of population on functioning of eco-systems.
6) Gifting of biodiversity services
In addition to farmer’s behavior of optimizing his objective function, it is assumed that nature
optimizes its behavior to achieve an optimal fitness. This is a key aspect in understanding
gifting. In the case of nature, energetic efforts for food acquisition by species are minimized.
This premise is adopted from Pethig et al. (2006) though similar arguments present in various
studies (Finnoff and Tschirhart, 2003). It should be noticed that it is a working hypothesis
(Eicher and Pethig, 2006), though it has shown already its potential in system analysis and
prediction (Pethig et al. 2006). By this working hypothesis of optimization we can make
verifiable predictions on behavior and system understanding. It can be understood, on the
species level for instance as feeding strategy, but also on the system level. Generally, we
presume that nature “designs” a species vector which correspond to a maximum attainable
ecological fitness, given the constraints. This assumption follows Eicher and Pethig (2006),
whose approach is modified using a programming approach. The essential step is to get a
behavioral response from nature in the gift exchange. The calibration of such a behavioral
function can be based on energy flows accounting in food webs. For instance, reconstruction
of a food web under the strategy of minimizing energetic losses through species can indicate a
particular species composition. The analogy is the revealed preference in economic modeling.
Our positivistic research component is: retrieving behavior from observation. It shall enable
us hitherto to make suggestions or envisage a future mutual beneficiary gift exchange, based
on reciprocity and inference.
A brief discussion on the initial state of ‘soil’ which is the background of gifting for soil
ecosystem services is required for further deliberations. Two very distinct situations may
prevail. In a first case a virgin soil where all functions is under control of nature can be
perceived. In a second case a deprived soil might be the starting point. In the presence of
human induced constraints, the prevalent species composition is eventually a second ‘best’
solution due to ‘deprivation’. An initially better performing nature might be perceivable, but
normally the reference is an already badly ‘performing’ nature. Hence, modeling is contingent
on state. Since a nature in poor conditions is most prevalent in interactions of humans with
nature, gifting offers a choice for improvement.
6.1 Programming the biodiversity services
Formally, the objective function of desired ‘energy retention’, i.e. minimization of energy loss
is reached by modulating species composition. The approach can be conducted from two
angles: first ‘cost’ (energy) minimization and second ‘revenue’ (fitness) maximization. It is
assumed that every species contributes to a certain amount of energy retention at individual
level and to a certain degree of a loss of energy at system level. For instance, feeding and
growth means dissipating energy to a certain percentage of already accumulated energy. Then
a new vector of species is accommodated on a second trophic level of the food chain. The
choice of species vector is dependent on energy (organic matter) transfer between trophic
levels that are optimized. (Static in the model, for dynamics see Gutierrez and Regev, 2005).
In the case of soil biota, organisms at the lower trophic level feeds on organic matter and then
the dead microbes are fed by organisms at upper trophic level and release the nutrients. In this
process they release various enzymes, hormones and substances that perform various
biological functions (Altieri, 1999). For the purpose of simplifying the analysis, we see a
fixed delivery of organic matter from the lower trophic level to the upper level. Also for
simplicity, we assume this lower level of species composition is already given. The subset of
micro organism species at upper trophic layer represents the gifting component of nature
(ecosystem service). It means a labor contribution in terms of land management practices by
humans (more service) is ultimately rewarded by a shift in the ‘optimal’ species composition.
This can be seen as reciprocity of nature because the resource constraint of nature is lifted by
gifts from humans. In the presented model only species of the upper trophic level are of
interest for humans. The ‘optimization’ represents a selection at a higher level and at the
expense of those species at the lower trophic level (Pethig et al. 2006). The system is bound
also to abiotic factors.
The gift of humans to nature eases limitations in processes of organic matter conversion
because it addresses the restraints. In principle, a number of land management practices could
be of benefit for nature. For example human labor for erosion prevention as well as soil
protection and practices such as minimum tillage, crop residue addition and crop rotation etc.
can relieve stress of nature in farming systems (Altieri, 1999). A vector of gifts reaches
nature. In response, a parallel vector of important species for humans is envisaged. The
advantage of using this approach is that we can generalize the programming framework
towards an inclusion of deliveries of ecosystem services. The deliveries are firstly given
exogenously, as requested set of species. In this respect fitness (or better expressed efficiency
of nature to transmit energy, which is the skill of an eco-system to organize itself) is defined
as the possibility to (re)produce a set of upper trophic level species at minimal loss of energy.
Fitness can be enhanced by land and labor contributions. A stepwise identification of
‘optimality’ shall help to establish functions. As before a starting point is a reference ‘nature’
which minimizes ‘c’ that is the energetic loss if higher trophic level microbial species (Sn) is
feeding on microbial species (xn ) at lower trophic level. It is a minimization problem (14).
L c ' x
s.t. A ' x  s
n
n
n
n
(14)
n ,a
where: xn = species of lower trophic level that are used by higher trophic level
Sn = species of higher trophic level
The species vector sn is a revealed “preference” of nature. In conjunction with ME
optimization it serves as a quasi statistical tool to reveal nature’s preference for the species
vector as an output. Input side preferences, which imply the dual of the above primal, are to
be revealed for a more comprehensive analysis. Dual and primal programming problems are
necessary to retrieve coefficients for behavioral equations (PMP/ ME). For the dual,
maximization applies, in case the primal is minimization.
V  s n,a ' 
n
A '
s.t.
n
n
(15)
c
n
where: λn = shadow ‘price’ measured in energy units
In this basic setting nature is independent from humans. In fact, we have to supplement the
constraint of the value generation by the availability of resources y. A vector of deliveries
V  s n,a '   co ' y
n
n
A '
s.t.
n
c
n
1
n
A2 '
n
B ' y
n
n
n
r
(16)
n
where additionally: yn = resource species for determination by lower bound
cn = per unit species for determination by lower bound
rn = resource constraints
is supported by the resource constrained species optimization of the lower tropic level. If system (16) is resource oriented, starting with the dual, it is suggested that a similar primal (17)
exists:
L c ' x  r ' 
n
n
s.t. A
x
n
n
n
n
B
1
n ,a
o  s
B
n
2
o
(17)
o  o
c
where additionally: λo = shadow price for lower bound
This new primal problem can be interpreted as a description of “value” creation for nature.
Here co is the ‘value’ of organic matter per species at the lower trophic level. As in the initial
primal solution the observable output of the natural system “s” and “r”, as inputs, are bench-
marks. This gives us the fit of the model, which presumably is calibrated for an ecology found
under semi-natural conditions. The idea, again, is that species and species diversity is “reconstructed” in a modeling approach, presuming minimization of energetic loss in the system.
Having calculated interactions and the behavioral background for an ideal, though “stylized”,
nature we can amend the behavioral description of this nature by the inclusion of gifts. Gifts
are given away to humans and gifts are received from humans. Given gifts, GG, are specified
as change in the output structure, and received gifts, RG are specified as changes in the input
structure.
V  s n,a '   co ' y
n
n
A '
s.t.
n
n
 B1  o  c
n
n
B 'y
n
n
n
2
n
r
C 'y l
n
n
l
(18)
For the time being, in the dual problem statement and in the amended version, ‘l’ is included
as a vector for deliveries (labor). Through including ‘l’, complementary constraints given by
the initial situation are substituted. Through the relaxation of the initial constraints on the
input side, the requested species vector for humans zh is now received. From the primal of
minimizing efforts, the dual on delivery of a specified output vector; i.e. the inclusion of a
desired output of species is framed.
L c ' x  r ' 
s.t. A x
Dx
n
n
n
n
n
s
n ,a
n

h
1
n
o
n
z
o
n n
A2 x  B   c
o
where additionally: zh = upper bound for desired species
(19)
The above presentation reflects a full integration of nature in the exchange system. As initially
said, the idea is to model a gradual revision of chances from zero participation to full participation, expressed as probabilities πn and counter probabilities (1-πn), and reckon the
knowledge on probabilities as a driving force for participation or strategic choice. In this vein
a generalization as in problem (20 and 21) enables the complete setup of the primal and dual
optimization.
L [1 n]'[c ' x
n
s.t.
c
c
c
n
n
A x
n
r '
n
 ]   n '[c ' x
n
c
n

n
n
n
n
n
n
A x
D x
B
n
n
n
r '
n
n
n
 cad '
n

B
n
o 

x ]
n
n
A x
a
n
n
n
o

s

z
(20)
n ,a
h
c
o
n

xf
x nn

t 1
x nn
Min! and
V [1 n]'[s n, n' nn  co ' y nn ]  n[s n, a ' 
s.t.
n
n
A ' nn 
c
n
 co '
A ' cn 
n
B 'y
n
n
n
C 'y
y
c
n
 ca '
y ]
a
n
c
B ' y '  B y
n

c
C 'y
c
(21)
n
n
a
a
C y
a
a
n
n

r

a
n
n
l
Max!
As before, the analysis is supplemented by a cost of change approach. Cost in a nature context
refers to an additional loss in energy if the vector of species offered by nature changes. Hence,
in the same vein of wording, nature tries to minimize additional cost if it has to adjust. For
adjustment we introduce δxnn as an additional variable in optimization. For a comparison with
the analysis of the programming of the farm, the nature approach is reduced to the
representation the gifted labor which augment the set of technologies pursued.
C ' y C y  l
n
n
a
a
n
n
l
(22)
6.2 Flexible response and Maximum Entropy
The outline on obtaining Maximum Entropy (ME) coefficients in a quadratic objective
function from the linear specification is similar as in the case of farmers. In the case of nature,
the optimization is minimization of energy losses. Moreover, the new species vector is a
response to gifts from humans. Both, species and deliveries, are subject to adjustments. To
maintain symmetry we consider the constraint with respect to received labor as the prime
criteria for adjustment of costs. The impact is that the new variable δxnn is a further activity to
be included. The quadratic behavioral equation of nature has to be built on the optimization
results of sn, yn, λn and λo given constraints sh, sn,a, rn, and lfn. I.e. using internal knowledge on
technology as coefficients, the system reduces to a constraint variable problem.
As before the constraint variable problem delivers a reduced form objective function as partial
solution for the internal optimization of activities and shadow prices as in objective function:
O    x    y   x   y   y   l   z  x '  x  y '  y
(23
 y '  y  l '  l  z '  z  x '  y  x '  y  x '  l  x '  z
 y '  y  y '  l  y '  z  y '  l  y '  z  l '  z
 [r ' , s ][ x   y   y   l   z   y ]
n
n
n
n
33
n ,l
n
31
n ,l
n ,a
n
n
n
n ,l
11
n
n
n
n
n
f
n
n ,l
n
n
n
n ,l
12
n
n
44
32
n
55
f
34
n
n
21
n ,l
21
n
n
n
n
n
n
63
n
n
31
n
n ,l
n
n ,l
n ,l
62
n
n
n
n
n ,l
61
n
f
n ,l
n ,l
11
f
23
42
n
n
n
n ,l
n
n
n ,l
n
n
n
n
f
11
n
n ,l
f
n
24
n ,l
n ,l
n
n
n ,l
22
n
n
25
n
n
51
n
n ,l
n
65
n
n
f
51
n
n
n
n
64
f
n ,l
n
41
n
41
n
66
n
)
The focus is now on an optimization towards “yielding” energy and the optimal use of energy,
notably on the second trophic layers. This determination of an objective function for soil
ecosystem helps us to establish an empirically retrievable analysis to describe a behavioral
equation system of nature. It includes responses to gifts and provides ecosystem services. In
response to gifting by humans lf nature offers sfe,o. The response is driven by expectations πne.
To clarify, because we still have a coordination problem, (24)
 
 On  xn  11
n ,l
n
n
y   l   z   r
 11 xn  21 y  23
n ,l
n ,l
11
n
n
n
24
n
n
25
f
n
61
n ,l
n
 71 sn  0
n ,l
…
 On 
n ,l
y
n
 12
n
 
n
y   l   z   r
 22 y  21 xn  31
n ,l
21
n ,l
n
n
n
32
n
f
n
34
n
62
n ,l
n
 72 sn  0 (24)
n ,l
is the mathematical expression of “behavior”. Elimination of x and y offers a reduced form

*
11
n


y '  z   l '  s
 21
*
11
n
*
h
*
n
*
n ,a
n
23
n
22
f
23
n
 22 r n '
*
n
(24a)
This form is based on probability of receiving a gift. Note that the change can be translated
into labor change
C 'y  y  l
n
n
c
n
l
and the equation for the second response and optimality criteria switches to:

*
11
n


*
11
l '  z
 21
*
n
*
h, g
f
23
n
 22 l f ' 22 sn  22 r n
*
n
*
n ,a
*
n
(25)
Hence this version of dynamic behavioral optimization recognizes the labor offered and the
response function (25) is dependent on exogenous variables characterizing the soil ecosystem. For the ecological side the probability is reflected by an adapting process:

e
t
 ]
 [1
11
e
t

 l
12
n,e
f,
(26)
Apparently these three conditions offer an access to an anticipated change in gifting of
ecological services from nature. The aspect of adapting in nature is part of evolutionary
processes and adjustment in ecology can be also understood as system adaptability to the
conditions provided by human gifting (comparable to learning from human point of view).
Though there could be disputes on adaptive capacity of nature, it should be possible to get
responses, given the built in objective function. In the given case only marginal changes in the
species composition are expected.
7) Dynamics and equilibrium
To simulate the convergence in gifting, the response functions have to be combined with
learning and adjusting behavior. The change in activities in order to gift and receive gifts
(change in farm activities in response and adjustment in nature (adaption)) is the core to
establish a dynamic equilibrium. The first step in delineating the convergence is to spell out
the variables that are endogenous to the adjusting system. The description of the willingness
to cooperate on the basis of a mutual gifting scheme is characterized by five variables viz. z, r,
l, π, and s. Moreover, conditional variables are represented by lagged variables (one period).
The equations that contain the behavioral response are,
l
n ,o
f ,t


 l
*
*
n ,o
21
f
 12
*
11

e
f ,t
 12 z f ,t  12 sn  12 r ft
*
*
h ,e
n ,n
*
(27a)
 22  f ,t  23z f  24 r f  25 sn  25 zn  25 l f  0
*
e
*
h ,e
*
h ,a
*
n ,n
*
n ,e
*
n ,o
(27b)


n

 [1  11] f ,t  12z f ,t  123l f ,
*
11
e
*
11
l
 21
*
n,e
f
' 23 zn  22 l f  22 sn  22 r n
e
f ,t


e
n,t
 ]
 [1
11
*
h, g
*
h ,e
e
n,t

n ,e
 l
12
n,e
f,
n ,e
*
n ,a
*
n
(27c)
(27d)
(27e)
In this, system variables represent changes on ecosystem services from nature and changes in
labor provision by humans. Offers for labor and expected changes of soil ecosystem services
are retrieved from past experiences (learning). Nevertheless, the expected and actual
deliveries are not equated while a balance in changes is visualized. Such a balancing can be
represented by the equation,
z
 21l f ,t 2  22 l f ,t 1  [1  21][z f ,t 1  z f ,t 2]
h ,a
n ,o
*
f ,t 1
n ,o
*
h ,a
*
(27f)
h ,a
The condition (27f) spells out humans’ anticipation in gifting, i.e. receiving eco-system services for labor. Importantly, by (27f), the observed change in receiving eco-system services is
linked to changes in labor offered. Equation (27f) is an ad-hoc statement; no theoretical
reasoning is provided. Here a gradual shift occurs with respect to the acceptance of
collaboration and change in strategies through learning of probabilities. The system is driven
by learning. Then, six variables are to be accommodated for a steady state or equilibrium
process.
l
n ,o
f ,t


 l
*
*
n ,o
21
f
 12
*
11

e
f ,t
 12 z f ,t  12
*
*
h ,e
z

z
 21
*
n,e
f
e
n,t
h ,a
f ,t 1
*
h ,e
*
h ,a
 ]
 [1
11
*
n ,n
*
h, g
h ,e
e
n,t

*
n ,e
*
n ,a
(27a)
n ,o
n ,e
 l
12
*
n ,o
This can also be presented as
n
n ,o
(27e)
n,e
f,
*
*
*
(27d)
n ,e
 21l f ,t 2  22 l f ,t 1  [1  21][z f ,t 1  z f ,t 2]
*
*
' 23 zn  22 l f  22 sn  22 r n
e
f ,t
n ,n
(27c)
*
11
l
*
 [1  11] f ,t  12z f ,t  13l f ,
e
*

e


 12 sn  12 r ft
(27b)
*
n
*
f ,t
 22  f ,t  23z f  24 r f  25 sn  25 zn  25 l f  0

11
h ,e
h ,a
h ,a
(27f)
 0
 *
 21
 *
 22
 *21

 13



 *
12











*
1  21








1


*
12
*

*

*
23
22
11
1


1
12
12
1

*
23

*
23

*
23

*
43

*
53










*
63
 a 
 lf   0
 e   *
 l n  25
 h ,e  
 zf  - *
 n.a  22
 zn  
 e  
 f  
e

 
  n  
n.a 

 z n 
 n ,l 
r n 
r 
 f 
 t 
l f 
 n ,n 
 sn 
 n 
an 
 n 
c 
 e 
c 

*

12
*

23
*
23

*
23
1
1   11
f

12
1   11
n










1
 a

l f

 e

l n

 h ,e  =
z
f


 n.a 
 zn 
 e 
 f 
 e 
 n 
n.a 

 z n 
(27)
The system (27) is a system of seven sub-vectors which constitute the differential equations.
In principle the system can be solved by dynamic analysis. At least as a technical solution, the
dynamics and equilibrium between the willingness to gift and to receive a gift can be
obtained. A simplistic solution is to assume that in equilibrium changes ‘δ…’ are zero (steady
state). Then the above system is
A1δy + A2y = A3x  A2y = A3x y = A2-1A2x
(28)
The meaning of this solution is that a probability exists with regard to humans, which is
optimal. Both, humans and nature maximize expected returns from gifting. For soil microbial
eco-system either fitness is maximized or energy losses are minimized. Again, these two pairs
in the argument are dual. Here, this goal of nature (like in Eicher and Pethig, 2006) is
extended by the concept of an ‘evolutionary’ learning. Probabilities of alternatives reflect the
spectrum for selection of an ‘optimal’ species vector. The shifting in species composition by
nature as a response to the ‘gifting’ of labor by humans (notable as reciprocal for gifts)
implies a change in the importance of species. The important point is that ‘evaluation’ by
nature can be anticipated which alters the spectrum of quasi goal oriented natural selection
(adaptation). ‘Valuation’ from the side of humans was a shadow price valuation of gifts from
nature and nature ‘values” the exchange of gifts through increased fitness (reduced energy
loss).
For further discussion: the Pethig hypothesis is extended for an inclusion of dynamics and
‘learning’. Putatively, in nature, there may be better principles of fitness adaptation, which go
beyond the subject matter of this paper. Extending the similarity between humans and nature,
for anticipating exchange and maintaining, the fitness hypothesis, for the moment, is
considered sufficient for information gathering. New priorities of resource use come as
adaptive learning (natural selection) process in nature. The simple consequence is that
’valuation’ shifts chances in nature to create better adapted species composition. This is the
major premise in this article.
8) Summary
This paper has presented a new approach to the delivery of soil eco-system services and
evaluation of nature in a gift exchange framework. The approach is based on the concept of a
gift economy as opposed to a valuation through a market. Gifting is to be mutually conducted
and a mechanism is presented which offers a coordination of gifting. The paper firstly
presented a programming approach which includes gifts and gifting from the human side. For
instance, gifts from soil biota are considered as ecosystem services in farming. Farmers are
offering labor in exchange (reciprocation) to ecosystem services reflected by the microbial
species vector. This provision is transferred into a non-linear analytical function under the
Maximum Entropy approach. Hence a flexible response function as a tool for gifting
optimization is obtained. The idea of a gift response function is also applied to nature. Soil
ecosystem is considered as fitness optimization unit and the optimization is supplemented by
gift exchange. Here also, firstly a linear programming approach is suggested and secondly this
approach is transferred into an analytical function. From this quasi objective function, a linear
response function for nature towards incremental gifting of eco-system services as response to
the receipt of labor can be derived. Finally based on the response functions it is shown how
the dynamics can be used to obtain a steady state which can be regarded an equilibrium.
9) References
Anderson, T. and Hill, P., 2002. Cowboys and Contracts. The Journal of Legal Studies, 31/2:
489-514.
Altieri, 1999, The ecological role of biodiversity in agroecosystems, Agriculture, Ecosystems
and Environment 74 : 19–31
Beals, R.L., 1970, Gifting, Reciprocity, Savings, and Credit in Peasant Oaxaca, Southwestern
Journal of
Anthropology, 26: 231-241
Chiurazzi, M., 2008, Microbial diversity as soil quality indicator in agricultural soils, Doctoral
thesis, Università degli Studi di Napoli Federico II
De Janvry, A., Fafchamp, M., and Sadoulet, E., 1991. Peasant household behaviour with missing markets: some paradoxes explained. The Economic Journal, 101/409: 1400-1417.
Eicher, T. and Pethig, R., 2006. A micro-foundation of predatory-prey dynamics. Natural
Resource Modeling, 19: 279-231.
Ellis, F. 2003. Peasant Economics, Farm Households and Agrarian Development, 2nd Ed.,
Wye Studies
in Agricultural and Rural Development, Wye (England).
Farber, S.C., Costanza, R. and Wilson, M. A., 2002, Economic and ecological concepts for
valuing ecosystem services, Ecological Economics 41 : 375–392.
Finnoff, D. and Tschirhart, J., 2003, Journal of Environmental Economics and Management
45: 589–611
Golan, A., Judge, G., and Miller, D., 1996. Maximum Entropy Econometrics. Wiley,
Chichester.
Gutierrez, A., Regev, U., 2005. The bioeconomics of tritrophic systems: applications to
invasive species. Ecological Economics, 52/3: 383– 396.
Hann, C.; 2006. The Gift and Reciprocity: Perspectives from Economic Anthropology.
“Handbook on the Economics of Giving, Reciprocity and Altruism”, 1. 207-223:
Heal, G., 2000, Valuing Ecosystem Services, Ecosystems, 3: 24-30.
Heckelei T., and Wolff, H., 2003. Estimation of Constrained Optimization Models
forAgricultural Supply Analysis Based on Generalised Maximum Entropy. European
Review of Agricultural Economics, 30/1: 27-50.
Herendeen, R., 1991, Do economic-like principles predict ecosystem behavior under changing
resource constraints?, in: T. Burns, M. Higashi (Eds.), Theoretical Studies
Ecosystems: The Network Perspective, Cambridge University Press, New York, 261–
287.
Lotka, A.J. ., 1925, Elements of Physical Biology, Williams and Wilkins Company,
Baltimore.
Norton, B. G. and Noonan D., 2007, Ecology and valuation: Big changes needed. Ecological
Economics, 63/4: 664-675.
Offer, A., 1997, Between the Gift and the Market: The Economy of Regard, Economic
History Review, 3: 450-476.
Paris, Q. and Howitt, R.E., 2000. The Multi-Output and Multi-Input Symetric Positive Equilibrium
Problem. In: Heckelei, T., H.P. Witzke, and W. Henrichsmeyer (eds.): Agricultural
Sector Modeling and Policy Information Systems. Proceedings 65th EAAE Seminar at Bonn
University, Kiel: 88-100.
Pashigian, P., 1970. Rational Expectations and the Cobb-Web-Theory. Journal of Political
Economy, 78: 338-352.
Pethig, R., Christiaans, T. and Eichner, T., 2006. On the dynamics of Tschirhart's predatorprey model, Ecological Modeling, 197: 52-58.
Sahlins, M., 1972. Stone Age Economics. Gruyter, London.
Underwood, D.A., 1998, The institutional origins of crises for economy and ecology, Journal
of Economic issues, 32: 513-522.
Wossink, G. A. A., Oude-Lansink, A. G. J. M. and Struik P. C., 2001. Non-separability and
heterogeneity in integrated agronomic–economic analysis of nonpoint-source pollution
Ecological Economics, 38/3: 345-357.
Wright, D. H. 1983, Species-energy theory: an extension of species-area theory, Oikos, 41:
496-506.