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Modeling Higher-Order Adaptive Evolutionary Processes by Multilevel Adaptive Agent Models

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In this paper, a fourth-order adaptive agent model based on a multilevel reified network model is introduced to describe different orders of adaptivity of the agent's biological embodiment, as found in a case study on evolutionary processes. The adaptive agent model describes how the causal pathways for newly developed features in this case study affect the causal pathways of already existing features, which makes the pathways of these new features one order of adaptivity higher than the existing ones, as they adapt a previous adaptation. A network reification approach is shown to be an adequate means to model this in a transparent manner.
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Modeling Higher-Order Adaptive Evolutionary Processes
by Multilevel Adaptive Agent Models
Jan Treur
Vrije Universiteit Amsterdam, Social AI Group
https://www.researchgate.net/profile/Jan_Treur
j.treur@vu.nl
Abstract. In this paper a fourth-order adaptive agent model based on a multilevel
reified network model is introduced to describe different orders of adaptivity of
the agent’s biological embodiment, as found in a case study on evolutionary pro-
cesses. The adaptive agent model describes how the causal pathways for newly
developed features affect the causal pathways of already existing features. This
makes these new features one order of adaptivity higher than the existing ones.
A network reification approach is shown to be an adequate means to model this.
1 Introduction
In the literature many examples can be found of first-order adaptive agent models, in
different (e.g., cognitive, mental, social) domains. The current paper focuses on a case
study of an adaptive agent model with biological embodiment to describe evolutionary
processes, and the orders of adaptation that are recognized in them; e.g., [3, 4]. The
case study addresses how the existence of pathogens has led to the adaptation of devel-
oping a defense system with an internal immune system and an external behavioural
immune system [1]. Pregnancy led to the adaptation of temporary suppression of the
internal defense system to give the (half-foreign) conceptus a chance to get embedded.
Moreover, above that, as another adaptation, for the first trimester of pregnancy a strong
feeling of disgust was developed to still strengthen the overall defense system by
strengthening, in particular, the external component of it; see [1].
The case study is analysed in some depth and modeled by a fourth-order adaptive
agent model making use of a multilevel reified network model. For this model different
scenarios were simulated. In Section 2 the case study itself is briefly discussed. In Sec-
tion 3 reified network models are briefly summarised. Section 4 introduces the fourth-
order adaptive agent model, and Section 5 the simulations with it. An Appendix ad-
dresses mathematical analysis of the model’s emerging behaviour and verification of
the model based on that; see https://www.researchgate.net/publication/335473231.
2
2 Higher-Order Adaptation in Evolutionary Processes
Viewed from a distance, an evolutionary process is an adaptation process that is chang-
ing the physical world by creating new causal pathways or blocking existing causal
pathways. This can be described as changing the causal connections in such causal
pathways from 0 or very low to high, or conversely. The adaptive aspect is exerted by
the selection pressure, which makes that for given circumstances organisms with more
favourable causal pathways for these circumstances become more dominant. Then they
determine more the average causal pathways of the population: this leads to a shift in
the average pathways by changes in the causal connections in these pathways. From [9]
it is suggested that three levels of adaptation might be considered applicable for the first
trimester of pregnancy. However, also the occurrence of pathogens can be considered
a form of adaptation for the wider ecological context. Therefore, the following four
adaptation orders can be distinguished:
First-order adaptation Pathogens occur, with causal pathways negatively affecting
the causal pathways for good health.
Second-order adaptation An internal defense system occurs, with causal pathways
which negatively affect the causal pathways used by pathogens.
Third-order adaptation For pregnancy, causal pathways are added to make the de-
fense system’s causal pathways less strong as the half-foreign conceptus might easily
be identified as a kind of parasite and attacked.
Fourth-order adaptation Disgust during (first trimester) pregnancy adds causal path-
ways by which potential pathogens in the external world are avoided so that less risks
are taken for entering of pathogens while the internal defense system is low functioning.
This strengthens the overall defense system by strengthening the external defense sys-
tem (the behavioural immune system) by which the pathogens are addressed outside
the body. this makes the causal pathway from (first trimester) pregnancy to suppress
the causal pathways of the overall defense system less strong as the external component
of the defense system strengthened by disgust is not addressed by it.
So, can this be used as a basis for a fourth-order reified adaptive network model?
This will be addressed in Section 4.
3 Reified Adaptive Temporal-Causal Network Models
The designed adaptive agent model to model these evolutionary processes makes use
of a Network-Oriented Modeling approach. The Network-Oriented Modeling approach
used is based on reified temporal-causal network models [7, 8]. A temporal-causal net-
work model in the first place involves representing in a declarative manner states and
connections between them that represent (causal) impacts of states on each other, as
assumed to hold for the application domain addressed. The states are assumed to have
(activation) levels, usually in the interval [0, 1], that vary over time. The following three
main characteristics connectivity, aggrgation, and timing of a network structure define
a conceptual representation of a temporal-causal network model [6, 9]:
3
Connectivity Each connection from a state X to a state Y has a connection weight value X,Y
representing the strength of the connection.
Aggregation For each state a combination function cY(..) is chosen to combine the causal
impacts of other states on state Y.
Timing For each state Y a speed factor Y is used to represent how fast state Y is changing
upon causal impact.
The notion of network reification [7] is a means to model adaptive networks in a
more transparent manner within a Network-Oriented Modelling perspective. This con-
cept is used in different scientific areas in which it has been shown to provide substan-
tial advantages in expressivity and transparency of models, and, in particular, within
AI; e.g., [2, 5, 13]. Specific cases of reification from a linguistic or logical perspective
are representing relations between objects by objects themselves, or representing more
complex statements by objects or numbers.
For network models, reification can be applied by reifying network structure cha-
racteristics for connectivity, aggregation and timing (e.g., X,Y, cY(..), Y indicated
above) in the form of additional network states (called reification states, indicated by
WX,Y, CY, HY, respectively) within an extended network. According to the specific net-
work structure characteristic represented, roles W, C, H are assigned to reification
states: connection weight reification, combination function reification, speed factor rei-
fication, or values, respectively. Also a role P for combination function parameters is
used. For more details, also see [10, 11], or the forthcoming book [12]. Multilevel rei-
fied networks can be used to model networks which are adaptive of different orders [8].
As discussed in Section 4.2 (see Box 1), a format based on role matrices mb (for base
role), mcw (for connection weight role W), mcfw (for combination function weight
role C), mcfp (for combination function parameter role P), and ms (for speed factor
role H), is used to specify a reified network model according to these roles.
4 An Agent Model for Fourth-Order Adaptive Processes
Inspired by the information in Section 2 but abstracting from specific details, a fourth-
order reified adaptive network for these evolutionary processes has been designed. As
pointed out in Section 2, evolutionary adaptation usually concerns affecting existing
causal pathways by adding new causal pathways that weaken or strengthen the existing
causal pathways. This makes that levels of adaptation are created where the causal path-
ways at one adaptation level are adapted by the causal pathways at the next level. The
adaptation of a causal pathway can be done by strengthening or weakening one or more
causal connections within such a causal pathway. This fits well in a reified network
architecture where for each level, for connection weights in causal pathways at that
level, reification states are introduced at the next level. The general pattern then be-
comes in a simple form (for the main example, see Fig. 1):
Base level: causal pathway by a causal connection from a to b
First adaptation level: causal pathway by a causal connection from a1 to Wa,b; this Wa,b rep-
resents the causal connection from a to b from the base level
4
Second adaptation level: causal pathway by a causal connection from a2 to Wa1,Wa,b; this
Wa1,Wa,b represents the causal connection from a1 to Wa,b from the first adaptation
level
Third adaptation level: causal pathway by a connection from a3 to Wa2,Wa1,Wa,b; this
Wa2,Wa1,Wa,b represents the connection from a2 to Wa1,Wa,b from the second adapta-
tion level
Fourth adaptation level: causal pathway by a causal connection from a4 to Wa3,Wa2,Wa1,Wa,b;
this Wa3,Wa2,Wa1,Wa,b represents the causal connection from a3 to Wa2,Wa1,Wa,b from
the third adaptation level
This general pattern for hierarchical adaptation processes for causal pathways will
be used to obtain a more specific reified network model for the multilevel adaptation
processes described in Section 2.
Fig. 1 Reified network model for fourth-order adaptation in an evolutionary context
In the considered reified network model four levels are considered, where for each
level its causal pathway can be changed by causal pathways at one level higher. To
limit the complexity of the overall model, the causal pathways at each level are kept
simple, modeled by just one causal connection covering the whole pathway. Table 1
explains the states of the network model. Fig. 1 shows a picture of the conceptual graph-
ical representation of the reified network model. It includes four reification states at
four levels which each reify the connection weight of the causal pathway one level
lower:
e1
s4
s3
s2
s1
s5
Ws5,e1
Ws1
,
Ws5,e1
Ws2
,
Ws1,Ws5,e1
Ws3,Ws2,Ws1,Ws5,e1
level
level
level
level
5
 first reification level state representing the causal connection from s5 to e1 from the
base level
 second reification level state representing the causal connection from s1 to
 from the first reification level
 third reification level state representing the causal connection from s2 to
 from the second reification level
 fourth reification level state representing the causal connection from s3 to
from the third reification level
Box 1 shows the role matrices mb (base connectivity), mcw (connection weights),
ms (speed factors), mcfw (combination function weights), mcfp (combination function
parameters). Each role matrix has a format in which in each row for the indicated state
it is specified which other states (red cells) or values (green cells) affect it, and accord-
ing to which role. In particular, in role matrix mcw the red cells indicate which states
Xi play the role of the reification states for the weights of the connection indicated in
that cell in mb.
Table 1. The states and their explanations
state
explanation
level
X1
s1
Occurrence of pathogens
X2
s2
Occurrence of interrnal defense system
X3
s3
Occurrence of pregnancy
Base
X4
s4
Occurrence of disgust
level
X5
s5
Contextual circumstances
X6
e1
Health level, on a causal pathway with a connection from s5 for
context
X7

Reification state for the weight of the base level connection
from s5 for context to e1 for health level, on a causal pathway
with a connection from s1 for pathogens
First reifi-
cation
level
X8

Reification state for the weight of the first reification level
connection from s1 for pathogens to , on a causal path-
way with a connection from s2 for interrnal defense system
Second rei-
fication
level
X9

Reification state for the weight of the second reification level
connection from s2 for internal defense system to ,
on a causal pathway with a connection from s3 for pregnancy
Third reifi-
cation
level
X10

Reification state for the weight of the third reification level
connection from s3 for pregnancy to , on a
causal pathway with a connection from s4 for disgust
Fourth rei-
fication
level
For the specific context described in Section 2, these elements are associated to the
following:
in environmental context s5 a causal pathway from s5 leads to a good health e1
pathogen state s1 leads to disturbing the causal pathway to a good health effect (e1)
well functioning internal defense system (s2) blocks the causal pathway for the effect of path-
ogens s1 on the health pathway to e1
pregnancy in the first trimester s3 needs less blocking of the effect of pathogens
disgust s4 is needed to compensate for the less blocking of foreign material
6
Box 1 Role matrices for the fourth-order adaptive network model
mb base
connectivity
1
X1
s1
X1
X2
s2
X 2
X3
s3
X 3
X4
s4
X 4
X5
s5
X 5
X6
e1
X 5
X7
51
X 1
X8
151
X 2
X9
2151
X 3
X10
3
2

151
X 4
mcfw
combination function
weights
1
alo-
gistic
2
comp
id
X1
s1
1
X2
s2
1
X3
s3
1
X4
s4
1
X5
s5
1
X6
e1
1
X7
51
1
X8
151
1
X9
2151
1
X10
3
2

151
1
mcfp combination
function parameters
function
1
2
alogistic
compid
parameter
1
2
1
2
X1
s1
18
0.2
X2
s2
18
0.2
X3
s3
18
0.2
X4
s4
18
0.2
X5
s5
18
0.2
X6
e1
8
0.5
X7
51
X8
151
X9
2151
X10
3
2

151
mcw connection
weights
1
X1
s1
1
X2
s2
1
X3
s3
1
X4
s4
1
X5
s5
1
X6
e1
X 7
X7
51
X8
X8
151
X9
X9
2151
X10
X10
3
2

151
1
ms speed
factors
1
X1
s1
0.08
X2
s2
0.05
X3
s3
0.015
X4
s4
0.008
X5
s5
0.2
X6
e1
0.5
X7
51
0.05
X8
151
0.05
X9
2151
0.004
X10
3
2

151
0.004
iv initial
values
1
X1
s1
0.2
X2
s2
0.1
X3
s3
0.11
X4
s4
0.1
X5
s5
0.5
X6
e1
0
X7
51
0.8
X8
151
0.8
X9
2151
0.8
X10
3
2

151
0.8
7
5 Simulation Experiments
Simulations have been performed using the dedicated software environment for reified
network models described in [10, 11] and in the forthcoming [12]. The scenario con-
sidered here focuses on a time period in which subsequently pathogens occur, a defense
system against them is developed, pregnancy occurs, and disgust (in the first trimester
of pregnancy) occurs. So, there are four orders of adaptation:
Adaptation 1 Pathogens are introduced first-order adaptation
Adaptation 2 Defense system is developed second-order adaptation
Adaptation 3 Pregnancy third-order adaptation
Adaptation 4 Disgust fourth-order adaptation
The red line in Fig. 2 indicates the health level. Before adaptation 1 health is good,
after adaptation 1 health becomes bad, after adaptation 2 health becomes good again,
after adaptation 3 health becomes worse again, and after adaptation 4 health becomes
better again. The simulation results for this scenario are shown in Fig. 2.
Fig. 2. Simulation with pathogens, internal defense system, pregnancy, and disgust occurring
6 Discussion
In this paper a fourth-order adaptive agent model based on a multilevel reified network
model was introduced to describe different orders of adaptivity found in a case study
on evolutionary processes; e.g., [3, 4]. The adaptive agent model describes how the
causal pathways for newly developed features in this case study affect the causal path-
ways of already existing features, which makes the pathways of these new features one
order of adaptivity higher than the existing ones, as they adapt the previous adaptation.
More details can be found at https://www.researchgate.net/publication/335473231. The
network reification approach has shown to be an adequate means to model this in a
transparent manner. In future research it can be explored how the adaptive agent model
introduced here can be extended and whether this also works for other evolutionary
case studies.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
050 100 150 200 250 300 350 400 450 500 550 600
X1 X2 X3 X4 X5
X6 X7 X8 X9 X10
8
From a more general perspective, this paper illustrates how higher-order adaptive
agent models can be designed making use of reified network models to specify their
functionality and a dedicated Network-Oriented Modeling environment [10, 11]. In the
current paper, the agent’s embodiment was addressed from a biological perspective.
Application for a similar approach to model higher-order adaptive mental and social
processes for agents can be found in [8], and in the forthcoming book [12].
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... The aim of the study reported here was to model from a Social Cognition perspective the influences on prisoner recidivism using an adaptive agent model based on an adaptive mental network, i.e., a network of mental states that describes the agent's socialcognitive functioning [18,19,23,24]. In Section 2 the designed adaptive social-cognitive agent model is introduced. ...
... A Network-Oriented Modeling approach was used to design the adaptive agent model with a focus on Social Cognition [18] [19], [23], [24]. This approach can be considered generic and was suitable to create a second-order adaptive agent model for the socialcognitive processes described in Section 1. ...
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Book
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This book addresses the challenging topic of modeling adaptive networks, which often have inherently complex behaviour. Networks by themselves usually can be modeled using a neat, declarative and conceptually transparent Network-Oriented Modeling approach. For adaptive networks changing the network’s structure, it is different; often separate procedural specifications are added for the adaptation process. This leaves you with a less transparent, hybrid specification, part of which often is more at a programming level than at a modeling level. This book presents an overall Network-Oriented Modeling approach by which designing adaptive network models becomes much easier, as also the adaptation process is modeled in a neat, declarative and conceptually transparent network-oriented manner, like the network itself. Due to this dedicated overall Network-Oriented Modeling approach, no procedural, algorithmic or programming skills are needed to design complex adaptive network models. A dedicated software environment is available to run these adaptive network models from their high-level specifications. Moreover, as adaptive networks are described in a network format as well, the approach can simply be applied iteratively, so that higher-order adaptive networks in which network adaptation itself is adaptive too, can be modeled just as easily; for example, this can be applied to model metaplasticity from Cognitive Neuroscience. The usefulness of this approach is illustrated in the book by many examples of complex (higher-order) adaptive network models for a wide variety of biological, mental and social processes. The book has been written with multidisciplinary Master and Ph.D. students in mind without assuming much prior knowledge, although also some elementary mathematical analysis is not completely avoided. The detailed presentation makes that it can be used as an introduction in Network-Oriented Modelling for adaptive networks. Sometimes overlap between chapters can be found in order to make it easier to read each chapter separately. In each of the chapters, in the Discussion section, specific publications and authors are indicated that relate to the material presented in the chapter. The specific mathematical details concerning difference and differential equations have been concentrated in Chapters 10 to 15 in Part IV and Part V, which easily can be skipped if desired. For a modeler who just wants to use this modeling approach, Chapters 1 to 9 provide a good introduction. The material in this book is being used in teaching undergraduate and graduate students with a multidisciplinary background or interest. Lecturers can contact me for additional material such as slides, assignments, and software. Videos of lectures for many of the chapters can be found at https://www.youtube.com/watch?v=8Nqp_dEIipU&list=PLF-Ldc28P1zUjk49iRnXYk4R-Jm4lkv2b.
Method
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For more background in network reification and how it can be applied to model adaptive networks of any order of adaptivity, see (Treur, 2018a) and (Treur, 2018b). The presented design fits well with Matlab as a programming environment, but can also be used for any other programming environment that allows the representation of basic mathematical concepts such as functions and matrices. The software architecture is illustrated for the developed Matlab software for reified temporal-causal networks. A version of this software itself can be found as an illustration in this document. Updated versions of the software will be provided later.
Conference Paper
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Network reification occurs when a base network is extended by adding explicit states representing the characteristics defining the structure of the base network. This can be used to explitly represent network adaptation principles within a network. The adaptation principles may change as well, based on second-order adaptation principles of the network. By reification of the reified network, also such second-order adaptation principles can be explicitly represented. This multilevel network reification construction is introduced and illustrated in the current paper. The illustration focuses on an adaptive adaptation principle from Social Science for bonding based on homophily; here connections are changing by a first-order adaptation principle which itself changes over time by a second-order adaptation principle.
Conference Paper
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In this paper the notion of network reification is introduced: a construction by which a given (base) network is extended by adding explicit states representing the characteristics defining the base network's structure. Having the network structure represented in an explicit manner within the extended network enhances expressiveness and enables to model adaptation of the base network by dynamics within the reified network. It is shown how the approach provides a unified modeling perspective on representing network adaptation principles across different domains. This is illustrated by a number of known network adaptation principles such as for Hebbian learning in Mental Networks and for network evolution based on homophily in Social Networks.
Article
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Network-Oriented Modeling has successfully been applied to obtain network models for a wide range of phenomena, including Biological Networks, Mental Networks, and Social Networks. In this paper it is discussed how the interpretation of a network as a causal network and taking into account dynamics in the form of temporal-causal networks, brings more depth. The basics and the scope of applicability of such a Network-Oriented Modelling approach are discussed and illustrated. This covers, for example, Social Network models for social contagion or information diffusion, adaptive Mental Network models for Hebbian learning and adaptive Social Network models for evolving relationships. From the more fundamental side, it will be discussed how emerging network behavior can be related to network structure. This paper describes the content of my Keynote lecture at the 10th International Conference on Computational Collective Intelligence, ICCCI'18.
Article
Disgust is an emotion intimately linked to pathogen avoidance. Building on prior work, we suggest disgust is an output of programmes that evolved to address three separate adaptive problems: what to eat, what to touch and with whom to have sex. We briefly discuss the architecture of these programmes, specifying their perceptual inputs and the contextual factors that enable them to generate adaptive and flexible behaviour. We propose that our sense of disgust is the result of these programmes and occurs when information-processing circuitries assess low expected values of consumption, low expected values of contact or low expected sexual values. This conception of disgust differs from prior models in that it dissects pathogen-related selection pressures into adaptive problems related to consumption and contact rather than assuming just one pathogen disgust system, and it excludes moral disgust from the domain of disgust proper. Instead, we illustrate how low expected values of consumption and contact as well as low expected sexual values can be used by our moral psychology to provide multiple causal links between disgust and morality. This article is part of the Theo Murphy meeting issue ‘Evolution of pathogen and parasite avoidance behaviours’.
Article
Raised progesterone during the menstrual cycle is associated with suppressed physiological immune responses, reducing the probability that the immune system will compromise the blastocyst's development. The Compensatory Prophylaxis Hypothesis proposes that this progesterone-linked immunosuppression triggers increased disgust responses to pathogen cues, compensating for the reduction in physiological immune responses by minimizing contact with pathogens. Although a popular and influential hypothesis, there is no direct, within-woman evidence for correlated changes in progesterone and pathogen disgust. To address this issue, we used a longitudinal design to test for correlated changes in salivary progesterone and pathogen disgust (measured using the pathogen disgust subscale of the Three Domain Disgust Scale) in a large sample of women (N = 375). Our analyses showed no evidence that pathogen disgust tracked changes in progesterone, estradiol, testosterone, or cortisol. Thus, our results provide no support for the Compensatory Prophylaxis Hypothesis of variation in pathogen disgust.