This document outlines ideas about mathematical models in population genetics. It provides examples of simple population genetics models involving alleles and their frequencies in a population. It discusses how models can describe mutation and selection over time. The document also discusses general ideas about mathematical models from a 1989 book. Models represent aspects of the real world in an abbreviated form by translating natural systems into mathematical systems. Successful models allow inferences in the mathematical system to predict behavior in the natural system.

1. Mendelian population as a model, intended as a
“stable target of explanation”
Emanuele Serrelli
emanuele.serrelli@unimib.it
1

2. 2

3. OUTLINE
• Some super-simple examples of usually-called “population genetics models”.
• Some ideas about mathematical models that were expressed in a 1989 book on modeling (Casti &
Karlqvist 1989), because we may still hold such ideas when we think to mathematical models.
• General pluralistic position on model notions (Leonelli 2003, 2007, Serrelli 2010, 2011).
• Report of the demarcation and defense of the notion of “model organism” (Ankeny & Leonelli 2011) as
opposed to “experimental organism”.
• Statement of a more general notion of a model as a “stable target of explanation” (Keller 2002) =>
several (though not all) requirements of “model organisms” end by falling into this notion.
• STE model notion describes also the essential part of population genetics, i.e. the Mendelian
population => proposal of revising the semantic extension of “model”; revisiting standard distinctions
like formal vs. material.
• Sketch of some interesting epistemological features and issues that pertain STE models are shared
by model organisms and Mendelian population.
3

4. OUTLINE
• Some super-simple examples of usually-called “population genetics models”.
• Some ideas about mathematical models that were expressed in a 1989 book on modeling (Casti &
Karlqvist 1989), because we may still hold such ideas when we think to mathematical models.
• General pluralistic position on model notions (Leonelli 2003, 2007, Serrelli 2010, 2011).
• Report of the demarcation and defense of the notion of “model organism” (Ankeny & Leonelli 2011) as
opposed to “experimental organism”.
• Statement of a more general notion of a model as a “stable target of explanation” (Keller 2002) =>
several (though not all) requirements of “model organisms” end by falling into this notion.
• STE model notion describes also the essential part of population genetics, i.e. the Mendelian
population => proposal of revising the semantic extension of “model”; revisiting standard distinctions
like formal vs. material.
• Sketch of some interesting epistemological features and issues that pertain STE models are shared
by model organisms and Mendelian population.
4

5. OUTLINE
• Some super-simple examples of usually-called “population genetics models”.
• Some ideas about mathematical models that were expressed in a 1989 book on modeling (Casti &
Karlqvist 1989), because we may still hold such ideas when we think to mathematical models.
• General pluralistic position on model notions (Leonelli 2003, 2007, Serrelli 2010, 2011).
• Report of the demarcation and defense of the notion of “model organism” (Ankeny & Leonelli 2011) as
opposed to “experimental organism”.
• Statement of a more general notion of a model as a “stable target of explanation” (Keller 2002) =>
several (though not all) requirements of “model organisms” end by falling into this notion.
• STE model notion describes also the essential part of population genetics, i.e. the Mendelian
population => proposal of revising the semantic extension of “model”; revisiting standard distinctions
like formal vs. material.
• Sketch of some interesting epistemological features and issues that pertain STE models are shared
by model organisms and Mendelian population.
5

6. OUTLINE
• Some super-simple examples of usually-called “population genetics models”.
• Some ideas about mathematical models that were expressed in a 1989 book on modeling (Casti &
Karlqvist 1989), because we may still hold such ideas when we think to mathematical models.
• General pluralistic position on model notions (Leonelli 2003, 2007, Serrelli 2010, 2011).
• Report of the demarcation and defense of the notion of “model organism” (Ankeny & Leonelli 2011) as
opposed to “experimental organism”.
• Statement of a more general notion of a model as a “stable target of explanation” (Keller 2002) =>
several (though not all) requirements of “model organisms” end by falling into this notion.
• STE model notion describes also the essential part of population genetics, i.e. the Mendelian
population => proposal of revising the semantic extension of “model”; revisiting standard distinctions
like formal vs. material.
• Sketch of some interesting epistemological features and issues that pertain STE models are shared
by model organisms and Mendelian population.
6

7. OUTLINE
• Some super-simple examples of usually-called “population genetics models”.
• Some ideas about mathematical models that were expressed in a 1989 book on modeling (Casti &
Karlqvist 1989), because we may still hold such ideas when we think to mathematical models.
• General pluralistic position on model notions (Leonelli 2003, 2007, Serrelli 2010, 2011).
• Report of the demarcation and defense of the notion of “model organism” (Ankeny & Leonelli 2011) as
opposed to “experimental organism”.
• Statement of a more general notion of a model as a “stable target of explanation” (Keller 2002) =>
several (though not all) requirements of “model organisms” end by falling into this notion.
• STE model notion describes also the essential part of population genetics, i.e. the Mendelian
population => proposal of revising the semantic extension of “model”; revisiting standard distinctions
like formal vs. material.
• Sketch of some interesting epistemological features and issues that pertain STE models are shared
by model organisms and Mendelian population.
7

8. OUTLINE
• Some super-simple examples of usually-called “population genetics models”.
• Some ideas about mathematical models that were expressed in a 1989 book on modeling (Casti &
Karlqvist 1989), because we may still hold such ideas when we think to mathematical models.
• General pluralistic position on model notions (Leonelli 2003, 2007, Serrelli 2010, 2011).
• Report of the demarcation and defense of the notion of “model organism” (Ankeny & Leonelli 2011) as
opposed to “experimental organism”.
• Statement of a more general notion of a model as a “stable target of explanation” (Keller 2002) =>
several (though not all) requirements of “model organisms” end by falling into this notion.
• STE model notion describes also the essential part of population genetics, i.e. the Mendelian
population => proposal of revising the semantic extension of “model”; revisiting standard distinctions
like formal vs. material.
• Sketch of some interesting epistemological features and issues that pertain STE models are shared
by model organisms and Mendelian population.
8

9. OUTLINE
• Some super-simple examples of usually-called “population genetics models”.
• Some ideas about mathematical models that were expressed in a 1989 book on modeling (Casti &
Karlqvist 1989), because we may still hold such ideas when we think to mathematical models.
• General pluralistic position on model notions (Leonelli 2003, 2007, Serrelli 2010, 2011).
• Report of the demarcation and defense of the notion of “model organism” (Ankeny & Leonelli 2011) as
opposed to “experimental organism”.
• Statement of a more general notion of a model as a “stable target of explanation” (Keller 2002) =>
several (though not all) requirements of “model organisms” end by falling into this notion.
• STE model notion describes also the essential part of population genetics, i.e. the Mendelian
population => proposal of revising the semantic extension of “model”; revisiting standard distinctions
like formal vs. material.
• Sketch of some interesting epistemological features and issues that pertain STE models are shared
by model organisms and Mendelian population.
9

10. OUTLINE
• Some super-simple examples of usually-called “population genetics models”.
• Some ideas about mathematical models that were expressed in a 1989 book on modeling (Casti &
Karlqvist 1989), because we may still hold such ideas when we think to mathematical models.
• General pluralistic position on model notions (Leonelli 2003, 2007, Serrelli 2010, 2011).
• Report of the demarcation and defense of the notion of “model organism” (Ankeny & Leonelli 2011) as
opposed to “experimental organism”.
• Statement of a more general notion of a model as a “stable target of explanation” (Keller 2002)
several (though not all) requirements of “model organisms” end by falling into this notion.
• STE model notion describes also the essential part of population genetics, i.e. the Mendelian
population => proposal of revising the semantic extension of “model”; revisiting standard distinctions
like formal vs. material.
• Sketch of some interesting epistemological features and issues that pertain STE models are shared
by model organisms and Mendelian population.
10

11. “Population genetics models”
• a, A = two alleles in a diallelic locus, in an indefinitely large population
11

12. “Population genetics models”
• a, A = two alleles in a diallelic locus, in an indefinitely large population
• q = the frequency of allele A in the population
11

13. “Population genetics models”
• a, A = two alleles in a diallelic locus, in an indefinitely large population
• q = the frequency of allele A in the population
• [(1-q)a+qA] = 1 relative frequencies of the two alleles
11

14. “Population genetics models”
• a, A = two alleles in a diallelic locus, in an indefinitely large population
• q = the frequency of allele A in the population
• [(1-q)a+qA] = 1 relative frequencies of the two alleles
• aa, Aa, AA zygotes -> what frequencies?
11

15. “Population genetics models”
• a, A = two alleles in a diallelic locus, in an indefinitely large population
• q = the frequency of allele A in the population
• [(1-q)a+qA] = 1 relative frequencies of the two alleles
• aa, Aa, AA zygotes -> what frequencies?
• Hardy-Weinberg equilibrium
(expansion of [(1-q)a+qA]2)
11

16. “Population genetics models”
• a, A = two alleles in a diallelic locus, in an indefinitely large population
• q = the frequency of allele A in the population
• [(1-q)a+qA] = 1 relative frequencies of the two alleles
• aa, Aa, AA zygotes -> what frequencies?
• Hardy-Weinberg equilibrium
(expansion of [(1-q)a+qA]2)
11

17. “Population genetics models”
• MUTATION
• Δq = -uq + v(1 - q) allele A’s frequency as a function of mutation
rates
12

18. “Population genetics models”
• MUTATION
• Δq = -uq + v(1 - q) allele A’s frequency as a function of mutation
rates
• SELECTION
• [(1-s)(1-q)a+qA]/[1-s(1-q)] = 1 relative frequencies in presence of
negative selection s on a
• Δq = [sq(1-q)]/[1-s(1-q)] change in the frequency of A
12

19. “Population genetics models”
• MUTATION
• Δq = -uq + v(1 - q) allele A’s frequency as a function of mutation
rates
• SELECTION
• [(1-s)(1-q)a+qA]/[1-s(1-q)] = 1 relative frequencies in presence of
negative selection s on a
• Δq = [sq(1-q)]/[1-s(1-q)] change in the frequency of A
• More and more complicated equations can be built...
12

20. “Population genetics models”
• Work in population genetics goes on and on still today, developing those
earlier ideas, as in the following example (Hartl & Clark 2007, pp. 97-98):
13

21. “Population genetics models”
• Work in population genetics goes on and on still today, developing those
earlier ideas, as in the following example (Hartl & Clark 2007, pp. 97-98):
• All this – basically, equations – is commonly referred to as “population
genetics models”
13

22. Ideas on mathematical models
• Every model, mathematical or otherwise, is a way of representing some aspects of the real world in an
abbreviated, or encapsulated, form. Mathematical models translate certain features of a natural system
N into the elements of a mathematical system M, with the goal being to mirror whatever is relevant
about N in the properties of M.
• The […] diagram shows the two essential aspects of a mathematical model: (i) An encoding
operation by which the explanatory scheme for the real-world system N is translated into the
language of the formal system M, and (ii) a decoding process whereby the logical inferences in M
are translated back into predictions about the temporal behavior in N.
(Casti & Karlqvist 1989 p. 3).
14

23. Ideas on mathematical models
• Every model, mathematical or otherwise, is a way of representing some aspects of the real world in an
abbreviated, or encapsulated, form. Mathematical models translate certain features of a natural system
N into the elements of a mathematical system M, with the goal being to mirror whatever is relevant
about N in the properties of M.
• The […] diagram shows the two essential aspects of a mathematical model: (i) An encoding
operation by which the explanatory scheme for the real-world system N is translated into the
language of the formal system M, and (ii) a decoding process whereby the logical inferences in M
are translated back into predictions about the temporal behavior in N.
(Casti & Karlqvist 1989 p. 3).
14

24. Ideas on mathematical models
• Every model, mathematical or otherwise, is a way of representing some aspects of the real world in an
abbreviated, or encapsulated, form. Mathematical models translate certain features of a natural system
N into the elements of a mathematical system M, with the goal being to mirror whatever is relevant
about N in the properties of M.
• The […] diagram shows the two essential aspects of a mathematical model: (i) An encoding
operation by which the explanatory scheme for the real-world system N is translated into the
language of the formal system M, and (ii) a decoding process whereby the logical inferences in M
are translated back into predictions about the temporal behavior in N.
(Casti & Karlqvist 1989 p. 3).
14

25. Ideas on mathematical models
• Every model, mathematical or otherwise, is a way of representing some aspects of the real world in an
abbreviated, or encapsulated, form. Mathematical models translate certain features of a natural system N
into the elements of a mathematical system M, with the goal being to mirror whatever is relevant about N
in the properties of M.
• The […] diagram shows the two essential aspects of a mathematical model: (i) An encoding operation by
which the explanatory scheme for the real-world system N is translated into the language of the formal
system M, and (ii) a decoding process whereby the logical inferences in M are translated back into
predictions about the temporal behavior in N.
(Casti & Karlqvist 1989 p. 3).
15

26. Ideas on mathematical models
• Every model, mathematical or otherwise, is a way of representing some aspects of the real world in an
abbreviated, or encapsulated, form. Mathematical models translate certain features of a natural system N
into the elements of a mathematical system M, with the goal being to mirror whatever is relevant about N
in the properties of M.
• The […] diagram shows the two essential aspects of a mathematical model: (i) An encoding operation by
which the explanatory scheme for the real-world system N is translated into the language of the formal
system M, and (ii) a decoding process whereby the logical inferences in M are translated back into
predictions about the temporal behavior in N.
(Casti & Karlqvist 1989 p. 3).
15

27. Ideas on mathematical models
• An “axiom of modeling faith” holds that it is possible to bring into harmony
the two worlds, i.e. the causal structure of the external world, and the
inferential structure of the internal world. Moreover, such harmony is seen
as the condition for a modeling relation to subsist between M and N
(Rosen, pp. 16-17).
16

28. Ideas on mathematical models
17

29. Ideas on mathematical models
17

30. Pluralism of model notions
• “Every model, mathematical or otherwise...” ???
18

31. Pluralism of model notions
• “Every model, mathematical or otherwise...” ???
• Leonelli (2007) defined the “single model approach” as “the tendency to
explain away, rather than value and analyse, the diversity among models”.
18

32. Pluralism of model notions
• “Every model, mathematical or otherwise...” ???
• Leonelli (2007) defined the “single model approach” as “the tendency to
explain away, rather than value and analyse, the diversity among models”.
• For Leonelli, the diversity of models is scientifically important: it secures
“several epistemic goals of potential interest to practicing scientists”, and
it allows biologists to combine them in order to pursue their research
outcomes.
18

33. Pluralism of model notions
• “Every model, mathematical or otherwise...” ???
• Leonelli (2007) defined the “single model approach” as “the tendency to
explain away, rather than value and analyse, the diversity among models”.
• For Leonelli, the diversity of models is scientifically important: it secures
“several epistemic goals of potential interest to practicing scientists”, and
it allows biologists to combine them in order to pursue their research
outcomes.
• Should we be permanently content of grouping heterogeneous activities
under the single term “modeling”?
18

34. Pluralism of model notions
• “Every model, mathematical or otherwise...” ???
• Leonelli (2007) defined the “single model approach” as “the tendency to
explain away, rather than value and analyse, the diversity among models”.
• For Leonelli, the diversity of models is scientifically important: it secures
“several epistemic goals of potential interest to practicing scientists”, and
it allows biologists to combine them in order to pursue their research
outcomes.
• Should we be permanently content of grouping heterogeneous activities
under the single term “modeling”?
• Surely a pluralistic account is the best thing we can do for now.
18

35. Model organisms
• Demarcating the concept “model organisms” vs. “experimental
organisms” (Ankeny & Leonelli 2011).
19

36. Model organisms
• Demarcating the concept “model organisms” vs. “experimental
organisms” (Ankeny & Leonelli 2011).
• Model organisms are non-human species that are extensively studied in
order to understand a range of biological phenomena, with the hope that
data and theories generated through use of the model will be applicable to
other organisms, particularly those that are in some way more complex than
the original model (p. 313).
19

37. Model organisms
• Demarcating the concept “model organisms” vs. “experimental
organisms” (Ankeny & Leonelli 2011).
• Model organisms are non-human species that are extensively studied in
order to understand a range of biological phenomena, with the hope that
data and theories generated through use of the model will be applicable to
other organisms, particularly those that are in some way more complex than
the original model (p. 313).
• Model organisms can be clearly distinguished from the broader class of
experimental organisms by several features.
19

38. Model organisms
• My view: several features identified by Ankeny & Leonelli fall into a more
general category - not experimental organism, but “stable target of
explanation”.
20

39. Model organisms
• My view: several features identified by Ankeny & Leonelli fall into a more
general category - not experimental organism, but “stable target of
explanation”.
• Two exclusive features of model organisms:
• Material features
• Representational target
20

40. Model organisms
• My view: several features identified by Ankeny & Leonelli fall into a more
general category - not experimental organism, but “stable target of
explanation”.
• Two exclusive features of model organisms:
to become (and remain) model, organisms
have to be suitable to be brood and tamed
cost-effectively; the “wild type strain” has to
• Material features
be isolated and standardized, so to assure
the comparability of results across a large
research community, etc.
• Representational target
20

41. Model organisms
• My view: several features identified by Ankeny & Leonelli fall into a more
general category - not experimental organism, but “stable target of
explanation”.
• Two exclusive features of model organisms:
• Material features
• Representational target
21

42. Model organisms
• My view: several features identified by Ankeny & Leonelli fall into a more
differs from representational
general category - not experimental organism, but “stable target of
scope
explanation”.
describes the conceptual reasons
• Two exclusive features of model organisms:
why researchers are studying a
• Material features
• Representational target
21

43. Model organisms
• My view: several features identified by Ankeny & Leonelli fall into a more
whole, intact organisms
general category - not experimental organism, but “stable target of
explanation”. …model organisms […] involve
attempts to generate complete
knowledge of the fundamental
• Two exclusive features of model organisms:processes at work […] including
the molecular, cellular, and
developmental processes; in this
• Material features sense the model organism is
understood as a test tube for
achieving a full understanding of
• Representational target all biological processes (p. 317).
22

44. Stable target of explanation (STE)
23

45. Stable target of explanation (STE)
• ...[model in experimental biology] is an organism, an organism that can be
taken to represent (that is, stand in for) a class of organisms. A model in this
sense is not expected to serve an explanatory function in itself, nor is it a
simplified representation of a more complex phenomenon for which we
already have explanatory handles. Rather, its primary function is to provide
simply a stable target of explanation (Keller 2002, p. 115).
24

46. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
{
25

47. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
{
25

48. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
3. stable: answers to the challenge of producing lawlike knowledge in fields such as experimental biology (Creager et
al. 2007, p. 5)
{
25

49. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
3. stable: answers to the challenge of producing lawlike knowledge in fields such as experimental biology (Creager et
al. 2007, p. 5)
{
4. representational scope
25

50. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
3. stable: answers to the challenge of producing lawlike knowledge in fields such as experimental biology (Creager et
al. 2007, p. 5)
{
4. representational scope
how extensively the results […] can be
projected onto a wider group of organisms
...the extent to which researchers see their
findings as applicable across organisms
(Ankeny & Leonelli, p. 315).
25

51. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
3. stable: answers to the challenge of producing lawlike knowledge in fields such as experimental biology (Creager et
al. 2007, p. 5)
{
4. representational scope is tendentially wide and changeable
26

52. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
3. stable: answers to the challenge of producing lawlike knowledge in fields such as experimental biology (Creager et
al. 2007, p. 5)
{
4. representational scope is tendentially wide and changeable
5. unified research community: ethos of sharing reinforces stability
26

53. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
3. stable: answers to the challenge of producing lawlike knowledge in fields such as experimental biology (Creager et
al. 2007, p. 5)
{
4. representational scope is tendentially wide and changeable
5. unified research community: ethos of sharing reinforces stability
6. socio-technical features: associated “experimental resources”, standardization, comparability, cumulative
establishment of techniques, practices, and results
26

54. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
3. stable: answers to the challenge of producing lawlike knowledge in fields such as experimental biology (Creager et
al. 2007, p. 5)
{
4. representational scope is tendentially wide and changeable
5. unified research community: ethos of sharing reinforces stability
6. socio-technical features: associated “experimental resources”, standardization, comparability, cumulative
establishment of techniques, practices, and results
7. artificiality: even model organisms “have been developed using complex processes of standardization that allow the
establishment of a standard strain which then serves as the basis for future research” (Ankeny & Leonelli, p. 316, cf.
e.g. Clarke & Fujimura 1992)
26

55. Stable target of explanation (STE)
1. targets of explanation: not immediately tools for explaining
2. autonomous: from theory and from data (Morgan & Morrison 1999)
3. stable: answers to the challenge of producing lawlike knowledge in fields such as experimental biology (Creager et
al. 2007, p. 5)
{
4. representational scope is tendentially wide and changeable
5. unified research community: ethos of sharing reinforces stability
6. socio-technical features: associated “experimental resources”, standardization, comparability, cumulative
establishment of techniques, practices, and results
7. artificiality: even model organisms “have been developed using complex processes of standardization that allow the
establishment of a standard strain which then serves as the basis for future research” (Ankeny & Leonelli, p. 316, cf.
e.g. Clarke & Fujimura 1992)
8. inexhaustedness: “…although model organisms are standardized in order to facilitate highly controlled biological
experimentation, their inherent complexity means that the systems are never fully understood and can continue to
generate surprising results” (Creager et al. 2007, p. 7)
26

56. How STE applies to population genetics
• To understand how the STE model notion
applies to mathematical population genetics,
we have to move our focus away from
equations, and recognize that there is
another, more fundamental object: the
Mendelian population.
• i.e., the large-scale derivation of Mendel’s
rules of inheritance.
27

57. How STE applies to population genetics
• To understand how the STE model notion
applies to mathematical population genetics,
we have to move our focus away from
equations, and recognize that there is
another, more fundamental object: the
Mendelian population.
• i.e., the large-scale derivation of Mendel’s
rules of inheritance.
27

58. How STE applies to population genetics
• To understand how the STE model notion
applies to mathematical population genetics,
we have to move our focus away from
equations, and recognize that there is
another, more fundamental object: the
Mendelian population.
• i.e., the large-scale derivation of Mendel’s
rules of inheritance.
27

59. How STE applies to population genetics
• Mendelian population is the space of all
possible individual combinations given a
number of loci and a number of alleles => a
combination space
• alleles
: : :
• loci
• individual combinations
28

60. How STE applies to population genetics
• Mendelian population is the space of all
possible individual combinations given a
number of loci and a number of alleles => a
combination space
• alleles
: : :
• loci
• individual combinations
• What is the relationship between this space
and population genetics equations?
An epistemological gap!
28

61. How STE applies to population genetics
• Only some positions in the combination space are
actually occupied at a certain time. Which
combinations are realized?
29

62. How STE applies to population genetics
• Only some positions in the combination space are
actually occupied at a certain time. Which
combinations are realized?
• With a minimally realistic number of loci and
alleles, the dimensionality of this space is so high
that no equation or algorithm can be developed.
29

63. How STE applies to population genetics
• Only some positions in the combination space are
actually occupied at a certain time. Which
combinations are realized?
• With a minimally realistic number of loci and
alleles, the dimensionality of this space is so high
that no equation or algorithm can be developed.
• Statistical equations address what happens to the
allele frequencies in one or two loci in a
population inhabiting an oversimplified di-allelic
Mendelian population space.
29

64. How STE applies to population genetics
• Only some positions in the combination space are
actually occupied at a certain time. Which
combinations are realized?
• With a minimally realistic number of loci and
alleles, the dimensionality of this space is so high
that no equation or algorithm can be developed.
• Statistical equations address what happens to the
allele frequencies in one or two loci in a
population inhabiting an oversimplified di-allelic
Mendelian population space.
• Even the more complicated population genetics
equations are incredibly partial statistical studies
of the Mendelian population space.
29

65. How STE applies to population genetics
• The Mendelian population (a combination
space) is, in my view, it is the model of
population genetics (at least of Mendelian
population genetics), it is the space equations
are about.
30

66. How STE applies to population genetics
• Review and apply STE features:
1. target of explanation
2. autonomous
3. stable
4. representational scope
5. unified research community
6. socio-technical features
7. artificiality
8. inexhaustedness
31

67. How STE applies to population genetics
• Review and apply STE features:
1. target of explanation
2. autonomous
3. stable
4. representational scope
5. unified research community
6. socio-technical features
7. artificiality the “connectedness” structure of
Mendelian population is very
8. inexhaustedness different from what we always
imagined intuitively
32

68. How STE applies to population genetics
• Review and apply STE features: this discovery enlarges the
representational scope of
1. target of explanation Mendelian population: from
adaptation to speciation too
2. autonomous
3. stable
4. representational scope
5. unified research community
6. socio-technical features
7. artificiality the “connectedness” among
genotypes in Mendelian population
8. inexhaustedness is very different from what we
always imagined intuitively
33

69. Issues about STE model notion
• Epistemological questions (dilemmas?).
If, as several authors point out (e.g., Creager et al. 2007), models are not
chosen because they are typical of a certain set of systems, nor they are
built to represent some other system by reduction, deduction, encoding
(Casti & Karlqvist 1989, Rosen 1989) or the like, how can they...
• REPRESENT?
• EXPLAIN?
• PREDICT?
34

70. Issues about STE model notion
• Discussing such relationships is not
essential within a notion of a model as a
stable target of explanation. That is, if we
choose this notion of model we can
provisionally remain silent on how and
what the model represents and explains.
35

71. Issues about STE model notion
• Discussing such relationships is not
essential within a notion of a model as a
stable target of explanation. That is, if we
choose this notion of model we can
provisionally remain silent on how and
what the model represents and explains.
• The most notable fact is that all the issues Formal Material
are shared between a formal and a material
models.
35

72. Issues about STE model notion
• Discussing such relationships is not
essential within a notion of a model as a
stable target of explanation. That is, if we
choose this notion of model we can
provisionally remain silent on how and
what the model represents and explains.
• The most notable fact is that all the issues Formal Material
are shared between a formal and a material
models.
35

73. THANK
YOU!
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