Genetic and physical testing used in genetic programs of common dog breeds.
\r\n\tThe major pathogenetic mechanisms resulting from RAAS overactivity include activation of the sympathetic nervous system, endothelial dysfunction, proinflammatory, and procoagulant states.
\r\n\tEmerging from basic science evidence, major clinical trials established the beneficial effects of inhibitors of the different components of RAAS such as angiotensin-converting enzyme (ACE) inhibitors, angiotensin receptor blockers (ARBs), aldosterone antagonists. These effects range from treatment of hypertension, diabetic nephropathy, CHF, as well as improvement of outcomes after myocardial infarction and improvement in glucose homeostasis and prevention of type 2 diabetes with some agents.
\r\n\tIn this book, written by a world-renowned scholar, we will address the major concepts and topics related to RAAS activation including the pathogenetic mechanisms underlying the deleterious effects of activated RAAS and the role of local tissue RAAS in various organ systems such as the heart and vasculature, the skeletal muscle, adipose tissues, pancreas and the angiotensinergic pathways in the brain. Cutting-edge information is provided that will address the need for a wide range of readers including a medical student, clinical practitioner, and basic science investigators alike. This book will be bridging the gap between basic science and clinical practice regarding the RAAS system, which is imminently critical and highly relevant to the practice of medicine.
\r\n\r\n\tFinally, with data emerging from the COVID-19 pandemic indicating overrepresentation of people with diseases associated with RAAS activation such as hypertension, chronic kidney disease, and diabetes, the role of RAAS activation and RAAS inhibition in the pathogenesis and clinical outcomes in COVID-19 has garnered a great deal of interest. In this book, we will dedicate a chapter addressing this topical and highly critical subject.
\r\n\t
The choice of initial attributes for description of an object in an artificial intelligence (AI) problem is the first stage of any simulation of an informational process (representation of information for its further use).
\nAt the 60–70th of the twentieth century, many authors (see, for example, [1]) offered to use predicate calculus for AI problem solving. The resolution method seemed to be a very easy and clear tool to solve problems dealing with compound objects, which can be described by properties of its elements and relations between these elements.
\nUntil the notion of NP-complete problem (in particular, described in [2, 3]) was not widely adopted, such an approach seemed to be very convenient, but many such-a-way formalized problems occurred to be NP-complete or even algorithmic unsolvable.
\nWhile developing the effective algorithms deciding discrete problems, determination of estimations for number of steps of their run becomes one of the important problems. The absence of the proved estimations for number of an algorithm run steps is considered as an insufficient research of this algorithm. It is especially relevant for problems with big input. It concerns, in particular, to the algorithms deciding various AI problems. At practical use of an algorithm, it is important that it has polynomial upper bound of number of its run steps. The NP-completeness or NP-hardness of a problem means now that the polynomial algorithm of its decision is not known.
\nIn 2007, the author proved NP-completeness of a series of AI problems formalized with the help of predicate calculus formulas [4], proved upper bounds for number of steps of algorithms solving these problems [5], and offered a level description of goal formulas for decreasing the number of proof steps [6]. Such a level description is based on the extraction of a common up to the names of its arguments sub-formula of the set of elementary conjunctions of atomic predicate formulas. These sub-formulas define generalized characteristics of an object.
\nExtraction of such sub-formulas allows to construct logic-predicate networks [7], which may change its configuration (the number of layers and the number of cells in the layer) during the process of training.
\nExtraction of these sub-formulas may serve as an instrument for constructing a multi-agent description of an object, when every agent can describe only a part of the object (these parts are intersected), but every agent gives its own names to the elements of the whole object [8].
\nHere, some AI problems formalized in such a way are under consideration. For these problems, the solving algorithms and upper bounds of their run are obtained. These upper bounds permit to point out the parameters of the problem, which mostly influence on the complexity of the algorithm, and to offer approaches permitting to decrease the complexity.
\nA model example illustrating the described approach and algorithms is given.
\nLet an investigated object be presented as a set of its elements ω = {ω1,…, ωt}. The set of predicates p1,…, pn (every of which is defined on the elements of ω) characterizes properties of these elements or relations between them. Logical description S(ω) of an object ω is a collection of all true formulas in the form \n
Let the set Ω of all investigated objects be a union of classes Ωk, (k = 1,…, K), i.e., Ω = \n
Here and below, the notation \n
The introduced descriptions allow to solve many artificial intelligence problems [9]. Main of these problems may be formulated as follows.
\nIdentification problem: to pick out all parts of the object ω that belongs to the class Ωk.
\nClassification problem: to find all such class numbers k that ω ∈ Ωk.
\nAnalysis problem: to find and classify all parts τ of the object ω.
\nThe solution of these problems may be reduced to the proof of logic sequents
\nrespectively, and determination of the values for \n
Note that the proof of any of the sequent (1), (2), or (3) answers only the question “whether it is true?” Strictly speaking, in the sequents (1)–(3), instead of the symbols \n
If one uses an exhaustive or a logical algorithm (derivation in a sequent calculus or proof by resolution method), the algorithm gives the values for \n
The proof of sequents (1) and (3) is based on the proof of the sequent
\nwhere \n
An exhaustive algorithm is widespread to prove (4). The total estimate for the number of steps (i.e., the number of comparisons) for the exhaustive algorithm solving (4) is
\nor, more roughly,
\nWhile using a logical algorithm (derivation in a predicate sequent calculus or proof by resolution method for predicate calculus), one must find unifier of the formula \n
The number of steps (i.e., the number of comparisons) required for the solution of the system and, hence, for the logical algorithm solving (4) is
\nai and si be the numbers of literals with the predicate pi in \n
where s′ = max{s1,…, sn}.
\nThe above-received estimations are exponential over the length of \n
The received estimations cannot be essentially decreased up to polynomial ones if P ≠ NP (classes P and NP are the classes of predicates checked in polynomial time by a deterministic or nondeterministic Turing machine respectively). More precisely, the problem (4) is NP-complete and, hence, the problems (1) and (3) are NP-complete, and the problems (4) and (5) are NP-hard [4, 5].
\nProblem (2) is strictly connected with the so-called “open” problem ISOMORPHISM OF GRAPHS [3], for which it is not proved neither its polynomiality nor its NP-completeness.
\nThese standard images allow to form a description (up to mirror image) of almost all boxes. Such a description is a disjunction of four elementary conjunctions containing, respectively, 10, 8, 10, 8 variables and 30 + 2, 23 + 1, 28 + 4, 33 + 4 atomic formulas with predicates V and L, respectively. The elementary conjunctions corresponding to the images are
\nGiven a “box” inside a complex contour image containing t nodes and s be the maximal number of occurrences of the predicate V in the description S(ω), it would be recognized (according to the estimations (5′) and (6′)) in O(t10) steps by an exhaustive algorithm and in O(s37) steps by a logical algorithm.
\nCan seem that many atomic formulas such as V(x5,x2,x4), V(x5,x3,x7), V(x5,x4,x7), and V(x5,x7,x2) in V(x5,x2,x3) & V(x5,x2,x4) & V(x5,x3,x7) & V(x5,x3,x10) & V(x5,x4,x7) & V(x5,x4,x10) & V(x5,x7,x2) & V(x5,x10,x2) are unnecessary. But if we delete such “unnecessary” formulas, it would be needed to add to a premise of a sequent, a condition that every point that belongs to a segment (y,z) may be substituted instead of y or z (be the second or the third argument) in every atomic formula with the predicate V. It would be another setting of a problem. Moreover, such “unnecessary” formulas can help to decrease the number of algorithm run steps if we use branch and bound algorithm inside the exhaustive algorithm or the reverse Maslov’s method for a logical one [11].
\nBelow, the designation \n
The notion of level description of classes was introduced in [6]. Such a description essentially allows to decrease the number of steps for an algorithm solving every of the above-formulated problems. This notion is based on the extraction of “frequently” appeared “sub-formulas” \n
Repeat the above-described procedure with all formulas \n
The solution of the problem of the form (4) with the use of the level description of classes is decomposed on the sequential (l = 1, …, L) implementation of the actions 1–4:
For every i (i = 1,…, nl) check Sl−1(ω) ⇒ \n
Introduce new l-level atomic formulas \n
Substitute \n
Add all constant atomic l-level formulas in the form \n
At last check SL(ω) ⇒ \n
The decreasing of the number of steps for an algorithm solving every of the above formulated problems (1)–(3) with the use of a level description follows from the fact that in items 1, 2, and 5, we solve the same problem as it was formulated in Section 1 and has the number (4). The estimations of number of steps exponentially depend on the parameters of the formula, i.e., on the right part of implication. That is why the term “small complexity” for \n
Why did we use quotation marks for the term “sub-formulas?” Such formulas (elementary conjunctions) \n
Definition 1. Elementary conjunctions P and Q are called isomorphic if there is an elementary conjunction R and substitutions λR,P and λR,Q of the arguments of P and Q, respectively, instead of the variables in R such that the results of these substitutions coincide up to the order of literals
\nThe substitutions λR,P and λR,Q are called unifiers of R with P and Q, respectively.
\nDefinition 2. Elementary conjunction C is called a common up to the names of arguments sub-formula of two elementary conjunctions A and B if it is isomorphic to some sub-formulas A′ and B′ of A and B, respectively
\nFor example, let A(x,y,z) = p1(x) & p1(y) & p1(z) & p2(x, y) & p3(x, z), B(x,y,z) = p1(x) & p1(y) & p1(z) & p2(x, z) & p3(x, z)
\nIs the formula P(u,v) = p1(u) & p1(v) & p2(u, v) their common sub-formula?
\nThe formula P(u,v) is their common up to the names of variables sub-formula with the unifiers λP,A—substitution of x and y instead of u and v, respectively, and λP,B—substitution of x and z instead of u and v, respectively. It is so because P(x,y) = p1(x) & p1(y) & p2(x,y) is a sub-formula of A(x,y,z) and P(x,z) = p1(x) & p1(z) & p2(x,z) is a sub-formula of B(x,y,z).
\nAn algorithm of extraction of a maximal (having a maximal number of literals) common up to the names of arguments sub-formula C of two elementary conjunctions A and B and determining the unifiers λc,A′ and λc,B′ is described in [12]. The number of steps of this algorithm is O(aa bb), where a and b are the numbers of literals in A and B, respectively. The minimal number of steps of this algorithm is O((ab)2), the middle estimate is O((ab)1/2 log(ab)).
\nThis algorithm allows to construct a level description for a set of goal elementary conjunctions. Essential difference between maximal common up to the names of arguments sub-formulas and sub-formulas in the level description consists in the fact that in the level description it is needed to extract sub-formulas with “small complexity” but not a maximal one. An algorithm of level description construction is in [6]. It consists in sequential pairwise extraction of common up to the names of variables sub-formulas of \n
Let N be the maximal number of literals \n
Return to the example in the previous section. There, we have seen a description of a class of “boxes” represented in Figure 1. According to these descriptions, we have received that given a “box” inside a complex contour image containing t nodes it would be recognized in O(t10) steps by an exhaustive algorithm and in O(s37) steps by a logical algorithm (here, s is the maximal number of occurrences of the same predicate in the object description S(ω)).
\nStandard different contour images of a “box”.
Pairwise extraction of common up to the names of variables of elementary conjunctions, corresponding to these images, allows to extract common up to the names of variables sub-formulas corresponding to the images represented in Figure 2
\nImages corresponding to extraction of common sub-formulas.
These sub-formulas contain, respectively, 8, 8, 7, 7, 7, 8 variables and 18, 15, 11, 11, 15, 16 atomic formulas.
\nThe following extraction by means of pairwise partial deduction between common sub-formulas corresponding to images ab, ac, ad, bc, bd, cd gives a sub-formula corresponding to the image represented in Figure 3.
\nImage corresponding to the second extraction of common sub-formulas.
Elementary conjunction P1(x1,x2,x3,x4,x5,x9,x10) = V(x1,x3,x2) & V(x2,x1,x5) & V(x3,x4,x1) & V(x3,x5,x1) & V(x3,x9,x4) & V(x3,x9,x5) & V(x3,x9,x1) & V(x5,x2,x4) & V(x5,x2,x3) & V(x9,x10,x3) & T(x4,x3,x5), corresponding to this image, defines a first-level predicate p1(x1). The first-level variable x1 is a variable for a list of seven initial variables x1 = (x1,x2,x3,x4,x5,x9,x10). The unifier of P1(x1,x2,x3,x4,x5,x9,x10) with the description of ab, ac, ad, ac, and bd is an identical substitution, but its unifier with the description of cd is a substitution of x6 instead of x5.
\nElementary conjunctions P12(x1,x1,x2,x3,x4,x5,x8,x9,x10), P22(x1,x4,x5,x6,x9,x10), P32(x1,x3,x4,x5,x10), P42(x1,x2,x5,x6,x10), corresponding to the images ab, ac, bd, cd and written with the use of the predicate p1(x1), define second-level predicates p12(x12), p22(x22), p32(x32), p42(x42) with the second-level variables x12 = (x1,x1,x2,x3,x4,x5,x8,x9,x10), x22 = (x1,x4,x5,x6,x9,x10), x32 = (x1,x3,x4,x5,x10), x42 = (x1,x2,x5,x6,x10).
\nFor example, a sub-formula corresponding to the image ab is P12(x1,x1,x2,x3,x4,x5,x8,x9,x10) = p1(x1) & V(x2,x5,x8) & V(x2,x1,x8) & V(x5,x4,x10) & V(x5,x3,x10) & V(x8,x2,x10) & V(x10,x8,x5) & V(x10,x5,x9) & V(x10,x8,x9). The unifier of P12(x1,x1,x2,x3,x4,x5,x8,x9,x10) with the description of a is an identical substitution, and with the description of b, it is a substitution of x4,x5,x6,x7,x8 instead of x2,x4,x5,x9,x10. Descriptions of images c and d are not unified with it.
\nThe three-level description of the image b takes the form Ab2(x12,x4,x5,x6,x7) = p12(x12) & V(x5,x4,x7) & V(x5,x7,x6) or Ab2(x32,x4,x5,x6,x7) = p32(x32) & V(x3,x2,x8) & V(x5,x4,x7) & V(x5,x7,x6).
\nGiven a “box” inside a complex contour image containing t nodes, the proof the sequence from S(ω) of elementary conjunction P1(x1,x2,x3,x4,x5,x9,x10) defining the first-level predicate p1(x1) and the denotation of variables x1,x2,x3,x4,x5,x9,x10 would be done in O(t7) steps by an exhaustive algorithm and in O(s11) steps by a logical algorithm.
\nElementary conjunctions P12(x11), P22(x11), P32(x11), P42(x11) contain respectively only 1, 1, 0, 1 “new” variables (not containing in the first-level variables) and 7, 4, 4, 5 “new” atomic formulas. The proof of the sequence from S1(ω ) of these elementary conjunctions defining the second-level predicates p12(x12), p22(x22), p32(x32), p42(x42), and the denotation of the “new” variables would be done in O(t) steps by an exhaustive algorithm and in O(s7) steps by a logical algorithm.
\nElementary conjunctions obtained from the class description by means of second-level predicates instead of the corresponding sub-formulas contain respectively 2, 0, 2, 2 “new” variables and 7, 4, 11, 16 “new” atomic formulas. The proof of the sequence from S2(ω ) of these elementary conjunctions and the denotation of the “new” variables would be done in O(t2) steps by an exhaustive algorithm and in O(s16) steps by a logical algorithm.
\nAs O(t7) + O(t) + O(t2) = O(t7) < O(t10) and O(s11) + O(s7) + O(s16) = O(s16) < O(s37) then both an exhaustive algorithm and a logical algorithm using the built level description of the class of “boxes” make the less number of steps then the same ones using the initial description. At the same time, the decreasing of number of steps of a logical algorithm is more noticeably.
\nTraditional neuron network deals with binary or many-valued characteristics of an object and is an adder of weighted inputs followed by a function mapping the result into the segment [0, 1]. The neuron network configuration is fixed and only the weights may be changed.
\nA logic-predicate network is described later. The inputs for this network are atomic formulas setting properties of the elements composing an investigated object and relations between them [7]. The proposed model of logic-predicate network has two blocks: a training block and a recognition block. The input of every block is an elementary conjunction of atomic predicate formulas or their negations. Configuration of the recognition block is formed after an implementation of the training block and may be changed with its help.
\nThe training block is a “slowly running” block. At the same time, the recognition block is a “quickly running” one. The base of the proposed predicate network is a logic-objective approach to AI problems and level description of classes.
\nThe scheme of the logic-predicate network is presented in Figure 4
\nScheme of the logic-predicate network.
At a training stage of logic-predicate network construction, we have a training set of objects. Let a training set of objects ω1,…, ωK be given to form an initial variant of the network training block. Replace every constant \n
Construct a level description for these goal formulas with the use of algorithm of level description. The first approximation to the recognition block is formed. Formulas \n
The recognition block tries to identify a new object according to the level description of classes, obtained in the training block.
\nIf after the “recognition block” run an object is not recognized or has wrong classification, then it is possible to train anew the network. The description of the “wrong” object must be added to the input set of the training block. The training block extracts common sub-formulas of this description and previously received formulas forming the recognition block. Some sub-formulas in the level description would be changed. Then, the recognition block is reconstructed.
\nGiven a training set for the class of contour images of “boxes” presented in Figure 1 (Section 2). Pairwise extraction of common up to the names of variables of elementary conjunctions, corresponding to these images, allows to extract common sub-formulas corresponding to the images presented in Figures 2 and 3 (Section 3). Fragments of the images corresponding to a three-level network are presented in Figure 5.
\nFragments of the images corresponding to a three-level network.
Given, a new image represented in Figure 6 for recognition, the network would not recognize it because the first-level predicate is not valid.
\nControl image.
Add the description of this control image to the input data of the training block. The extraction of common sub-formulas for this description and the formula defining the first-level predicate gives a formula corresponding to the image represented in Figure 7.
\nImage corresponding to the new first-level predicate.
New second-level predicates correspond to three images represented in Figure 8.
\nImages corresponding to three new second-level predicates.
The set of the third-level predicates coincides with the set of previous second-level predicates. So, the recognition block is constructed anew and represents four-level description of the class. Fragments of the images corresponding to a four-level network are presented in Figure 9.
\nFragments of the images corresponding to a four-level network.
A problem of multi-agent description of a complex object is under consideration in this section. It is supposed that every agent knows only a part of an investigated object description. Moreover, she does not know the true names of elements and gives them names arbitrary. It is similar to the parable about tree blind men who feel an elephant. To overcome such a paradox, it is supposed that every two agents have information concerning some common part of an object. The main difficulty in this problem is to find and identify these parts [8].
\nLet an investigated object is represented as a set of its elements \n
Information (description) of an object is an elementary conjunction of atomic formulas with predicates p1,…, pn and some constants as arguments.
\nThere are m agents a1,…, am which can measure some values for some predicates of some elements of ω. The agent aj does not know the true number of the ω elements and suppose that she deals with the object \n
As every agent uses her own notifications for the names of the object elements, it is needed to find all common up to the names of arguments sub-formulas Cij of the information \n
Below, the arguments of information will be omitted. Let every agent aj has information Ij about the described object ω (j = 1,…, m). To construct a description of ω the following algorithm is offered.
Change all constants in I1,…, Im by variables in such a way that different constants are changed by different variables and the names of variables in Ii and Ij (i ≠ j) does not coincide. Obtain I′1,…, I′m.
For every pair of elementary conjunctions I′i and I′j (i = 1,…, m − 1, j = i + 1, …, m) find their maximal common up to the names of arguments sub-formula Cij and unifiers λi,ij and λj,ij. Every argument of Cij has a unique name.
For every pair i and j (i > j) check if I′i and I′j contain a contradictory pair of atomic formulas or two sub-formulas which cannot be satisfied simultaneously (for example, “x is green” and “x is red”). If such a contradiction is established, then delete from Cij atomic formulas containing the variables, which are in the contradictory sub-formulas. Change the unifiers by means of elimination of these variables.
For every i, identify the variables in Cij (i ≠ j) which are substituted in I′i and I′j instead of the same variable. The names of the identified variables are changed in unifiers by the same name.
With the use of the unifiers obtained in items 2–4 change the names of variables in I′1,…, I′m. Obtain I″1, …, I″m.
Write down the conjunction I″1 & … & I″m and delete the repeated atomic formulas.
To estimate the number of the algorithm run steps, we estimate every item of the algorithm.
Item 1 requires not more than \n
Item 2 requires \n
“steps” for an algorithm based on the derivation in the predicate calculus.
It is needed to summarize the above estimates for i = 1,…, m − 1, j = i, …, m. So, we have \n
Consistency checking of the formulas Ii and Ij requires \n
For every i, identification of the variables in Cij (i > j) consists in the comparison of the replaced part of the unifiers λi,ij and λj,ij. It requires not more than (m − i)ti2 “steps.” Summarizing it for i = 1,…, m we have not more than \n
The number of “steps” required for the changing of the names of variables in I1, …, Im is linear under \n
The number of “steps” required for the deleting of the repeated conjunctive terms is not more than \n
The whole number of the algorithm run steps is O(tt 2s m2) for an exhaustive algorithm and O(ss + 3 m2) for an algorithm based on the derivation in the predicate calculus.
\nThe analysis of the received estimation shows that the main contribution is made by the summarized number of partial deduction checking (item 2).
\nLet the initial predicates be V and L described in Section 2. Each of the three agents has a description of one of the fragment presented in Figure 10.
\nFragments of the image received by three agents.
According to the item 1 of the algorithm, all constants in the fragment descriptions are replaced by variables in such a way that different constants are changed by different variables and the names of variables in Ii and Ij (i ≠ j) does not coincide. The fragment descriptions take the form:
\nI′1(x1,…,x6) = V(x1,x2,x4) & V(x1,x5,x4) & V(x1,x3,x2) & V(x1,x3,x5) & V(x1,x3,x4) & V(x2,x1,x3) & V(x2,x3,x5) & V(x3,x2,x1) &V(x3,x6,x2) & V(x3,x6,x1) & L(x2,x1,x5),
\nI′2(y1,…,y6) = V(y3,y1,y4) & V(y1,y2,y3) & V(y1,y5,y3) & V(y1,y6,y2) & V(y1,y6,y5) & V(y1,y6,y3) & L(y2,y1,y5),
\nI′3(z1,…,z8) = V(z1,z5,z3) & V(z1,z3,z2) & V(z1,z5,z2) & V(z3,z1,z7) & V(z3,z1,z6) & V(z3,z7,z4) & V(z3,z6,z4) & V(z3,z4,z1) & V(z4,z2,z3) & V(z4,z3,z8) & V(z4,z2,z8) & L(z7,z6,z3).
\nAccording to the item 2 of the algorithm, find maximal common up to the names of arguments sub-formula of formulas I′1(x1,…,x6) and I′2(y1,…,y6). It is C12(u0,…,u4) of the form C12(u0,…,u4) = V(u0,u1,u2) & V(u0,u3,u2) & V(u0,u4,u1) & V(u0,u4,u3) & V(u0,u4,u2) & L(u1,u0,u3).
\nIt has unifiers λI1,C12—substitution of u0, u1, u4, u2, u3 instead of x1, x2, x3, x4, x5, respectively, and λI2,C12—substitution of u0, u1, u2, u3, u4 instead of y1, y2, y3, y5, y6, respectively. Besides,
\nI′1(u0,u1,u2,u3,u4,x6) = V(u1,u0,u4) & V(u1,u4,u3) & V(u4,u1,u0) & V(u4,x6,u1) & V(u4,x6,u0) & C12(u0, …, u4),
\nI′2(u0,u1,u2,y4,u3,u4) = V(u2,u0,y4) & C12(u0,…,u4).
\nMaximal common up to the names of arguments sub-formula of I′2(y1,…,y6) and I′3(z1,…,z8) is C23(v0,v2,v4,v5,v6,v7) of the form
\nC23(v0,v2,v4,v5,v6,v7) = V(v6,v2,v7) & V(v2,v4,v6) & V(v2,v5,v6) &V(v2,v0,v4) & V(v2,v0,v5).
\nIt has unifiers λI2,C23—substitution of v2, v4, v6, v7, v5, v0 instead of y1, y2, y3, y4, y5, y6, respectively, and λI3,C23—substitution of v0, v2, v6, v5, v4, v7 instead of z1, z3, z5, z6, z7, z8, respectively. Besides,
\nI′2(v2,v4,v6,v7,v5,v0) = V(v2,v0,v6) & L(v4,v2,v5) & C23(v0,v2,v4,v5,v6,v7),
\nI′3(v0,z2,v2,v6,z5,v5,v4,v7) = V(v2,v6,v0) & V(v0,z5,v2) & V(v0,v2,z2) & V(v0,v5,z2) & V(v6,z2,v2) & V(v6,v2,v7) & L(v4,v5,v2) & C23(v0,v2,v4,v5,v6,v7).
\nAs I′2(v2,v4,v6,v7,v5,v0) contains V(v2,v0,v6) and I′3(v0,z2,v2,v6,z5,v5,v4,v7) contains V(v2,v6,v0) and according to the definition of the predicate V, the formula V(x,y,z) & V(x,z,y) is a contradiction, so substitutions with this unifiers cannot give a consistent description of the object. After deleting from I′2(y1,…,y6) and I′3(z1,…,z8), the variables y1 and z3, respectively, a new maximal common up to the names of arguments their sub-formula C’23(v0,v2,v4,v5,v6,v7) of the form C’23(v0,v1,v2) = L(v1,v0,v2) will be received with the unifiers λI2,C’23— substitution of v0, v1, v2 instead of y1, y2, y3, respectively, and λI3,C’23—substitution of v2, v0, v1 instead of z3, z6, z7, respectively. Besides,
\nI′2(v0,v1,v2,y4,y5,y6) = V(v2,v0,y4) & V(v0,v1,v2) & V(v0,y5,v2) & V(v0,y6,v1) &V(v0,y6,y5) & V(v0,y6,v2) & C’23(v0,v1,v2),
\nI′3(z1,z2,v2,z4,z5,v0,v1,z8) = V(z1,z5,v2) & V(z1,v2,z2) & V(z1,z5,z2) & V(v2,z1,v1) & V (v2,z1,v0) & V(v2,v1,z4) & V(v2,v0,z4) & V(v2,z4,z1) & V(z4,z2,v2) & V(z4,v2,z8) & V(z4,z2,z8) & C’23(v0,v1,v2).
\nMaximal common up to the names of arguments sub-formula of I1(x1,…,x6) and I3(z1,…,z8) is C13(w0, …,w6) in the form
\nC13(w0, …,w6) = V(w2,w4,w6) & V(w2,w5,w6) & V(w2,w0,w4) & V(w2,w0,w5) & V(w0,w1,w2).
\nIt has unifiers λI1,C13— substitution of w2, w4, w0, w6, w5, w6 instead of x1, x2, x3, x4, x5, x6, respectively, and λI3,C13—substitution of w0, w2, w6, w1, w5, w2 instead of z1, z3, z4, z5, z6, z7, respectively. Besides,
\nI′1(w2,w4,w0,w6,w5,w1) = V(w2,w0,w6) & V(w0,w1,w4) & V(w0,w4,w2) & L(w2,w4,w5) & C13(w0,…,w6),
\nI′3(w0,z2,w2,w6,w1,w5,w4,z8) = V(w0,w2,w3) & V(w0,w1,w3) & V(w2,w6,w0) & V(w6,w3,w2) & V(w6,w2,w7) & V(w6,w3,w7) & C13(w0,…,w6).
\nAs I′1(w2,w4,w0,w6,w5,w1) contains V(w2,w0,w6), I3(w0,z2,w2,w6,w1,w5,w4,z8) contains V(w2,w6,w0) and according to the definition of the predicate V, the formula V(x,y,z) & V(x,z,y) is a contradiction, so substitutions with this unifiers cannot give a consistent description of the object.
\nAfter deleting from I′1(x1,…,x6) and I′3(z1,…,z8) literals with the variables x1 and z3, respectively, a new maximal common up to the names of arguments their sub-formula
\nC′13(w0,w1,w2) of the form C’13(w0,w1,w2) = L(w1,w0,w2)
\nwill be received with the unifiers λI1,C’13—substitution of w0, w1, w2 instead of x1, x2, x5, respectively, and λI3,C’13—substitution of w2, w1, w0 instead of z3, z4, z5 respectively. Besides,
\nI′1(w0,w1,x3,x4,w2,x6) = V(w0,w1,x4) & V(w0,w2,x4) & V(w0,x3,w1) & V(w0,x3,w2) & V(w0,x3,x4) & V(w1,w0,x3) & V(w1,x3,w2) & V(x3,w1,w0) & V(x3,x6,w1) & V(x3,x6,w0) & C’13(w0,w1,w2),
\nI′3(z1,z1,w2,w1,w0,z6,z7,z8) = V(z1,w0,w2) & V(z1,w2,z2) & V(z1,w0,z2) & V(w2,z1,z7) & V(w2,z1,z6) & V(w2,z7,w1) & V(w2,z6,w1) & V(w2,w1,z1) & V(w1,z2,w2) & V(w1,w2,z8) & V(w1,z2,z8) & C′13(w0,w1,w2).
\nAccording to the item 4 of the algorithm, we identify new variables substituted instead of the same initial variable. That is we identify the following variables:
\nu0 and w0 (are substituted instead of the variable x1),
u1 and w1 (are substituted instead of the variable x2),
u2 and w2 (are substituted instead of the variable x4),
u0 and v0 (are substituted instead of the variable y1),
u1 and v1 (are substituted instead of the variable y2),
u2 and v2 (are substituted instead of the variable y3),
v0 and w0 (are substituted instead of the variable z6),
v1 and w1 (are substituted instead of the variable z3),
v2 and w2 (are substituted instead of the variable z7).
The identified variables denote as α 0, α 1, and α 2. So, we have the equalities u0 = v0 = w0 = α 0, u1 = v1 = w1 = α 1, u2 = v2 = w2 = α 2.
\nAs a result, we have the following descriptions of the fragments:
\nI″1(α 0, α 1,u4,u2, α 2,x6) = V(α 0, α 1,u2) & V(α 0, α 2,u2) & V(α 0,u4, α 1) & V(α 0,u4, α 2) & V(α 0,u4,u2) & V(α 1, α 0,u4) & V(α 1,u4, α 2) & V(x3, α 1, α 0) & V(u4,x6, α 1) & V(u4,x6, α 0) & L(α 1, α 0, α 2),
\nI″2(α0, α 1,u2,y4, α 2,u4) = V(u2, α 0,y4) & V(α 0, α 1,u2) & V(α 0, α 2,u2) & V(α 0,u4, α 1) & V(α 0,u4, α 2) & V(α 0,u4,u2) & L(α 1, α 0, α 2),
\nI″3(z1,z2, α 2,z4,z5, α 0, α 1,z8) = V(z1,z5, α 2) & V(z1, α 2,z2) & V(z1,z5,z2) & V(α 2,z1, α 1) & V(α 2,z1, α 0) & V(α 2, α 1,z4) & V(α 2, α 0,z4) & V(α 2,z4,z1) & V(z4,z2, α 2) & V(z4, α 2,z8) & V(z4,z2,z8) & L(α 1, α 0, α 2).
\nTheir conjunction
\nV(α0, α 1,u2) & V(α 0, α 2,u2) & V(α 0,u4, α 1) & V(α 0,u4, α 2) & V(α 0,u4,u2) &
\nV(α 1, α 0,u4) & V(α 1,u4, α 2) & V(x3, α 1, α 0) & V(u4,x6, α 1) & V(u4,x6, α 0) &
\nV(u2, α 0,y4) & V(z1,z5, α 2) & V(z1, α 2,z2) & V(z1,z5,z2) & V(α 2,z1, α 1) &
\nV(α 2,z1, α 0) & V(α 2, α 1,z4) & V(α 2, α 0,z4) &V(α 2,z4,z1) & V(z4,z2, α 2) &
\nV(z4, α 2,z8) & V(z4,z2,z8) & L(α 1, α 0, α 2)
\nallows to “stick together” the images of fragments according to the same variable. The image corresponding to the result of “sticking” is presented in Figure 11.
\nImage corresponding to the result of “sticking”.
If a description of the investigated object is presented in the database, it may be found according the principle “the nearest neighbor” with the use of metric for predicate formulas presented in [13].
\nLogic-predicate approach to an AI problem has a rather powerful capability, essentially when an investigated object is a compound one and is characterized by properties of its elements and relations between them.
\nSetting of pattern recognition problems considered in Section 2 (except the problem (2)) differs from the classical one. The setting of the problems (1) and (3), in which it is needed to find parts of an investigated object, turns out to be a rather difficult one in the frameworks of a standard approach in the frameworks of which an object is regarded as a whole indivisible one.
\nIn particular, an exponential estimation for number of propositional variables in a formula simulating a predicate formula in a finite domain for planning problems T·|Act|·OP is mentioned in [14]. Here, T is the number of time stages, |Act| is the number of schemes of actions, O is the number of objects in the domain, P is the maximal number of parameters in schemes of actions. In Section 2, the analogous estimate (5′) was received for an exhaustive algorithm solving the problem (4).
\nThe problem (2) is polynomial equivalent to an “open” problem ISOMORPHISM OF GRAPHS [3] and the problems (1) and (3) are NP-complete.
\nA notion of level description of classes has been introduced in Section 3 in order to decrease the number of steps of algorithms solving these problems. Such a description reduces the solution of the main problem to a series of solutions of the same form problems with the inputs with the essentially less notation lengths. At the same time, the constructing of a level description still deals with big input data. So, a problem with big input data is solving only once, and then the problem with the essentially less input data is solving repeatedly.
\nThe idea of decomposition of a problem to a series of the “less dimension” problems is not a new one and is frequently used. The difficulty consists in a precise definition of the term “common sub-formula of small complexity.”
\nThe development of a precise definition and of an algorithm for the extraction of a common up to the names of arguments sub-formula of two elementary conjunctions (and their unifiers) allows not only to work out an algorithm of level description construction but also to find an approach to the solution of some else AI problems.
\nNote that the extracted sub-formulas define generalized characteristics of an object. This has an analogy in medical diagnostics: initial characteristics are symptoms and the generalized ones are syndromes.
\nLevel description of classes allowed to introduce the notion of logic-predicate network described in Section 4. Such a network may be regarded as a self-training network which changes its configuration after an additional training. It corresponds to the fact that in the process of a man training, new notions and relations between them are formed in a human brain.
\nThe presence of an algorithm for the extraction of a common up to the names of arguments sub-formula of two elementary conjunctions (and their unifiers) allows to find an approach to a problem of multi-agent description of an object described in Section 5. Just an extraction of such sub-formulas and determining of their unifiers with the input formulas makes possible to “stick together” such parts of descriptions in which different agents gives different names to one element of the whole object.
\nNote that the formulation of the problem (1) from Section 2 coincides with the one for a well-known problem CONJUNCTIVE BOOLEAN QUERY from [3]. The difference is in the implementation of these problems. While repeated implementation of the problem (1) the premise S(ω) of the sequent \n
While repeated implementation of the problem CONJUNCTIVE BOOLEAN QUERY, the premise S(ω) of the sequent \n
The possibility of reduction of an object description length by means of adding a formula setting some properties of initial predicates to the premise of a sequent was mentioned in the model example in Section 2. Properties of initial predicates also were used in the item 3 of the algorithm of multi-agent description. In fact, in the both cases instead the sequent of the form (4) \n
To solve the problem (2) and to extract a maximal common up to the names of arguments sub-formula of two elementary conjunctions it is needed to check whether two elementary conjunctions are isomorphic. A polynomial in time rough algorithm for such a checking was offered in [12] by Petrov. Numerical experiments with this algorithm give over 99.95% of valid results.
\nIn recent years, genetic studies on dog genomics have multiplied worldwide. Currently, there are over 50 international laboratories which are involved in canine genome projects and several applications will be available in the near future from these studies. These new findings will improve our understanding of the selection process of the dogs and provide useful information for the study and control of genetic diseases.
The single-control characters are influenced by genes located in a locus on one of the pairs of the chromosomes (78 in the dog) and have a binomial distribution. For example, the hair length in dogs is coded by two genes present at an autosomal locus. Short-haired animals have genotype LL (dominant homozygotes), while, long-haired animals have genotype ll (recessive homozygotes). From their mating originates short-haired animals with genotype Ll (heterozygotes), indistinguishable from short-haired parents. Even those characters that express different degrees of dominance, different from the Mendelian inheritance, are considered simple characters (e.g. incomplete or partial dominance). The simple characters are not influenced by the environment and, therefore, to each genotype corresponds a certain phenotype (P = G, where P = phenotype and G = genotype). The study of simple characters includes also multiple alleles (several alleles present in a population), pleitropy, association or linkage and incomplete penetrance. For characters with simple inheritance, it is easier to make selection than for multiple control characters. The multiple control characters are also called quantitative or polygenic characters. These characters are influenced by many genes distributed on several loci and they are influenced by environmental factors. The strong artificial selection exercised by man during the domestication process and during the creation of the different breeds has led to the setting of several characters. Color inheritance illustrates the case of separate loci that control the expression of the phenotype. The coat of dogs consists of two parts: top coat (protective function) and undercoat (heat-insulating function). Some breeds have no undercoat (e.g. Yorkshire). The color of the coat depends on the characteristics of the pigments contained in the medullary and cortical layers of the hair [1]. According to Willis [1], it is possible to explain all the colors by means of two chemical pigments: hemoglobin and melanin. More specifically, melanin is differentiated into eumelanin (black-brown) and pheomelanin (yellow-reddish). The synthesis of pigments in the hair of mammals depends on the interaction between the Agouti protein and the Melanocortin 1 receptor [2]. The coat colors in the dog are linked to the presence/absence of two types of melanin and their possible combinations. It is important to underline that melanin do not show a precise time of formation and they develop during the different phases of the fetal development and after birth [1]. The knowledge of the genetic inheritance of the morphological traits is very important in order to establish suitable selection objectives in the different breeds.
Measurement of F coefficient (consanguinity) in a population can be considered as a measure of the increase in the proportion of homozygous individuals following an inbreeding mating (between relatives) [3]. The coefficient of consanguinity F can be calculated with the following methods: 1) pedigree 2) run of homozigosity (ROH); 3) genomic kinship matrix; 4) SNP genotyping [4, 5]. Inbreeding can occur in small closed populations due to mating between related animals. In a closed population, the decrease in the fraction of heterozygotes from one generation to the next may be referred to as ΔF. This value varies in relation to the size of the population: ΔF = 1 / 2Ne where Ne is the effective number or effective size of the population. In a population, Ne depends on the number of males (Nm), and on the number of females (Nf), in the following relationship:
The inbreeding coefficient, at a given t generation, can be calculated as a function of ΔF and t as:
which shows the decrease (ΔF) of heterozygotes that occurs at each generation following inbreeding [6]. Lewis et al. [7] reported for 221 breeds of the UK Kennel Club a Ne that varies between 23.8 of the Manchester terrier breed to 918 of the Borzoi breed and an average value of F equal to 0.06. The deleterious effects of inbreeding are universally known. They can be summarized briefly in the increase in the frequency of all genetic defects and abnormalities (reproductive sphere, resistance to diseases, longevity, etc.). These findings are based on the results of experiments carried out on different breeds and for several generations. Leroy et al. [8] showed that the increase in inbreeding in the population has an effect on individual survival and litter size of different breeds. Deleterious effects begin to occur when the value of F is about 0.375. Lower values are not to be considered dangerous. It is worth noting that this is the level of inbreeding that is achieved in only two generations of full sibling mating. For this reason, it is recommended to avoid mating between close relatives. Consanguinity is influenced by the number of individuals used per generation [9]. As a general rule, individuals whose numbers are lower in the breeding population they exert a proportionately greater effect on consanguinity. This is true both in relation to the male/female ratio (depend more on the number of males) and the different numbers of breeders in the various generations. The actual number of breeding animals is the parameter used in small populations to determine the expected inbreeding coefficient. Since the less numerous sex is the most important, the actual number of the population can be calculated even if the number of the larger sex is not known (e.g. 2 males and the number of females is assumed to be infinite: 1/Ne = 1/ 4Nf = 1/4 (2) =1/8 * F = 1/16 = 0.0625). The family size is the number of offspring in each family who become parents in the next generation. In ideal conditions, the size of the population will remain constant in subsequent generations if each parent is replaced by another individual. In this case, the average number of offspring per parent is equal to 1 with an average family size of 2 (two parents). The Ne is also function of the variance of the family size. If males mate with more than one female, the number of offspring and thus the variance of the family size will differ between the two sexes. Several measures can be implemented to keep consanguinity within acceptable limits in the population: increase the number of breeders; mating of one male with a female (since the number within the sexes is the same, Ne will be maximized), reduce the variance size of the family (for a constant number of offspring for each family, the variance is equal to 0 and the Ne is double); avoid mating between siblings or cousins; avoid mating individuals in generations that overlap as inbreeding increases. If the management program includes the genetic improvement of one or more characters, selection must be carried out using selection indices that take into account of the level of relationship. The goal is to find the optimal number of offspring for each breeding animal and determine if a young animal (a candidate for selection) should be selected for breeding or not. This is done in an optimal way using the software EVA [10] that guarantees the achievement of the genetic progress and the maintenance an optimal genetic diversity in the population.
The general actions to be taken in a program for the genetic improvement within a breed should include: 1) genomic identification and characterization of individuals, highlighting their potential in terms of their contribution to maintaining biodiversity, aptitude and use 2) monitoring of demographic parameters and assessment of the risk of reduced genetic variability 3) characterization and evaluation of the intra-breed genetic variability for proper management activities. Modern molecular techniques can be helpful for the improvement of management strategies, even for small breeds and for qualitative traits. The current hypothesis is to add molecular data to classical schemes (assisted selection) to improve their accuracy. The first step in planning an improvement program consists of: 1) a clear definition of the objectives 2) identification of the traits to be recorded 3) evaluation of the gene effect of the characters to be selected 4) estimate of the effect of the environment (epigenetic effect) on the characters to be selected. In Table 1 are reported the genetic and physical testing used in genetic programs of several dog breeds [11].
Breed | DNA test | Physical test |
---|---|---|
Basenji | Fanconi | Eye assessment |
Hip score | ||
Progressive Retinal Atrophy | Thyroid | |
Heart assessment | ||
Hemolytic anaemia | ||
Pyruvate kinase deficiency | ||
DNA inbreeding coefficient Factor | ||
DNA identification Thyroid | ||
Border Collie | Neuronal Ceroid Lipofuscinosis | Elbow score |
Trapped Neutrophil Syndrome | Hip score | |
Collie Eye Anomaly | Eye assessment | |
Multi-Drug Resistance Gene 1 | General vet check | |
Imerslund-Grasbeck Syndrome | Chiropractor vet check | |
Degenerative Myelopathy | Collie collaps | |
Parentage (Orivet) | Hearing test | |
Glaucoma | ||
German Shepherd | Degenerative Myelopathy | Hip score |
Ivermectin Sensitivity | Elbow score | |
Long stock coat gene | ||
Canine Renal Dysplasia | ||
Dwarfism | ||
Haemophilia | ||
Golden Retriever | ||
Ichthyosis | Hip score | |
Progressive Retinal Atrophy 1 | Eye assessment | |
Progressive Retinal Atrophy 2 | Heart assessment | |
Progressive Rod Cone Degeneration | Elbow score | |
Dentition assesment |
Genetic and physical testing used in genetic programs of common dog breeds.
In general, genetic diseases result from a mutation in a gene. In most cases, the mutations are traits that follow a simple Mendelian inheritance model (autosomal recessive, autosomal dominant or sex chromosome-linked character). Other hereditary diseases can be more complex and show reduced penetrance or multiple loci (multigenic disease). Genetic disorders can result from new mutations, but in most cases they result from old mutations passed on from one generation to the next. Mutated alleles can persist within a population for many reasons: 1. they can confer particular advantages in the state of heterozygotes; 2. the symptomatological signs can appear late 3. the mutation can be a recessive trait and therefore the defective allele can be spread in the population by healthy carriers. Without a mutation screening program, the carrier status can become evident only after the production of sick offspring.
The canine genome contains approximately 19,000 genes spread over 39 pairs of chromosomes (38 homologous chromosomes and 2 sex chromosomes). To date, nearly 400 hereditary diseases have been recognized in dogs. However, the precise ways in which these diseases are inherited are known for only about a third of them. In most cases, they are linked to autosomal recessive mutations. Bellumori et al. [12] report the prevalence of major genetic diseases in the United States for pure and mixed breeds. Pure breeds show more markedly some diseases including elbow dysplasia, cardiomyopathy, hypothyroidism and cataracts. The identification of the carriers can be implemented with the aid of two types of information: by pedigree or from a progeny test. In the first case, an animal showing the dominant phenotype (dominant phenotype) is known to be a carrier if one of the parents has the homozygous recessive genotype. In the second case, the farmer uses the information obtained from the offspring for the determination of the animal’s genotype. Let us admit that a male is believed to be carrying a recessive allele. Special methods are required for the identification (and rejection) of carriers of the gene (suspected). This requires a reproduction test (test cross or progeny test) to determine whether the individual is dominant (suspected) or heterozygous. The genetic study of a hereditary diseases can follow additional strategies. Several genetic tests are now available for the identification of some hereditary disease [13]. The DNA-based diagnostic technique can be used to uniquely distinguish between sick and healthy subjects. These techniques allow the exclusion from reproduction of the carriers of frequent hereditary pathologies and they are a useful tool in validating the genealogical data reported in the pedigree.
The candidate gene approach consists in selecting a particular gene considered as the most likely site of a mutation. The main criteria for selecting a gene as a candidate are the following: 1) genes are selected because they are defective in similar animal species (usually humans or mice) 2) genes are selected based on their function. The analysis of the candidate gene consists in sequencing the entire gene and comparing two groups (healthy vs sick animals). However, the presence of a mutation in a gene is not in itself sufficient to identify the cause of the disorder. Unfortunately, for many genetic diseases the relative candidate gene has not been identified and very similar hereditary diseases can result from mutations on completely different genes. As an example, in the Bedlington terrier dog breed, the hereditary copper toxicosis is phenotypically identical to the Wilson’s disease in humans. However, the gene involved in the human disease is not responsible for the disease in dogs. In conclusion, the approach with candidate genes has the advantage of allowing the identification of the specific mutation and therefore the creation of a targeted genetic tests.
The method of linkage analysis is based on completely different assumptions from the candidate gene approach. The main difference is that no assumptions are made about which gene is responsible for the disease, nor, more generally, the chromosomal tract involved. In this method, the whole genome is potentially subjected to analysis, without directing attention to any particular region. The search for the causal mutation takes place through the use of genetic markers whose chromosomal position is known. The more such markers are physically close to the mutation site, the more likely they will be co-inherited together with the mutation from one parental generation to the next. In a very simplified way, linkage analysis evaluates whether any of the variants of the markers appear in the population is associated with the presence of the disease. The ideal markers, and normally used to perform this type of study, are microsatellites, considered as practically ideal genetic markers because they are abundantly scattered throughout the genome and generally highly polymorphic. The number of microsatellites used to perform a linkage analysis is not fixed but generally the higher it is, the higher the probability that the study has success. This assumption derives from the fact that not directing attention towards specific genes and particular chromosomal portion, genome screening it must be as large as possible, i.e. it must contain the highest possible number of markers in order to understand the whole genome (so-called genome-wide screening). Generally, to perform a linkage study within a family tree informative are employed between 200 and 300 microsatellites using pedigrees with at least a hundred animals. For a given area of the genome, the probability of a recombination event occurring between a marker and a disease gene is directly proportional to their distance. The probability of occurrence of this event is expressed as a recombination fraction (θ). If θ is equal to 0.5, the marker and the disease gene are not linked and are therefore independently segregated. In other words, the probability that the marker and gene are inherited, associated or separated is identical. Conversely, if the marker and disease gene are linked together, the θ is less than 0.5. The lod score (Z) is the parameter which is used to estimate the linkage between 2 genetic loci. Z is the logarithm of the ratio between the probability that the 2 loci are linked (θ <0.5) and the probability that the 2 loci are randomly recombined (θ = 0.5). Traditionally the linkage is accepted if the lod score is at least 3. Linkage analysis leads to the identification of a chromosomal region where the locus of the disease is probably located. The analysis must continue with the so-called refinement, that is, a further linkage analysis. Only later, the analysis proceeds through a gene candidate approach. All the genes of the region are identified and a sequence analysis is performed.
Animal mtDNA is a cycular molecule ranging from 14,000 to 26,000 bp. The mtDNA codes for 13 proteins. Mitochondria contain most of the genes that code for cell energy production and electron transfer (NADH deydrogenase subunits, cytochrome oxidase subunits, ATPase 6 and 8, cytochrome b, rRNAr, RNA, 12S and 16S) [14, 15]. The choice of the sequence to be used for the genetic analysis depends on the phylogenetic hypothesis to be tested: D loop, sequences that evolve rapidly; cytocrome b, sequences that evolve moderately; Cytocrome oxidase I, sequences that evolve slowly. The mitochondrial control region (CR) sequence is the most popular marker. The mtDNA is uniparental (maternal line), characterized by a high evolution rate (5–10 times higher than nuclear genes) and the lack of introns and recombinations. The mtDNA is used to clarify the direction of hybridization and the incidence of introgression. In the case of hybridization, erroneous inferences can be obtained only using the evolutionary history of the females. In phylogeographic studies, information from various loci of the nuclear genome are also included [16, 17, 18]. The use of both parents allows a better analysis of the population structure.
Nuclear microsatellites (one to six in tandem repeated nucleotides) are used in population genetics for the description of the population structure and kinship identification [19]. The reason for the wide use of microsatellites is due to the fact that are co-dominant, multi-allelic, highly reproducible and with a high resolution. The information per locus is about 10 times more informative than SNP markers. The most common repeats are di, tri and tetra-nucleotides. Microsatellite loci with a di-nucleotide motif are generally used, since they are easier to isolate and high density (on average every 30–50 kb) [20]. Microsatellites are also known as SSR (Simple Sequence Repeats) or STRs (Short Tandem Repeats). The maximum length is about 200 bp. Microsatellites are distributed throughout the genome with greater prevalence in non-coding regions. They are neutral in terms of selection. The typical problems encountered in the genotyping analysis are: homoplasy (condition of equality in the type and number of microsatellite repeats between two alleles) [21]; stutters (in the form of allelic pre-peaks); null alleles (NA) (possible mutations in the pairing site of the primers can prevent the pairing to the target sequence, causing the non-amplification of some alleles. The genetic analysis of microsatellites produce the following data: the distribution of allele frequencies for each microsatellite locus, the percentage of expected (HE) and observed (HO) heterozygosity, the estimates of the Fst values; Nei distances; conformity to the Hardy–Weinberg equilibrium (HWE) of the allele frequencies for each locus.
Starting in the 2000s, the analysis of SNPs led to the beginning of a new era in molecular genetics. The direct study of the genome using SNPs markers allows to integrate the genealogical information and to obtain high levels of accuracy in the estimation of the main genetic parameters of the population. The development of new sequencing techniques has made it possible to study the consequences of gene flow using a larger number of markers. At the beginning, the Sanger’s technology was used to sequence the genomes of different animal species. This sequencing technique produces reads (>700 bp) with a very low error (<0.01%) and high cost (>600 US $ per Gb). This technique was subsequently improved through the use of the Celera assembler with a significant reduction in time and costs. New generation sequencing technologies (Next Generation Sequencing - NGS), also known as High Throughput Sequencing (HTS) technologies, have evolved rapidly offering an ever greater number of sequenced bases at a lower cost. In 2006, the first second-generation NGS technologies (Second-Generation Sequencing - SGS) appeared. Illumina (MiSeq, HiSeq and NovaSeq) is the most popular platform, due to its high performance and low cost. This technology is based on the fragmentation of DNA, amplification in multiple reactions in parallel, obtaining short reads, between 100 and 300 bp. Depending on the library, it is possible to sequence only one end of the fragment, single reads (single end) or both ends. The distance between the read pairs is called insert size (mate pair (2–5 kb); paired end (<1 kb)). Since 2013, the third-generation NGS techniques emerged, also known as the Single Molecule Sequencing (SMS) method. Single molecule sequencing produces long reads with higher costs (>2000 US$ per Gb). These techniques do not require the library amplification step and they are capable of directly sequencing a single DNA molecule, without applying any enzymatic or hybridization process. The main platforms of the third generation are Pacific Biosciences (PacBio) and Oxford Nanopore Technologies (ONT). These platforms produce longer reads than the previous ones (5–50 kb) but have a much higher error rate. The Pacbio platform routinely generates reads with an N50 > 1 Mb and it has recently reduced the error rate with a new technique (circular consensus sequencing) and the production of high fidelity reads of 15 Kb. The most popular softwares used for the bio-informatic analysis are Canu; Marvel and Mecat Flye. Then, results obtained are cleaned with some software such as Racon; Nanopolish and Pilon. Figure 1 shows an example of workflow using long reads.
Example of NGS bioinformatic analysis (long read sequencing).
After identifying the putative protein coding regions (CDSs), UCEs (Ultra Conserved Elements), it is possible to infer the correct reading pattern (Open Reading Frames, ORF) and translate the nucleotide sequences into amino acids [22]. In this way, we will obtain the set of predicted proteins encoded by the study genome. BLAST (nucleotide, protein, translated, genomes), HMMER or InterProScan databases can be used to functionally annotate these proteins. InterProScan provides the information on functional processes (GO terms) and metabolic pathways (KEGG). Once the functional and structural annotation has been obtained, the analysis of the functional elements of interest such as polymorphic positions or genes with differential expression can be performed. Figure 2 shows an example of workflow for the genomic annotation analysis.
Example of NGS annotation analysis.
Orthmcm, Orthofinder; EggNog sofwares can be used for the homology analysis. Several studies, in recent years, have shown that the best way to understand complex systems (for example diseases) is to combine different omic data together. Figure 3 shows a detailed analysis using omic data (genomic, transcrptomics, proteomics and metabolomics).
Example of OMICs analysis (genomics,transcrptomics, proteomics and metabolomics).
Several new techniques have been developed in the last decade. The most popular is the restriction-site-associated DNA sequencing (RAD-Seq) [23] and the genotyping by sequencing method (GBS) [24]. The main advantage of RRGS methods is that it reduces the cost of analysis with an high coverage compared to the traditional sequencing methods. The de novo analysis does not require a priori knowledge of the reference genome sequence. Several applications of the RAD-Seq methods have been reported: population genetics studies (phylogenetic and phylogeographic), linkage mapping (fine scale) and genome scaffolding [25]. To avoid or reduce the bias, some variations of the original RAD Seq protocol have been proposed: ddRAD, ezRAD, 2b-RAD. Classic RAD reads are obtained between the restriction site and a random site while the ddRAD reads are obtained between two restriction sites. In particular, the ddRAD-SEq method increases the number of samples per sequencing line and develops a tagging approach by combining pairs of adapters. Another advantage is the selection of the fragment sizes. This reduces duplicate sampling of a region, thus requiring only half the reads to effectively achieve high levels of confidence for each SNP associated with a restriction enzyme cleavage site. All these properties make the ddRAD-Seq method robust, allowing to search for a smaller number of reads. The bio-informatic analysis of RAD-Seq data includes the following phases: quality control, trimming, reference genome or de novo mapping methods, SNP filtering/annotation. The results of RAD-Seq analysis are analyzed with different softwares such as Stacks, Ig-Tree, Uneak (Tassel), Pyrad; Ddocent; 2brad and Aftrrad. The most popular software is the Stacks program. RRL methods, in relation to the production of short reads, are not very useful for the construction of phylogenetic trees but are generally used for the analysis of SNPs.
In the recent years, the availability of massive genomic data obtained from the last generation sequencing techniques allowed the efficient identification of a large number of SNPs [26]. The GWAS is a method of investigation that allows to examine the entire genome by analyzing the single nucleotide polymorphism of genomic markers (SNPs) with the use of high density SNP arrays [27] (the last versions Illumina Canine HD SNP 170 K have hundreds of thousands of SNPs distributed throughout the genome). The study identified the genetic structure of the populations present in Italy and the selection signatures. Reduction of genotyping costs is achieved using inference methods such as the imputation. Imputation techniques allow to transfer information from DNA from high density bead chips to low density ones.
The genome-wide association studies (GWAS) have been proposed as an effective approach for the identification of many causative mutations and genetic factors that constitute the main traits. Unlike linkage studies, which consider the phenomenon of inheritance of chromosomal regions linked to the presence of a trait within a family, association studies consider instead the difference between the frequency of SNPs affecting the trait of interest. Association studies may be conducted through two approaches: direct and indirect. A direct association study is to catalog and test one by one all the possible causal mutations. However, the direct approach presents some practical problems. This strategy involves genome-wide identification of all genes (up to 19,000 genes) as well as of all SNPs. For these reasons, the use of the direct method is limited to a few cases and it has almost always replaced with the application of the indirect method. The indirect strategy avoids the need to catalog all mutations that could potentially give predisposition to a given trait and instead relies on the association between a giver phenotype and markers located near a strategic locus. These associations are obtained from studies of linkage disequilibrium (LD) between marker loci. The indirect strategy, then employs a dense map of polymorphic markers to explore the genome in a systematic way. The choice of markers differentiates further the indirect approach in two different strategies. In the first, markers are chosen very close to exon regions of known genes. The second employs markers located in large regions, virtually anywhere in the genome, thus considering the chromosomes in their entirety, including intronic regions. The choice of the marker falls on bi-allelic SNPs because of their high frequency in the animal genomes, for the low rate of mutation and for the ease with which it can be analyzed. Linkage means the presence of genes in closed loci on the same chromosome. LD is a combination of alleles at two or more loci that occurs more often than it does happen by chance. Two markers are in LD when they occur together in the same individual more frequently than would be expected by chance. The presence of a LD thus indicates co-segregation of two markers. In generally, the LD between two SNPs decreases with the physical distance and the extent of LD varies strongly among the regions of the genome. LD analysis is a valuable tool for fine mapping. Doherty [28] conducted an GWAS analysis using 9700 SNPs on 72,000 dogs (63 breeds). Eight SNPs were significantly correlated with the live weight and five SNPs with cancer mortality. Plassais [29] analyzed the genomes (WGS) of 722 dogs and used the Illumina canine HD SNP BeadArray to identify over 91 million SNPs. In this way the main SNPs coding for body weight and main morphological characters were identified. In Table 2 is reported an example of SNP genotyping using a SNP chip array in dogs [30].
Genomic analysis |
---|
Illumina CanineHD SNP chip (San Diego, CA) |
Genotype SNP calls using Illumina’s Genome Studio |
Selection of samples with a >90% SNP call rate |
SNPs with Gentrain scores >0.4 |
Minor allele frequency >1% |
Bio-statistical analysis |
FlashPCA - Principal components (PCs) |
Admixture - two to ten adjusted cluster ancestry models |
Beagle – calculation of IBD haplotype sharing analysis and phasing |
VCFtools – calculation of the inbreeding coefficient |
TreeMix – construction of a maximum likelihood tree - windows of 1000 SNPs using the flags -bootstrap and -k 1000 functions |
R studio – construction of graphs and plots for all the analyses |
SNP genotyping using a SNP chip array in dogs.
The domestic dog is thought to be the most recent species of the canine family, within which three phylogenetic groups, or clades, are distinguished: the domestic dog belongs to the same clade as the gray wolf, coyote and jackals [31]. It is thought that the dog appeared about 40,000 years ago, and that the first steps in its domestication took place in East Asia [32]. Most of the domestic breeds we know today, however, are the result of human selection over the past two or three centuries. Many of the most popular modern breeds were created in Europe in the 19th century. Some of the breeds were already present in the ancient world as the greyhound and the dog of the pharaohs. Studies conducted at the genomic level have highlighted a stratification of genetic variability within dog breeds. The recent sequencing methods and the use of SNP arrays allow the screening of the whole genome for the presence of signatures of selection. Sequencing data are aligned to the reference genome to identify selective sweeps. The presence of genes with a large number of outliers indicates a positive or negative effect of selection. A genome scan approach can be used to distinguish genome-wide processes (expected to mainly reflect demographic histories) from processes at individual loci. Genome scans may suffer from inflated numbers of false positives under hierarchical spatial structure coupled with isolation by-distance dynamics. In the case of positive selection, there is an increase in the fitness of the population due to a new (or rare) mutation. In the case of hard sweeps, there is an increase in the frequency of some variants and in the linkage disequilibrium. Kim et al. [33] compared 127 dogs (sport-hunting vs. terrier) for sporting characteristics. Results of the study showed the main SNPs (cardio-circulatory, muscular and neuronal systems) and selection signature that are involved in the sport-hunting breeds. In Table 3 is reported an example of GWAS and selective sweep analysis in dogs [29].
Dataset of 268 dogs representing 130 breeds |
---|
Phenotypes used in the study: canids catalog, kinship, aggressiveness, boldness, bulky, drop ears, furnishing, hairless, height, large ears, lengh of fur, life span, long legs, muscled, tail curl, weight, white chest, white head |
GWAS |
Samples with ≥10x coverage, selecting two males and two females |
Gemma - linear-mixed model methods; elimination of variants with missing value >1 |
R Studio – Manhattan correlation and box-plots |
Identification of positively selected genes |
Vcftools60 |
Beagle - infer the haplotype phase |
Xpclr - phased genotype input; non-overlapping windows (50 kb), 600 SNPs within each window; correlation level cutoff of 0.95. |
XP-EHH - splitting the genome into non-overlapping segments of 50 kb |
Example of GWAS and selective sweep analysis in dogs.
The canine genome project was launched in the early 1990s. After some preliminary results, in 2003, a fist sequence of the dog’s genome was obtained from a female boxer which is now the reference sequence for the dog [34]. The availability of a high quality canine genome has revolutionized the way in which geneticists operate. The first version of the boxer’s genome, carried out with a coverage of 7.5x, covered nearly 99 percent of the animal’s genome. The genome sequence provided a first description of the organization, number of genes and the presence of repeated elements. To some surprise, they found a high presence of short interspersed nuclear elements (SINEs) throughout the genome, sometimes located in locations from which they could affect gene expression. For example, the insertion of a SINE into the gene encoding the hypocretin receptor (a neuropeptide hormone found in the hypothalamus) causes narcolepsy in the Doberman. Similarly, the insertion of a SINE element into the silv gene, which is known to be linked to the pigmentation process, is responsible for a particular mottled color called merle. The 2003 sequence comprises approximately 2.4 billion of bases and revealed the existence of approximately 19,000 genes. For about 75% of genes, the homology (resulting from shared ancestral material) between the dog, man and mouse is very high. The study also found that many genes have no gaps in their sequence, which is beneficial if you would like to study the correlation between a given gene and a disease. During its evolution, the dog’s genome has accumulated more than two million of SNPs. These markers are proving crucial in understanding the role of genetic variability within one breed and in different breeds. SNPs, analyzed by means of DNA microarrays or bead arrays, can make an important contribution to GWAS (association studies) aimed at identifying the genes responsible for complex traits in dogs. A microarray with around 170,000 SNPs is currently available. By comparing data from dogs with a certain disease with healthy individuals, it is possible to quickly identify the genes responsible for the disease. Dog breeds differ not only in the overall body size but also in leg length, head shape and many other morphological characteristics. In the dog, the phenotypic variability of several traits is very high compared to the other living terrestrial mammals. The first molecular study on the genetic aspects of dog morphology was conducted at the University of Utah [35, 36]. Called Georgie Project (in memory of a dog), the study focused on the Portuguese water dog breed, ideal for this type of study because it comes from a small number of ancestors. In the project, DNA samples of more than a thousand dogs were collected. A completed genome scan using 500 microsatellite markers was carried out. For these animals, in addition to the genealogical and medical data, more than 90 anatomical measurements were obtained from a series of five radiographs taken on each animal during the first phase of the study. Based on the analysis of these data, four primary main components (CP) have been identified (Figure 4).
Example of PCA (principal component analysis) of genotypic data (autosomal) of three dog populations.
The analysis of the genome scans and principal components (CPs) revealed 44 putative QTLs (quantitative trait loci associated with a particular quantitative trait) on 22 chromosomes. QTLs are identified by means of a complicated statistical analysis and identify the genome regions that contribute to the expression of a certain trait. Of particular interest is the gene CFA15 on chromosome 15 which showed a strong association with the body size. Although, it is only one of seven loci thought to affect the body size, it was chosen as the starting point. To find the gene CFA15, several SNPs were identified and then the resulting set of genome-wide markers were genotyped. The distribution of these markers showed a single peak near the insulin-like growth factor-1 (IGF 1) gene, which codes for insulin-like growth factor which is known to code for the body size in humans and mice. IGF 1 was analyzed in detail, discovering that there are only two specific combinations of alleles (called haplotypes) and one of them is present in 96% of the population. The haplotype associated with the small size was called B, while the one associated with the largest size was called I. Homozygous dogs for the haplotype B showed a smaller average body size while, dogs homozygous for I were larger. Heterozygous dogs showed an intermediate size. The Georgie Project is important for the number of genes discovered. In addition to the genes related to the head shape, body size, leg length and many other traits, additional genes were discovered that control the sexual dimorphism [37, 38]. This dimorphism is observed in almost all mammals but its mechanisms it is not yet fully known. Indeed, it was found a gene on chromosome 15 which interacts with other genes to make males larger and females smaller. On average, females of the Portuguese water dog breed are 15% smaller than the males.
In the past fifteen years, tremendous progress has been made in dog genomics [39, 40, 41]. Several genetic aspects of cancer, heart disease, hip dysplasia, vision and hearing problems in dogs have been investigated and studied in detail. Genome-wide associative studies have made possible to identify several genes associated with diseases, morphological and behavioral traits. The Dog10K project will produce 10,000 new dog genomes (20x) within five years [42]. The mapping of disease-associated genes will hopefully lead to the production of new genetic tests and improve the management of running breeding programs, which in turn will produce healthier and longer-living dogs. It will be easier to select for specific physical traits such as the size or coat color. Finally, perhaps we will be able to identity which genes are responsible for the typical behaviors of each breed.
Authors are listed below with their open access chapters linked via author name:
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\\n\\nFei Wei 2016-18
\\n\\nIoannis Xenarios 2017, 2018
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\\n\\nXin-She Yang 2017, 2018
\\n\\nYulong Yin 2015, 2017, 2018
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\n\n\n\n\n\n\n\n\n\nJocelyn Chanussot (chapter to be published soon...)
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\n\nIoannis Xenarios 2017, 2018
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