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Мутации и спирали эволюции

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13

Содержание

1. Частота ошибок при последовательной репликации

2. Стохастика процессов эволюции

3. Игра в имитацию

4.Заключение

1. Частота ошибок при последовательной репликации

Процессы конкуренции и отбора имеют фундаментальное значение для
процессов эволюции, но сами по себе они еще не приводят к эволюции.
Естественно возникает вопрос: какие механизмы необходимо привести в
действие для того, чтобы система, обладающая свойствами
самовоспроизведения, мультистабильности, конкуренции и отбора, обрела
способность к эволюции? Таким механизмом служат мутации, т. е. случайное
производство альтернативных возможностей. Одна отдельная мутация, как
правило, означает ухудшение скорее, чем улучшение системы в смысле
эволюции. Но если случайно возникает новая благоприятная возможность и
она усиливается, то эволюция делает шаг вперед. Такие благоприятные
возможности называются инновациями. Механизм мутаций присущ
самовоспроизводящимся системам. Причина заключается в физических законах
квантовой механики и статистической термодинамики, лежащих в основе
каждого процесса воспроизведения. Эти законы гарантируют возможность
появления ошибки, первопричиной которой могут быть как
квантово-механические, так и термодинамические флуктуации. Потенциальные
возможности возникновения новых первичных структур при репродукции
биополимеров практически неисчерпаемы.

Число возможностей составить биополимер длины v из ? различных сортов
мономеров составляет

W = ?v (1)

Число возможных первичных структур для полинуклеотида длиной 1000
составляет величину

W = 41000 10600 (2)

Это — астрономически большое число. Некоторое представление о его
величине дает следующее замечание: все водоемы Земли не могут вместить
более 1040 молекул биополимера. Тем самым резервуар возможностей
практически неисчерпаем.

Как показал Эйген, мутации являются единственным источником новых
структур и новой информации. Тейяр де Шарден был неправ, когда он писал
об эволюции: «… Ничто в мире не может возникнуть внезапно после ряда
эволюционных процессов, если его не было ранее в зародыше». Такая точка
зрения приводит только к процессам конкуренции и отбора, представляющим
собой чистое «развитие» имеющихся возможностей, но не к мутационным
процессам. С помощью случайных процессов эволюция может порождать
совершенно новые структуры: благодаря им эволюция обретает творческий и
скачкообразный характер. Возникновение новой сущности всегда происходит
скачком, в некий дискретный момент времени. Например, возникновение
нового сорта действительно является «внезапным» скачком. Мутация, как
правило, является результатом одного-единственного элементарного
молекулярного процесса.

Различают микромутации (точечные мутации), затрагивающие лишь один или
несколько нуклеотидов, и макромутации (макроповреждения), охватывающие
значительные участки генома. Примером точковых мутаций может служить
замещение оснований (одного или нескольких оснований какими-то другими
основаниями) и сдвиг растра (вставка или выпадение нескольких
нуклеотидов). Примером макроповреждений может служить дупликация
(удвоение фрагмента последовательности нуклеотидов), делеция (утрата
фрагмента последовательности), инверсия (обращение последовательности
нуклеотидов в фрагменте) и инсерция (вставка чуждого гену фрагмента).
Различают хромосомные и плоидные мутации. Типичным и в том и в другом
случае является элементарный молекулярный характер мутации.
Преобладающим действием мутаций являются отрицательные изменения в
фенотипе, ведущие к вымиранию варианта. В относительно редких случаях,
когда мутаций ведут к улучшениям, этот микроскопический эффект
претерпевает макроскопическое усиление в результате отбора новых
вариантов. В этом заключается содержание фундаментального принципа
усиления.

Взаимодействие мутаций и отбора в процессах эволюции разыгрывается по
следующей общей схеме. Каждая мутация означает возмущение в
установившемся на некоторое время равновесии (рис. 1). Мутант приводит к
проверке системы на устойчивость относительно появления нового сорта.
Если мутация не дает никаких преимуществ по сравнению с существовавшими
ранее сортами, то новый сорт исчезает в результате процесса отбора.
Система оказывается устойчивой относительно возмущения. Отбор ведет к
уничтожению нового сорта, и система возвращается в исходное состояние.
Но если оказывается, что мутант обладает определенным преимуществом по
сравнению с первоначально имевшимися штаммовыми сортами, то отбор ведет
к росту нового сорта. Система оказывается неустойчивой относительно
возмущения. Усиливая эти возмущения (мутанты), система постепенно
переходит в новое селекционное равновесие, соответствующее переходу на
более высокий уровень эволюции (рис. 1). Следовательно, процесс отбора
описывает замкнутые петли и открытые спирали, причем последние выводят
систему на более высокий уровень эволюции (рис.2).
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13

Эта картина напоминает нарисованную Гегелем принципиальную схему
диалектического подхода к эволюции. Согласно гегелевской схеме, эволюцию
надлежит воспринимать как процесс, развивающийся по восходящей линии,
переход от простого к сложному, от низких свойств к высшим, как единство
непрерывных и скачкообразных изменений, и путем повторения стадий
процесса на более высоком уровне обнаруживается его спиралеобразная
структура. Согласно гегелевской точке зрения, эволюция не означает
автоматически развития по возрастающей, она содержит также элементы
стагнации и развития вспять, но при этом отличительная особенность
процессов эволюции заключается в возникновении новых фундаментальных
свойств (инноваций). Тем самым эволюция означает возникновение новых
качеств, по крайней мере, как тенденции. Развитая выше схема игры
мутаций и отбора в ходе эволюционных процессов весьма удачно вписывается
в общую концепцию гегелевской теории эволюции. Следует заметить, однако,
что рассматриваемые процессы протекают в основном на самом низком —
молекулярном — уровне эволюции. Основным элементом служат биологические
макромолекулы, которые, как показывают соотношения (1) и (2), могут
образовывать невообразимо большое число изомерных форм молекул с
различными первичными структурами.

Известно, что 3—4 миллиарда лет назад в условиях Праземли спонтанно
могло возникать огромное число биомолекул — полипептидов,
полинуклеотидов, Сахаров и жирных кислот. Однако вследствие невообразимо
большого числа различных первичных структур практически исключено
случайное образование биологически значимого множества первичных
структур. Даже если бы вся масса Вселенной, составляющая около 1079 масс
протона, превратилась бы в биомолекулы с молекулярным весом около 106,
то и тогда было бы испробовано около 1073 вариантов. Это число до
смешного мало в сравнении с числом возможных первичных структур,
которое, как было показано, для одних лишь полинуклеотидов составляет
величину около 10600. В то время как остальные этапы биогенеза и в
особенности период химической эволюции ныне известны достаточно
досконально, самоорганизацию биополимеров, т. е. возникновение
биологически значимых структур, до сих пор удалось понять лишь отчасти.
Именно этой проблеме посвящены фундаментальные работы Эйгена. По Эйгену,
самоорганизация биополимеров является результатом процессов эволюции в
условиях Праземли. Гипотеза Эйгена служит основой физической
интерпретации процессов, которые происходили в глубокой древности на
Земле и привели к возникновению жизни. В этом гипотеза Эйгена намного
превосходит различные другие гипотезы. Например, Вигнер, Йордан и
Эльзассер, исходя из оценки чрезвычайно малой вероятности спонтанной
самоорганизации биополимеров, пришли к заключению о том, что биогенез
должен был содержать нефизические акты или, иначе говоря, что в рамках
биогенеза должны были протекать процессы, прямо противоречащие законам
физики. Разумеется, такое предположение противоречило бы развиваемому
нами основному тезису, согласно которому законы физики никогда и нигде
не нарушаются. Не может удовлетворить и выдвинутая Моно гипотеза,
согласно которой возникновение жизни есть однократное, совершенно
невероятное случайное событие. Гипотеза Эйгена, которая, несмотря на все
неясности, содержит «прозрачную» физическую концепцию возникновения
жизни.

Гипотеза Эйгена исходит из предпосылки, согласно которой в «протосупе»,
образовавшемся 3—4 миллиарда лет назад в водах, омывавших Праземлю,
образовались условия для молекулярной эволюции. Процессы эволюции могут
протекать только в том случае, если выполняются следующие условия:

— способность к экспорту энтропии, например, с помощью постоянного
притока свободной энергии;

— способность к самовоспроизведению структур;

— мультистабильность как предпосылка хранения информации и введения
историчности;

— конкуренция вариантов и отбор благоприятных структур;

— мутации, приводящие к возникновению все новых и новых структур.

Показано, что на Праземле действительно установились перечисленные выше
физические условия. Под воздействием ультрафиолетового излучения,
высоких температур и электрических разрядов, выступавших в качестве
источников свободной энергии, в восстановительной про-тоатмосфере,
содержавшей водород, азот, водяной пар, метан, аммиак, двуокись углерода
и т. д., могли образовываться аминокислоты, пиримидиновые и пуриновые
основания, сахара, жирные кислоты и т.д. Следовательно, структурные
компоненты биомолекул могли возникать спонтанно и в достаточных
количествах. Показано также, что в этих условиях могла происходить
полимеризация аминокислот в простейшие «заготовки» протеинов — так
называемые протеноиды — и полимеризация нуклеотидов в более или менее
длинные цепи. Под нуклеотидами мы понимаем основные структурные единицы
нуклеиновых кислот, состоящих их пуриновых (аденина и гуанина) или
пиримидиновых (цитозина, тимина к урацила) оснований, а также пентоз и
фосфатных групп. Эти еще примитивные протеноиды и нуклеиновые кислоты
образовывались преимущественно в водах, омывавших Праземлю. В свою
очередь из них (главным образом из протеноидов) возникали компактные
образования — так называемые коацерваты. Решающее значение имело то, что
протеноиды обладали простыми каталитическими свойствами, хотя те были
выражены в миллионы раз слабее, чем у современных ферментов. При
каталитической поддержке протеноидов синтез полинуклеотидов должен был
происходить интенсивнее, причем уже имевшиеся цепочки нуклеотидов
служили матрицами для синтеза последующих цепочек. Таким или близким к
описанному путем протополимеры обрели способность к самовоспроизведению.
В результате ошибок при репродуцировании возникали все новые и новые
структуры, которые в результате естественного отбора вступали между
собой в конкуренцию. Выживали только такие, которые лучше всего
приспосабливались к окружающей природной среде, обладали способностью к
быстрому и относительно стабильному воспроизведению. На рис. 3
представлена формальная схема замещения структур нуклеиновых кислот
новыми, все более совершенными. К строгому изложению предложенной
Эйгеном концепции ценности мы сможем приступить лишь в последующих
разделах. Упомянем пока лишь некоторые качественные аспекты. Способность
нуклеиновых кислот к хранению информации (способность, в основе которой
лежит мультистабильность первичных структур нуклеиновых кислот),
несомненно, играет важную роль при определении «ценности» конкретной
первичной структуры для процесса эволюции. «Ценность» с этой точки
зрения должна быстро возрастать с увеличением длины v
последовательностей и, следовательно, их информационной емкости W = ?v.
Более длинные нуклеиновые кислоты обладают более развитым аппаратом
кодирования протеинов ферментативного характера, необходимых для их
стабилизации и самовоспроизводства. Простейшим из существующих ныне
бактерий требуется для обеспечения своего существования, обмена и
размножения около 103 ферментов; у высокоорганизованных организмов той
же работой занято 104-105 ферментов, лишь малую долю которых удалось
выделить и исследовать. Тенденция к возрастанию длины и тем самым
информационной емкости нуклеиновых кислот противодействует спонтанно
происходящим мутациям. Эволюция развертывается в диалектическом поле
напряжений противоречивых тенденций. Однако роль мутаций в игре эволюции
имеет фундаментальное значение: не будь мутаций, эволюция оставалась бы
на достигнутом уровне.

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cfffffffffffffffffffffffffff8001ffffffffcfffcfffe3f1ffffffffffffffffffff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ffff8001ffffffff8ff8ffe7f9e7fffffffffffffffffffffffffffe798ff8fc78c7c67f
ffffffffffff8e3cffffffffffffffffffffffffffff8001ffffffff8ff9ffe3f8e7ffff
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ffffffffffff8001ffffffffcff9e3f3f8c7fffffffffffffffffffffffffffe78cff1fc
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ffffffffffffffffffff8001ffffffffcff39cc3f8cfffffffffffffffffffffffffffff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1ff1f1ffffffffffffffe3fffff1ffffffffffffffffffffffff8001ffffffff8cffffff
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fffe3fff1fe3f9ffffffffffffffc3fe7ff8ffffffffffffffffffffffff8001ffffffff
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fffffffffffc7fff1fe7f9ffffffffffffffc3fc7ffcffffffffffffffffffffffff8001
ffffffff89fffffffc3ffffffffffffffffffffffffffffffffc7fff1fc7f9ffffffffff
ffff81fc7ff8ffffffffffffffffffffffff8001ffff0f9fc1fffffffc3fffffffffffff
fffffffffffffffffffcffff1fc7f9ffffffffffffff9bfc7fffffffffffffffffffffff
ffff8001fffe0607c1fffffffc3ffffffffffffffffffffffffffffffffcffff1f8ff9ff
ffffffffffff9ffc7ffcffffffffffffffffffffffff8001fffff267c3fffffff83fffff
fffffffffffffffffffffffffffcffff1f9ff9ffffffffffffff9cfc7ffc7fffffffffff
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fc9ffffffffffffffffffffffffffffffff8ffff8f0ffcffffffffffffff8c7e7ffe3fff
ffffffffffffffffffff8001ffffe271c0fffffffc9fffffffffffffffffffffffffffff
fffcffff8f9ff8ffffffffffffff1e7e7ffe3fffffffffffffffffffffff8001ffff8273
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fffffffffff9ffffff3ffcffffffffffffff1f3c7fff3fffffffffffffffffffffff8001
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fffffffffffffffffff1ffff8e3ff8ffffffffffffff3f1c7fff3fffffffffffffffffff
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ffffffffffff3f9effff3fffffffffffffffffffffff8001ffffe7cfc1fffffff88fffff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cf3ffffff3c7fffffffffffffffffffffffffffffe7fffffe1fffff1fffffffffff9ffff
ffffc78e3fffffffffffffffffff8001ffffffffcf1fffffe3e7ffffffffffffffffffff
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ffffffffcf9fffffe3e7fffffffffffffffffffffffffffffcffffffff3ffff8ffffffff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Рис. 3. Схема смены структур S1 ? S3 ? S7 ? S8 ? S9 и т.д.

Если бы в некоторой нуклеиновой кислоте с определенной структурой
воплотился псевдопотенциал безошибочного самовоспроизводства, то для
дальнейшей эволюции она не имела бы особого значения: через несколько
поколений ее «настигла бы и перегнала» менее совершенная
самовоспроизводящаяся структура. Таким образом, установление физической
концепции ценности должно включать в явном виде способность к мутации.
То, что самовоспроизведение молекул должно сопровождаться ошибками
копирования, физически самоочевидно: выполняющиеся в процессе репликации
молекул законы квантовой механики и статистической термодинамики
обусловливают неустранимый «внутренний шум», который с необходимостью
приводит к ошибкам копирования. В том же направлении оказывают свое
действие и неизбежные внешние возмущения — «внешний шум», создаваемый,
например, квантами излучения. Как сказываются ошибки в копировании на
длине самовоспроизводящихся полимерных молекул? Если обозначить через q
вероятность правильного построения фрагментов в копии заданного эталона,
и через 1 – q — вероятность ошибки, то вероятность получения правильной
копии всей молекулы длиной v определяется величиной

Q = qv = [1 – (1 – q)]v 1 – v(1 – q). (3)

При простом самовоспроизведении нуклеиновых кислот, без участия
специализированных ферментов, построение дополнительной копии основано
только на образовании относительно сильных водородных связей между
дополнительными парами оснований А—У, А—Т и Ц—Г. Однако при нормальной
температуре селективность таких взаимодействий не очень велика. В табл.
1 представлены константы ассоциации различных пар оснований в неполярном
растворителе.

Таблица 1

Частота ошибок при последовательной репликации

CCl4

С6Н6УАЦГУ45

15550 0 может
возникнуть новый сорт, который до этого вообще не был представлен в
системе, т. е. до мутации должно выполняться равенство Ni = 0, а после
мутации — равенство Ni = 1. С физической точки зрения, мутации всегда
приводят к возникновению новых сортов молекул, не существовавших прежде
в системе; с математической точки зрения, появление новых сортов
соответствует расширению пространства состоянии за счет включения в него
новых размерностей. Необходимо исходить из того, что пространство
состояний макромолекулы имеет размерность порядка 10600. Так как во всей
«Вселенной» число нуклонов достигает лишь 1079, а из них можно построить
не более чем 1073 макромолекул, мы заключаем, что по крайней мере для
10527 размерностей должны выполняться равенства Nk = 0, или, иначе
говоря, что представляющая точка состояния всегда должна лежать на одной
из граней определяемой уравнениями симплициальной решетки. Таким
образом, мутация означает, что представляющая точка удаляется от грани в
новой, еще не занятой, размерности, а возникающий процесс отбора
соответствует движению по новой грани при условии, что речь идет об
инновации, т. е. о благоприятной мутации (рис. 7).
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effc7e2ffffffc3ffffffffffffffffffff00101ffffffff1fffffffffffffc7ffffffff
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fe0ffffffffefc47fffffcfffffffffffffffffffff00101ffffffff1fffffffffffff8f
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ffffffffffffffffffff1ffe3f8fbff1ffdfe1fffc7fc7fffffffffffffffffffff00101
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8ffc7ffffffffffffffffffffff00101ffffffff3fffffffffffc7ffffffffffffffffff
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fff83fff9ff8fffffffffffffffffffffff00101ffffffff3fffffffffff8fffffffffff
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cffffe3ff3f81ffffff1fffffffffffffffffffffff00101ffffffff1fffffffffff1fff
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ff8fe7fe3fffe0e7fffffffffffffffffffffffffff00101ffffffff3ffffff8fffff889
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040000002701ffff030000000000

Рис.6 Пространство состояний и элементарные переходы в стохастическом
процессе эволюции при постоянном числе (размерность 2)

Рис.7 Решетка-симплекс пространства состояний с примером траектории,
образовавшейся после мутации.

Существует альтернативный вариант графического представления связанных с
мутацией и отбором стохастических процессов в пространстве нуклеотидов,
или последовательностей. В основе его лежит идея, предложенная
Рехенбергом. Это представление исходит из того, что каждый нуклеотид в
последовательности длиной v может находиться только в четырех
состояниях: Г, А, Т, Ц. Для представления состояния такой
последовательности можно воспользоваться v -мерным гиперкубом, состоящим
в каждом направлении из трех «поставленных» один на другой элементарных
кубов. На рис. 8 показан пример для случая v = 2.

picscalex120010009000003981800000000860d00000000860d000026060f00021b574d
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0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c0000000000000008400005d8020000cc0200000210c0db0100000000000000
0000000000000000000000000100000089504e470d0a1a0a0000000d49484452000000c6
000000c40100000000ec2863fb0000000467414d410000b18e7cfb519300000009704859
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fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ffffffffff
ffcfffffffffffffe7ffffffffffff1ffc010101fffff3ffffffffffffcfffffffffffff
e7ffffffffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1f
fc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ff
ffffffffffcfffffffffffffe7ffffffffffff1ffc000101fffff3ffffffffffffcfffff
ffffffffe7fffffffffffe0ffc010101fffff3ffffffffffffcfffffffffffffe7ffffff
fffffe0ffc000101fffff3ffffffffffffcfffffffffffffe7fffffffffffe0ffc010101
fffff3ffffffffffffcfffffffffffffe7fffffffffffe1ffc000000fffff3ffffffffff
ffcfffffffffffffe7fffffffffffe1ffc010101fffff3ffffffffffffcfffffffffffff
e7ffffffffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1f
fc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ff
ffffffffffcfffffffffffffe7ffffffffffff1ffc000000fffff3ffffffffffffcfffff
ffffffffe7ffffffffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffff
ffffff1ffc000001fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101
fffff3ffffffffffffcfffffffffffffc7ffffffffffff1ffc010101fffff3ffffffffff
ffcfffffffffffffe7ffffffffffff3ffc010101fffff3ffffffffffffcfffffffffffff
e7ffffffffffff3ffc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff3f
fc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ff
ffffffffffcfffffffffffffe7ffffffffffff1ffc010101ff0ff3ffffffffffffcfffff
ffffffffe7ffffffffffff1ffc010101ff0ff3ffffffffffffcfffffffffffffefffffff
ffffff1ffc010101ff9ff3ffffffffffffcfffffffffffffefffffffffffff3ffc010101
ff1fe1ffffffffffff87ffffffffffffc7fffffffffffe1ffc010101ff9fc00000000000
000001ffffffffff83fffffffffffc1ffc010101ff1fc000000000000000000000000000
000000000000001ffc010101ff1fc1ffffffffffff07fffffffffffb800000000000041f
fc010101ff1fc1ffffffffffff87ffffffffffff83fffffffffffe1ffc010101ff1ff3ff
ffffffffffcfffffffffffffc7fffffffffffe3ffc010101f39df3ffffffffffffcfffff
ffffffffcffffffffffffe3ffc010101f001f3ffffffffffffcfffffffffffffcfffffff
fffffe3ffc010101f801f3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101
fffff3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101fffff3ffffffffff
ffcfffffffffffffcffffffffffffe3ffc010101ffffe3ffffffffffffcfffffffffffff
cffffffffffffe3ffc010101fffff3ffffffffffffcfffffffffffffcffffffffffffe3f
fc010101fffff3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101fffff3ff
ffffffffffcfffffffffffffcffffffffffffe3ffc010101fffff3ffffffffffffcfffff
ffffffffcffffffffffffe3ffc010101fffff3ffffffffffffcfffffffffffffcfffffff
fffffe3ffc010101ffffe3ffffffffffff8fffffffffffffcffffffffffffe3ffc010101
ffffe3ffffffffffffcfffffffffffffcffffffffffffe3ffc010000ffffe3ffffffffff
ff8fffffffffffffcffffffffffffe3ffc010101ffffe3ffffffffffff8fffffffffffff
cffffffffffffe3ffc010101ffffe3ffffffffffff8fffffffffffffcffffffffffffe3f
fc010101ffffe3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101fffff3ff
ffffffffffcfffffffffffffcffffffffffffe3ffc010101ffffe3ffffffffffff8fffff
ffffffffcffffffffffffe3ffc010101ffffc3ffffffffffff8fffffffffffffcfffffff
fffffe3ffc010101ffffc1ffffffffffff8fffffffffffffcffffffffffffe3ffc000000
ffffc1ffffffffffff8fffffffffffffcffffffffffffe3ffc000000ffff81ffffffffff
ffdfffffffffffffcffffffffffffe3ffc000000ffffc1ffffffffffffdfffffffffffff
cffffffffffffe3ffc010101fffff3ffffffffffff9fffffffffffffcffffffffffffe3f
fc000001ffffe7ffffffffffff9fffffffffffffcffffffffffffe3ffc010101ffffe3ff
ffffffffff9fffffffffffffcffffffffffffe3ffc010101ffffe3ffffffffffff9fffff
ffffffffcffffffffffffe3ffc010100ffffe3ffffffffffff9fffffffffffffcfffffff
fffffe3ffc000000ffffe3ffffffffffff9fffffffffffffcffffffffffffe3ffc000000
ffffe3ffffffffffff9fffffffffffffcffffffffffffe3ffc000000ffffe7ffffffffff
ff9fffffffffffffcffffffffffffe3ffc000000ffffe7ffffffffffff9fffffffffffff
cffffffffffffe3ffc010101ffffe3ffffffffffff9fffffffffffffcffffffffffffe3f
fc000000ffffe3ffffffffffff9fffffffffffffcffffffffffffe3ffc010101ffffe7ff
ffffffffff9fffffffffffffcffffffffffffe3ffc010101ffffe3ffffffffffff9fffff
ffffffffcffffffffffffe3ffc000000ffffe7ffffffffffff9fffffffffffffcfffffff
fffffe7ffc000000ffffe3ffffffffffff9fffffffffffffcffffffffffffe7ffc000000
ffffe3ffffffffffff9fffffffffffffcffffffffffffe7ffc000000ffffe7ffffffffff
ff9fffffffffffffcffffffffffffe7ffc000000fff9e7ffffffffffff9fffffffffffff
cffffffffffffe7ffc010101fffbe3ffffffffffff9fffffffffffffcffffffffffffe7f
fc010101e003e3ffffffffffff9fffffffffffffcffffffffffffe7ffc010101e003e3ff
ffffffffff9fffffffffffffcffffffffffffe7ffc010101e1c7c3ffffffffffff9fffff
ffffffffcffffffffffffe7ffc010101e1c78046fbffffffff0fffffcfffffffcfffffff
fffffc3ffc010101e3c78000000000000000000807ffffff87ffffffffffe03ffc000000
e3c78000000000000000000000000000000000000000001ffc010101e3c7c3ffffffffff
7e07f20000000000000000000000003ffc010101e3c7e7ffffffffffff0fffff87ffffff
07fffffffffffc3ffc010101e3c7ffffffffffffffffffffefffffffcfffffffffffff7f
fc010101f3c7fffffffffffffffffffffffffffffffffffffffffffffc010101e1c7ffff
fffffffffffffffffffffffffffffffffffffffffc010101fbc7ffffffffffffffffffff
fffffffffffffffffffffffffc010101ffffffffffffffffffffffffffffffffe7ffffff
fffffffffc010101fffffffffffffffffffffffffffffffffffffffffffffffffc010101
fffffffffffffffffffffffffffffffffffffffffffffffffc010101ffffffffffffffff
fffffffffffffffffffffffffffffffffc0101014c000000640000000000000000000000
7d0000007c00000000000000000000007e0000007d0000002900aa000000000000000000
0000803f00000000000000000000803f0000000000000000000000000000000000000000
000000000000000000000000220000000c000000ffffffff460000001c00000010000000
454d462b024000000c000000000000000e00000014000000000000001000000014000000
0400000003010800050000000b0200000000050000000c027d007e00030000001e000400
0000070104000400000007010400dd0a0000410b2000cc00c400c600000000007d007e00
0000000028000000c6000000c40000000100010000000000000000000000000000000000
020000000000000000000000ffffff00ffffffffffffffffffffffffffffffffffffffff
fffffffffc010101fffffffffffffffffffffffffffffffffffffffffffffffffc010101
fffffffffffffffffffffffffffffffffffffffffffffffffc010101ffffffffffffffff
fffffffffffffffffffffffffffffffffc010101fc1fffffffffffffff7fffffffffffff
fffffffffffffffffc010101fe3ffffffffffffffe3e1fffffffffffffffffffffffffff
fc010101fe3fffffffffffffff3e3fffffffffffe1fffffffffffffe7c010101fe3fffff
ffffffffff3e3fffffffffffe3ffffffffffff007c010101fe3fffffffffffffff807fff
ffffffffe3ffffffffffff007c010101fe3fffffffffffffff80ffffffffffffe3ffffff
ffffff18fc010101fe3fffffffffffffffc8ffffffffffffe3ffffffffffff18fc010101
fe3fffffffffffffffc8ffffffffffffe3ffffffffffff18fc010101fe3fffffffffffff
ffe1ffffffffffffe3ffffffffffff18fc010101fe39ffffffffffffffe1ffffffffffff
e3ffffffffffff18fc010101fc01fffffffffffffff1ffffffffffffe3ffffffffffff18
fc010101fe03fffffffffffffff3fffffffffffee37fffffffffff18fc010101ffffffff
fffffffffffffffffffffffe003fffffffffff18fc010101ffffffffffffffffffffffff
ffffffff007fffffffffff18fc010101ffffffffffffffffffffffffffffffffffffffff
ffffff18fc010101ffffffffffffffffffffffffffffffffffffffffffffff1cfc010101
fffffffffffffffffffffffffffffffffffffffffffffffffc010101fffff0ffffffffff
ffe1ffffffffffffe3fffffffffffffffc010101fffff000000001ffffc0ffffffffffff
c1ffffffffffffcffc010101ffffe00000000000000000000000000000bf9fffffffff87
fc010101fffff07ffffffffff0000000000000000000000000000003fc010101fffff07f
ffffffffffe1ffffffffffff807ffffdc8800007fc010101fffff9fffffffffffff3ffff
ffffffff027fffffffffff87fc010101fffff9fffffffffffff3ffffffffffff127fffff
ffffff8ffc010101fffff9fffffffffffff3ffffffffffff123fffffffffffcffc000001
fffff9fffffffffffff3ffffffffffff123fffffffffffcffc010101fffff9ffffffffff
fff3ffffffffffff323fffffffffffcffc010101fffff9fffffffffffff3ffffffffffff
323fffffffffffcffc010101fffff9fffffffffffff3ffffffffffff323fffffffffffcf
fc010101fffff9fffffffffffff3ffffffffffff323fffffffffffcffc010101fffff9ff
fffffffffff3ffffffffffff323fffffffffffcffc010101fffff9fffffffffffff3ffff
ffffffff333fffffffffffcffc010100fffff9fffffffffffff3ffffffffffff323fffff
ffffffcffc010101fffff9fffffffffffff3ffffffffffff323fffffffffffcffc010101
fffff9fffffffffffff3ffffffffffff323fffffffffffcffc010101fffff9ffffffffff
ffe3ffffffffffff323fffffffffffcffc010101fffff9ffffffffffffe3ffffffffffff
323fffffffffffcffc010101fffff9ffffffffffffe3ffffffffffff323fffffffffffcf
fc010101fffff9ffffffffffffe3ffffffffffff323fffffffffffcffc010101fffff9ff
ffffffffffe3ffffffffffff323fffffffffff8ffc010101fffff9ffffffffffffe3ffff
ffffffff323fffffffffff8ffc010101fffff9ffffffffffffe7ffffffffffff323fffff
ffffff8ffc010101fffff9ffffffffffffe7ffffffffffff323fffffffffff8ffc010101
fffff9ffffffffffffe3ffffffffffff323fffffffffff8ffc010101fffff9ffffffffff
ffe3ffffffffffff341fffffffffff9ffc010101fffff9ffffffffffffe7ffffffffffff
340fffffffffff9ffc010000fffff9ffffffffffffe7ffffffffffff361fffffffffff8f
fc010101fffff9ffffffffffffe7fffffffffffe361fffffffffff8ffc010101fffff9ff
ffffffffffe7fffffffffffe161fffffffffff8ffc000101fffff9ffffffffffffc1ffff
fffffffe023fffffffffff9ffc010101fffff9ffffffffffffc1fffffffffffc163fffff
ffffff9ffc010101fffff9ffffffffffffc1fffffffffffc163fffffffffff9ffc010101
fffff9ffffffffffffc3fffffffffffe123fffffffffff9ffc010101fffff9ffffffffff
ffe3ffffffffffff363fffffffffff9ffc010101fffff9ffffffffffffe3ffffffffffff
367fffffffffff9ffc010101fffff9ffffffffffffe3ffffffffffff267fffffffffff9f
fc000000fffff9ffffffffffffe7ffffffffffff267fffffffffff9ffc010101fffff9ff
ffffffffffe7ffffffffffff267fffffffffff9ffc000101fffff9ffffffffffffe7ffff
ffffffff267fffffffffff9ffc010101fffff9ffffffffffffe7ffffffffffff267fffff
ffffff9ffc000000fffff9ffffffffffffe7ffffffffffff367fffffffffff9ffc010101
fffff9ffffffffffffe7ffffffffffff267fffffffffff9ffc010101fffff9ffffffffff
ffe7ffffffffffff267fffffffffff9ffc000000fffff9ffffffffffffe7ffffffffffff
267fffffffffff9ffc010101fffff9ffffffffffffe7ffffffffffff267fffffffffff9f
fc010100fffff1ffffffffffffe7ffffffffffff267fffffffffff9ffc010101fffff9ff
ffffffffffe7fffffffffffe267fffffffffff9ffc000001f9f1f9ffffffffffffe7ffff
ffffffff267fffffffffff9ffc010101f0f0f9ffffffffffffe7ffffffffffff267fffff
ffffff9ffc010101f9f1f9ffffffffffffe7fffffffffffe267fffffffffff9ffc010101
fcf3f1ffffffffffffc7fffffffffffe267fffffffffff9ffc010101fc03e0ffffffffff
ffc7ffffffcfffff267fffffffffff9ffc010101fc03c000000002038783ffffffc1ffff
007ffffff7ffff9ffc010101fe47c0fb5000000000000000000000000002dffff07fff0f
fc010101fe07e0ffffffffffff00000000000000000000000000000ffc000101ff0ff9ff
ffffffffff83ffffffc0ffff818800000000000ffc010101ff1ffbffffffffffffe7ffff
ffefffffc3fffffff07fff0ffc010101ff9ff3ffffffffffffe7ffffffffffffe7ffffff
f3ffff9ffc010101ff9ff3ffffffffffffe7ffffffffffffe7ffffffffffff9ffc010101
fffff3ffffffffffffe7ffffffffffffe7ffffffffffff9ffc010101fffff3ffffffffff
ffe7ffffffffffffe7ffffffffffff9ffc010101fffff3ffffffffffffc7ffffffffffff
e7ffffffffffff9ffc010100fffff3ffffffffffffcfffffffffffffe7ffffffffffff9f
fc010101fffff3ffffffffffffefffffffffffffe7ffffffffffff9ffc010101fffff3ff
ffffffffffc7ffffffffffffe7ffffffffffff9ffc010101fffff3ffffffffffffefffff
ffffffffe7ffffffffffff9ffc010101fffff3ffffffffffffcfffffffffffffe7ffffff
ffffff9ffc010101fffff3ffffffffffffefffffffffffffe7ffffffffffff9ffc010101
fffff3ffffffffffffcfffffffffffffe7ffffffffffff9ffc010101fffff3ffffffffff
ffcfffffffffffffe7ffffffffffff9ffc010101fffff3ffffffffffffcfffffffffffff
e7ffffffffffff9ffc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff9f
fc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff9ffc010101fffff3ff
ffffffffffcfffffffffffffe7ffffffffffff9ffc010101fffff3ffffffffffffcfffff
ffffffffe7ffffffffffff9ffc010101fffff3ffffffffffffcfffffffffffffe7ffffff
ffffff9ffc010000fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101
fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ffffffffff
ffcfffffffffffffe7ffffffffffff9ffc010101fffff3ffffffffffffcfffffffffffff
e7ffffffffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1f
fc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ff
ffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ffffffffffffcfffff
ffffffffe7ffffffffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffff
ffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc000101
fffff3ffffffffffffcfffffffffffffe7fffffffffffe0ffc010101fffff3ffffffffff
ffcfffffffffffffe7fffffffffffe0ffc000101fffff3ffffffffffffcfffffffffffff
e7fffffffffffe0ffc010101fffff3ffffffffffffcfffffffffffffe7fffffffffffe1f
fc000000fffff3ffffffffffffcfffffffffffffe7fffffffffffe1ffc010101fffff3ff
ffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ffffffffffffcfffff
ffffffffe7ffffffffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffff
ffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc000000
fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101fffff3ffffffffff
ffcfffffffffffffe7ffffffffffff1ffc000001fffff3ffffffffffffcfffffffffffff
e7ffffffffffff1ffc010101fffff3ffffffffffffcfffffffffffffc7ffffffffffff1f
fc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff3ffc010101fffff3ff
ffffffffffcfffffffffffffe7ffffffffffff3ffc010101fffff3ffffffffffffcfffff
ffffffffe7ffffffffffff3ffc010101fffff3ffffffffffffcfffffffffffffe7ffffff
ffffff1ffc010101fffff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101
ff0ff3ffffffffffffcfffffffffffffe7ffffffffffff1ffc010101ff0ff3ffffffffff
ffcfffffffffffffefffffffffffff1ffc010101ff9ff3ffffffffffffcfffffffffffff
efffffffffffff3ffc010101ff1fe1ffffffffffff87ffffffffffffc7fffffffffffe1f
fc010101ff9fc00000000000000001ffffffffff83fffffffffffc1ffc010101ff1fc000
000000000000000000000000000000000000001ffc010101ff1fc1ffffffffffff07ffff
fffffffb800000000000041ffc010101ff1fc1ffffffffffff87ffffffffffff83ffffff
fffffe1ffc010101ff1ff3ffffffffffffcfffffffffffffc7fffffffffffe3ffc010101
f39df3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101f001f3ffffffffff
ffcfffffffffffffcffffffffffffe3ffc010101f801f3ffffffffffffcfffffffffffff
cffffffffffffe3ffc010101fffff3ffffffffffffcfffffffffffffcffffffffffffe3f
fc010101fffff3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101ffffe3ff
ffffffffffcfffffffffffffcffffffffffffe3ffc010101fffff3ffffffffffffcfffff
ffffffffcffffffffffffe3ffc010101fffff3ffffffffffffcfffffffffffffcfffffff
fffffe3ffc010101fffff3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101
fffff3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101fffff3ffffffffff
ffcfffffffffffffcffffffffffffe3ffc010101ffffe3ffffffffffff8fffffffffffff
cffffffffffffe3ffc010101ffffe3ffffffffffffcfffffffffffffcffffffffffffe3f
fc010000ffffe3ffffffffffff8fffffffffffffcffffffffffffe3ffc010101ffffe3ff
ffffffffff8fffffffffffffcffffffffffffe3ffc010101ffffe3ffffffffffff8fffff
ffffffffcffffffffffffe3ffc010101ffffe3ffffffffffffcfffffffffffffcfffffff
fffffe3ffc010101fffff3ffffffffffffcfffffffffffffcffffffffffffe3ffc010101
ffffe3ffffffffffff8fffffffffffffcffffffffffffe3ffc010101ffffc3ffffffffff
ff8fffffffffffffcffffffffffffe3ffc010101ffffc1ffffffffffff8fffffffffffff
cffffffffffffe3ffc000000ffffc1ffffffffffff8fffffffffffffcffffffffffffe3f
fc000000ffff81ffffffffffffdfffffffffffffcffffffffffffe3ffc000000ffffc1ff
ffffffffffdfffffffffffffcffffffffffffe3ffc010101fffff3ffffffffffff9fffff
ffffffffcffffffffffffe3ffc000001ffffe7ffffffffffff9fffffffffffffcfffffff
fffffe3ffc010101ffffe3ffffffffffff9fffffffffffffcffffffffffffe3ffc010101
ffffe3ffffffffffff9fffffffffffffcffffffffffffe3ffc010100ffffe3ffffffffff
ff9fffffffffffffcffffffffffffe3ffc000000ffffe3ffffffffffff9fffffffffffff
cffffffffffffe3ffc000000ffffe3ffffffffffff9fffffffffffffcffffffffffffe3f
fc000000ffffe7ffffffffffff9fffffffffffffcffffffffffffe3ffc000000ffffe7ff
ffffffffff9fffffffffffffcffffffffffffe3ffc010101ffffe3ffffffffffff9fffff
ffffffffcffffffffffffe3ffc000000ffffe3ffffffffffff9fffffffffffffcfffffff
fffffe3ffc010101ffffe7ffffffffffff9fffffffffffffcffffffffffffe3ffc010101
ffffe3ffffffffffff9fffffffffffffcffffffffffffe3ffc000000ffffe7ffffffffff
ff9fffffffffffffcffffffffffffe7ffc000000ffffe3ffffffffffff9fffffffffffff
cffffffffffffe7ffc000000ffffe3ffffffffffff9fffffffffffffcffffffffffffe7f
fc000000ffffe7ffffffffffff9fffffffffffffcffffffffffffe7ffc000000fff9e7ff
ffffffffff9fffffffffffffcffffffffffffe7ffc010101fffbe3ffffffffffff9fffff
ffffffffcffffffffffffe7ffc010101e003e3ffffffffffff9fffffffffffffcfffffff
fffffe7ffc010101e003e3ffffffffffff9fffffffffffffcffffffffffffe7ffc010101
e1c7c3ffffffffffff9fffffffffffffcffffffffffffe7ffc010101e1c78046fbffffff
ff0fffffcfffffffcffffffffffffc3ffc010101e3c78000000000000000000807ffffff
87ffffffffffe03ffc000000e3c78000000000000000000000000000000000000000001f
fc010101e3c7c3ffffffffff7e07f20000000000000000000000003ffc010101e3c7e7ff
ffffffffff0fffff87ffffff07fffffffffffc3ffc010101e3c7ffffffffffffffffffff
efffffffcfffffffffffff7ffc010101f3c7ffffffffffffffffffffffffffffffffffff
fffffffffc010101e1c7fffffffffffffffffffffffffffffffffffffffffffffc010101
fbc7fffffffffffffffffffffffffffffffffffffffffffffc010101ffffffffffffffff
ffffffffffffffffe7fffffffffffffffc010101ffffffffffffffffffffffffffffffff
fffffffffffffffffc010101ffffffffffffffffffffffffffffffffffffffffffffffff
fc010101fffffffffffffffffffffffffffffffffffffffffffffffffc0101010c000000
40092900aa000000000000007d007e0000000000040000002701ffff030000000000

Рис. 8. Пространство нуклеотидов для последовательности пар и один из
путей эволюции

Нетрудно видеть, что каждому из 16 состояний соответствует одна из
пар-последовательностей ГГ, ГА, ГТ, ГЦ, АГ, АА, AT, АЦ, ТГ, ТА, ТТ, ТЦ,
ЦГ, ЦА, ЦТ, ЦЦ — вершины прилегающих друг к другу квадратов. В случае
последовательностей длины v = 3 необходимо включить еще тре тье
измерение, в результате чего возникает куб с 64 вершинами,
соответствующими 64 различным последовательностям-тройкам. Точковая
мутация соответствует сдвигу вдоль ребра, параллельного одной из осей.
Длины элементарных ребер не имеют непосредственного значения, так как
априори все переходы Г ? А, Г? Т, Г ? Ц, А ? Т, А ? Ц, А ? Г, Ц ? Г, Ц ?
А, Ц ? Т равнозначны. Эволюционный nyi от одной последовательности
нуклеотидов к другой, состоящий, вообще говор из многих мутаций, т. е.
из многих шагов вдоль ребер, соответствует некоторок связному пути по
гиперкубу. Примером может служить изображенный на рис. 8 эволюционный
путь от АГ к ГТ. Если рассматривать популяции, то числу представителей
Ni последовательности определенного типа i = А1 … Аv может бы
сопоставлено скопление точек мощности Ni в непосредственной окрестности
о ответствующей i вершины (или жирная точка). Эволюция популяции
описываетcя блужданием скопления точек по пространству нуклеотидов.
Графическое представление в пространстве нуклеотидов особенно удобно для
наглядного истолкования путей эволюции и при обсуждении стратегий
эволюции. На языке теории автоматов переходы в пространстве нуклеотидов
могут быть описаны как процессы в автоматах Рабина-Скотга.

Подойдем теперь к определению вероятностей элементарных переходов (8) в
единицу времени. При этом будем следовать более ранним работам, в
которых вероятности переходов были получены сначала для более простых
эволюционных процессов Эйгена, а позднее уточнены с учетом образования
гиперциклов.
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 (9)

Здесь aij — входящие в выражение (9) скорости мутаций, еi — скорости
репродукции нуклеиновых кислот, bij — коэффициенты гиперциклических
связей. Пренебрегая каталитическим действием протеинов, положим просто
bij=0, еi = Ei и aij = Aij и получим бы вероятности перехода.
Приведенные выше вероятности перехода позволяют легко вычислить
стохастические траектории в пространстве состояний при заданных
начальных условиях. Ценные выводы относительно исследуемого случайного
процесса могут быть получены с помощью методов стохастической динамики,
т. е. путем систематического исследования большого числа индивидуальных
траекторий. Трудности, возникающие при применении этих методов к
процессам эволюции, сводятся по существу с тому, что коэффициенты в
выражении (8) известны лишь в очень грубом триближении. Другой метод
исследования случайного процесса эволюции состоит в исследовании
распределения вероятности

P(N1,N2, …; t) (9)

как функции времени. Для этого необходимо предварительно записать
основное ;инетическое уравнение.

picscalex100010009000003d50400000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00f802c1200000026060f001a00ffffffff00001000
0000c0ffffffafffffff402c00004f0f00000b00000026060f000c004d61746854797065
0000b00309000000fa02000010000000000000002200040000002d010000050000001402
50024000050000001302500203020500000014020a01141c0500000013029603141c0500
0000140270057d1e050000001302fc077d1e050000001402dc08d021050000001302680b
d02115000000fb0240fe0000000000009001000000000402001054696d6573204e657720
526f6d616e000081040000002d01010008000000320a990e072202000000292e09000000
320a990e901d040000002e2e2e2c08000000320a990e101d010000002c000a000000320a
990e1d18050000002c2e2e2e2c000a000000320a990e8e13050000002c2e2e2e2c000800
0000320a990e0f1101000000280008000000320a920a962a01000000290008000000320a
920a2727010000002c0008000000320a920a0c24010000002c0008000000320a920adb1e
010000002c0008000000320a920a251e01000000310008000000320a920a501901000000
2c0008000000320a920a9a1801000000310008000000320a920a4e140100000028000900
0000320a2607c324040000002e2e2e2908000000320a26074324010000002c0009000000
320a2607d31f040000002e2e2e2c08000000320a2607531f010000002c0008000000320a
26079d1e0100000031000a000000320a26078519050000002c2e2e2e2c000a000000320a
2607a613050000002c2e2e2e2c0008000000320a26070f1101000000280008000000320a
c002302901000000290008000000320ac0025126010000002c0008000000320ac0029b25
01000000310008000000320ac002c020010000002c0008000000320ac0020a2001000000
310008000000320ac0021f19010000002c0008000000320ac0020416010000002c000800
0000320ac002781301000000280008000000320ac002ad0c01000000290009000000320a
c002e609040000002e2e2e3b08000000320ac0021e09010000002c0008000000320ac002
0806010000002c0008000000320ac002710301000000280015000000fb02c0fe00000000
00009001000000000402001054696d6573204e657720526f6d616e000081040000002d01
020004000000f001010008000000320a090fd81201000000310008000000320a1c0c7711
010000002c0008000000320a1c0c6110010000002c0008000000320a9607cf1801000000
310008000000320a9607f01201000000310008000000320a4a04a110010000002c000800
0000320a4a048b0f010000002c0008000000320a30034f0801000000320008000000320a
3003520501000000310015000000fb02c0fe000000000000900101000000040200105469
6d6573204e657720526f6d616e000081040000002d01010004000000f001020008000000
320a090f2721010000006b0008000000320a090f601c010000006a0008000000320a090f
8b1701000000690008000000320a1c0ce311010000006b0008000000320a1c0c09110100
00006a0008000000320a1c0cf90f01000000690008000000320a020bb629010000006b00
08000000320a020b8f26010000006a0008000000320a020b7a2301000000690008000000
320a020bda20010000006b0008000000320a020bd31b010000006a0008000000320a020b
481601000000690008000000320a96076a23010000006b0008000000320a9607c81d0100
00006a0008000000320a9607a31701000000690008000000320a4a040d11010000006b00
08000000320a4a043310010000006a0008000000320a4a04230f01000000690008000000
320a30035028010000006b0008000000320a30034323010000006a0008000000320a3003
be1d01000000690008000000320a30031e1b010000006b0008000000320a300387180100
00006a0008000000320a3003721501000000690015000000fb0240fe0000000000009001
010000000402001054696d6573204e657720526f6d616e000081040000002d0102000400
0000f001010008000000320a990ed91f010000004e0008000000320a990ed61a01000000
4e0008000000320a990e4716010000004e0008000000320a990ead11010000004e000800
0000320a990ef00f01000000500008000000320a920a6828010000004e0008000000320a
920a0525010000004e0008000000320a920a3622010000004e0008000000320a920a8c1f
010000004e0008000000320a920a491a010000004e0008000000320a920a041501000000
4e0008000000320a920a951201000000570008000000320a26071c22010000004e000800
0000320a26073e1c010000004e0008000000320a26075f16010000004e0008000000320a
2607c511010000004e0008000000320a2607f00f01000000500008000000320ac0020227
010000004e0008000000320ac002b921010000004e0008000000320ac0027a1c01000000
4e0008000000320ac002d019010000004e0008000000320ac002fd16010000004e000800
0000320ac0022e14010000004e0008000000320ac002bf1101000000570008000000320a
c002130c01000000740008000000320ac0020107010000004e0008000000320ac0022704
010000004e0008000000320ac002520201000000500008000000320a1c045e0101000000
740010000000fb0240fe0000000000009001000000020002001053796d626f6c00020400
00002d01010004000000f001020008000000320a990e0c0f01000000d70008000000320a
920ad72b01000000d70008000000320ab20aa61001000000e50008000000320a920ae61c
010000002d0008000000320a920a5517010000002b0008000000320a920ad90e01000000
2d0008000000320a26072127010000002d0008000000320a26070c0f01000000d7000800
0000320ac002712a01000000d70008000000320ae002d00f01000000e50008000000320a
c0025624010000002b0008000000320ac002cb1e010000002d0008000000320ac002bb0d
010000003d0008000000320a1c04520001000000b60008000000320aa801ae0001000000
b60010000000fb02c0fe0000000000009001000000020002001053796d626f6c00020400
00002d01020004000000f001010008000000320a96072218010000002d000a0000002606
0f000a00ffffffff01000000000010000000fb021000070000000000bc02000000cc0102
022253797374656d00cc040000002d01010004000000f0010200030000000000 (10)

Распределение вероятности представляет собой поверхность, построенную
над симплициальной решеткой; описанием деформации этой поверхности во
времени служит случайный процесс эволюции. Разумеется, высказать
определенное утверждение относительно распределения вероятности в
пространстве столь высокой размерности необычайно трудно. К этому
добавляется еще принципиальная трудность применения метода основного
кинетического уравнения к общему эволюционному процессу: при заданных
начальных распределениях, сосредоточенных на относительно узкой области
пространства состояний (симплициальной решетки), основное кинетическое
уравнение описывает систематическую тенденцию к относительно
равномерному распределению вероятностей на всем пространстве состояний
необычайно высокой размерности. Соответственно, возможные утверждения
носят достаточно расплывчатый характер, а конечное стационарное
распределение, к которому стремится система, по существу лишено
определенного физического смысла. С другой стороны, основное
кинетическое уравнение особенно хорошо подходит для изучения таких
специальных вопросов, как выживание новых сортов и сосуществование новых
сортов. Покажем, что основное кинетическое уравнение согласуется с
детерминистическим уравнением . Для этого умножим уравнение (10) на Nk и
просуммируем по всем числам заполнения. В результате мы получим
уравнение для средних чисел заполнения:
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 (11)

Факторизуя средние значения и деля на объем, получаем из уравнения (11)
уравнения для средней плотности Xk = (Nk)/V. Тем самым доказано, что
стохастическое описание согласуется с детерминистическим. Исследуем
теперь вопрос о вымирании или выживании нового сорта, возникающего в
системе вследствие мутации. Ограничимся сначала простыми эйгеновскими
системами без гиперцикцических связей. Предположим, что в системе
имеется только один штаммовый сорт со скоростью воспроизведения Е1 и
только один представитель мутантов со скоростью воспроизведения E2, т.
е. в начальном состоянии t = 0 выполняются равенства N1 = N – 1, N2 = 1.

Условимся рассматривать N2 как независимую переменную и пренебрегать в
основном кинетическом уравнении всеми членами выше первой степени по N2
(что вполне допустимо, если учесть начальные условия). В результате мы
получим упрощенное уравнение
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(12)

Известно решение этого уравнения при начальном условии
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 (13)

Если интересует вероятность вымирания мутанта по истечении времени t, то
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 (14)

Введем для удобства записи фактор преимущества
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 (15)

и найдем вероятность выживания нового сорта:
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 (16)

Если определить n = Elt как меру числа поколений, которые выживают
мутанты, то получится очень простая формула
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 (17)
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aa00000000000000ac00310100000000040000002701ffff030000000000

Рис. 9. Вероятность выживания мутанта через n поколений как функция
фактора выживания (сплошные линии — стохатическая теория; штриховые
линии — детерминистическая теория)

На рис. 9 показана зависимость вероятности выживания от фактора
преимущества и числа поколений. В то время как в детерминистической
теории лучшие мутанты с > 0 заведомо выживают, а худшие с 0 не очень существенно
отличаются от

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