Supplementary Material
Evolution of trophic structure
Bell: Evolution of trophic structure
Supplementary Information
Part 1: Principles of operation of Uqbar
Part 2. Uqbar procedures
Part 3. Basic operation manual for Uqbar
Part 4. Output files
Part 5. Free parameters
Part 6. Elementary properties of Uqbar
Part 7. Optimal number of SIL
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Part 1: Principles of operation of Uqbar
Uqbar is an artificial electronic ecosystem containing organisms that consist of a few
lines of computer code. This code specifies the identity of an individual, and determines
how it will acquire resources, reproduce, and interact with other individuals.
The
behaviour of the individual is otherwise under the control of the CPU, which sets system
parameters and manipulates individuals according to the instructions they bear.
Ecosystem. The habitable part of the ecosystem comprises an ordered list of ‘slots’. The
number of slots is fixed and may take any value: the simulations reported typically use
100,000 slots. Each slot is either vacant, or is occupied by a single entity. There are two
types of entity: organisms and substrates.
A substrate consists of a number of different resources in fixed proportions;
different substrates are made up according to different recipes. Each exists in the form of
single packets containing a fixed quantity of each resource, made up from ingredients
obtained from the Resource Pool. This is a separate compartment, which communicates
with the ecosystem but is not habitable. Resources enter the pool either from the
ecosystem, through recycling, or as exogenous input from an undefined outside world.
The current contents of the resource pool determine the quantities of different resources
available to the ecosystem, so that new packets of any given substrate can be formed only
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if the necessary resources are available from the resource pool. A new substrate packet
enters the ecosystem from the resource pool with given probability in each move. It is
eventually removed from its slot when it decomposes or is consumed by an organism.
Extraneous supply of
resources at fixed rate
External
community
chemical synthesis
Resource
Pool
Substrate Packet
Recycling of unconsumed
substrate and dead bodies
decomposes
UQBAR
consumed
Producer
starves
immigration
maintenance,
respiration
consumed grows and
reproduces
Predator
starves
consumed grows and
reproduces
Bell Fig 1
This figure shows the main ecological processes in Uqbar.
irreversibly lost
from system
The ways in which resource supply,
decomposition, recycling, maintenance, consumption, reproduction, death and immigration are simulated
are described in the text below.
Organisms exist as individuals that are able to acquire resources. Some species (called
collectively Producers) grow exclusively by consuming substrate packets; others (called
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Predators) by consuming other organisms. Growth beyond a certain point is followed by
reproduction, when the parent gives rise to a newborn individual that is allocated a
separate ecosystem slot. Individuals eventually die when they starve to death, having
been unable to find sufficient, or appropriate, substrates, or when they are consumed by a
predator. The resources contained in dead bodies may leave the system, or may be
recycled to the resource pool.
The number of ecosystem slots is fixed, and a new individual or substrate packet
can enter the system only if a slot is available.
Structure of entities. Entities are constructed on a common plan, but regions present in
some types of entity are lacking in others.
The two principal types of entity are
organisms and substrates, but an organisms may be a Producer or a Predator (Figure 2).
The most complicated entity is an Producer, which consists of four distinct regions.
(1) A single identity locus (IDL). This bears a binary number of given
length (i.e. given number of bits) that labels the individual as belonging to a particular
species. All individuals bearing the same identity number have identical genotypes, that
is are identical in state at all other loci.
(2) A set of social interaction loci (SIL). Each SIL bears a binary number
of given length.
The SIL determine the outcome of pairwise interactions between
individual organisms.
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(3) A set of resource acquisition loci (RAL). This is a second set of loci
each bearing a binary number of given length. The RAL determine the outcome of an
interaction between an individual Producer and a resource package. They occur only in
Producers.
(4) The resource storage sites (RSS). A series of sites each of which holds
the individual’s supply of a certain resource. Resources are acquired and expended
through interactions or attempted interactions with other organisms or with substrates.
The current value and composition of RSS determine whether an individual will
reproduce and whether it will die.
A Predator has precisely the same structure, except that it lacks RAL.
A substrate
package consists of two regions only: a single SIL, and a set of RSS. The RSS of a
substrate packet have fixed contents that correspond to a particular substrate SIL.
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ID
L
RAL
1
RAL
2
SIL
1
SIL
2
SIL
3
SIL
4
ID
L
SIL
1
SIL
2
SIL
3
SIL
4
RSS
1
RSS
1
RSS
2
RSS
2
SIL
1
RSS
1
RSS
2
PRODUCER
PREDATOR
SUBSTRATE
Figure 2. The Uqbar entities. This is the same as Figure 1 of the article.
Ecosystem operation. The ecosystem list is used as an ordered queue, with execution
proceeding from lower-numbered to higher-numbered slots. In each new move the entity
occupying the next highest-numbered slot is selected as the ‘Agent’. A second slot is then
selected from the ecosystem list. In the present study the second slot is selected at
random, but the program provides the option of selecting it from a limited ‘home range’
centred on the slot occupied by the Agent. The entity that occupies this slot is called the
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‘Patient’. Agent and Patient then interact according to the rules described below, and
their status adjusted appropriately. When the top of the ecosystem list is reached,
terminating a “cycle” of moves, execution continues from the bottom; the list is thus
essentially circular, with no definite limit to the number of cycles that may occur.
Each move consists of a series of external events that may affect the ecosystem,
followed by an internal procedure. The external events are as follows; each occurs with
some defined probability in each move.
(1) Exogenous supply to the resource pool. A given quantity of each resource
enters the resource pool from outside.
(2) Substrate supply to the ecosystem. A single random substrate packet is added
to the ecosystem from the resource pool.
(3) Immigration.
A single random individual enters the ecosystem from an
external species pool. This individual is chosen at random from the initial
community used to set up Uqbar.
(4) Disturbance. Individuals are liable to be killed by some arbitrary extraneous
event.
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(5) Invasion.
Evolution of trophic structure
Bell
A large number of individuals enters the ecosystem from an
external species pool, displacing residents.
The probabilities of each of these events can be defined, so that Uqbar is affected to a
greater or lesser extent by external perturbation. In the limit, it can be completely closed
and self-contained.
The internal procedure depends on the nature of the Agent. If the Agent is a
vacant slot, execution proceeds directly to the next slot in sequence. If it is a substrate
packet, then the packet may decompose spontaneously and its constituent resources may
then be recycled to the resource pool. The probabilities of decomposition and recycling
influence the availability of resources in the ecosystem. If the Agent is an organism, then
it incurs a metabolic cost represented by the expenditure of fixed quantities of each
resource during the move. These resources are recycled to the resource pool with a
specified probability. They are expended even if the Agent encounters only a vacant slot;
if it encounters an entity, then the consequences depend on the outcome of the interaction
between Agent and Patient.
Interaction. All interactions are based on the notions of complementarity and
compatibility at the SIL and RAL. Two individuals are complementary if a recognition
locus of one bears precisely the opposite pattern of bits to a corresponding locus of the
other. Thus, 00101 and 11010 are complementary patterns. If Agent and Patient are
complementary in this sense, then their interaction is antagonistic. When an Producer
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encounters a substrate packet, the Producer consumes the substrate if any of its RAL are
complementary to the single SIL of the substrate. The substrate packet is not consumed if
the agent is a non-complementary Producer or a Predator. When two organisms
encounter one another, their interaction is antagonistic if one or more of their SIL are
complementary.
The specificity of interactions between predator and prey is governed by the
length of SIL and the rules for complementarity. For simplicity, I distinguish Long
systems (with 4 SIL of 5 bits each) from Short systems (with 10 SIL of 2 bits each), with
the same quantity of information initially encoded by each individual being the same (20
bits). In either case, any given Predator SIL may interact with a single defined Producer
SIL only (interaction
in cis) or with all Producer SIL (interaction in trans). This gives four
cases as a framework for experiments: Long-Cis, Long-Trans, Short-Cis and Short-Trans
(see Fig).
The relationship between the extent of complementarity and the probability of
capture of a prey organism or a substrate packet is determined by a function that is not
liable to change. Any function may be specified; I have assumed that increasing
complementarity meets with diminishing returns, and that this can be expressed by the
two-parameter nonlinear function
Probability of capture = L [1 - exp(- i * complementarity) ]
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where L is the limiting probability of capture when complementarity is very large, and i
is an interaction coefficient that determines how rapidly prey capture probability
increases with complementarity. A similar function (whose parameter values may differ)
is used to tune the complementarity of producer with substrate packet. This is the only
equation-driven process in Uqbar.
When two complementary individuals meet, a rule must decide which consumes
the other. A Predator always consumes an Producer rather than vice versa; the difficulty
comes when two Predators meet. Three kinds of rule might operate. The first is
phenotypic and invokes a state that varies among individuals of the same species: the
larger or stronger individual (that with greater RSS contents) consumes the smaller or
weaker. RSS contents are not inherited, so the system cannot evolve. The second
possible rule is a genetic criterion that is invariant within a species and consistent for
pairwise combinations of species: the individual with the greater value at IDL consumes
the other. This has two drawbacks: IDL is not heritable in any straightforward way
(because it is a label that distinguishes a descendant from an ancestral taxon), and
interactions are forced to be transitive (in the sense that if A eats B and B eats C then C
cannot eat A). The final possibility is a genetic criterion that is invariant within a species
but not necessarily consistent for pairwise combinations of species: the individual with
the greater value at complementary SIL consumes the other. This allows heritability and
does not force transitivity, and for these reasons is the rule adopted here, although the
other two can be invoked as options in Uqbar.
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Two individuals are compatible if all the SIL of one are identical to the
corresponding SIL of the other (first with first, second with second, and so forth). This
will be the case if they belong to the same species (that is, have identical IDL); their
interaction is sexual. Recombination occurs through random breakage and reunion of SIL
and (in Producers) RAL. Two individuals may also be compatible, however, even if they
belong to different species: their interaction is then mutualistic. Mutual benefit is created
by the possibility of reproducing together even though neither can reproduce alone. Both
individuals reproduce if their combined RSS contents are adequate to produce an
offspring each; otherwise, neither reproduces. Compatible interactions, whether sexual
or mutualistic, are not considered further in this initial report.
Individuals that are neither complementary nor compatible are neutral; neither is
consumed and neither reproduces. Whether or not consumption occurs, however, the
maintenance cost is exacted from any organism involved in a move, whether as Agent or
as Patient. This applies even when the Agent encounters an empty slot. The cost of
maintenance is not fixed, but depends on the resource-gathering potential of an
individual: the maintenance of a Producer is proportional to the number of RAL it bears,
and that of a Predator on the number of SIL. In addition, SIL may be more (or less)
expensive than RAL, so that heterotrophy is intrinsically more (or less) expensive than
autotrophy.
Life Cycle.
Individuals reproduce when they possess sufficient quantities of each
resource; the overall rate of reproduction thus depends on both the required quantity of
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each and on the amount of each available in substrate packets. When the RSS of an
individual all exceed the threshold quantity, an ecosystem slot is allocated to the
offspring. Only slots that are not occupied by organisms are available. If the slot is
occupied by a substrate packet, this is removed, and its contents may be recycled to the
resource pool. The genome of the parent (IDL, SIL and, in the case of an Producer, RAL)
are then copied to the vacant slot and the appropriate header affixed.
Finally, the
newborn is provided with a basic ration of each resource, this amount being subtracted
from the parent’s stores. If no slot is available, no reproduction can occur.
Genetics. The contents of the SIL and RAL are copied with a certain probability of error,
representing mutation. Three types of mutation may occur. The first is deletion, the
omission of a complete SIL (from a Predator) or RAL (from an Producer). The second is
duplication, the addition of a new SIL or RAL with the same structure as the parental
locus.
Deletion and duplication parallel changes in body size, because the cost of
metabolism is borne per locus – per SIL in Predators and per RAL in Producers. The third
kind of mutation is point mutation, with each bit of each SIL and RAL being liable to be
flipped from one state to the other. When mutation occurs the IDL may be reset to a new
random value not possessed by any other organism, subject to the species concept in
operation.
Two aspects of mutational variation need to be emphasized. The first is that
unequivocally beneficial mutations are not allowed. Thus, increasing the number of RAL
increases the range of substrates that an Producer could consume. It also increases the
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cost of maintenance, however, and is allowed for this reason. Decreasing the number of
SIL,
on the other hand, would reduce the vulnerability of an Producer to predation with no
countervailing disadvantage, and for this reason is not allowed. Deletion of SIL in
Predators, on the other hand, is allowed because although it reduces both the cost of
maintenance and the range of possible predators, it also reduces the range of possible
prey. The second aspect is that macroevolution is not permitted. Producer and Predator
are fixed categories, and organisms are not permitted to evolve from the one into the
other. Instead, a Producer that loses all its RAL or a Predator that loses all its SIL by
deletion is unable to feed and eventually starves to death.
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Part 2. Uqbar Procedures
Uqbar operates in conventional fashion by calling subroutines. They are as follows.
Initialization
GetVariables
Set parameter values
CheckVariables
Screen parameter input for errors
Capital
Initial allocation of resources to resource pool
Tabledhote
Random definition of substrate packets (dishes)
Alacarte
Specification of substrate packets
Feed
Initial allocation of substrate packets to ecosystem
Colonists
Random definition of aboriginal taxa
Delegates
Specification of aboriginal taxa
Stock
Initial allocation of individuals to ecosystem
Subroutines executed (once) each cycle
AdvanceScores
Advance cumulative scores and reset move counters
Existence
Confirm that at least one taxon exists
Supply
Exogenous input to resource pool
Restock
Add single immigrant to community with fixed probability
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Resin
Distribute substrate to ecosystem throughout history
Disturbance
Simultaneous arbitrary threat of death at all slots
Invasion
Simultaneous arbitrary threat of displacement
Subroutines executed (often repeatedly) each move
Patient
Select ecosystem slot with which to interact
Vacant
Agent is a vacant slot
Decomposition
Agent is substrate packet
AgentNeutral
Agent is individual that does not interact with Patient
PatientNeutral
Patient is individual that does not interact with Agent
AgentEatsSubstrate
Agent is autotroph able to consume substrate
Mutual
Agent and Patient are different species but SIL-identical
AgentEatsPatient
Agent is heterotroph able to consume Patient
PatientEatsAgent
Patient is heterotroph able to consume Agent
Recombination
Genetic recombination
Maintain
Individual pays metabolic costs of maintenance
Death
Individual dies
Birth
Individual reproduces, giving birth to single offspring
Both
Two mutualists each give birth
Mutation
Genome of newborn is subject to heritable alteration
ChangeWeb
Change web membership of taxon in complex system.
ConfigureWebs
Read in characteristics of subsystems from an input file.
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Output
Record
Record of initial state of Uqbar
Census
Carry out census of ecolist
Report
Report on types of activity, nutrient flows, list contents
InitialSystem
Description of initial source foodweb
FinalSystem
Description of final source foodweb
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Part 3. Basic operation manual
When you open Uqbar, you will be presented with a series of forms that specify the type
of ecosystem to be simulated, the values of the parameters, and the initial configuration
of the system. This brief text goes through each form in turn and explains how you
should complete them.
StartForm. This form appears when you start the program, and specifies that it is
being used for academic purposes (not that any others have yet been discovered). Click
“Enter Uqbar” to proceed.
OutputForm. This form specifies the location of the output files. There are several of
these, which are described further in Supplementary Information Part 4. Use the
scrollbars to specify where you want them stored. I find it convenient to create a folder
“Uq Out” on the Desktop to hold them temporarily.
The EcoList and the extensive web listings can create large and unwieldy files; check
them only if you need them for analysis.
PPForm. This form specifies how individuals that meet decide whether one can
consume the other.
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Choosing one of the options in the first block of four specifies as simple system
with a single food web. This is the default. In a simple system with a single food web,
two individuals which meet, and are complementary, must decide which is the predator
and which they prey. If one is a Producer and the other a Predator, the Predator always
eats the Producer. If both are Predators, then the issue is decided as follows.
(a) IDL-based recognition. The individual whose IDL has the greater
value is the Predator. Note that this creates completely transitive
trophic relastionships.
(b) SIL-based recognition. The individual whose value for SIL summed
over all complementary loci is the greater is the Predator. This does
not necessarily give rise to transitive trophic relationships.
At this point you also specify whether interactions are evaluated in cis (between
homologous SIL only) or in trans (between all pairwise combinations of SIL). These
modes of interaction are explained more fully in Supplementary information Part 1 and in
the text.
Alternatively, choose the fifth button (in separate box) to specify a complex
system with several separate food webs. Individuals assigned to one food web cannot
consume nor be consumed by individuals assigned to another food web. You must set
the values of three parameters.
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(a) the number of component source webs (subsystems).
(b) The “web mutation rate”. This re-allocates species to different subsystems,
for the following reason. If all Predators in one subsystem become extinct, all
Producers in this subsystem are released from predation, and are then likely to
replace all others, leading to a rapid loss of trophic complexity. It seems more
reasonable to assume that other Predators would eventually evolve so as to be
able to consume them. Accordingly, each species of Producer in the depleted
subsystem is reassigned randomly to another subsystem with given
probability in each cycle. You specify this probability as the web mutation
rate. It is not applied to subsystems which include Predators.
(c) The number of resources in substrate packets. The structure of substrate
packets is explained in more detail in Supplementary Information Part 1. This
parameter is set in a later form (MainForm) for simple systems. The
minimum value allowed is 1 and the maximum 4.
When you have selected the option and (if appropriate) set parameter values, press
“Proceed”. If you have selected a simple system, this takes you to the next form. If you
have selected a complex system, you are prompted (on the right-hand side of PPForm) to
specify the characteristics of the subsystems, for as many as you have specified. For each
subsystem, these characteristics are as follows.
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(a) the frequency of the subsystem: the fraction of all EcoList slots initially
occupied by organisms that will be occupied by members of this subsystem.
This frequency is of course likely to change during the run. Click in the text
box, enter the frequency of the first subsystem, then press Enter. The value
that you have specified will then appear in the list box below, so that you can
keep track of the configuration you are specifying. It does not matter what the
frequencies you enter add up to: they are re-normalized to sum to unity by the
program.
(b) The mode of interaction, either cis or trans, specified as 0 or 1. Specify one of
these and then (and for all subsequent choices) press Enter.
(c) The mode of identifying predator and prey, either IDL-based or SIL-based.
(d) The number of SIL.
(e) The length of each SIL.
(f) The interaction coefficient I that influences the probability of prey capture
(see Supplementary Information Part 1).
(g) The second interaction coefficient L (see Supplementary Information Part 1).
(h) The metabolic cost for each resource: this is the quantity of this resource
expended for maintenance in each move.
Note that all of these parameters are input in a later form (ParameterInputForm) in the
case of ac simple system.
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SpeciesForm. This form specifies how species are defined. You can choose either a
sexual or an asexual system. The sexual species concept has been written into the
program but has not yet been investigated or debugged; it is recommended that at this
point you choose one of the two Asexual options
(a) Only a point mutation in SIL or RAL (altering the interaction with other
species or substrates) creates a new species, of which the mutant individual is
the first member. This is the default setting.
(b) Deletion or duplication (altering only the strength of affinity and perhaps the
cost of maintenance) also result in the creation of a new species.
ParameterInputForm. This large and complex form sets the values of most of the
parameters in Uqbar. The complete set of parameters, under the headings used on the
form, is described below. If you have already specified some of these after choosing a
complex system in PPForm, the corresponding boxes will not be visible.
(a) EXTENT
(1) EcoList. The number of slots in the EcoList
(2) ComList The maximum allowable number of taxa existing at any one
time.
(3) History The number of cycles performed in the run.
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(b) DIVERSITY
(4) Res The number of different resources that make up a substrate packet.
The minimum value is 1 and the maximum value is 4.
(5) Menu. The number of different kinds of substrate packaet, each with a
different mix of resources.
(6) MaxAbun. The maximum number of individuals of any genotype in the
initial population.
(7) Diverse. The number of taxa in the initial population.
(8) DivAuto. The number of taxa of Producers in the initial population.
(c) GENETICS
(9) IdlL The length of each IDL
(10)
SilL The length of each SIL
(11)
RalL The length of each RAL
(12)
SilN The number of SIL
(13)
RalN The number of RAL
(14)
MaxSIL The maximum number of SIL that can be borne by an
individual
(15) MaxRAL The maximum number of RAL
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(d) NUTRIENT FLOW
(16)
Plate. The maximum quantity of resource in a a given kind of
substrate packet.
(17)
Ifeed. The initial number of substrate packets.
(18)
Mfeed. The probability that a substrate packet is added in each
move.
(19)
Recycle. The probability that the resources remaining in an
indiidual that has starved to death are recyucled to the system, by being
added to the Resource Pool.
(20)
Decompose. The probanbility that a substrate, when selected as
Agent, decomposes. If it does decompose, it may be recycled or not.
(21)
XREs1 – Xres4. The quantity of (up to) four resources added to
the Resource Pool per move.
(e) RATIONS
(22)
Brat. The quantity of each resource that a newborn individual
receives from its parent.
(23)
Dcrit. The minimum quantity of each resource compatible with
life. If any resource falls below this value, the individual starves to death.
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Bcrit. The minimum level of each resource required for an
individual to give birth. Reproduction is permitted only whemn all
resources meet or exceed this threshold.
(25)
Meta. The cost of maintenance. This quantity of each resource is
expended per move, regardless of the outcome of the move.
(26)
Heta. The factor by which the cost of maintenance of a Predator
exceeds that of a Producer; this can be greater or less than unity.
(f) INTERACTION
(27)
InterSub. The coefficient I in the interation between Producer and
substrate packet.
(28)
LimitSub. The coefficient ILin the interation between Producer
and substrate packet.
(29)
InterAct. The coefficient I in the interaction between two
organisms.
(30)
LimitAct. The coefficient L in the interation between two
organisms.
(g) IMMIGRATION: check Allowed if immigration is to occur.
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Migrant. The probability that a single random organism is added
to the system from an external pool, per move. The species composition
of the external pool is that of the initial population.
(h) DISTURBANCE: check Allowed if disturbance is to occur.
(32)
Disturb. The probability that the system is disturbed (by putting
each of its occupants at risk) per cycle.
(33)
Fatal. The probability that any given individual is killed by a
disturbance.
(i) INVASION: check Allowed if invasion is to occur.
(34)
Invade. Probability that an invasion occurs, per cycle. The
invaders are the external pool, with the same composition as the initial
community.
(35)
Incomer. The probability that in the event of an invasion a
resident is displaced by a random invader, per slot.
(j) RECOMBINATION: check Allowed if recombination is to occur.
(36)
RecSIL. Probability of recombination for SIL.
(37)
RecRAL. Probability of recombination for RAL.
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Note: recombination has not yet been adequately checked.
(k) SPECIATION: check Allowed if speciation is to occur.
(38)
SpeciationRate. The probability given a Sexual species concept
that a newborn individual belongs to a new species.
(l) MUTATION: check Allowed if mutationis to occur; check Reversible if
reversion is allowed.
(39)
DelR. The probability that a SIL or RAL present in the parent is
lost in the newborn individual.
(40)
DupR. The probability that a SIL or RAL present in the parent is
duplicated in the newborn individual.
(41)
RalMutR. The probability that any given bit in a RAL is flipped
in the genome of a newborn individual.
(42)
SilMutR. The probability that any given bit in a RAL is flipped
in the genome of a newborn individual
(m) SPATIAL
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Bell
Disperse. The probability that a newborn individual is allocated a
slot at random (rather than being allocated a slot as near as possible to its
parent).
(44)
Homer. Home range: the region (in slots) on either side of the
Agent within which the Patient is chosen; usaed to create local ecological
interactions.
(45)
Patch. The probabiolity that an incoming substrate packet is
assigned to a pre-defined local patch, or region within the EcoList, rather
than being assigned top a random slot. Used to create environmental
heterogeneity.
`(m) RANDOMIZATION
(46) seed. The random number seed used to minitialize the experiment if
“0” is entered the timer is used.
The default values assigned to most of these parameters will favour the development of a
persistent trophically complex community, although they do not guarantee this. All can
be changed at will.
StartOverForm. This form can be used to start a new run, to continue with a run that
has ended, or to end a run permanently, without the possibility of restarting it. Choose
the option you want.
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UqbarMainForm. This form, which contains most of the code for operating Uqbar,
sets up the initial community. There are three ways of doing this.
(a) As a random community. In this case, the specified number of Producers and
Predators are assembled at random, that is, with random SIL and RAL
sequences. A special case is the origin of a community from a single random
Producer; such a community never develops trophic structure, and this option
is used to configure Uqbar for population genetics.
(b) As a community specified by the comlist_input (organisms) and sublist_input
(substrates) files. These are files that have been created by a previous run,
and this option enables you to investigate more fully any past experiment.
Note: there is a slight bug in this version that makes it necessary to add one
more line of code to each of these input files in order for them to be read in
correctly.
(c) As a community specified by nominating a list of substrates and genotypes
directly in the box on the right-hand side of the form.. You will be prompted
to give the following information. Type the values that you have selected for
each parameter, followed by Enter.
(1) Random number seed (over-rides any previous choice)
(2) The quantity of each “dish” (recipe for substrate packet)
(3) The amount of each resource in each substrate packet
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(4) The abundance of each kind of organism
(5) The number of SIL for each species
(6) The number of RAL for each species
(7) The genotype at each SIL for each species
(8) The genotype at each RAL of each species
When the message box announcing that Uqbar has been configured appears, press “OK”
to begin the experiment
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Part 4. Output and Input Files
Output files
All output files are in csv (comma-dseparated variable) format. In the text box on the
OutputForm, type any string “X” once you have selected a path for files. They will be
then saved as “X “ followed by the following file name.
meter.csv
Output
#1
Parameter values for run
stock.csv
Output
#2
Initial community composition
run.csv
Append
#3
Update of progress of run
activity.csv
Output
#4
summary of different kinds of events
comlist.csv
Output
#5
list of taxa
sublist.csv
Output
#6
list of substrates
ecolist.csv
Output
#7
complete list of occupants of slots
FinalSystem.csv
Output
#8
the food web at the end of the run
InitialSystem.csv
Output
#9
the food web at the beginning of the run
state.csv
Append
#12
population genetics for single genotype
Input
#10
specified menu of substrates
Input files
sublist_input.csv
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comlist_input.csv
Input
#11
specified initial species composition
web_input.csv
Input
#13
characteristics of webs in complex system
In addition, a running summary is printed in the Immediate window. By default this
includes the following variables for each cycle:
Cycle
Number of slots available for occupation
Number of taxon names available
Number of vacant slots
Number of slots occupied byv substrate
Number of slots occupied by Producers
Number of slots occupied by Predators
Number of Producer taxa
Number of predator taxa
Total quantity of resources entering system
Total quantity of resources leaving system
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Part 5. Free parameters in Uqbar
Parameter
Type
Definition
AbList
Long
Number of taxa available for speciation
BCrit(4)
Single
Threshold of resource() for birth
BRat(4)
Single
Ration of resource() donated to newborn
ComList
Long
Number of potential taxa in community
DCrit(4)
Single
Threshold of resource() for survival
Decompose
Single
Prob that substrate Agent decomposes
DelR
Single
Prob that locus is deleted
Disperse
Single
rob of random long-distance dispersal
Disturb
Single
Prob of disturbance per cycle
DisturbPermit
Boolean
Turns disturbance on or off
DivAuto
Integer
Initial number of autotrophic taxa
Diverse
Integer
Initial number of taxa
DupR
Single
Prob that locus is duplicated
EcoList
Long
Number of slots in ecosystem
Fatal
Single
rob that occupant of slot is killed by disturbance
Heta
Single
Excess metabolic cost of heterotrophs
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History
Long
Number of cycles in run
Homer
Single
Region near Agent where Patient can be found
IdlL
Integer
Length in bits of IDL
Ifeed
Long
Initial number of substrate packets
Incomer
Single
Prob incomer arrives, each slot
InteractionMode
String
Sets interactions in trans or in cis
InterAnt
Double
InterAnt = i for predator-prey *
InterSub
Double
InterSub = i for autotroph-substrate *
Invade
Single
Prob of invasion, each cycle
InvadePermit
Boolean
Turns invasion on or off
LimitAnt
Double
LimitAnt = L for predator-prey *
LimitSub
Double
LimitSub = L for autotroph-substrate *
MaxAbun
nteger
Max initial abundance of taxon
MaxRal
Integer
Max number of RAL possible
MaxSil
Integer
Max number of SIL possible
Menu
Integer
Combinations of resources (substrates)
Meta(4)
Single
Metabolic cost per move for resource()
Mfeed
Single
Prob of adding substrate packet per move
Migrant
Single
Prob of adding migrant from pool, each move
MigrantPermit
Boolean
Turns immigration on or off
MutatePermit
Boolean
Allow mutation or not
Patch
Single
Prob that substrate is allocated to local patch
Plate
Long
Max quantity of resource per substrate packet
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PPTransitive
Boolean
True for IDL-based interaction, False for SIL-based
RalL
Integer
Length in bits of each RAL
RalMutR
Single
Prob of point mutation per bit at RAL
RalN
Integer
Number of RAL among aborigines
RecombinePermit
Boolean
Allows recombination or not
RecRal
Single
Prob of recombination in RAL region
RecSil
Single
Prob of recombination in SIL region
Recycle
Single
Prob that resources recycled from starved organisms
Res
Integer
Number of distinct kinds of resource
Revert
Boolean
Point mutation reversible
Seed
Long
Random number seed
SetUpMode
String
Random or Specified input
SilL
Integer
Length in bits of each SIL
SilMutR
Single
Prob of point mutation per bit at SIL
SilN
Integer
Number of SIL among aborigines
SourceWebNumber
Integer
number of separate source webs in complex systems
SpeciationPermit
Boolean
Sexual speciation permitted
SpeciationRate
Single
Prob sexual speciation per birth
SpeciesConcept
String
Sexual or Asexual species concept
TaxBroad
Boolean
Nature of asexual species concept
VacList
Long
Number of slots available for occupation
WebMutation
Single
Prob per cycle that taxon is assigned to new web
XRes(4)
Single
Quantity of 4 resources added to rpool per move
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* Interaction model is a two-parameter negative exponential:
Prob of interaction = L [1 - exp(- i * silfit)]
where silfit is number of complementary matches between SIL of Agent and Patient, i
is the coefficient of interaction and L is the limiting probability approached as the number
of matches becomes large. L and i for interactions with substrates and with other
organisms are different.
This is the only equation in Uqbar
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Part 6. Elementary properties of Uqbar
The purpose of Uqbar is to explore the behaviour of evolvable communities that lie
beyond the range of current models. It can be a credible simulacrum, however, only if its
behaviour in simple situations conforms to well-established theory.
A series of
elementary exercises were therefore conducted to validate more ambitious experiments.
1. No organisms, single substrate. With no decomposition there is no loss of substrate
from the system, which persists indefinitely unchanged.
With no external input of
resources, decomposition reduces the quantity of substrate until the system is empty.
Recycling substrate resources to the resource pool slows down this process but cannot
prevent the emptying of the system. When resources are supplied to the Resource Pool
from an external source, the concentration of substrate in the ecosystem depends on the
rate of supply relative to the resource content of a resource package.
2. No organisms, two substrates. The frequency of the resources in the ecosystem
approaches their frequency in the menu. If any resource required to make substrate has
no external source of supply, substrate levels in the ecosystem fall to zero.
3. Single Producer, single substrate. A single Producer able to consume the substrate
grows logistically, while resource concentration declines asymptotically towards some
positive value. The rate of growth and the carrying capacity depend on the input of
substrate to the system, and are affected by the rate of extraneous resource input to the
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resource pool, the rate of transfer of substrate from the pool, the proportion of resources
recycled and the rate of spontaneous decomposition of substrate in the ecosystem. These
interact in a straightforward manner. Thus, the system is resource-limited through the
Resource Pool when the demand created by input to the ecosystem is large relative to
allochthonous supply. When this demand is relatively small, population growth depends
on the rate of substrate input. Population number depends on the rate of substrate
decomposition, with fewer individuals supported when the rate of decomposition is high.
The efficiency of substrate use depends on the metabolic cost, which is
determined by the number of RAL and the metabolic cost per RAL. Population increases
as metabolic cost declines. Moreover, populations with lower metabolic cost drive down
substrate to lower levels.
4. Two identical Producers, single substrate.
When two identical Producers are
introduced at equal frequency the outcome depends on the extent of the ecosystem. If the
ecosystem is fairly extensive (more than 5000 slots) the two coexist for long periods of
time (thousands of cycles) with little fluctuation in frequency. In smaller ecosystems the
fluctuations become greater, until in very small systems (less than 50 slots) one or the
other becomes extinct through demographic stochasticity within a few tens or hundreds
of cycles .
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5. Disturbance and rescue by migration. Severe disturbance destroys the community,
which can then regrow from migrants. Immigration also prevents permanent stochastic
extinction of species.
6. Two dissimilar Producers, single substrate. The type with fewer RAL increases in
frequency because its maintenance cost is lower. As it does so, substrate declines as the
more efficient form spreads, before stabilizing at a lower level once the less efficient
form has been eliminated. The log frequency ratio of the two forms declines linearly
through time. The slope of this plot can be used to estimate the selection coefficient; it is
–0.03 when the two forms differ by a single RAL, and is additive for larger differences.
7. Obstruction of selection by immigration and invasion. Immigration (defined on p
7) slows down the fixation of the fitter type and may prevent the loss of the less fit type.
Invasion (defined on p 8) creates a jagged change in frequency through time because it
causes the replacement of a fraction of the resident population by a cohort with the
composition of the base population.
8. Interaction strength. All the above results were obtained with strong interaction in
which a single complementary RAL assured resource capture. Weaker interaction retards
the replacement of a less efficient with a more efficient type.
9. Two Producers on two substrates. If there is no substrate decomposition, two
specialized Producers consuming different substrates coexist, forming two separate
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systems. Each grazes its substrate down to the point where resupply from the Resource
Pool balances consumption. When the two are equally efficient the replacement level is
the same for both substrates. If decomposition occurs, then the type specializing on the
substrate with the lower supply rate is eliminated. Thus, the dynamics of two complete
and exclusive specialists is determined by the accumulation of substrate.
When
accumulation is undisturbed by decomposition then each substrate constitutes a refuge
and selection is negatively frequency-dependent, with the frequencies of the types
approaching substrate input frequencies.
When there is little or no accumulation
frequency-dependence disappears and the type specializing on the substrate with the
greater rate of supply is fixed.
10. Three Producers on two substrates. Two Producers are complete and exclusive
specialists; the third is a generalist able to consume both substrates. In the simplest case,
the two substrates have equal resource composition. The cost of generalization is then the
number of extra RAL required by the generalist. If there is no cost, the generalist is fixed.
If the cost just balances the benefit (e.g. 2 RAL for the generalist and 1 RAL for each
specialist, with equal supply rates of the two substrates) there is a neutral equilibrium. If
the cost falls short of the benefit, the generalist is fixed. Otherwise, the crucial factor in
competition is the variance of resource composition among substrates, which favours the
generalist: the greater the variance, the more rapidly the generalist spreads, unless the
metabolic cost of carrying more RAL prevents this.
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11. One Producer on a single substrate, with mutation.
Bell
There is a progressive
decrease in the number of RAL through deletion, so that increasingly frugal types evolve,
ending in the fixation of the optimal single-RAL type.
12. One Producer on two substrates, with mutation. A type able to exploit the unused
resource soon emerges by point mutation and spreads to equal frequency if the substrates
have equal rates of production.
13. One substrate, one Producer, one Predator. The predator-prey interaction can be
tuned through the strength of interaction between predator and prey, or between organism
and substrate, or through the additional metabolic cost of heterotrophy.
(a) Strong interaction. Dynamics are always oscillatory. With single SIL there
is a narrow zone of coexistence where Predators have high metabolic cost relative
to Producers. If this cost is too great, the Predator becomes extinct fairly rapidly.
If the cost is low, there are feeble cycles with either the Predator or the Producer
going extinct; if the Producer goes extinct first the Predator soon follows, of
course. The system is readily rescued by low rates of immigration.
(b) Weak interaction between predator and prey. There are persistent, rather
low-amplitude cycles even when the additional metabolic burden of predation is
low. Thus, weaker predator-prey interaction stabilizes dynamics in a region that
would otherwise be unstable.
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14. One substrate, one Producer, one Predator, with mutation.
RAL,
Bell
Beginning with a 4-
4-SIL Producer with one RAL capable of binding to the sole available substrate, and
a 4-SIL Predator capable of eating the Producer, with strong interaction in cis, the
consequences of genetic change are as follows.
(a) Superfluous RAL and SIL tend to be removed by deletion, since this
reduces metabolic cost. Deletion of the sole RAL or SIL required for resource
exploitation is lethal, however.
(b) Duplications are deleterious because they increase metabolic cost. They
are conditionally deleterious, in that they might provide a basis for adaptive
divergence in the future, given a beneficial point mutation.
(c) Point mutations are usually neutral, because no alternative substrates or
prey exist. Mutations at required SIL or RAL are lethal. One class of point
mutation is highly beneficial, however: mutation of the Producer RAL to a state
that the Predator does not recognise.
The initial community of two genotypes quickly diversifies, principally through neutral
point mutations, mildly deleterious duplications, and beneficial deletions. The crucial
event is a point mutation to resistance in the Producer, which spreads rapidly in the
population. As it does so, selection continues to favour more frugal genotypes among the
still numerous susceptible Producers and the Predators. With the rise of the resistant type
the population of Predators declines, and a new virulent type able to consume the new
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resistant Producers usually fails to appear. This seems to be mainly because its rate of
reproduction is very low in the absence of susceptible prey, and mutation occurs only at
replication. (Note that the effects of mutation on fitness are asymmetrical: any random
change in SIL sequence makes a Producer resistant to its current Predators, whereas only
the single appropriate mutation in a Predator will restore its ability to capture the Prey.)
The Producer, on the other hand, has a high birth rate because it is able to consume
substrate, even though it has a high death rate if it is vulnerable to predation. The type
with the greater rate of turnover thus has the evolutionary edge, and the Predator becomes
extinct sooner or later. Resistant and susceptible Producers are then neutral, and frugal
deleted versions of both increase in frequency, eventually dominating the population.
15. One substrate, two Producers, two specialist Predators. The most interesting
system is that in which the more frugal Producer is vulnerable to the more efficient
Predator. This was accomplished by letting Producer 1 have a single RAL and Producer 2
two identical RAL, while under weak predator-prey interaction Predator 1 has two SIL
both complementary to Producer 1 whereas Predator 2 had two SIL only one of which
was complementary to Producer 2. The source web Producer 1 - Predator 1 is then more
frugal in pure culture than the alternative source web Producer 2 - Predator 2, because
Producer 1 is reduced to lower levels by its predator. The complete system is highly
oscillatory (given strong interaction in cis), the more frugal component Producer 1 Predator 1 having the greater variance because it involves the stronger interaction. The
usual outcome is that Predator 1 suffers stochastic extinction, releasing Producer 1, which
then completely displaces Producer 2 - Predator 2. The system persists longer when the
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Producer-substrate interaction is weak, although sooner or later a deeper trough than
usual in the Producer 1 population results in the loss of Predator 1.
Weak interaction
together with a modest level of immigration secures long-term persistence; with an
immigration rate of 0.001 per move only about 5% of new creatures are immigrants (and
only 0.5% are Predator 1 immigrants), but an ecosystem with 10,000 slots maintained
diversity with no sign of a systematic trend in frequencies for 5000 cycles.
16. Many Producers and many Predators. Communities with hundreds of different
species may or may not retain trophic complexity, depending on the values of parameters
that affect metabolism and prey capture. Figure 4 of the article shows how capture
probability affects the persistence of Predators, given a moderate maintenance cost that
permits about ten attempts to locate and capture prey before an individual starves to
death. When capture probabilities are low, Predators starve and are maintained only as
rare immigrants at very low levels. At modest capture probabilities, however, Predators
are able to survive, and the community remains trophically complex. Thus, the long-term
persistence of complex food webs in Uqbar does not require some unrealistic or unduly
restrictive combination of parameters. It is only for the highly specific interactions in
Long-Cis systems that very high capture probabilities are required. These high capture
probabilities generate strong coupled oscillations in Predator and Producer, which in
closed systems often leads rapidly to the extinction of Predators, with or without the
extinction of Producers. The community is readily rescued, however, and retains trophic
complexity, by very low levels of immigration, of the order of a single individual per
cycle.
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Part 7. Optimal number of SIL
The model used for the probability of capture Pcap as a function of complementarity k is:
Pcap = L (1 – exp(-ik)) … (1)
where L and i are given parameters. Define E as the probability of encounter with
potential prey, C as the metabolic cost per move, and B as the benefit derived by the
predator (metabolic content of prey). The expected gain G per move is then:
G = E Pcap B - C … (2)
This is affected by the number of SIL borne by the Predator, Npred, through
complentarity k and metabolic cost C, both of which increase with Npred.
Complementarity will be equal to the product of the probability that a given Predator SIL
is complementary with a given prey SIL (equal to the reciprocal of the length of the SIL,
SILL), the number of potentially complementary prey SIL (Nprey, determined by cis or
trans interaction), and the number of predator SIL. Hence dk/dNpred = Nprey/SILL. If
each additional SIL incurs the same incremental metabolic cost, then dCmet/dNpred = C.
Substituting these results in (2) yields
dG/dNpred = Ebi(L -= Pcap) (Nprey/SILL) - C … (3)
Setting this to zero and substituting for Pcap gives the optimal number of SIL as
Npred = - K loge [(1/E) (C/B) K] … (4)
where K = (1/iL) (SILL/Nprey}.
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