Creation of Worlds — Appendices. Recommended Notation in Population-Ecological Models

Recommended Notation in Population-Ecological Models
The notation listed below is used in the population-ecological models constructed throughout this course. The Latin alphabet letters that appear in this notation list are highlighted in colour: A a B b C c D d E e F f G g H h I i J j K k L l M m N n O o P p Q q R r S s T t U uV v W w X x Y y Z z. As you can see, few unused letters remain...
In many models in this course, the steps of restructuring the model population during a single cycle are denoted using Greek letters. For example, changes occurring in the abundance of a particular group of individuals at cycle t may be represented as follows: αtnga → βtnga → γtnga → δtnga → ωtnga. Here n denotes the abundance of a particular group; α and other Greek letters denote steps of restructuring within the cycle; t denotes the cycle; g denotes the genotype or other characteristic by which the given group of individuals is distinguished; a denotes the age of individuals in that group.
In many cases an uppercase letter denotes a characteristic of the entire model population, while the corresponding lowercase letter denotes the same characteristic for some subgroup. Thus, of3 is the fecundity of three-year-old females of genotype f; oF3 is the fecundity of all three-year-old females (when it is identical for individuals of different genotypes); and O is the total number of offspring in the entire model population. However, in some cases uppercase and lowercase letters denote different characteristics. For example, P denotes the number of pairs, while p denotes probability.
To make the proposed notation easier to remember, in most cases each symbol is associated with an English word. Some of the notation presented here is used in modelling hemiklonal population systems (HPS) of the hybridogenetic complex of water frogs (Pelophylax esculentus complex).
A — age. The uppercase letter is used in equations of linear individual growth: ~L = a + b*A; here a and b are the coefficients of the linear equation.
a — age (in notation associated with population dynamics).
nga — abundance of individuals of genotype g and age a.
mataf — age of onset of reproductive participation for females of female genotype g.
matam — age of onset of reproductive participation for males of male genotype m.
maxag — maximum lifespan of individuals of genotype g.
B — big — in individual growth equations, notation for the large-size strategy: ~BL = Ba + Bb*A.
b — breed — fecundity of females; the number of offspring a female can produce in one reproductive cycle.
bf3 — fecundity of three-year-old females.
c — competitiveness — relative competitive ability. Relative competitive ability cga is specified instead of absolute competitive ability c'ga, because c'ga depends on the composition of all individuals in the habitat.
maxc' — maximum competitive ability; the competitive ability of the group of individuals for which the probability of surviving the competitive reduction step is maximal.
cga — relative competitive ability: the ratio of the probability of an individual of genotype g and age a surviving competitive population reduction to the corresponding probability for the most competitive individuals: cga = c'ga / maxc'.
c'ga — competitive ability: the probability of an individual of genotype g and age a remaining alive after competitive population reduction.
D — demand — total resource demand of all individuals in the model. D = Σ(nga × dga).
dga — resource demand of individuals of genotype g and age a.
E — esculentus — in models describing population systems of water frogs, the presence of Pelophylax esculentus in the hemiklonal population system (HPS).
E — explanation — in descriptions of model structure, an information field containing the model name and necessary explanatory notes.
e — effectiveness — coefficient of male reproductive probability. Specified instead of the actual male reproductive probability e'ma, which depends on the composition of all males in the habitat.
maxe' — maximum reproductive probability, characteristic of the most reproductively successful group of males.
ema — coefficient of reproductive probability for males of male genotype m and age a; the ratio of the reproductive probability of these males to that of the males for which it is maximal: ema = e'ma / maxe'.
F — females — total abundance of sexually mature females.
f — female — a particular female genotype.
G — gap — discrepancy between the model approximation and empirical data.
g — genotype — a particular genotype.
H — hermaphrodites — total abundance of hermaphrodites.
h — hermaphrodite — a particular hermaphroditic genotype.
I — invariant — in descriptions of model structure, the invariant part of the model.
i — inbound — the number of individuals arriving at a given habitat; immigrants.
tiga — the number of immigrants of genotype g and age a arriving at cycle t.
j — the number of resource categories in the model.
jpg — the probability that a unit of resource of category j is consumed by an individual g (or an individual of genotype g).
K — carrying capacity of the environment; the number of individuals that can survive in the given habitat.
k — total number of genotypes considered in the model.
L — lessonae — in models describing population systems of water frogs, the genome of Pelophylax lessonae; the presence of Pelophylax lessonae in the hemiklonal population system (HPS).
L — length — in models describing growth of individual organisms, body length. With a tilde, the calculated body length expected on the basis of a particular individual growth equation: ~L = a + b*A.
l — loveliness — coefficient of female reproductive probability. Specified instead of the actual female reproductive probability l'fa, which depends on the composition of all females in the habitat.
maxl' — maximum reproductive probability, characteristic of the most reproductively successful group of females.
lfa — coefficient of reproductive probability for females of female genotype f and age a; the ratio of the reproductive probability of these females to that of the females for which it is maximal: lfa = l'fa / maxl'.
M — males — total abundance of sexually mature males.
m — male — a particular male genotype.
N — number — total abundance of individuals in the habitat. If abundance changes at different stages of the model cycle, Greek letters are used to denote it at different stages: αN → βN → γN → δN → εN → … → ωN. Here αNg = Σ(αnga), etc.
n — number — abundance of a particular group. nga — abundance of individuals of genotype g and age a. nF2 — abundance of two-year-old females. If group abundance changes at different stages of the model cycle, Greek letters are used: αnga → βnga → γnga → δnga → εnga → … → ωnga.
O — offspring — total number of offspring per reproductive cycle.
Og — number of offspring of genotype g.
o — offspring — proportion of offspring of a given genotype produced by a given pair of parents.
og(ff,mm) — proportion of offspring of genotype g produced by a female of female genotype f and a male of male genotype m.
P — pairs — number of pairs.
p — probability.
1p1-3 — cumulative probability of consumption of one unit of category-1 resource by individuals (or groups of individuals) 1 through 3.
q — quota — relative probability. The ratio of relative probabilities of consuming a given resource unit is proportional to the ratio of the probabilities of such consumption: jpg = jqg / Σ(jqg).
R — ridibundus — in models describing population systems of water frogs, the genome of Pelophylax ridibundus; the presence of Pelophylax ridibundus in the hemiklonal population system (HPS).
r — reproduction — the Malthusian parameter; biotic potential.
S — small — in individual growth equations, notation for the small-size strategy: ~SL = Sa + Sb*A.
s — survival — survivorship. A parameter describing non-competitive mortality.
sga — the proportion of individuals of genotype g and age a that, in the absence of competitive mortality, survive to the next modelling cycle.
T — treason — the number of females that one male can fertilise in a single reproductive cycle.
t — time — time; cycle number of the model.
αtnga — initial abundance of individuals of genotype g and age a at cycle t of model operation.
U — use — the amount of resource consumed during a given cycle by all individuals in the model. U = Σ(nga × uga).
uga — the amount of resource consumed by individuals of genotype g and age a.
V — volume — total amount of resources available to the model population.
V — variable — in descriptions of model structure, the variable part of the model, which contains the assumptions tested during modelling.
W — way — the mode or scenario of population reduction for a given set of individuals during competitive reduction.
W — in descriptions of model structure, the system of transformations that converts input parameters into output parameters: W(X) = Y.
w — wad — the proportion of eggs in a clutch that a male is capable of fertilising.
wma — fertilisation capacity of a male of male genotype m and age a.
X — designation of the female sex chromosome and the genome carrying it.
XR — the genome of Pelophylax ridibundus with the female sex chromosome.
X — in descriptions of model structure, input parameters.
x — the number of female genotypes considered in the model.
Y — designation of the male sex chromosome and the genome carrying it.
YL — the genome of Pelophylax lessonae with the male sex chromosome.
Y — in descriptions of model structure, output parameters.
y — the number of male genotypes considered in the model.