七鳃鳗种群模型分析

翻译这篇摘要
Population analysis of lampreys: a discrete population dynamics model based on age grouping
Abstract
In this paper, we model the ecosystem of lampreys and analyze the impacts of changes in the
sex ratio of lampreys on populations and ecosystems.First, we establish a discrete population dynamics model with age groups. Based on the biological characteristics of lampreys, we divide
the lampreys population into seven age groups, and consider the ecosystems in which they live as
well as bait for larvae, competitors for larvae, bait for adults, competitors for adults, and artificial
fisheries. The model takes into account the fact that the sex ratio varies according to the external
environment.
For task 1, we focus on the effects of changes in the sex ratio of lampreys on the larger ecosystem. The results of the discrete population dynamics model reflect that the changeable sex ratio of
lampreys is conducive to the stabilization of its population size, making it dominant in the ecosystem. Compared with the changes in population size before and after the invasion of lampreys in an
ecosystem, we conclude that the variable sex ratio of lampreys as an invasive species is detrimental
to the native population of the ecosystem, but at the same time, the larvae of lampreys can purify
the water quality and promote nutrient cycling in the benthic environment.
For task 2, we apply our model by focusing on the advantages and disadvantages of the biological characteristics of variable sex ratio, metamorphosis, one-time reproduction and migration of
lampreys for their own populations. Through the discrete population dynamics model to calculate
the situation of changing environmental resources and sudden changes in the external environment,
we obtain that the population of lampreys with metamorphic and variable sex ratio is more stable,
and the population of lampreys with metamorphic is more capable of realizing the full use of environmental resources. By simulating the impacts of human influence on the migratory spawning
process of lampreys and the drastic decrease in the number of spawners in a given year, we conclude
that the migratory characteristics of lampreys and the disadvantages of one-time reproduction are
that the migratory process may be dangerous, and that the larvae of lampreys are habitat-dependent,
and that the low survival rate of a given generation puts the entire population at risk.
For task 3, we pay a close attention on the effects of the variable sex ratio of lampreys on
ecosystem stability. We take the resistance stability, resilience stability and sustainability of the
ecosystem as evaluation indexes. Numerical simulations of the discrete population dynamics model
show that: the degree of ecosystem fluctuation is 23.28% and 33.19% respectively when the number
of lampreys and plankton populations with variable sex ratios is abruptly changed, and the recovery
time is 18 years and 28 years respectively. Compared with the numerical simulation results when
the sex ratio of lampreys is not variable, the lampreys population with variable sex ratio makes
the ecosystem have stronger resistance stability and recovery stability. The ecosystems in which
the lampreys population with variable sex ratio are sustainable after the introduction of artificial
interventions.
For task 4, we mainly analyze the effects of variable sex ratios of lampreys on other species with
our model. We add parasite populations to a discrete population dynamics model, and the model
results show that the variable sex ratio of lampreys favors other parasite organisms and populations.
In conclusion, the changes in the sex ratio of lampreys are beneficial to ensure the stability of
their population numbers when facing harsh environments. This, in turn, contributes to the stability
and sustainability of the larger ecosystem.
Keywords: Discrete Population Dynamics Modeling; Lampreys Sex Ratio; Lampreys Metamorphosis; Ecosystem Stability

继续翻译目录
Contents
1 Introduction 3
1.1 Problem Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Restatement of the Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Our Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Assumptions and Notations 4
2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 The Lampreys Ecosystem Model 5
3.1 Model Preparation: Age Grouping of the Lampreys Population . . . . . . . . . . . 5
3.1.1 Age Profile of Lampreys and its Subgroups . . . . . . . . . . . . . . . . . 5
3.1.2 Lampreys Ecosystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Discrete Population Dynamics Model Based on Grouping with Age . . . . . . . . 6
3.2.1 Ecosystem Modeling of Larval Populations in Lampreys . . . . . . . . . . 6
3.2.2 Lampreys Ecosystem Modeling of Adult Populations . . . . . . . . . . . . 8
3.2.3 External Artificial Intervention Model . . . . . . . . . . . . . . . . . . . . 8
3.3 Model Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Task1: Impact on the Larger Ecological System 10
4.1 Analysis of Changes in Population Gender Ratio . . . . . . . . . . . . . . . . . . 10
4.2 The Impact of the Ecosystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3 Result Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 Task2: Advantages and Disadvantages of Populations 14
5.1 Advantages of Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2 Disadvantages of Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6 Task3: Impact of Sex Ratio on Ecosystem Stability 17
6.1 Classification of Ecosystem Stability . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.2 Ecosystem Resistance Stability and Resilience Stability . . . . . . . . . . . . . . . 18
6.3 Sustainability of Ecosystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
7 Task4: Impact of Changing Sex Ratio on Other Species 21
7.1 Add Parasite Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
7.2 Model Solution and Result Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 21
8 Analysis on Model’s Sensitivity 23
8.1 Impact Analysis of Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . 23
8.2 Effects of Human Intervention and Parasite Populations on Models . . . . . . . . . 23
8.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
9 Strengths and Weaknesses 24
References 25

继续翻译

1 Introduction
1.1 Problem Background
In nature, the sex ratio of different species is different. Most species have a sex ratio of 1:1, but
the sex ratio of sea lampreys changes in response to changes in the external environment. We call
this phenomenon of changing the sex ratio of a species to adapt to environmental demands adaptive
sex ratio change.
Lampreys live mainly in coastal and freshwater areas in most temperate regions. Lampreys
significantly impact ecosystems as parasites in several lake habitats, and as a member of the food
chain, providing a source of food for areas such as Scandinavia, the Baltic Sea, and the Pacific
Northwest of North America.
The rate of development of the larval stages of lampreys determines their sex ratio, and their
growth rate is affected by food availability. When the food supply is insufficient, the population’s
sex is dominated by males, with a proportion of about 78%; when the food supply is sufficient, the
proportion of males is about 56%, and the proportion of males and females is almost equal.
Figure 1: Sex Ratio of Lampreys in Different Environments
1.2 Restatement of the Problems
For the problem of sex ratios in lampreys and their dependence on local conditions, we develop
plausible mathematical models that provide insights into the interactions that arise in ecosystems
and answer the following questions:
• Analyze the effects on the ecosystems in which lampreys are found when their sex ratio is
correlated with their population size.
• Analyze and justify the strengths and weaknesses of the lampreys population with the model
that has been developed accordingly.
• Analyze the impact of the lampreys sex ratio on ecosystem stability, considering that it varies
according to the external environment.
• Explain whether lampreys can provide an advantage to other species in the ecosystem (e.g.
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parasites) based on the specificity of the sex ratio of their populations

2 Assumptions and Notations
2.1 Assumptions
• Assumption 1: We assume that all lampreys were bred in the seventh year and that the
parents died at the end of the breeding.
Justification: The lampreys are one-time reproducing organisms and have a lifespan of seven
years, so to make it easier to calculate the number of newborn hatchlings produced by the
lampreys’ reproduction, we assume that all of them reproduce in their seventh year.
• Assumption 2: We assume that lampreys’ change of gender is accomplished the instant they
enter their fifth year.
Justification: We have grouped lampreys by age in our model and calculated the population
size of lampreys of each age in yearly intervals, so for easy calculation of the number, we
consider the behavior of changing the sex of lampreys to be done instantaneously.
• Assumption 3: We assume that lampreys have no natural predators, i.e., we do not consider
lampreys as bait but are mainly threatened by human activities.
Justification: Larval lampreys live in relatively secretive environments and are largely pro￾tected from regular predation, and adult lampreys are relatively less exposed to threats from
natural enemies due to their size and habits. We therefore do not consider predator popu￾lations of lampreys, but instead add an artificial intervention term to model the impact of
lampreys populations on human activities.
• Assumption 4: We assume that the parasite population of lampreys only parasitizes lam￾preys’ mature bodies.
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Justification: Existing studies on parasites of lampreys show that more than 80% of parasites
are found in lampreys’ mature body populations, and only 11% of parasites are present in
lampreys’ juvenile populations, so to simplify the model we mainly consider the effect of
parasites on lampreys mature body populations.
2.2 Notations
Table 1: Notations Description
Notations Definition
Mt Proportion of females
βm Natural mortality rate of larvae
βB Natural mortality rate under bait deprivation
α Reproduction coefficient
rx Natural rate of growth