在未來 50 年之內， 什麼是人類面臨的最大挑戰？

1. 在未來50年之內，什麼是人類面臨的最大挑戰？在未來50年之內，什麼是人類面臨的最大挑戰？ “由梅肯研究院 (Milken Institute)所主辦的 「2006年全球展望大會」上，來自全球逾2600名各專業領域代表一致認為， 環保將是最大的挑戰， 水及能源短缺會直接衝擊全球文化、生活、經濟等多個層面。” (95/5/15 國科會國際科技合作簡訊電子報) 水域生態系研究!

2. Why do we use ecological models? 生態模式是真實世界的簡化版，模擬未來 Understanding Data synthesize Model Questions ( Future) prediction management model computer simulation ( Past and Now)

3. Ocean Scienceat the new millennium The NSF’s summary in July 2001 • “The development of models with multiple application is a priority. A special effort is needed to develop models that link different parts of the ocean system. Linked models that tie together physical, geological, biological and chemical systems show great promise and are likely to grow in importance in oceanographic research.”

4. IntroductionThemes of ecological modeling • What is an ecological model? Ecology is concerned with the interactions between an organism and its environment and the consequences of these interactions. An ecological model must be able to describe changes in numbers to varying degree of accuracy and generality.

5. Reasons formathematical language • Ecological models are phrased in mathematical language. • Brevity and formality of description • Manipulation of the model • Discovery of emergent properties not apparent from non-mathematical reasoning

6. Realistic models • Tactical models (戰術模式): Attempt to measure all the relevant factors and determine how they interact with the target population or community. • A black box: we do not know why it produces the answer • The main value is that it can speed up natural processes (100 years). • Two options nearer to the mechanism • Strip down the model to its statistically significant components • Alter variables systematically and see the output responds quantitatively

7. Unrealistic models • Strategic models (策略模式) • Using mathematical modelling as a way of formalizing generalizations about the ecological systems of interest. • Example: Lotka and Volterra predator-prey models • If we do not understand the mode of operation of strategic models, then we can never understand why the particular realistic models do what they do.

8. Discrete and Continuous time • Continuous time: it can be divided up into smaller units Appropriate to populations of individuals with asynchronous and continuous reproduction Differential equations • Discrete time: indivisible in units of e.g. years Appropriate to populations composed of individuals with synchronized reproduction at regular time intervals Difference equations

9. Deterministic vs. Stochastic Processes • Deterministic models (確定性模式): In a deterministic world everything should be predictable. • Stochastic models (機率模式): entirely random in their occurrence. • The randomness of these events may depend on the time-scale used. • Emphasize the deterministic modelling for two reasons: • The analysis of stochastic processes is more complex • We prefer to think of a primarily deterministic world clouded by stochasticity where the use of the simplest realistic model is appropriate.

10. Testing ecological models • Straightforward: the output of a model should be compared to the observed dynamics in the field. • In practice, there are two problems: • Model and field will show some agreement. • There are rarely sufficient field data • field, microcosm and mesocosm experiments may complement the modelling. • Not only can experiments be used to parameterize and test the predictions of models and suggests the construction of new models, but also models can be used to indicate the design of field experiments.

11. Applications of ecological models • Physiological ecology Foraging, digestion rates, allometric growth, rates of translocation and transpiration • Population ecology Biological control, harvesting of species, spread of invasive species, disease • Community ecology Community stability and diversity, coexistence and species richness • Ecosystem ecology Nutrient cycling, effects of global change

12. P-I curve Pm GCPP (P) P = Pm × tan h (α × I / Pm) P: GCPP (Gross community primary productivity) Pm: maximum GCPP α: initial slope of curve I: light intensity α Light intensity (I) (Jassby & Platt, 1976)

13. Life tables and survivorship curves • To determine how long, on average, and individual of a given age could be expected to live are called life tables. • One way to construct a life table is to follow the fate of a cohort, a group of individuals of the same age, from birth until all are dead. • A graphic way of representing some of the data in a life table is to draw a survivorship curve, a plot of the numbers in a cohort still alive at each age.

14. Population Growth Models • Under ideal conditions, the population grows at the fastest rate possible, because all members have access to abundant food and are free to reproduce at their physiological capacity. This maximum population growth rate, called the intrinsic rate of increase, is symbolized as rmax. • Population increase under these conditions is called exponential population growth. dN/dt = rmax N

15. A logistic model of population growth incorporates the concept of carrying capacity • There is a limit to the number of individuals that can occupy a habitat. Ecologists define carrying capacity as the maximum population size that a particular environment can support with no net increase of decrease over a relatively long period of time. • Carrying capacity, K, is a property of the environment. It varies over space and time with the abundance of limiting resources.

16. The logistic growth equation • A model of logistic population growth incorporates the effect of population density on r, allowing it to vary from rmax under ideal conditions to zero as carrying capacity is reached. • (K – N) tells us how many additional individuals the environment can accommodate, and (K – N)/K tells us what fraction of K is still available for population growth. • dN/dt = rmax N [(K-N)/K]

17. How well does the logistic model fit the growth of real populations? • Some of the basic assumptions do not apply to all populations. • Allee effect, in which individuals may have a more difficult time surviving and reproducing if the population size is too small. • The logistic model also makes the assumption that populations approach carrying capacity smoothly.

18. The occurrence and severity of density independent factors are unrelated to population density • Density-independent factors are unrelated to population size; they affect the same percentage of individuals regardless of population density. • Fires and hurricanes

19. A mix of density-dependent and density-independent factors probably limits the growth of most populations • Populations were reasonable stable over the three-decade span, but major declines occurred following unusually cold winters. • The relative importance of density-dependent and density-independent controls may also vary seasonally. • A synergistic combination of density-dependent and density-independent factors accounts for marked fluctuations in some populations of the Dungeness crab.

20. Regular boom and bust cycles • Some populations of insects, birds, and mammals fluctuate in density with remarkable regularity. • One idea is that crowding regulates cyclical populations, perhaps by affecting the organisms’ endocrine systems. • Another hypothesis is that population cycles are caused by a time lag in the response to density-dependent factors, creating large fluctuations of population size above and below carrying capacity. • An alternative hypothesis for the snowshoe hare cycle is that high hare population density causes a deterioration in the quality of their food.

21. Dynamics of ecological communities • Ecological community（群集）：all individuals of interacting species in a given area. • Guilds（同功群）：具有相似要求和覓食習慣，因而在群落中具有相似角色的族群。 優點：種間競爭可能發生在這些族群之中。 • 舉例：群落包含，以一種植物為食的食草昆蟲依賴集團，植物本身，以及食草昆蟲的天敵。 • 目的：發展模式以處理兩種以上的族群間關係。個別族群的動態與整個群落的動態、穩定性與結構。

22. Three related problems • consider the full range of interactions between species.(0/＋/－) • assign a strength to these interactions.(＋＋) • the sheer number of species which may be involved.

23. Models of interspecific competition 舉例：Crombie(1945，1946)，beetles confused flour beetles (Tribolium confusum ) 雜擬穀盜（擬步甲科） sawtoothed grain beetle (Oryzaephilus surinamensis) 鋸穀盜（鋸穀盜科）2.5-3.5mm

26. logistic equation dNi / dt = ri Ni (1- Ni / Ki ) β12= the coefficient of competition example β12 ＝ 0.5 each individual of species 2 is equivalent to 1/2 of an individual of species 1.

27. =0 zero growth isoclines 等傾線dN1 / dt = 0 and dN2 / dt = 0 N1*=K1-β12N2*

28. 種間競爭的結果 dN1 / dt = 0

29. Models of succession Succession is the directional change in plant and animal species over time in a particular area. Mathematical models of this phenomenon have represented it as a Markov chain. This involves determining the probability that these replacement probabilities do not change with time. For example, Horn (1975,1981)gave the values for 50-year tree-by-tree replacement between four species.(Table 5.4a)

30. The model can be represented in matrix form: = (transition probabilities) Vt+1transition probability matrix Vt The models predict a stationary end-point, i.e. there will be a fixed ratio of GB to B to RM to M.

31. Iterations over different periods of time and the end-point of the Horn example are given in Table 5.4(b). The predicted end-point compares favorably with the observed composition in old growth forest.

32. Frelich et al.(1993) examined the long-term effects of tree-by-tree replacement processes on spatial patterns in a forest. Transition probabilities were found to be depend on the species composition of a local neighborhood (10m radius). • Simulations were undertaken demonstrating that the patches of sugar maple and hemlock observed in the field could have developed from an initial random mix.

34. Future projections for Mexican faunas under global climate change scenarios by A. T. Peterson et al. Nature 416: 626-629, 2002

35. 全球氣候變化非常迅速，且無法預期會帶來什麼樣的結果全球氣候變化非常迅速，且無法預期會帶來什麼樣的結果 影響生物多樣性 分布的限制（distributional limitation) 分布的改變 (distributional shifts) 生物多樣性的減損 (biodiversity losses) • 然而，不論模式（modelling）的焦點是在單一物種或是整個生態系，雖然有一些動物相（fauna-wide）的初步監測資料，以及一些物種為了調適氣候變化而遷移（climate change-mediated shifts）的證據， • 但是對於氣候變化對物種分布（species’ distributions）的影響仍了解不多，甚至對於群落層級（community-level）更是幾乎完全沒有探討

36. 灰色 –appropriate both at present and under the scenario of change 白色 –inappropriate both 紅色 –appropriate at present, but predicted to become inappropriate 藍色 –inappropriate at present, but predicted to become appropriate 圓點 – known occurrence points 黑線內區域 – present geographic limits to species’ distribution 黑線外區域 – correspond to other Ortalis species and overprediction owing to historical factors • universal dispersal abilities (not a good assumption) • conservative : less habitable area -- 22.7% decline • liberal: more habitable area -- 75.1% increase • contiguous or no dispersal abilities (more realistic limited dispersal assumptions) • two scenarios more closely -- conservative:33.7% decrease; liberal: 29.7% decrease

37. averaging across the two climate-change scenarios colonization 白色: <25 灰色: 25-48 粉紅: 49-71 紅色: 72-95 深紅: 96-119 species richness 白色: <155 灰色: 155-306 粉紅: 307-458 紅色: 459-610 深紅: 611-763 species turnover 白色: <10% 灰色: 10-20% 粉紅: 20-30% 紅色: 30-40% 深紅: >40 local extinctions 白色: <29 灰色: 29-56 粉紅: 57-84 紅色: 85-112 深紅: 113-140

38. predictions of the effects ofglobal climate change on distributions • 預測的結果，絕種及劇烈範圍的減少的情形不多 • 但在一些區域的群落種類置換（species turnover）比率卻很高（>40% 的物種） • suggesting that severe ecological perturbations may result